# Pair Of Linear Equations In Two Variables Questions

We provide pair of linear equations in two variables practice exercises, instructions, and a learning material that allows learners to study outside of the classroom. We focus on pair of linear equations in two variables skills mastery so, below you will get all questions that are also asking in the competition exam beside that classroom. #### List of pair of linear equations in two variables Questions

Question NoQuestionsClass
1A number consist of two digits whose
sum is ( 11 . ) The number formed by reversing the digits is 9 less than the original number. Find the number.
10
2Solve the following pair of simultaneous equations:
( frac{a}{4}-frac{b}{3}=0 ; frac{3 a+8}{5}=frac{2 b-1}{2} )
A ( . a=-4.5, b=12 )
в. ( a=4, b=-5 )
c. ( a=14, b=10.5 )
D. ( a=12, b=11.5 )
10
3Two straight lines passing through the point ( A(3,2) ) cut the line ( 2 y=x+3 ) and
x-axis perpendicularly at ( P ) and ( Q ) respectively. The equation of the line PQ
is
A. ( 7 x+y-21=0 )
B. ( x+7 y+21=0 )
( mathbf{c} cdot 2 x+y-8=0 )
D. ( x+2 y+8=0 )
10
4If ( 7 x+13 y=27 ) and ( 13 x+7 y=33 )
find ( x+y )
10
5Reduce the equation ( 2 x+3 y-4=0 )
to slope-intercept form and find its slope and ( y- ) intercept
10
6A rectangular ( A 4 ) size paper is kept on cartesian plane coinciding the points ( (3,0),(-1,0),(0,-2) . ) Find the area of the paper in sq. units.
A . 12
B. 8
c. 16
D. 10
10
7Solve the following pair of linear (simultaneous) equations by the method of elimination:
( boldsymbol{x}+mathbf{8} boldsymbol{y}=mathbf{1 9}, mathbf{2} boldsymbol{x}+mathbf{1 1} boldsymbol{y}=mathbf{2 8} )
A. ( x=3 ) and ( y=2 )
B. ( x=12 ) and ( y=5 )
c. ( x=1 ) and ( y=6 )
D. ( x=9 ) and ( y=-6 )
10
8Solve graphically the following pairs of
equations
( boldsymbol{y}=mathbf{2} boldsymbol{x}+mathbf{1} ; boldsymbol{y}+mathbf{3} boldsymbol{x}-mathbf{6}=mathbf{0} )
( mathbf{A} cdot(1,3) )
B ( cdot(2,3) )
( mathbf{c} cdot(4,3) )
D. None of these
10
9The equations ( a x+b y+c=0 ) and
( boldsymbol{d} boldsymbol{x}+boldsymbol{e} boldsymbol{y}+boldsymbol{f}=boldsymbol{0} ) represent the same
straight line if and only if
A ( cdot frac{a}{d}=frac{b}{c} )
в. ( c=f )
c. ( frac{a}{d}=frac{b}{e}=frac{c}{f} )
D. ( a=d, b=e, c=f )
10
10Solve for ( boldsymbol{x}, boldsymbol{y} )
( (a+2 b) x+(2 a-b) y=2,(a- )
2b) ( x+(2 a+b) y=3 )
A. ( x=(5 b-2 a), y=10 a b )
в. ( x=frac{5 b-2 a}{10 a b}, y=frac{a+10 b}{10 a b} )
c. ( x=frac{5 b-2 a}{10 a b}, y=frac{5 a+10 b}{10 a b} )
D. ( x=frac{5 b+2 a}{10 a b}, y=frac{a+10 b}{10 a b} )
10
11Solve the following pair of simultaneous equations:
( frac{mathbf{3}}{mathbf{a}}+frac{mathbf{4}}{mathbf{b}}=mathbf{2} ; frac{mathbf{9}}{mathbf{a}}-frac{mathbf{4}}{mathbf{b}}=mathbf{2} )
A ( . a=3, b=4 )
в. ( a=1, b=-2 )
c. ( a=5, b=-3 )
D. ( a=0, b=6 )
6
10
12Find the value of ( ^{prime} x^{prime} ) and ( ^{prime} y^{prime} ) for the equations ( frac{a^{2}}{x}-frac{b^{2}}{y}=0 ; frac{a^{2} b}{x}+frac{b^{2} a}{y}= )
( boldsymbol{a}+boldsymbol{b} ) where ( boldsymbol{x}, boldsymbol{y} neq mathbf{0} )
A . ( x=a^{2}, y=b^{2} )
B . ( x=b^{2}, y=a^{2} )
c. ( x=frac{b}{a}, y=frac{a}{b} )
D. ( x=frac{1}{b}, y=frac{1}{a} )
10
13Solve the following pair of equations:
( frac{5 y}{2}-frac{x}{3}=8 )
( frac{y}{2}+frac{5 x}{3}=12 )
( mathbf{A} cdot x=2 ; y=7 )
B. ( x=4 ; y=3 )
( mathbf{c} cdot x=6 ; y=4 )
D. ( x=7 ; y=3 )
10
14Draw the graph of the above linear
equation having Celsius on X-axis and Fahrenheit on Y-axis.
10
15If the point (3,2) lies on the graph of the
equation ( 5 x+a y=19, ) then find ( a )
( mathbf{A} cdot mathbf{5} )
B. 7
( c . )
D. 2
10
16If ( mathrm{I}, mathrm{m}, mathrm{n} & mathrm{I}^{prime}, mathrm{m}^{prime}, mathrm{n}^{prime} ) be the direction cosines
of two lines which include an angle ( boldsymbol{theta} )
then
( mathbf{A} cdot cos theta=l l^{prime}+m m^{prime}+n n^{prime} )
B . ( sin theta=l l^{prime}+m m^{prime}+n n^{prime} )
( mathbf{c} cdot cos theta=m n^{prime}+m^{prime} n+n l+n^{prime} l+l m^{prime}+l^{prime} m )
( mathbf{D} cdot sin theta=m n^{prime}+m^{prime} n+n l+n^{prime} l+l m^{prime}+l^{prime} m )
10
17toppr
(i) ( frac{-}{2 x}+frac{-}{3 y}=2 ; frac{-}{3 x}+frac{-}{2 y}=frac{-}{6} )
(ii) ( frac{mathbf{2}}{sqrt{boldsymbol{x}}}+frac{mathbf{3}}{sqrt{boldsymbol{y}}}=mathbf{2} ; frac{mathbf{4}}{sqrt{boldsymbol{x}}}-frac{mathbf{9}}{sqrt{boldsymbol{y}}}=-mathbf{1} )
(iii) ( frac{4}{x}+3 y=14 ; frac{3}{x}-4 y=23 )
(iv) ( frac{mathbf{5}}{boldsymbol{x}-mathbf{1}}+frac{mathbf{1}}{boldsymbol{y}-mathbf{2}}=mathbf{2} ; frac{mathbf{6}}{boldsymbol{x}-mathbf{1}}- )
( frac{3}{y-2}=1 )
( (v) frac{7 x-2 y}{x y}=5 ; frac{8 x+7 y}{x y}=15 )
(vi) ( 6 x+3 y=6 x y ; 2 x+4 y=5 x y )
(vii) ( frac{mathbf{1 0}}{boldsymbol{x}+boldsymbol{y}}+frac{mathbf{2}}{boldsymbol{x}-boldsymbol{y}}=mathbf{4} ; frac{mathbf{1 5}}{boldsymbol{x}+boldsymbol{y}}- )
( frac{5}{x-y}=-2 )
(viii) ( frac{1}{3 x+y}+frac{1}{3 x-y}= )
( frac{3}{4} ; frac{1}{2(3 x+y)}-frac{1}{2(3 x-y)}=frac{-1}{8} )
10
18A man starts his job with a certain monthly salary and a fixed increment
every year. If his salary will be Rs. 11000
after 2 years and Rs. 14000 after 4 years of his service. What is his starting salary and what is the annual increment?
A. Starting salary is Rs. 7500 and increment is Rs. 2500
B. Starting salary is Rs.5000 and increment is Rs. 1800
C. Starting salary is Rs. 8000 and increment is Rs. 1500
D. Starting salary is Rs. 7000 and increment is Rs. 1300
10
19A man starts his job with a certain monthly salary and earns a fixed increment every year. If his salary was
Rs 1500 after 4 year of service and Rs
1800 after 10 years of service, what was
his starting salary and what is the annual increment?
10
20Solve the simultaneous equations by
substitution method.
( -boldsymbol{x}+mathbf{2} boldsymbol{y}=mathbf{0} ; mathbf{1 0} boldsymbol{x}+mathbf{1 5} boldsymbol{y}=mathbf{1 0 5} )
10
21No. of Solutions for:
( frac{4}{3} x+2 y=8 )
[
2 x+3 y=12
]
10
22Solve the following equations by substitution method.
( boldsymbol{x}=mathbf{2} boldsymbol{y}-mathbf{1} ; boldsymbol{y}=mathbf{2} boldsymbol{x}-mathbf{7} )
A. ( x=8, y=3 )
в. ( x=2, y=3 )
c. ( x=5, y=3 )
D. ( x=1, y=3 )
10
23Solve the equations ( frac{5}{x-1}+frac{1}{y-2}=2 ) and ( frac{6}{x-1}- )
( frac{3}{y-2}=1 )
10
24The pair of equations ( boldsymbol{y}=mathbf{0} ) and ( boldsymbol{y}=-mathbf{7} )
have :
A. one solution
B. two solutions
c. infinitely many solutions
D. no solution
10
25For what value of ” ( c^{prime prime} ) will the equations
( 3 x-4 y=7 ) and ( x+c y=13 ) have no
solution?
A ( cdot frac{3}{4} )
B. ( frac{4}{3} )
( c .-4 )
D. ( frac{-4}{3} )
10
26If ( 2 x+3 y=6 sqrt{3} ) and ( 2 x-3 y=6, ) find
the value of ( x y ? )
A. ( x y=3 )
в. ( x y=2 )
c. ( x y=1 )
D. ( x y=7 )
10
27Solve the following system of equation for ( x ) and ( y ) ( frac{5}{x-1}+frac{1}{y-2}=2, frac{6}{x-1}-frac{3}{y-2}=1 )10
28Solve the equations using elimination method:
( x-y=2 ) and ( -x y=-10 )
A. (6,-4)
()
в. (6,4)
c. (-6,-4)
D. (-6,4)
10
29Reduce the equation ( 4 x+6 y-7=0 )
to intercept form.Hence find the length of the segment intercepted between the
axes.
10
30Determine the value of ( k ) so that the
following linear equations has no
solution:
( (3 k+1) x+3 y-2=0 ) and ( left(k^{2}+right. )
1) ( boldsymbol{x}+(boldsymbol{k}-mathbf{2}) boldsymbol{y}-mathbf{5}=mathbf{0} )
A. ( k=-1 )
B. ( k=3 )
c. ( k=-7 )
D. ( k=8 )
10
31( frac{boldsymbol{x} boldsymbol{y}}{boldsymbol{x}+boldsymbol{y}}=frac{boldsymbol{6}}{mathbf{5}} )
( frac{x y}{y-x}=6 )
A. ( x=-2, y=3 )
в. ( x=3, y=2 )
c. ( x=2, y=3 )
D. ( x=-3, y=-2 )
10
32Solve: ( 37 x+29 y=45 ; 29 x+37 y=21 )10
33Graph ( ( i v ) ) is represented by which
equation?
( (i) )
(i)
(iii)
(iv)
A ( cdot y=2 x )
B. ( y+x=2 )
( mathbf{c} cdot y=2+x )
D. ( x=y+22 )
10
34Equation of a straight line passing through the point (2,3) and inclined at an angle of ( tan ^{-1} frac{1}{2} ) with the line ( y+ ) ( 2 x=5, ) is:
( mathbf{A} cdot y=3 )
B. ( x=2 )
c. ( 3 x+4 y-18=0 )
D. ( 4 x+3 y-17=0 )
10
35Determine the values of a and ib for
which the given system of equations has infinitely many solutions:
( (2 a-1) x-3 y=5 ) and ( 3 x+(b- )
2) ( y=3 )
10
36Find ( p ) for which given equation has
unique solution
( 4 x+p y+8=0 )
( 2 x+2 y+2=0 )
10
37Solve the following system of equations ( frac{mathbf{6}}{boldsymbol{x}+boldsymbol{y}}=frac{mathbf{7}}{boldsymbol{x}-boldsymbol{y}}+mathbf{3}, frac{mathbf{1}}{mathbf{2}(boldsymbol{x}+boldsymbol{y})}= )
( frac{1}{3(x-y)} ) where ( x+y neq 0 ) and ( x )
( boldsymbol{y} neq mathbf{0} )
10
38Draw the graph of the straight line given
by the equation ( 4 x-3 y+36=0 )
Calculate the area of the triangle formed by the line drawn and the coordinate axes.
A. Area ( =45 ) sq. units
B. Area = 54 sq. units
c. Area ( =48 ) sq. units
D. Area = 58 sq. units
10
39Find the equations of the lines for which ( cot theta=frac{1}{2}, ) where ( theta ) is the angle of
inclination of the line and ( y- ) intercept
is ( frac{-3}{2} )
10
40Solve the following puzzles using the
equations:

The present age of Beena is 2 years
more than Reeta.The present age of Teena is 3 years more than Beena.If the
sum of the ages of Reeta, Beena, and Teena is 79 years, find the present age of all the three of them.
A. Reeta 24 years, Beena 26 years, Teena 29 years
B. Reeta 24 years, Beena 21 years, Teena 29 years
c. Reeta 24 years, Beena 29 years, Teena 29 years.
D. Reeta 24 years, Beena 26 years, Teena 30 years

10
41Solve: ( 3 x-5=x-5 )10
42Solve ( boldsymbol{x}+mathbf{4} boldsymbol{y}=mathbf{2 4} boldsymbol{x} boldsymbol{y}, boldsymbol{x}+mathbf{2} boldsymbol{y}=mathbf{2} mathbf{1} boldsymbol{x} boldsymbol{y} )10
43The cost of 7 erasers and 5 pencils is Rs
( mathbf{5 8} ) and the cost of 5 erasers and 6
pencils is Rs.56. Formulate this problem algebraically and solve it graphically.
10
44Reduce the equation ( 3 x+4 y-5=0 )
to intercept form.Hence find the length of the segment intercepted between the
axes.
10
45Solve the following pair of equations by cross multiplication rule.
( boldsymbol{x}+boldsymbol{y}=boldsymbol{a}+boldsymbol{b}, boldsymbol{a} boldsymbol{x}-boldsymbol{b} boldsymbol{y}=boldsymbol{a}^{2}-boldsymbol{b}^{2} )
A . ( x=1, y=a b )
в. ( x=a+b, y=b )
c. ( x=a, y=b )
D. ( x=b, y=1 )
10
46The number of solutions for ( 2 x+3 y= )
10 and ( 4 x+6 y=25 ) are
10
47Intersection point of lines ( boldsymbol{x}=mathbf{2}, boldsymbol{x}= )
-2 is
A. (0,0)
(年) ( 0,0,0,0,0,1, )
в. (1,1)
c. It does not exist
D. None
10
48A two-digit number is 3 more than six times the sum of its digits. If 18 is added to the number obtained by
interchanged by interchanging the digits, we get the original number. Find
the number
A . 25
B. 45
c. 75
D. None of these
10
49( a, b, c(a>c) ) are the three digits, from left to right of a three digit number. If the number with these digits reversed is subtracted from the original number, the resulting number has the digit 4 in its unit’s place. The other two digits
from left to right are –
A. 5 and 4
B. 5 and 9
c. 4 and 5
D. 9 and 5
10
50Find the point of intersection of the
lines represented by ( 3 x-2 y=6 ) and
the y-axis.
10
51If the lines given by ( 3 x+2 k y=2 ) and
( mathbf{2} boldsymbol{x}+mathbf{5} boldsymbol{y}+mathbf{1}=mathbf{0} ) are parallel, then the
value of ( k ) is
A ( cdot frac{-5}{4} )
B. ( frac{2}{5} )
c. ( frac{15}{4} )
D. ( frac{3}{2} )
10
52( A ) and ( B ) each have a certain number of
mangoes. A says to B “If you give me 30 of your mangoes, I will have twice as many as left with you.” B replies, “If you give me ( 10, ) I will have thrice as many as left with you.” How many mangoes does each have?
10
53If we divide the unknown two-digit number by the number consisting of the same digits written in the reverse order,
we get 4 as a quotient and 3 as a remainder. Now if we divide the
required number by the sum of its
digits, we get 8 as a quotient and 7 as a remainder. Find the number.
10
54Represent the following pair of equations graphically and write the coordinates of points where the line intersects ( boldsymbol{y} ) -axis
( boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{6} )
( 2 x-3 y=12 )
10
55( A ) and ( B ) are friends and their ages differ
by 2 years. A’s father D is twice as old as A and B is twice as old as his sister ( C ).
The age of ( D ) and ( C ) differ by 40 years. Find the ages of ( A ) and ( B )
10
56For which value of the given system of equations have infinitely many solution ( (k-3) x+3 y=k ) and ( k x+k y=12 )
A . -6
B. 6
( c cdot 0 )
D. 3
10
5711. The ratio of the present ages of
Sunita and Vinita is 4 : 5. Six
years hence, the ratio of their
ages will be 14 : 17. What will
be the ratio of their ages 12
years hence ?
(1) 17:19 (2) 15 : 19
(3) 13:15 (4) 16:19
10
58Solve the following simultaneous equations by substitution method and find the value of ( x 3 x-2 y=4 ; 6 x+ )
( 7 y=19 )
10
59Solve the simultaneous equations:
( frac{1}{x}+frac{1}{y}=12, frac{3}{x}-frac{2}{y}=1 )
10
60Reduce the equation ( 9 x+7 y-3=0 )
to intercept form.Hence find the length of the segment intercepted between the
axes.
10
61Solve ( : boldsymbol{x}+boldsymbol{y}=mathbf{1 1 0}, boldsymbol{y}=boldsymbol{x}+mathbf{4} )10
62A pair of linear equations in two
variables ( x ) and ( y ) is ( a_{1} x+b_{1} y+c_{1}=0 )
and ( a_{2} x+b_{2} y+c_{2}=0, ) such that
( frac{a_{1}}{a_{2}} neq frac{c_{1}}{c_{2}}, ) then it has
A. Unique solution
B. No solution
c. Infinitely many solutions
D. Can’t say
10
63Solve the following pair of linear (simultaneous) equations by the method of elimination:
( boldsymbol{y}=boldsymbol{4} boldsymbol{x}-mathbf{7} )
( 16 x-5 y=25 )
A ( cdot x=frac{3}{2}, y=6 )
B・ ( x=frac{5}{2}, y=3 )
c. ( _{x}=frac{7}{4}, y=2 )
D. ( x=frac{9}{2}, y=0 )
10
6464. If 32x – y = 3*+y = 27. then the
value of 3x-y will be
(1) 3
(2) ja
10
65Solve: ( 4 x+frac{6}{y}=15 ) and ( 6 x-frac{8}{y}= )
( mathbf{1 4} )
A. ( x=2 ; y=3 )
В. ( x=3 ; y=2 )
c. ( x=1 ; y=5 )
D. ( x=4 ; y=1 )
10
66Solve the given pair of equations by substitution method:
( boldsymbol{x}+boldsymbol{y}=mathbf{0} )
( boldsymbol{y}-boldsymbol{x}=boldsymbol{6} )
A. (2,7)
(i)
в. (-3,3)
c. (4,9)
(年. (4,9)
D. (-6,2)
10
67f we write equation as ( a x+b y+c=0 )
then ( a=? )
4
B.
( c )
( D )
10
68Use the graphical method to find the
value of ( k, ) if ( (5, k-2) ) lies on the
straight line ( boldsymbol{x}-mathbf{2} boldsymbol{y}+mathbf{1}=mathbf{0} )
A .2
B. 3
( c cdot 4 )
D. 5
10
69Given ( 3 x-4 y=7 ) and ( x+c y=13 ) for what value of “c” will the two equation not have a solution?
A ( cdot frac{3}{4} )
B. ( frac{4}{3} )
( c cdot-4 )
D. ( frac{-4}{3} )
10
70Find the equations to the straight lines which pass through the origin and are
inclined at ( 75^{circ} ) to the straight line ( (x+y) sqrt{3}+y-x=a )
10
71Equation of a straight line passing through the point (2,3) and inclined at an angle of ( tan ^{-1}left(frac{1}{2}right) ) with the line ( y+ ) ( 2 x=5 ) is
This question has multiple correct options
( mathbf{A} cdot y=3 )
B. ( x=2 )
c. ( 3 x+4 y-18-0 )
D. ( 4 x+3 y-17=0 )
10
72Write the equation of a line which is parallel to ( x- ) axis at a distance of 5
units from it, and another line parallel
to ( y- ) axis at a distance of 7 units from
it. Draw the graphs and write the coordinates of point of intersection.
10
73Solve the following systems of equations graphically:
( boldsymbol{x}+boldsymbol{y}=boldsymbol{6} )
( boldsymbol{x}-boldsymbol{y}=mathbf{2} )
10
74Identify the system of equations: ( 2 x- )
( 2 y=2 ) and ( x-y=1 )
A. inconsistent
B. consistent
c. dependent
D. non-linear
10
75In the system of equations ( boldsymbol{x}+boldsymbol{y}=mathbf{4} boldsymbol{x} boldsymbol{y} )
and ( frac{1}{x}+frac{2}{y}=10, ) the value of ( x ) and ( y )
will be
A ( cdot-frac{1}{3} ) and ( frac{1}{6} )
B ( cdot frac{1}{5} ) and ( frac{1}{6} )
c. ( -frac{1}{2} ) and ( frac{1}{6} )
D. ( +frac{1}{3} ) and ( -frac{1}{2} )
10
76Write a pair of linear equations which has the unique solution ( x=-1, y=3 . ) How many such pairs can you write?
A. ( x+y=2 & x-y=-4 ; ) infinite
B. ( 2 x+y=6 & 2 x-3 y=6 ; 3 )
c. ( 5 x-8 y=13 ) & ( x+3 y=7 ; 8 )
D. Cannot be determined
10
77Find the common solution:
( 2 x+y=8 )
( boldsymbol{x}-boldsymbol{y}=mathbf{1} )
10
78What is the nature of the graphs of a system of linear equations with exactly
one solution?
A. Parallel lines
B. Perpendicular lines
c. coincident lines
D. Intersecting lines
10
79The graph of ( 2 x+3 y=6 ) is
represented by
( A )
3
c. ॥
D. IV
10
80A member of these family with positive
gradient making an angle of ( frac{pi}{4} ) with the line ( 3 x-4 y=2, ) is
A. ( 7 x-y-5=0 )
B. ( 4 x-3 y+2=0 )
c. ( x+7 y=15 )
D. ( 5 x-3 y-4=0 )
10
81Rohit says to Ajay “Give me a hundred, I shall then become twice as rich as you.” Ajay replies “If you give me ten, I shall be
six times as rich as you.” How much does each have originally?
A. Rohit has Rs. 20 and Ajay has Rs. 90
B. Rohit has Rs. 50 and Ajay has Rs. 200
c. Rohit has Rs. 40 and Ajay has Rs. 170
D. Rohit has Rs. 56 and Ajay has Rs. 190
10
82Solve the following pairs of equations by reducing them to a pair of linear equations:
( frac{7 x-2 y}{x y}=5 )
( frac{8 x+7 y}{x y}=15 )
10
83Solve the simultaneous equation:
( frac{2}{x}+frac{2}{3 y}=frac{1}{6} ; frac{3}{x}+frac{2}{y}=0 )
10
84What is the value of ( x ) for the following
equations: ( x-5 y=10 ) and ( x+y=4 ? )
(Use cross multiplication method)
( mathbf{A} cdot x=5 )
B. ( x=4 )
c. ( x=3 )
D. ( x=2 )
10
85Draw the graph of straight line ( y= )
( -2 x+3 . ) Use your graph to find the
area between the line and co-ordinate
axes.
A. 4.66 sq.units
B. 3.25 sq.units
c. 2.25 sq.units
D. 5.66 sq.units
10
86Equation of one of the sides of an isosceles right angled triangle whose hypotenuse is ( 3 x+4 y=4 ) and the
opposite vertex of the hypotenuse is ( (2,2), ) will be ( ? )
A. ( x-7 y+12=0 )
в. ( 7 x+y-12=0 )
c. ( x-7 y+16=0 )
D. ( 7 x+y+16=0 )
10
87Find the equations of the lines for which ( tan theta=frac{1}{sqrt{2}}, ) where ( theta ) is the angle of
inclination of the line and ( x- ) intercept
is 3
10
88solve the equation using substitution method:
( 2 x+3 y=13 ) and ( 4 x+5 y=23 )
A ( cdot(-2,3) )
B. (2,3)
c. (2,-3)
D. (-2,-3)
10
89( A equiv(1,2) ) and ( B equiv(7,10) ) are two points. If ( boldsymbol{P}(boldsymbol{x}, boldsymbol{y}) ) is a point such that
( angle A P B=60^{circ} ) and area of ( Delta A P B ) is
maximum, then which of the following is (are) TRUE?
This question has multiple correct options
A. ( P ) lies on any line perpendicular to ( A B )
B. ( P ) lies on the perpendicular bisector of ( A B )
c. ( P ) lies on the line ( 3 x+4 y=36 )
D. Radius of circumcircle of ( Delta P A B ) is 10 units
10
90If we divide a two-digit number by the
sum of its digits, we get 6 as a
quotient and 2 as a remainder. Now if
we divide it by the product of its digits,
we get 5 as a quotient and 2 as a remainder. Find the number.
10
91Find the equations of the lines for which ( tan theta=frac{1}{3}, ) where ( theta ) is the angle of
inclination of the line and ( y- ) intercept
is ( frac{-1}{2} )
10
92Solve :
( frac{4}{x}+frac{5}{y}=7 ; frac{3}{x}+frac{4}{y}=5 )
10
93If the line ( 2 x+3 y+12=0 ) cuts the
axes at ( A ) and ( B ), then the equation of
the perpendicular bisector of ( A B ) is
A. ( 3 x-2 y+5=0 )
B. ( 3 x-2 y+7=0 )
c. ( 3 x-2 y+9=0 )
D. ( 3 x-2 y+8=0 )
10
94If ( boldsymbol{y}=boldsymbol{a}+frac{boldsymbol{b}}{boldsymbol{x}}, ) where ( boldsymbol{a} ) and ( boldsymbol{b} ) are
constants and if ( boldsymbol{y}=mathbf{1} ) when ( boldsymbol{x}=-mathbf{1} )
and ( y=5 ) when ( x=-5, ) what is the
value of ( a+b ? )
A. -1
B. 0
( c cdot 1 )
D. 11
10
95Solve the systems of equations:
( frac{boldsymbol{x}-mathbf{2}}{mathbf{4}}+frac{boldsymbol{y}+mathbf{1}}{mathbf{3}}=mathbf{2} ; frac{boldsymbol{x}+mathbf{1}}{mathbf{7}}+frac{boldsymbol{y}-mathbf{3}}{mathbf{2}}= )
( frac{1}{2} )
A ( cdot(6,2) )
в. (2,2)
c. (2,3)
(年. (2,3,3)
D. (3,4)
10
96A two-digit number is thrice as large as the sum of its digits, and the square of that sum is equal to the trippled required number. Find the number10
97Through the point (3,4) are drawn two
straight lines each inclined at ( 45^{circ} ) to
the straight line ( x-y=2 . ) Find their
equations and find also the area included by the three lines.
10
98Solve ( : frac{3}{x+y}+frac{2}{x-y}=2 ) and
( frac{9}{x+y}-frac{4}{x-y}=1 )
A. ( x=frac{2}{5} ; y=frac{7}{2} )
B. ( x=frac{5}{2} ; y=frac{1}{2} )
c. ( x=frac{6}{7} ; y=frac{4}{3} )
D. ( x=frac{7}{3} ; y=frac{1}{2} )
10
99Solve
( frac{33}{u+2}+frac{12}{v-3}=123 )
and ( frac{12}{u+2}+frac{33}{v-3}=102 )
10
100Given that both ( x ) and ( y ) are positive
integers. Solve the following systems of equations. ( boldsymbol{x}^{2}+boldsymbol{x} boldsymbol{y}=mathbf{1 5}, boldsymbol{y}^{2}+boldsymbol{x} boldsymbol{y}=mathbf{1 0} )
10
101Solve the following pairs of equations, graphically:
( 2 x-3 y=-6 ) and ( x-frac{y}{2}=1 )
( mathbf{A} cdot(3,2) )
в. (3,3)
c. (4,4)
D. (3,4)
10
102The perpendicular bisector of the line segment joining ( boldsymbol{P}(1,4) ) and ( boldsymbol{Q}(boldsymbol{k}, boldsymbol{3}) )
has ( boldsymbol{y}- ) intercept ( -4 . ) Then a possible
value of ( k ) is ( ? )
A . -2
B. -4
c.
D. 2
10
103f we write equation as ( a x+b y+c=0 )
then ( b=? )
4
B.
( c )
( D )
10
104Yamini and Fatima, two students of
Class IX of a school, together contributed Rs 100 towards the
Prime Minister’s Relief Fund to help the earthquake victims. Write a linear equation which the given data will satisfy and also plot its graph.
A. ( x+y=100 )
в. ( x+y=112 )
c. ( x+y=50 )
D. ( x+2 y=100 )
10
105Find the equations of the lines for which ( tan theta=frac{1}{4}, ) where ( theta ) is the angle of
inclination of the line and ( y- ) intercept
is ( frac{-3}{2} )
10
106Which of the following pairs of linear equations has unique solution, no solution, or infinitely many solutions. In case there is a unique solution, find it by using cross multiplication method?
( 3 x-5 y=20,6 x-10 y=40 )
A. No solutions
B. Unique solutions, ( x=0 ) and ( y=1 )
c. Infinitely many solutions
D. Data insufficient
10
107Solve the following pairs of equations by reducing them to a pair of linear
equations:
( frac{4}{x}+3 y=14, frac{3}{x}-4 y=23 )
10
108Solve the following pair of equation by
the elimination method.
( boldsymbol{x}+boldsymbol{y}=mathbf{1 4}, boldsymbol{x}-boldsymbol{y}=mathbf{4} )
10
109Solve the following pairs of linear (simultaneous) equation by the method of elimination by substitution: ( 2 x+ )
( mathbf{3} boldsymbol{y}=mathbf{8}, mathbf{2} boldsymbol{x}=mathbf{2}+mathbf{3} boldsymbol{y} )
A ( cdot x=2, y=frac{3}{2} )
в. ( x=3, y=5 )
c. ( _{x}=frac{5}{2}, y=1 )
D. ( x=frac{3}{2}, y=4 )
10
110Solve
( boldsymbol{x}+boldsymbol{y}=mathbf{3} )
( boldsymbol{x}-boldsymbol{y}=mathbf{1} )
10
111( frac{1}{3} x-frac{1}{6} y=4 )
( 6 x-a y=8 )
In the system of equations above, ( a ) is a
constant. If the system has no solution,
what is the value of ( boldsymbol{a} )
A ( cdot frac{1}{3} )
B.
( c .3 )
D.
10
112Is the following situation possible? If so, determine their present ages.

The sum of the ages of two friends is 20 years.Four years ago, the product of their ages in years was 48
A. Not Possible
B. Yes, 8 and 6
c. Yes ( , 12 ) and 4
D. none

10
113Solve the following equations graphically
[
begin{array}{l}
mathbf{2 x}+boldsymbol{y}=mathbf{6} \
mathbf{2 x – y}+mathbf{2}=mathbf{0}
end{array}
]
10
114Based on equations reducible to linear
equations

Solve for ( x ) and ( y: 9+25 x y=53 x ) and
( 27-4 x y=x )
A. ( x=1, y=4 )
в. ( x=2, y=7 )
c. ( x=6, y=2 )
D. ( x=3, y=2 )

10
115The equation of the straight line cutting off an intercept 8 on ( x ) -axis and making
an angle of ( 60^{circ} ) with the positive
direction of ( y- ) axis is
A ( . x-sqrt{3} y-8=0 )
B. ( x+sqrt{3} y=8 )
c. ( y-sqrt{3} x=8 )
D. ( y+sqrt{3} x=8 )
10
116The equation of the straight line which passes through (1,1) and making angle ( 60^{circ} ) with the line ( x+sqrt{3} y+2 sqrt{3}=0 )
is/are.
A. ( y=1 )
B. ( x=1 )
c. ( x+y=2 )
D. ( x+sqrt{3} y-sqrt{3}-1=0 )
10
117The equation of perpendicular bisector of the line segment joining the points
(1,2) and (-2,0) is-
A ( .5 x+2 y=1 )
B. ( 4 x+6 y=1 )
c. ( 6 x+4 y=1 )
D. None of these
10
118Using substitution method find the value of ( x ) and ( y: )
( 4 x+9 y=5 ) and ( -5 x+3 y=8 )
A. -1 and ( frac{-2}{5} )
B. -1 and ( frac{2}{5} )
c. -1 and 1
D. 1 and ( frac{2}{5} )
10
119If the equations ( 4 x+7 y=10 ) and
( 10 x+k y=25 ) represent coincident
lines, then the value of ( k ) is
A . 5
в. ( frac{17}{2} )
c. ( frac{27}{2} )
D. ( frac{35}{2} )
10
120Find the equation to, and the length of the perpendicular drawn from the point
(1,1) upon the straight line ( 3 x+4 y+ )
( 5=0, ) the angle between the axes being
( 120^{circ} )
10
121Solve the following simultaneous equations:
( frac{27}{x-2}+frac{31}{y+3}=85 ; quad frac{31}{x-2}+ )
( frac{27}{y+3}=89 )
A ( cdot x=frac{3}{4}, y=4 )
B. ( x=frac{5}{2}, y=-2 )
c. ( _{x}=frac{4}{3}, y=3 )
D. ( x=frac{7}{2}, y=6 )
10
122Find the value of ( p, ) if ( p q+12=3 p+ )
( p r ) and ( q-r=7 )
A . -3
B. -4
( c cdot frac{1}{3} )
D.
E. ( -frac{6}{5} )
10
123If ( boldsymbol{x}+boldsymbol{y}=mathbf{2 5} ) and ( frac{mathbf{1 0 0}}{boldsymbol{x}+boldsymbol{y}}+frac{mathbf{3 0}}{boldsymbol{x}-boldsymbol{y}}=mathbf{6} )
then the value of ( x-y ) is
A . 18
B . 20
c. 15
D. 10
10
124Two perpendicular lines are intersecting at ( (4,3) . ) One meeting coordinate axis at ( (4,0), ) find the
coordinates of the intersection of other
line with the cordinate axes.
A ( .(0,3) )
B. (1,3)
D. None of these
10
125Akhila went to a fair in her village. She
wanted to enjoy rides on the Giant
Wheel and play Hoopla (a game in which you throw a ring on the items kept in the stall, and if the ring covers any object completely you get it). The number of times she played Hoopla half the number of rides she had on the
Giant Wheel. Each ride costs ( R s .3 ), and
a game Hoopla costs ( R s .4 . ) If she spent
Rs.20 in the fair, represent this situation algebraically
10
126Solve the following pairs of equations by
reducing them to a pair of linear
equations:
( frac{2}{sqrt{x}}+frac{2}{sqrt{y}}=2, frac{4}{sqrt{x}}-frac{9}{sqrt{y}}=-1 )
10
127Find the values of ( x ) and ( y, ) if ( frac{mathbf{2}}{boldsymbol{x}}+frac{mathbf{6}}{boldsymbol{y}}=mathbf{1 3} ; quad frac{mathbf{3}}{boldsymbol{x}}+frac{boldsymbol{4}}{boldsymbol{y}}=mathbf{1 2} )
A ( cdot x=frac{1}{6}, y=frac{2}{3} )
B. ( x=frac{1}{3}, y=frac{2}{3} )
c. ( x=frac{1}{7}, y=frac{2}{3} )
D. ( x=frac{1}{2}, y=frac{2}{3} )
10
128The number of solutions for the system of equations ( 2 x+y=4,3 x+2 y=2 )
and ( boldsymbol{x}+boldsymbol{y}=-boldsymbol{2} ) is
( mathbf{A} cdot mathbf{1} )
B . 2
( c cdot 3 )
D. infinitely many
E .
10
129A line passes through the origin and makes an angle of ( pi / 4 ) with the line
( boldsymbol{x}-boldsymbol{y}+mathbf{1}=mathbf{0} . ) Then
This question has multiple correct options
A. Equation of the line is ( x=0 )
B. The equation of the line is ( y=0 )
C. The point of intersection of the line with the given line ( s(-1,0) )
D. The point of intersection of the line with the given line is (0,1)
10
130Solve the following pair of simultaneous equations:
( 4 x+frac{3}{y}=1 ; 3 x-frac{2}{y}=5 )
A. ( x=-6, y=7 )
в. ( x=-3, y=1 )
c. ( x=1, y=-1 )
D. ( x=2, y=0 )
10
131Kate and Nora each have a sum of
money. The ratio of the amount of
money Kate has to that of Nora is 3: 5
After Nora gives Rs. 150 to Kate, the ratio of the amount of money Kate has to that of Nora becomes ( 7: 9 . ) Find the
sum of money Kate had initially.
10
132Solve: ( 4 x+frac{6}{y}=15 ) and ( 6 x-frac{8}{y}=14 )
Hence find the value of ( k, ) if ( y=k x-2 )
A ( cdot x=4, y=1 ) and ( k=frac{2}{3} )
в. ( x=5, y=3 ) and ( k=frac{3}{5} )
c. ( _{x}=3, y=2 ) and ( k=frac{4}{3} )
D. ( x=1, y=2 ) and ( k=frac{9}{2} )
10
133On comparing the ratios ( frac{boldsymbol{a}_{1}}{boldsymbol{a}_{2}}, frac{boldsymbol{b}_{1}}{boldsymbol{b}_{2}} ) and ( frac{boldsymbol{c}_{1}}{boldsymbol{c}_{2}} )
find out whether the following pairs of linear equations are consistent, or inconsistent.
( mathbf{5} boldsymbol{x}-mathbf{3} boldsymbol{y}=mathbf{1 1} ;-mathbf{1 0} boldsymbol{x}+mathbf{6} boldsymbol{y}=mathbf{2 2} )
A. Consistent
B. Inconsistent
c. Ambiguous
D. Data insufficient
10
134Find the value of ( a, ) so that the following
system of equations bears no solution ( 2 y-6 x=28 )
( 4 y-a x=28 )
A . -12
B. – –
( c cdot 3 )
D. 6
( E cdot 12 )
10
135The equation of perpendicular bisector of the line segment joining the points (-1,-2) and (2,0) is
A ( .5 x+2 y=1 )
в. ( 4 x+6 y=-1 )
c. ( 6 x+4 y=-1 )
D. none of these
10
136Solve for ‘u’ and ‘v’, 2 ( (3 u-v)=5 u v )
and ( 2(u+3 v)=5 u v )
10
137Solve the equations ( 2 x-3 y=9 )
( 4 x+6 y=18 )
10
138If ( 2 x=t+sqrt{t^{2}+4} ) and ( 3 y=t- )
( sqrt{t^{2}+4} ) then the value of ( y ) when ( x=frac{2}{3} )
is
A . -2
B. 1
( c cdot-1 )
D.
10
139Reduce the equation ( x+2 y-6=0 ) to
slope-intercept form and find its slope
and ( boldsymbol{y}- ) intercept.
10
140A particular work can be completed by 6 men and 6 women in 24 days; whereas the same work can be completed by 8 men and 12 women in 15 days, according to the amount of work done one man is equivalent to how many women?
A ( cdot_{frac{1}{2}} ) women
в. ( 5 frac{1}{3} ) women
( ^{mathrm{c}} cdot_{5} frac{2}{3} ) women
D. ( frac{3}{2} ) women
10
141Coordinates of a square are:
( (2,2),(-2,2),(-2,-2) . ) Find the length of the side of square
A .4
B . 2
( c cdot 6 )
D. None of these
10
142Solve: ( 8 x-7=6 )10
143If ( boldsymbol{y}=boldsymbol{a}+frac{boldsymbol{b}}{boldsymbol{x}}, ) where ( boldsymbol{a} ) and ( boldsymbol{b} ) are
constants, and if ( boldsymbol{y}=mathbf{1} ) when ( boldsymbol{x}=-mathbf{1} )
and ( y=5 ) when ( x=-5, ) then ( a+b )
equals.
A . -1
B.
c.
D. 10
E. 11
10
144If one line of the pair of lines ( a x+ )
( 2 b x y+b y^{2}=0 ) bisects the angle bet.
( A cdot a-b=12 b )
B. ( a+b=-2 b )
( c cdot a+b=2 b )
D. ( (a-b)^{2}=4 b^{2} )
10
145If ( 2 x+y=23 ) and ( 4 x-y=19 ; ) find
the values of ( x-3 y ) and ( 5 y-2 x )
A. The values of ( x-3 y ) and ( 5 y-2 x ) are -20 and 31 respectively
B. The values of ( x-3 y ) and ( 5 y-2 x ) are 0 and 3 respectively
c. The values of ( x-3 y ) and ( 5 y-2 x ) are 14 and -9
respectively
D. The values of ( x-3 y ) and ( 5 y-2 x ) are 5 and 23 respectively
10
146Reduce the equation ( x+2 y-3=0 ) to
slope-intercept form and find its slope
and ( boldsymbol{y}- ) intercept.
10
147A line passing through the origin and making an angle ( frac{pi}{4} ) with the line ( y- ) ( mathbf{3} boldsymbol{x}=mathbf{5} ) has the equation
This question has multiple correct options
A. ( x+2 y=0 )
в. ( 2 x=y )
c. ( x=2 y )
( mathbf{D} cdot y+2 x=0 )
10
148Draw a graph for the following pair of
linear equations in two variables and find their solution from the graph.
( 2 x+y=5 )
( 3 x-2 y=4 )
10
149Choose the correct options for the figure
This question has multiple correct options
A. Point A is substitute into the equation for line ( l_{2} )
B. Point A is substitute into the equation for line ( l_{1} )
C. Point ( C ) is substitute into the equation for line ( l_{1} )
D. Point ( C ) is substitute into the equation for line ( l_{2} ).
10
150Solve the following pair of linear equations by the substitution method.
(i) ( boldsymbol{x}+boldsymbol{y}=mathbf{1 4} ; boldsymbol{x}-boldsymbol{y}=mathbf{4} )
(ii) ( s-boldsymbol{t}=mathbf{3} ; frac{boldsymbol{s}}{mathbf{3}}+frac{boldsymbol{t}}{mathbf{2}}=mathbf{6} )
(iii) ( 3 x-y=3 ; 9 x-3 y=9 )
(iv) ( 0.2 x+0.3 y=1.3 ; 0.4 x+0.5 y= )
( mathbf{2 . 3} )
(v) ( sqrt{mathbf{2}} boldsymbol{x}+sqrt{mathbf{3}} boldsymbol{y}=mathbf{0} ; sqrt{mathbf{3}} boldsymbol{x}-sqrt{mathbf{8}} boldsymbol{y}=mathbf{0} )
(vi) ( frac{mathbf{3} boldsymbol{x}}{mathbf{2}}-frac{mathbf{5} boldsymbol{y}}{mathbf{3}}=-mathbf{2} ; frac{boldsymbol{x}}{mathbf{3}}+frac{boldsymbol{y}}{mathbf{2}}=frac{mathbf{1 3}}{mathbf{6}} )
10
151The sum of the digits of a two digit number is ( 15 . ) If 9 is added to the
number, the digit are reversed. Find the number.
10
152Based on equations reducible to linear
equations Solve for ( x ) and ( y: frac{2}{x-1}+frac{y-2}{4}= ) ( 2 ; frac{3}{2(x-1)}+frac{2(y-2)}{5}=frac{47}{20} )
A ( . x=3, y=6 )
в. ( x=1, y=5 )
c. ( x=2, y=-7 )
D. ( x=5, y=-9 )
10
153By the graphical method, find whether
the following pair of equations are consistent or not. If consistent, solve
them.
( boldsymbol{x}+boldsymbol{y}=mathbf{3} ) and ( mathbf{3} boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{9} )
10
154Solve the equations using graphical
method: ( boldsymbol{x}-boldsymbol{y}=mathbf{3} ) and ( boldsymbol{x}+boldsymbol{y}=mathbf{1 1} )
A ( .(7,4) )
в. (-7,3)
c. (7,-4)
D. (-7,4)
10
15526. The number of values of k, for which the system of
equations :
[JEE M 2013]
(k+1)x+8y=4k
kox + (k+3) y = 3k-1
has no solution, is
(a) infinite
(b) 1
(c) 2
(d) 3
10
156The graph of ( x+2=0 ) is a line parallel
to ( ldots ldots . . . ) axis.
This question has multiple correct options
A . ( x )
B. ( y )
c. ( x-2=0 )
D. None of these
10
157Solve graphically: ( 2 x+y-7=0, x+ )
( 3 y-11=0 )
10
158Find the equations of the straight lines which pass through (3,2) and make an
angle of ( 45^{circ} ) with the line ( x=2 y+4 )
10
159Show graphically the given system of equations
( 2 x+4 y=10 ) and ( 3 x+6 y=12 ) has no
solution.
10
160Solve the equations using cross
multiplication method: ( x-y=12 ) and
( boldsymbol{x}+boldsymbol{y}=mathbf{1 4} )
A . ( x=13, y=1 )
В. ( x=13, y=-1 )
c. ( x=-13, y=-1 )
D. ( x=-13, y=1 )
10
161Reduce the equation ( 2 x-3 y+5=0 )
to intercept form.Hence find the length of the segment intercepted between the
axes.
10
162Based on cross-multiplication method, solve the following pair of equations by cross multiplication rule ( mathbf{5} boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{3 5}, mathbf{2} boldsymbol{x}+mathbf{4} boldsymbol{y}=mathbf{2 8} )
Then
A. ( x=4, y=5 )
B. ( x=5, y=4 )
c. ( x=6, y=3 )
D. ( x=3, y=6 )
10
163Solve :
( frac{mathbf{5}}{boldsymbol{x}+boldsymbol{y}}-frac{mathbf{2}}{boldsymbol{x}-boldsymbol{y}}+mathbf{1}=mathbf{0} )
( frac{15}{x+y}+frac{7}{x-y}-10=0 )
10
164A man sold two paintings at ( R s 924 )
each. On one he gains ( 20 % ) and on the
other he loses ( 20 % ). How much does he
gain or lose in the whole transaction?
10
165Consider the following statements: The system of equations ( .2 x-y=4 ) and
( boldsymbol{p} boldsymbol{x}-boldsymbol{y}=boldsymbol{q} )
I. has a unique solution if ( y neq 2 )
Il. has infinitely many solutions if ( boldsymbol{p}= )
( 2, q=4 ) Of these statements:
A. I alone is correct
B. II alone is correct
c. I and II are correct
D. I and II are false
10
166Find the equation of the line passing
through the point (2,3) and perpendicular to the straight line ( 4 x- )
( mathbf{3} boldsymbol{y}=mathbf{1 0} )
A. ( 3 x+4 y=18 )
в. ( 3 x-4 y=18 )
c. ( 3 x+4 y=-18 )
D. ( 4 x-3 y=-18 )
10
167If ( frac{x+y-8}{2}=frac{x+2 y-14}{3}=frac{3 x-y}{4} )
then the values of ( x ) and ( y ) is
A ( . x=1, y=3 )
B. ( x=5, y=2 )
c. ( x=3, y=3 )
D. ( x=2, y=6 )
10
168The graph of the linear equation ( 2 x- )
( y=4 ) cuts ( x ) -axis at
A ( .(2,0) )
в. (-2,0)
c. (0,-4)
D. (0,4)
10
169Find the equation of the line having an
inclination ( 60^{circ} ) with the positive direction of ( X ) axis and cut off an
intercept of 4 on the positive side of ( Y )
axis.
10
170A line is perpendicular to ( 3 x+y=3 )
and passes through a point ( (2,2) . ) Its ( y ) intercept is
A ( cdot 2 / 3 )
в. ( 1 / 3 )
c. 1
D. ( 4 / 3 )
10
171The cost of ( 2 mathrm{kg} ) of apples and ( 1 mathrm{kg} ) of grapes on the day was found to be Rs.
160. After a month the cost of ( 4 mathrm{kg} ) of
apples ( 2 mathrm{kg} ) of grapes is ( mathrm{Rs} .300 ) Represent the situation algebraically.
10
172[
begin{array}{l}
2 x-5 y=8 \
4 x+k y=17
end{array}
]
For which of the following values of ( k )
will the system of equations above have no solution?
A . -10
в. -5
c. 0
D. 5
E . 10
10
173Solve the following system of equations
for ( boldsymbol{x} ) & ( boldsymbol{y} )
( frac{5}{x-1}+frac{1}{y-2}=2, frac{3}{x-1}=1 )
10
174Solve: ( 4 x+frac{6}{y}=15 ) and ( 6 x-frac{8}{y}= )
( mathbf{1 4} )
Hence, find ‘a’ if ( boldsymbol{y}=boldsymbol{a} boldsymbol{x}-boldsymbol{2} )
A ( cdot x=1, y=6 ) and ( a=3 frac{2}{5} )
B. ( x=3, y=12 ) and ( a=7 frac{6}{5} )
c. ( _{x}=3, y=2 ) and ( a=1 frac{1}{3} )
D. ( x=12, y=16 ) and ( a=4 frac{31}{3} )
10
175Find the value of ( x ) and ( y ) using cross multiplication method:
( boldsymbol{x}+boldsymbol{y}=mathbf{0} ) and ( boldsymbol{x}-boldsymbol{y}=mathbf{2} )
( A cdot(1,1) )
B . (-1,1)
( c cdot(1,-1) )
D. (-1,-1)
10
176Solve the following simultaneous
equations:
( 217 x+131 y=913 )
( 131 x+217 y=827 )
A. ( x=7, y=3 )
В. ( x=2, y=1 )
c. ( x=3, y=2 )
D. ( x=1, y=5 )
10
177Solve the following simultaneous equations:
( frac{7}{2 x+1}+frac{13}{y+2}=27, frac{13}{2 x+1}+ )
( frac{7}{y+2}=33 )
10
178( f-2 x=4 y+6 ) and ( 2(2 y+3)=3 x- )
5What is the solution ( (x, y) ) to the
system of equation above?
10
179A square paper is kept on cartesian plane coinciding the points ( (2,0),(4,0),(0,2) . ) Find the perimeter of the paper.
A. 8 Units
B. 12 Units
c. 16 Units
D. None of these
10
180Draw the graph of ( 2 x+3 y=12 )10
181Solve graphically the following pairs of
equations
( 4 x-y-5=0 ; x+y-5=0 )
( mathbf{A} cdot(2,3) )
B ( cdot(3,3) )
( mathbf{c} cdot(4,3) )
D. None of these
10
182The solution of the equations ( frac{boldsymbol{m}}{boldsymbol{x}}+ ) ( frac{n}{y}=a ) and ( frac{n}{x}+frac{m}{y}=b ) is given by
A ( x=frac{n^{2}+m^{2}}{a m-b n}, y=frac{m^{2}-n^{2}}{b m-a n} )
B. ( _{x}=frac{m^{2}-n^{2}}{a m-b n}, y=frac{n^{2}-m^{2}}{b m-a n} )
c. ( _{x}=frac{m^{2}-n^{2}}{a m-b n}, y=frac{m^{2}-n^{2}}{b m-a n} )
D. ( x=frac{n^{2}-m^{2}}{a m-b n}, y=frac{n^{2}-m^{2}}{b m-a n} )
10
183Find whether the lines representing the following pair of linear equation
intersect at a point, are parallel or coincident ( cdot frac{3 x}{2}-frac{5 y}{3}=-2 ; frac{x}{3}+frac{y}{2}= )
( mathbf{1 3} )
( mathbf{6} )
10
184Determine the values of ( mathrm{m} ) and ( n ) so that
the following system of linear equations have infinite number of solutions:
( (2 m-1) x+3 y-5=0 )
( 3 x+(n-1) y-2=0 )
10
185The equation of line bisecting perpendicularly the segment joining the points (-4,6) and (8,8) is
( mathbf{A} cdot y=7 )
в. ( 6 x+y-19=0 )
c. ( x+2 y-7=0 )
D. ( 6 x+2 y-19=0 )
10
186The equation of ( y ) axis is
A ( . quad x=0 )
( mathbf{B} cdot y=0 )
( mathbf{c} cdot x=k )
D. None of these
10
187Father says to son “I am 9 times as old
as you were when i was as old as you are”. If the sum of their present ages is
50 years. What is the age of father?
10
188A straight line passes through the points (2,4) and ( (5,-2) . ) Taking ( 1 c m= ) 1 units, mark these points on a graph
paper and draw the straight line through these points. If points ( (boldsymbol{m},-mathbf{4}) )
and ( (3, n) ) lie on the drawn line, find the
values of ( m ) and ( n )
A. ( m=1 ) and ( n=2 )
B. ( m=3 ) and ( n=2 )
c. ( m=6 ) and ( n=2 )
D. ( m=9 ) and ( n=2 )
10
189One says, “Give me a hundred, friend! shall then become twice as rich as you.”.”
The other replies, “lf you give me ten, shall be six times as rich as you.” Tell
me what is the amount of their (respective) capital? [From the Bijaganita of Bhaskara II]
10
190The line joining two points ( A(2,0), B(3,1) ) is rotated about ( A ) in anti-clockwise direction through an
angle of ( 15^{circ} . ) The equation of the line in the now position, is
A ( cdot sqrt{3} x-y-2 sqrt{3}=0 )
B. ( x-3 sqrt{y}-2=0 )
c. ( sqrt{3} x+y-2 sqrt{3}=0 )
D. ( x+sqrt{3} y-2=0 )
10
191Solve ( 0.2 x+0.3 y=1.3 )
( mathbf{0 . 4 x}+mathbf{0 . 5 y}=mathbf{2 . 3} )
A. ( x=-2 ) and ( y=3 )
B. ( x=3 ) and ( y=3 )
c. ( x=2 ) and ( y=3 )
D. None of these
10
192Find the value of ( x ) and ( y ) using cross
multiplication method:
( 5 x+y=15 ) and ( 2 x+6 y=34 )
A. (-2,5)
в. (2,-5)
( c cdot(2,5) )
D. (-2,-5)
10
193Solve the following pair of linear equation:
( frac{1}{3 x+y}+frac{1}{3 x-y}=frac{3}{4}, frac{1}{2(3 x+y)} )
( frac{1}{2(3 x-y)}=frac{-1}{8}, 3 x+y neq 0,3 x- )
( boldsymbol{y} neq 0 )
10
194The angle between lines joining the original to the point of intersection of the line ( sqrt{mathbf{3}} x+boldsymbol{y}=mathbf{2} ) and the curve
( y^{2}-x^{2}=4 ) is
A ( cdot tan ^{-1} frac{2}{sqrt{3}} )
B. ( frac{pi}{6} )
( ^{mathrm{c}} tan ^{-1}left(frac{sqrt{3}}{2}right) )
D. ( frac{pi}{2} )
10
195Draw the graph for the equation given below. Hence find the co-ordinates of
the points where the graph drawn meets the co-ordinate axes:
( frac{1}{3} x+frac{1}{5} y=1 )
( mathbf{A} cdot(6,3) ) and (5,0)
B ( cdot(3,5) ) and (2,0)
c. (3,0) and (0,5)
( mathbf{D} cdot(2,0) ) and (0,7)
10
196Solve the following equation using the
trial and error method.
( 2 x+4=8 )
10
197Solve ( : frac{2}{x}+frac{2}{3 y}=frac{1}{6} ) and ( frac{3}{x}+frac{2}{y}=0 )
Hence, find ‘ ( m^{prime} ) for which ( y=m x-4 )
A ( . x=3 ; y=-5 ) and ( m=2 )
B. ( x=6 ; y=-4 ) and ( m=0 )
c. ( x=2 ; y=-3 ) and ( m=0 )
D. ( x=4 ; y=-4 ) and ( m=2 )
10
198f ( x+y=6 ) and ( 3 x-y=4, ) then ( x-y )
is equal to:
A . -1
B.
( c cdot 2 )
D.
10
199Find the equation of the line passing
through the point (-6,10) and perpendicular to the straight line ( 7 x+ )
( 8 y=5 )
10
200The system of equation ( 3 x-4 y=12 ) and ( 6 x ) ( 8 y=48 )
A. 2 solution
B. 1 solution
c. infinite number of solutions
D. no solutuion
10
201Solve graphically the pair of equations ( x+3 y=6, ) and ( 3 x-5 y=18 . ) Hence
find the value of ( boldsymbol{K} ) if ( mathbf{7} boldsymbol{x}+mathbf{3} boldsymbol{y}=boldsymbol{K} )
A. ( x=-3, y=1, K=13 )
В. ( x=-8, y=5, K=8 )
c. ( x=1, y=2, K=29 )
D. ( x=6, y=0, K=42 )
10
202Solve :
( (x+y-4)^{2}+(x-y-2)^{2}=0 )
A ( . x=1, y=1 )
в. ( x=4, y=1 )
c. ( x=3, y=1 )
D. ( x=5, y=1 )
10
203Fill in the blanks: The graph of line ( x+2 ) ( =0 ) is parallel to ( ldots ldots . . . . ) axis.10
204Solve the following equation
( 3 x-4 y=1 )
( -2 x+frac{8}{3} y=5 )
10
205What is the value of ( a ) for the following
equation: ( 3 a+4 b=13 ) and ( a+3 b=1 )
( ? )
(Use cross multiplication method)
( mathbf{A} cdot a=5 )
B. ( a=6 )
( mathbf{c} cdot a=mathbf{7} )
( mathbf{D} cdot a=8 )
10
206The equation to a straight line referred
to axes inclined at ( 30^{circ} ) to one another is
( y=2 x+1 . ) Find its equation referred to
axes inclined at ( 45^{circ}, ) the origin and axis
of ( x ) being unchanged.
10
207Solve the following simultaneous linear equations by method of reduction.
( boldsymbol{x}+mathbf{2} boldsymbol{y}+boldsymbol{z}=mathbf{8} )
( 2 x+3 y-z=11 )
( 3 x-y-2 z=5 )
10
208Solve for ( x ) and ( y ) by using method of
substitution:
( mathbf{0 . 2 x + 0 . 3 y}=mathbf{1 . 3 ; 0 . 4 x + 0 . 5 y}=mathbf{2 . 3} )
A. -2,-3
B. 2,-3
c. 2,3
D . -2,3
10
209Solve ( 4 x+frac{6}{y}=15 ) and ( 6 x-frac{8}{y}=14 )
and hence find ‘p’, if ( boldsymbol{y}=boldsymbol{p} boldsymbol{x}-boldsymbol{2} )
10
210If ( 2 x+y=23 ) and ( 4 x-y=19, ) find
the values of ( 5 y-2 x ) and ( frac{y}{x}-2 )
A ( cdot 36,-frac{1}{3} )
в. ( _{31,-frac{5}{7}} )
c. ( _{38, frac{6}{7}} )
D. None of these
10
211Solve: ( frac{mathbf{2 0}}{boldsymbol{x}+boldsymbol{y}}+frac{mathbf{3}}{boldsymbol{x}-boldsymbol{y}}=mathbf{7} ) and
( frac{8}{x-y}-frac{15}{x+y}=5 )
A. ( x=3 ) and ( y=2 )
B. ( x=2 ) and ( y=7 )
c. ( x=9 ) and ( y=4 )
D. ( x=1 ) and ( y=9 )
10
212Solve: ( 4 x+frac{6}{y}=15 ) and ( 6 x-frac{8}{y}=14 )
Hence, find ( boldsymbol{a} ) if ( boldsymbol{y}=boldsymbol{a} boldsymbol{x}-boldsymbol{2} )
A ( cdot x=2 ; y=26 ) and ( a=2 frac{5}{3} frac{5}{3} )
B・ ( x=3 ; y=2 ) and ( a=1 frac{1}{3} )
c. ( _{x}=1 ; y=5 ) and ( a=2 frac{7}{3} )
D. ( x=5 ; y=1 ) and ( a=5 frac{1}{8} )
10
213Solve the following linear equations. ( boldsymbol{x}-boldsymbol{y}=mathbf{3} ; mathbf{4} boldsymbol{x}+mathbf{2} boldsymbol{y}=mathbf{0} )10
214Find the equations of the lines for which ( tan theta=frac{3}{5}, ) where ( theta ) is the angle of
inclination of the line and ( x- ) intercept
is -8
10
215Draw the graph for the linear equation given below:
( mathbf{2} boldsymbol{x}-mathbf{7}=mathbf{0} )
Which of the following points lie on this line?
This question has multiple correct options
A. (3.5,0)
в. (3,0)
c. (-2,2)
D. (3.5,2)
10
216If a line passes through the point
( P(1,2) ) makes an angle of ( 45^{circ} ) with the x-axis and meets the line ( x+2 y-7= )
0 in ( Q, ) then ( P Q ) equals-
A. ( sqrt{3} )
B. ( frac{3 sqrt{2}}{2} )
( c cdot frac{2 sqrt{2}}{3} )
D. ( sqrt{2} )
10
217Solve for ( x ) and ( y: 6 x+3 y=6 x y ) and
( 2 x+4 y=5 x y )
10
218Solve: ( a x+b=0 )10
219Show that the equation of the line passing through the origin and making an angle ( theta ) with the line ( y=m x+c ) is
( frac{boldsymbol{y}}{boldsymbol{x}}=frac{boldsymbol{m} pm tan boldsymbol{theta}}{1 mp boldsymbol{m} tan boldsymbol{theta}} )
10
220One diagonal of a square is the portion of ( frac{x}{97}+frac{y}{79}=1 ) intercepted between
the axes. ( boldsymbol{p}_{1}, boldsymbol{p}_{2} ) are the lengths of the perpendiculars from the vertices of the other diagonal on the axis of ( y ) then ( p_{1}^{2}+p_{2}^{2} ) is equal to
10
221Solve the equations using graphical
method: ( x+y=7 ) and ( 2 x-3 y=9 )
( A cdot(6,-1) )
B. (-6, 1)
( c cdot(6,1) )
D. (-6,-1)
10
222The equation of the line with inclination
( 45^{0} ) and passing through the point (-1,2)
is
A. ( x+y+3=0 )
в. ( x-y+3=0 )
c. ( x-y-3=0 )
D. ( x+y-3=0 )
10
223Differentiate the following function with
respect to ( x ) ( sin ^{2} x )
( A cdot cos x )
B. ( sin 2 x )
( mathbf{c} cdot sin 3 x )
D. ( sin ^{2} x cos x )
10
224Is the point (0,3) lie on the graph of the
linear equation ( 3 x+4 y=12 ? )
10
225Solve the following simultaneous equations:
( frac{mathbf{1 6}}{boldsymbol{x}+boldsymbol{y}}+frac{mathbf{2}}{boldsymbol{x}-boldsymbol{y}}=mathbf{1} ; quad frac{mathbf{8}}{boldsymbol{x}+boldsymbol{y}}- )
( frac{12}{x-y}=7 )
A ( . x=2, y=3 )
B. ( x=6, y=1 )
c. ( x=7, y=4 )
D. ( x=3, y=5 )
10
226Find the equation of the line passing
through the point (2,3) and perpendicular to the straight line ( 4 x- ) ( mathbf{3} boldsymbol{y}=mathbf{1 0} )
10
227A piece of cloth costs rupees ( 75 . ) If the piece is four meters longer and each
meter costs rupees 5 less, the cost remains unchanged. What is the length of the piece?
A. 12 meters
B. 8 meters
c. 10 meters
D. 6 meters
10
228The solution of the equations ( 2 x- )
( 3 y=7 ) and ( 4 x-6 y=20 ) is
A. ( x=18, y=12 )
В. ( x=0, y=0 )
c. No solution
D. ( x=8, y=5 )
10
229If the equations ( (boldsymbol{b}+boldsymbol{c}) boldsymbol{x}+(boldsymbol{c}+boldsymbol{a}) boldsymbol{y}+(boldsymbol{a}+boldsymbol{b})= )
( mathbf{0}, boldsymbol{c} boldsymbol{x}+boldsymbol{a} boldsymbol{y}+boldsymbol{b}=mathbf{0} ) and ( boldsymbol{a} boldsymbol{x}+boldsymbol{b} boldsymbol{y}+boldsymbol{c}=mathbf{0} )
are consistent, then show that either
( boldsymbol{a}+boldsymbol{b}+boldsymbol{c}=boldsymbol{0} ) or ( boldsymbol{a}=boldsymbol{b}=boldsymbol{c} )
10
230The axes being inclined at an angle of
( 30^{circ}, ) find the equation to the straight line which passes through the point
(-2,3) and is perpendicular to the
straight line ( boldsymbol{y}+mathbf{3} boldsymbol{x}=mathbf{6} )
10
231Find all two-digit numbers such that the sum of the digits constituting the number is not less than ( 7 ; ) the sum of
the squares of the digits is not greater than ( 30 ; ) the number consisting of the same digits written in the reverse order is not larger than half the given number
10
232Find the value of ( k ) for which the given
system of equations has infinite number of solutions.
( mathbf{5} boldsymbol{x}+mathbf{2} boldsymbol{y}=mathbf{2} boldsymbol{k} ) and ( mathbf{2}(boldsymbol{k}+mathbf{1}) boldsymbol{x}+boldsymbol{k} boldsymbol{y}= )
( (3 k+4) )
A . 4
B. 7
( c cdot 3 )
D. 6
10
233Find the equations to the straight lines
which pass through the point ( (h, k) ) and
are inclined at an angle ( tan ^{-1} m ) to the
straight line ( boldsymbol{y}=boldsymbol{m} boldsymbol{x}+boldsymbol{c} )
10
234A rectangular ( A 4 ) size paper is kept on cartesian plane coinciding the points ( (3,0),(-1,0),(0,-2) . ) Find the
perimeter of the paper.
A. 10 Units
B. 16 Units
c. 9 units
D. 12 Units
10
235Based on cross-multiplication method,
solve the following pairs of equations by cross multiplication rule. ( frac{x}{2}-frac{y}{3}+4=0, frac{x}{2}-frac{5 y}{3}+12=0 )
Then ( x+y ) is equal to
10
236The values of and ( y ) satisfying the two
equations ( 32 x+33 y=31,33 x+ )
( 32 y=34 ) respectively will be
A. -1,2
в. 2,-1
c. 0,0
D. 2,3
10
237One pendulum ticks 57 times in 58 seconds and another 608 times in 609
seconds. If they start simultaneously, find the time after which will they tick
together?
A ( cdot frac{211}{19} )
в. ( frac{1217}{19} s )
c. ( frac{1218}{19} s )
D. ( frac{1018}{19} s )
10
238The equations representing the given
graph is
A. ( 7 x+2 y=11 ; y-2 x=3 )
B. ( 2 x+7 y=11 ; 5 x+(35 y / 2)=25 )
c. ( 3 x-7 y=10 ; 8 y-6 x=4 )
D. ( 3 x-4 y=1 ; 3 x-4 y x+2=0 )
10
239A line passes through (5,-6) and it is
parallel to ( y- ) axis.Find its equation.
10
240A Father is four times as old as his son.
The age of the father at the time of the
birth of his son was ( 30 . ) Find the age of
his son
10
241Solve the set of equations: ( 3(2 u+v)= )
( mathbf{7} boldsymbol{u} boldsymbol{v} ) and ( boldsymbol{3}(boldsymbol{u}+boldsymbol{3} boldsymbol{v})=mathbf{1 1} boldsymbol{u} boldsymbol{v} )
A ( cdot u=1 ; v=frac{3}{2} )
в. ( u=2 ; v=frac{1}{2} )
c. ( u=2 ; v=frac{5}{4} )
D. ( u=5 ; v=frac{7}{4} )
10
242If the equations ( k x+4 y+1=0, x+ )
( k y+1=0 ) and ( 2 x-3 y+1=0 ) are
consistent, then show that the value of
( k ) is not a real number.
10
243The ages of ( A ) and ( B ) are in the ratio 8: 3
Six years hence, their ages will be in the ratio 9: 4 Find the sum of their present
ages.
10
244Solve graphically:
( 2 x-3 y=7 ) and ( 5 x+y=9 )
A. ( x=2, y=-6 )
в. ( x=8, y=-9 )
c. ( x=0, y=-3 )
D. ( x=2, y=-1 )
10
245A man is 24 years older than his son. 12 years ago, he was five times as old as
his son. Find the present ages of both.
A. Present age of father is 44 years and Present age of son is 20 years
B. Present age of father is 42 years and Present age of son is 18 years
c. Present age of father is 60 years and Present age of son is 36 years
D. Present age of father is 48 years and Present age of son is 24 years
10
246On comparing the ratios ( frac{a_{1}}{a_{2}}, frac{b_{1}}{b_{2}} ) and ( frac{c_{1}}{c_{2}} )
find out whether the lines representing the following pairs of linear equations intersect at a point, are parallel or coincident.
( mathbf{6} boldsymbol{x}-mathbf{3} boldsymbol{y}+mathbf{1 0}=mathbf{0} ; mathbf{2} boldsymbol{x}-boldsymbol{y}+mathbf{9}=mathbf{0} )
A. Intersect at a point
B. Parallel
c. coincident
D. Data insufficient
10
247Based on equations reducible to linear
equations Solve for ( x ) and ( y frac{1}{3 x}-frac{1}{7 y}=frac{2}{3} ; frac{1}{2 x}- )
( frac{1}{3 y}=frac{1}{6} )
A. ( x=1 / 8, y=1 / 2 )
в. ( x=1 / 3, y=1 / 6 )
c. ( x=1 / 7, y=1 / 8 )
D. ( x=1 / 5, y=1 / 7 )
10
248Solve the equation: ( -4 x+8 y=12 ) and
( -2 x+4 y=6 ) and then identify the
system of equation. This question has multiple correct options
A. Consistent
B. Inconsistent
c. Dependent
D. None the above
10
249Write the nature of the lines
representing the linear equation ( 2 x- )
( boldsymbol{y}=mathbf{3} ) and ( mathbf{4} boldsymbol{x}-boldsymbol{y}=mathbf{5} )
10
250The distance between two places is 900 km. An ordinary express train takes 5
hours more than a superfast express train to cover this distance. If the speed of the superfast express train is 15 km/hr more than that of the ordinary express train, find the speed of the trains.
10
251Solve the following pair of linear (simultaneous) equations by the method of elimination:
( 8 x+5 y=9 )
( mathbf{3} boldsymbol{x}+mathbf{2} boldsymbol{y}=mathbf{4} )
A. ( x=1 ) and ( y=-2 )
B. ( x=1 ) and ( y=-5 )
c. ( x=3 ) and ( y=6 )
D. ( x=-2 ) and ( y=5 )
10
252Reduce the equation ( 2 x-3 y-5=0 )
to slope-intercept form and find its slope and ( y- ) intercept
10
253Draw the graph of straight line ( y= )
( -2 x+3 . ) Use graph to find the
intercept on ( y ) -axis.
A . 3
B . 2
c. 0
D.
10
254Solve the following system of equations:
( boldsymbol{x}+boldsymbol{y}=boldsymbol{a}-boldsymbol{b} )
( boldsymbol{a} boldsymbol{x}-boldsymbol{b} boldsymbol{y}=boldsymbol{a}^{2}+boldsymbol{b}^{2} )
10
255The line joining two points ( A(2,0) ) and
( B(3,1) ) ir rotated about ( A ) about in the anticlock wise direction through an
angle of ( 15^{circ} . ) The equation of the line in the new position is:
A ( . x-sqrt{3} y-2=0 )
В. ( x-2 y-2=0 )
c. ( sqrt{3} x-y-2 sqrt{3}=0 )
D. ( sqrt{2} x-y-2 sqrt{2}=0 )
10
256Solve the following pair of equations by
reducing them to a pair of linear
equations:
( frac{1}{(3 x+y)}+frac{1}{(3 x-y)}= )
( frac{3}{4}, frac{1}{2(3 x+y)}-frac{1}{2(3 x-y)}=frac{-1}{8} )
A ( . x=2, y=7 )
в. ( x=5, y=0 )
c. ( x=1, y=1 )
D. ( x=2, y=3 )
10
257For what value of ( boldsymbol{K} ) will the following
pair of linear equations have infinitely many solutions?
( boldsymbol{K} boldsymbol{x}+boldsymbol{3} boldsymbol{y}-(boldsymbol{K}-boldsymbol{3})=mathbf{0} )
( mathbf{1 2} boldsymbol{x}+boldsymbol{K} boldsymbol{y}-boldsymbol{K}=mathbf{0} )
10
258Solve ( 8 x-2 y=28 ) and ( x+4 y=-5 )10
259Based on equations reducible to linear equations Solve for ( x ) and ( y: frac{16}{x+3}+frac{3}{y-2}= ) ( mathbf{5} ; frac{mathbf{8}}{boldsymbol{x}+mathbf{3}}-frac{mathbf{1}}{boldsymbol{y}-mathbf{2}}=mathbf{0} )
A. ( x=5, y=3 )
В. ( x=7, y=2 )
c. ( x=1, y=5 )
D. None of these
10
260The straight line passing through the point of intersection of the straight lines
( boldsymbol{x}-mathbf{3} boldsymbol{y}+mathbf{1}=mathbf{0} ) and ( mathbf{2} boldsymbol{x}+mathbf{5} boldsymbol{y}-mathbf{9}=mathbf{0} )
and having infinite slope and and at a distance 2 units from the origin has the
equation
( mathbf{A} cdot x=2 )
В. ( 3 x+y-1=0 )
( mathbf{c} cdot y=1 )
D. None of these
10
261Solve the following equations:
( y+sqrt{x^{2}-1}=2 )
( sqrt{boldsymbol{x}+mathbf{1}}-sqrt{boldsymbol{x}-mathbf{1}}=sqrt{boldsymbol{y}} )
This question has multiple correct options
A. ( x=2 ; y=5 )
в. ( x=1 ; y=2 )
c. ( _{x}=frac{5}{3} ; frac{2}{3} )
D. ( x=3 ; y=3 )
10
262Show that the equations to the straight
lines passing through the point (3,-2) and inclined at ( 60^{circ} ) to the line ( sqrt{3} x+ ) ( boldsymbol{y}=1 ) are ( boldsymbol{y}+boldsymbol{2}=boldsymbol{0} ) and ( boldsymbol{y}-sqrt{mathbf{3}} boldsymbol{x}+ )
( mathbf{2}+mathbf{3} sqrt{mathbf{3}}=mathbf{0} )
10
26354. ‘x number of men can finish a
piece of work in 30 days. If there
were 6 men more, the work
could be finished in 10 days less.
The original number of men is
(1) 6
(2) 10
(3) 12
(4) 15
10
264Find the equations of the lines for which ( tan theta=frac{2}{3}, ) where ( theta ) is the angle of
inclination of the line and ( x- ) intercept
is 5
10
265Find the value of ( mathrm{m} ) and ( mathrm{n} ) using cross multiplication method:
( 3 m+n=15 ) and ( m+2 n=10 )
( A cdot(4,3) )
B. (-4,3)
( c cdot(-4,-3) )
D. (4,-3)
10
266The length of the sides of a triangle are ( mathbf{2} boldsymbol{x}+frac{boldsymbol{y}}{mathbf{2}}, boldsymbol{5} frac{boldsymbol{x}}{mathbf{3}}+boldsymbol{y}+frac{mathbf{1}}{mathbf{2}}, boldsymbol{2} frac{boldsymbol{x}}{mathbf{3}}+mathbf{2} boldsymbol{y}+frac{mathbf{5}}{mathbf{2}} )
the triangle is equilateral. Then its
perimeter is ( frac{m}{2} . ) Find ( m )
10
267Equation of a straight line passing through the origin and making with ( x- ) axis an angle twice the size of the angle
made by the line ( y=0.2 x ) with the ( x- )
axis, is :
A. ( y=4.0 x )
В. ( y=frac{5}{12} x )
c. ( 6 y-5 y=0 )
D. none of these
10
268Solve
( 2 x+3 y=8 )
( 2 x=2+3 y )
10
269For what value of ( alpha, ) the system of
equations ( boldsymbol{alpha} boldsymbol{x}+mathbf{3} boldsymbol{y}=boldsymbol{alpha}-boldsymbol{3} )
( 12 x+alpha y=alpha )
will have no solution
( mathbf{A} cdot alpha=5 )
B . ( alpha=-6 )
c. ( alpha=-4 )
D. ( alpha=2 )
10
270ff ( x+y=5 ) and ( x=3 ), then the value of
( boldsymbol{y} )
10
271Area of triangle formed by angle bisectors of coordinate axes and the
line ( y=6 ) in sq.units is
A . 36
B . 24
( c cdot 72 )
D. 16
10
272Find the value of ( x ) and ( y ) using elimination method:
( frac{x}{2}+frac{y}{3}=1 ) and ( frac{x}{4}+frac{y}{7}=2 )
A. (44,-63)
В . (-41,63)
c. (44,63)
D. (-44,-63
10
273Solve: ( frac{34}{3 x+4 y}+frac{15}{3 x-2 y}=5 ) and
( frac{25}{3 x-2 y}-frac{8.50}{3 x+4 y}=4.5 )
A. ( x=7 ; y=2 )
в. ( x=5 ; y=2 )
c. ( x=1 ; y=2 )
D. ( x=3 ; y=2 )
10
274The value of ( k ) for which the system of equations ( 3 x+5 y=0 ) and ( k x+ )
( 10 y=0 ) has a non-zero solution, is
( A cdot 0 )
B . 2
( c cdot 6 )
D. 8
10
275Based on equations reducible to linear
equations Solve for ( x ) and ( y: frac{24}{2 x+y}-frac{13}{3 x+2 y}= ) ( 2 ; frac{26}{3 x+2 y}+frac{8}{2 x+y}=3 )
A. ( x=-2, y=6 )
в. ( x=-5, y=3 )
c. ( x=3, y=2 )
D. ( x=1, y=0 )
10
276Which option of linear equation is inconsistent?
( mathbf{A} cdot x+y=1 )
( 2 x+y=0 )
B. ( x-y=2 )
( 2 x-2 y=1 )
c. ( 2 x-3 y=0 )
( 2 y+x=1 )
D. 2x – 4 ( y=19 ) ( -2 x+y=0 )
10
277State whether the given statement is true or false:

A pair of linear equations is given by ( boldsymbol{a}_{1} boldsymbol{x}+boldsymbol{b}_{1} boldsymbol{y}+boldsymbol{c}_{1}=boldsymbol{0} ) and ( boldsymbol{a}_{2} boldsymbol{x}+boldsymbol{b}_{2} boldsymbol{y}+ )
( c_{2}=0 ) and ( frac{a_{1}}{a_{2}}=frac{b_{1}}{b_{2}}=frac{c_{1}}{c_{2}} )
In this case, the pair of linear equations is consistent.
A. True
B. False

10
278Fill in the blanks: The graph of line ( y+3 ) ( =0 ) is parallel to axis.10
279Solve the equations ( frac{mathbf{1 0}}{boldsymbol{x}+boldsymbol{y}}+frac{mathbf{2}}{boldsymbol{x}-boldsymbol{y}}=4, frac{mathbf{1 5}}{boldsymbol{x}+boldsymbol{y}}-frac{mathbf{5}}{boldsymbol{x}-boldsymbol{y}}= )
-2
10
280Solve: ( 2 A-B=-2 C ) and
( boldsymbol{A}-boldsymbol{B}=-boldsymbol{C} )
Find ( A ) and ( B ).
10
281Solve the following simultaneous equations using graphical method ( boldsymbol{x}+boldsymbol{y}=boldsymbol{6} )
( boldsymbol{x}-boldsymbol{y}=mathbf{2} )
10
282If ( A=2 y^{2}+3 x-x^{2}, B=3 x^{2}-y^{2} )
and ( C=5 x^{2}-3 x y ) then find
( B-C )
10
283Solve:
( boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{4} )
( 2 x-y=1 )
10
284If ( 2^{2 x-y}=32 ) and ( 2^{x+y}=16 ) then ( x^{2}+ )
( y^{2} ) is equal to
( mathbf{A} cdot mathbf{9} )
B. 10
c. 11
D. 13
10
285The following pair of linear equations consistent. State true and false:
( boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{1 1} ; mathbf{2}(mathbf{2} boldsymbol{x}+mathbf{6} boldsymbol{y})=mathbf{2 2} )
A. True
B. False
10
286The equation ( a x^{2}+b y^{2}+c x+c y=0 )
represents a pair of straight lines, when This question has multiple correct options
( mathbf{A} cdot a+b=0 )
B . ( c=0 )
c. ( a+c=0 )
D. ( c(a+b)=0 )
10
287Solve each pair of equation by using the substitution method.
( boldsymbol{x}+frac{mathbf{6}}{boldsymbol{y}}=mathbf{6} )
( mathbf{3} boldsymbol{x}-frac{mathbf{8}}{boldsymbol{y}}=mathbf{5} )
A ( . x=3 ) and ( y=-2 )
в. ( x=30 ) and ( y=2 )
c. ( x=3 ) and ( y=2 )
D. None of these
10
288Two perpendicular lines are intersecting at ( (4,3) . ) One meeting coordinate axis at ( (4,0), ) find the distance between origin and the point of intersection of other line with the
cordinate axes.
A . 4
B. 7
( c .3 )
D. 5
10
289Solve graphically the following pairs of
equations. ( boldsymbol{y}-mathbf{2} boldsymbol{x}+mathbf{2}=mathbf{0} ; boldsymbol{y}=mathbf{4} boldsymbol{x}-mathbf{4} )
( mathbf{A} cdot(1,0) )
B ( cdot(2,0) )
( mathbf{c} cdot(3,0) )
D. None of these
10
290( frac{mathbf{2 2}}{boldsymbol{x}+boldsymbol{y}}+frac{mathbf{1 5}}{boldsymbol{x}-boldsymbol{y}}=mathbf{5} )
( frac{mathbf{5 5}}{boldsymbol{x}+boldsymbol{y}}+frac{mathbf{4 5}}{boldsymbol{x}-boldsymbol{y}}=mathbf{1 4} )
A. ( x=-8, y=3 )
в. ( x=-3, y=8 )
c. ( x=8, y=3 )
D. ( x=8, y=-3 )
10
291Solve the equations using elimination method:
( 2 x+3 y=15 ) and ( 3 x+3 y=12 )
A ( cdot(-3,-7) )
в. (-3,7)
c. (-3,6)
D. (3,-7)
10
292The sum of two numbers is 80 and the
greater number exceed twice the
smaller by 11. Find the larger numbers.
10
293Draw the graphs of equations ( 2 x+y= )
7 and ( 2 x+y=8 . ) If they intersect, write
the co-ordinates of the point of their intersection.
10
294Solve for ( x ) and ( y, ) if ( x+y=7 ) and ( 2 x+ )
( 3 y=18 )
A ( . x=3, y=4 )
в. ( x=2, y=5 )
c. ( x=1, y=6 )
D. ( x=4, y=3 )
10
295Solve the following pair of equations:
( frac{a}{x}-frac{b}{y}=0 )
( frac{a b^{2}}{x}+frac{a^{2} b}{y}=a^{2}+b^{2} )
A. ( x=a b ) and ( y=b )
B. ( x=a ) and ( y=b )
c. ( x=b ) and ( y=a )
D. ( x=b-a ) and ( y=a b )
10
296Draw the graph of each of the equations ( 2 x+3 y+5=0 ) and ( 5 x+4 y+1=0 )
and find the coordinates of the point where the lines meet.
10
297If ( 2 a=b, ) the pair of equations ( x+ )
( 2 y=2 a-6 b, a x+b y=2 a^{2}-3 b^{2} )
possess solution(s)
A. No
B. Only one
c. only two
D. An infinite number of slutions
10
298The ratio of income of two persons is 9:
7 and the ratio of their expenditure is
( 4: 3 . ) If each of them manages to save
Rs. 2000 per month, find their monthly income.
A. ( R s .18,000, ) Rs.14, 000
B. ( R s .1,000, R s .14,000 )
c. ( R s .18,000, ) Rs.1, 000
D. None of these
10
299f ( 3 x-2 y=5 ) and ( 3 y-2 x=3 ) then
find the value of ( (boldsymbol{x}+boldsymbol{y}) )
10
300Solve the following system of equation:
( frac{1}{2 x}-frac{1}{y}=-1 )
( frac{1}{x}+frac{1}{2 y}=8, ) where ( x neq 0, y neq 0 )
10
301If ( boldsymbol{x}=boldsymbol{m}+mathbf{1} ) and ( frac{mathbf{1}}{mathbf{3}}(mathbf{6} boldsymbol{x}-mathbf{3})-(mathbf{8}- )
( mathbf{3} boldsymbol{x})=mathbf{1 1} ; ) find the value of ( mathbf{m} )
A ( . m=2 )
в. ( m=3 )
c. ( m=7 )
D. ( m=5 )
10
302Draw the graph of equation ( 3 x+2 y=6 ) Find the sum of the co-ordinates of the
point where the graph intersects the ( Y ) axis.
10
303Find the equations of the lines for which ( tan theta=sqrt{2}, ) where ( theta ) is the angle of
inclination of the line and ( y- ) intercept
is -1
10
304Find the value of ( k ) so that the line ( 2 x- )
( k y-7=0 ) may be parallel to ( 3 x+ )
( 4 y+7=0 )
10
305The value of ( k ) for which the system of
equations
( 2 x+3 y=5 )
( 4 x+k y=10 )
has an infinite number of solutions, is
( mathbf{A} cdot mathbf{1} )
B. 3
( c cdot 6 )
D. 0
10
306Solve for ( x ) and ( y )
( boldsymbol{m} boldsymbol{x}-boldsymbol{n} boldsymbol{y}=boldsymbol{m}^{2}+boldsymbol{n}^{2}, boldsymbol{x}-boldsymbol{y}=boldsymbol{2} boldsymbol{n} )
A. ( x=m+n ; y=m-n )
в. ( x=m-n ; y=m n-n )
c. ( x=m+m n ; y=m+n )
D. ( x=m n-n ; y=m-n )
10
307Find the values of ( alpha & beta ) for which the
following system of linear equations has infinite number of solution.
( 2 x+3 y=7 )
( 2 alpha x+(alpha+beta) y=28 )
10
308Solve the following pair of equations by cross multiplication rule.
( frac{x}{a}+frac{y}{b}=0, frac{x}{a}-frac{y}{b}=4 )
A. ( x=2 a, y=-2 b )
в. ( x=-3 a, y=-b )
c. ( x=a, y=2 b )
D. None of these
10
309When a bucket is half full, the weight of
the bucket and the water is 10 kg. When the bucket is two-thirds full, the total
weight is 11 kg. What is the total weight, in kg, when the bucket is completely full?
A . 12
в. ( 12 frac{1}{2} )
( c cdot_{12} frac{2}{3} )
D. 13
10
310Solve the following pair of linear equations by the elimination method and the substitution method:
(i) ( x+y=5 ) and ( 2 x-3 y=4 )
(ii) ( 3 x+4 y=10 ) and ( 2 x-2 y=2 )
(iii) ( 3 x-5 y-4=0 ) and ( 9 x=2 y+7 )
(iv) ( frac{x}{2}+frac{2 y}{3}=-1 ) and ( x-frac{y}{3}=3 )
10
311If ( 2 a=b, ) the pair of equations ( a x+ )
( b y=2 a^{2}-3 b^{2}, x+2 y=2 a-6 b )
possess
A. no solution
B. only one solutions
c. only two solutions
D. an infinite number of solutions
10
312The sum of the two digits of a two digit number is 12. The number obtained by interchanging the digits exceeds the given number by 18. Find the number.10
313If the product of two numbers is 10 and
their sum is ( 7, ) which is the greatest of the two numbers?
A . -2
B. 2
( c .5 )
D. 4
10
314The equation of a straight line passing through the point of intersection of ( x- )
( boldsymbol{y}+mathbf{1}=mathbf{0} ) and ( mathbf{3} boldsymbol{x}+boldsymbol{y}-mathbf{5}=mathbf{0} ) and
perpendicular to one of them, is?
A. ( x+y+3=0 )
в. ( x-y-3=0 )
c. ( x-3 y-5=0 )
D. ( x-3 y+5=0 )
10
315Show that the following system of linear equations is consistent and also find their solution:
( mathbf{5} boldsymbol{x}+mathbf{3} boldsymbol{y}+mathbf{7} boldsymbol{z}=mathbf{4} )
( mathbf{3} boldsymbol{x}+mathbf{2 6} boldsymbol{y}+mathbf{2} boldsymbol{z}=mathbf{9} )
( mathbf{7} boldsymbol{x}+mathbf{2} boldsymbol{y}+mathbf{1 0} boldsymbol{z}=mathbf{5} )
10
316In a factory, the cost of manufacturing ( x )
article is ( R s 20+2 x ) and the selling
price of ( x ) articles is ( R s(2.5) x . ) Draw the graph and determine.
(i) Number of articles to be
manufactured and sold to reach break-
even point (no profit and no loss situation);
(ii) The profit made when 60 articles are manufactured and sold
10
317Draw the graph of equation2 ( y+x=7 )
and ( 2 x+y=8 ) on the same ( c o )
ordination system. Write the pt of intersection.
10
318Represent the solution of each of the
following inequalities on the real number line:
( 7-x leq 2-6 x )
10
319The slope of one of the lines given by ( a x^{2}+2 h x y+b y^{2}=0 ) is ( k ) times the
other, then
A ( cdot 4 k^{2} h=a b(1+k) )
B . ( k h^{2}=4 a b(1+k)^{2} )
C. ( k h^{2}=2 a b(1+k)^{2} )
D. ( 4 k h^{2}=a b(1+k)^{2} )
10
320Aftab tells his daughter, “Seven years ago, I was seven times as old as you were then. Also, three years from now, shall be three times as old as you will be.” Is not this interesting? Represent this situation algebraically.10
321If the system of equations ( 2 x+3 y- )
( mathbf{5}=mathbf{0}, mathbf{4} boldsymbol{x}+boldsymbol{k} boldsymbol{y}-mathbf{1 0}=mathbf{0} ) has an infinite
number of solutions, then
A ( cdot k=frac{3}{2} )
в. ( _{k neq frac{3}{2}} )
c. ( k neq 6 )
D. ( k=6 )
10
322A train covered a certain distance at a
uniform speed. If the train would have been ( 6 mathrm{km} / mathrm{h} ) faster, it would have taken
4 hours less than the scheduled time.
And, if the train were slower by ( 6 mathrm{km} / mathrm{h} )
it would have taken 6 hours more than
the scheduled time. Find the length of
the journey.
10
32311. For what values of m, does the system of equations
3x + my=m
2x-5x=20
has solution satisfying the conditions x > 0, y>0. (1980)
10
324From Delhi station, if we buy 2 ticket for
station ( A ) and 3 tickets for station ( B ), the
total cost is Rs.77. But if we buy 3 tickets for station ( A ) and 5 tickets for
station ( mathrm{B} ), the total cost is Rs. 124. What
are the fares from Delhi to station ( A ) and
to station B ?
A. ( A=R s .12 ; B=R s .17 )
в. ( A=R s .13 ; B=R s .17 )
c. ( A=R s .18 ; B=R s .17 )
D. ( A=R s .19 ; B=R s .17 )
10
325Determine, graphically, the vertices of the triangle formed by the lines
( boldsymbol{y}=boldsymbol{x}, mathbf{3} boldsymbol{y}=boldsymbol{x}, boldsymbol{x}+boldsymbol{y}=mathbf{8} )
B . (0,0),(4,4),(0,2)
D. (0,0),(4,4),(6,2)
10
326Use graph paper for this question. Take
( 2 c m=2 ) units on ( x ) -axis and ( 1 c m=1 )
unit on ( y ) -axis. Solve graphically the following
equations:
( 3 x+5 y=12 ; 3 x-5 y+18=0 )
(Plot only three points per line)
A. ( x=-1 ; y=3 )
в. ( x=-1 ; y=7 )
c. ( x=-1 ; y=5 )
D. ( x=-1 ; y=2 )
10
3271250 persons went to see a circus-show
Each adult paid Rs. 75 and each child
paid Rs. 25 for the admission ticket Find the number of adults and number
of children, if the total collection from them amounts to Rs. 61,250
A. Adults ( =600 ) and children ( =650 )
B. Adults = 300 and children = 450
c. Adults ( =800 ) and children ( =700 )
D. Adults ( =640 ) and children ( =800 )
10
328Show graphically that the pair of
equations ( 3 x+4 y=6,6 x+8 y=12 )
represents coincident lines
10
329Solve the following equations by graphical method ( 2 x+3 y=0 )10
330Solve: ( 3(2 x+y)=7 x y ) and
( mathbf{3}(boldsymbol{x}+mathbf{3} boldsymbol{y})=mathbf{1 1} boldsymbol{x} boldsymbol{y} )
where, ( boldsymbol{x} neq mathbf{0}, boldsymbol{y} neq mathbf{0} )
A ( cdot x=3 ; y=frac{1}{2} )
в. ( x=1 ; y=frac{3}{2} )
c. ( x=4 ; y=2 )
D. ( x=3 ; y=4 )
10
331If the system of equations ( 2 x+3 y=7 )
( 2 a x+(a+b) y=28 )
has infinitely many solutions, then
A ( . a=2 b )
B. ( b=2 a )
c. ( a+2 b=0 )
( mathbf{D} cdot 2 a+b=0 )
10
332Solve the following system of equations by the method of substitution:
( mathbf{3} boldsymbol{x}-mathbf{4} boldsymbol{y}=mathbf{1 0}, mathbf{4} boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{5} )
10
333Solve the following pair of equations
graphically; ( 2 x-3 y=1, & 4 x-3 y+ )
( mathbf{1}=mathbf{0} )
A. ( x=1 y=-1 )
В. ( x=-1 y=-1 )
c. ( x=-1 y=1 )
D. ( x=1 y=1 )
10
334Nitya and Satya have some marbles with them. Nitya says to Satya, “If you give one marble to me, we will have equal number of marbles. Satya says to Nitya, “If you give me one marble, I will have twice the number of marbles you
have”. How many marbles do Nitya and Satya have respectively?
A ( cdot 4,6 )
в. 5,7
( c cdot 6,4 )
D. 7,5
10
335Solve: ( 3 x+4 y=10,2 x-2 y=2 ) by the
method of elimination.
10
336Find the equations of the straight line
which passes through the point (-3,8) and cut positive intercepts on the coordinates axes whose sum is 7 .
10
337The graph of ( x=2 ) is a line parallel to
axis.
( A )
в. ( y=2 )
c. ( y )
D. None of these
10
338Solve the following simultaneous equations using graphical method ( boldsymbol{x}+boldsymbol{y}=boldsymbol{6} )
( boldsymbol{x}-boldsymbol{y}=boldsymbol{4} )
10
339Solve the following system of equations by the method of substitution:
( 3 x-7 y=7,11 x+5 y=87 )
10
340Solve the following pairs of equations.
( mathbf{3} boldsymbol{x}+mathbf{2} boldsymbol{y}=mathbf{4} ; mathbf{9} boldsymbol{x}+mathbf{6} boldsymbol{y}-mathbf{1 2}=mathbf{0} )
A. Many solution
B. No solution
c. Unique solution
D. None of these
10
341A purse contains only 25 paise and 10 paise coins. The total amount in the
purse is ( R s .8 .25 . ) If the number of 25
paise coins is one-third the number of 10 paise coins, then the total number of
coins in the purse is:
10
342Solve each of the following pairs of equations by the elimination method. ( 2 x+3 y=8 )
( 4 x+6 y=7 )
10
343inflated with both helium and nitrogen
gas. Between the two gases, the balloon
can be inflated up to 8 liters in volume.
The density of helium is 0.20 grams per
liter, and the density of nitrogen is 1.30 grams per liter. The balloon must be
filled so that the volumetric average
density of the balloon is lower than that
of air, which has a density of 1.20 grams per liter. Which of the following system of inequalities best describes
how the balloon will be filled, if ( x )
represents the number of liters of
helium and ( y ) represents the number of
liters of nitrogen?
A ( cdotleft{begin{array}{l}x+y>8 \ 20 x+130 y>120end{array}right. )
B. ( left{begin{array}{l}x+y=8 \ frac{0.2 x+1.30 y}{2}<1.20end{array}right. )
c. ( left{begin{array}{l}x+y leq 8 \ 0.20left(frac{x}{x+y}right)+1.30left(frac{y}{x+y}right)<1.20end{array}right. )
D ( cdotleft{begin{array}{l}x+y leq 8 \ 0.20 x+1.30 y<1.20end{array}right. )
10
344The coach of a cricket team buys 3 bats
and 6 balls for ( c 3900 ). Later, she buys
another bat and 3 more balls of the
same kind for ( c 1300 . ) Represent this situation algebraically and geometrically
10
345Find the equations of the lines for which ( tan theta=-1, ) where ( theta ) is the angle of
inclination of the line and ( x- ) intercept
is 4
10
346The sum of the present ages of the father and his son is 45 years. 5 years ago, the age of the father was 6 times
that of son. What is the present age of
the son?
10
347Draw the graph of i) ( y=2 x+5, ) ii)
( boldsymbol{y}=mathbf{2} boldsymbol{x}-mathbf{5}, ) iii) ( boldsymbol{y}=mathbf{2} boldsymbol{x} ) and find the
point of intersection on ( x ) -axis. Is the ( x )
coordinates of these points also the zero of the polynomial?
10
348( frac{5}{x+y}-frac{2}{x-y}=-1 )
( frac{15}{x+y}+frac{7}{x-y}=10 )
10
349Solve:
( mathbf{3}(mathbf{2 u}+boldsymbol{v})=mathbf{7} boldsymbol{u} boldsymbol{v} ) and
( mathbf{3}(boldsymbol{u}+mathbf{3} boldsymbol{v})=mathbf{1 1} boldsymbol{u} boldsymbol{v} )
10
350If ( a m neq b l, ) then the system of
equations ( a x+b y=c ) and ( l x+m y= )
( n ) has:
A. A unique solution
B. No solution
c. Infinitely many solutions
D. May or may not have a solution
10
351The difference of the slopes of the lines
represented by ( 6 x^{2}-5 x y+y^{2}=0 ) is
( mathbf{A} cdot mathbf{1} )
B . 2
( c .3 )
D.
10
352f ( 2 x+y=9 ) and ( 3 x-y=6 ) then find
the value of ( x )
10
353Find the value of ( p ) for which the given
simultaneous equation has unique solution:
( mathbf{8} boldsymbol{x}-boldsymbol{p} boldsymbol{y}+mathbf{7}=mathbf{0} ; quad mathbf{4} boldsymbol{x}-mathbf{2} boldsymbol{y}+mathbf{3}= )
( mathbf{0} )
A. All values of ( p ) except 4
в. ( p=7 )
( mathbf{c} cdot p=6 )
D. All values of ( p ) except 5
10
354Given set of equations is ( mathbf{1} . mathbf{3} boldsymbol{g}+mathbf{1} . mathbf{7} boldsymbol{h}=mathbf{5} )
( 3 h=20+13 g )
Based on the system of equations
above, determine the value of ( h )
( ^{A} cdot frac{7}{2} ) or 3.5
B. 3
c. ( frac{9}{2}=4.5 )
D. 4
10
355Find the value of ( x ) and ( y ) using elimination method:
( 2 x+3 y=-6 ) and ( b x+2 y=-10 )
A ( cdotleft(2, frac{-2}{3}right) )
B ( cdotleft(-2, frac{2}{3}right) )
c. ( left(2, frac{2}{3}right) )
D. ( left(-2, frac{-2}{3}right) )
10
356The equation of the straight line passing through the point (4,3) and making intercepts on the cordinate axes whose sum is ( -1, ) is :
A ( cdot frac{x}{2}+frac{y}{3}=-1 ) and ( frac{x}{-2}+frac{y}{1}=-1 )
B. ( frac{x}{2}-frac{y}{3}=-1 ) and ( frac{x}{-2}+frac{y}{1}=-1 )
c. ( frac{x}{2}+frac{y}{3}=-1 ) and ( frac{x}{-2}+frac{y}{1}=1 )
D. ( frac{x}{2}-frac{y}{3}=1 ) and ( frac{x}{-2}+frac{y}{1}=1 )
10
35762. The equations
3x + 4y = 10
– x + 2y = 0
have the solution (a, b). The val-
ue of a + b is
(1) 1
(2) 2 b y
(3) 3
(4) 4 –
10
358The work done by a body on application of a constant force is directly
proportional to the distance traveled by the body. Express this in the form of an equation in two variables and draw the graph of the same by taking the
constant force as 5 units. Read from the
graph, the work done when the distance traveled by the body is 0 units.
A. 0 units
B. 2 units
c. 1 units
D. 3 units
10
359If the straight line draw through the point ( P(sqrt{3}, 2) ) and inclined at an angle ( frac{pi}{6} ) with the ( x ) -axis,meets the line ( sqrt{3} x- ) ( 4 y+8=0 ) at Q.Find the length ( P Q ? )10
360Solve the following equations by substitution method.
( mathbf{5} boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{2} mathbf{1} ; mathbf{2} boldsymbol{x}-boldsymbol{y}=mathbf{4} )
A. ( x=3, y=2 )
в. ( x=-3, y=2 )
c. ( x=3, y=-2 )
D. None of these
10
361Plot the graph of line ( x=5 )10
362Equations of the two straight lines
passing through the point (3,2) and
making an angle of ( 45^{circ} ) with the line
( x-2 y=3, ) are
A. ( 3 x+y-7=0 ) and ( x+3 y+9=0 )
B. ( 3 x-y-7=0 ) and ( x+3 y-9=0 )
C ( . x+3 y-7=0 ) and ( x+3 y-9=0 )
D. none of these
10
363Five years later, the father’s age will be
three times the age of his son. Five years ago, father was seven times as old
as his son. Find their present ages.
10
364Give the graphical representation of the following equation
(a) On the number line and
(b) On the
Cartesian plane ( 2 x-9=0 )
10
36551. r *+1-and i+ya
Ex-Y
then the value of 1 + xay is
(1)
2ab
2-62
(2
a2_62
2ab
2ab
ab
10
3668 times a 2 digit number is equal to 3 times the number obtained by reversing
the order of the digit. If the difference
between digit is 5 then find the number.
10
367Solve the following pair of linear equations:
( frac{10}{x+y}+frac{2}{x-y}=4 ; frac{15}{x+y}-frac{5}{x-y}= )
-2
10
368If the perimeter of rectangle is ( 24 mathrm{m} ) represent this in the form of equation.10
369Solve the following pair of equations by reducing them to a pair of linear equations:
( frac{1}{2 x}+frac{1}{3 y}=2, frac{1}{3 x}+frac{1}{2 y}=frac{13}{6} )
A ( cdot x=frac{1}{4} ) and ( y=frac{1}{7} )
B. ( x=frac{2}{5} ) and ( y=frac{1}{3} )
c. ( _{x}=frac{3}{7} ) and ( y=frac{1}{7} )
D. ( x=frac{1}{2} ) and ( y=frac{1}{3} )
10
370Solve the following equations by the substitution method
( 11 x-8 y=27,3 x+5 y=-7 )
A. ( x=0, y=1 )
в. ( x=0, y=-5 )
c. ( x=2, y=3 )
D. ( x=1, y=-2 )
10
371( f frac{x}{a}+frac{y}{b}=1 ) and ( frac{x^{2}}{a^{2}}+frac{y^{2}}{b^{2}}=frac{a b}{a+b} )
then prove that ( frac{boldsymbol{x}^{boldsymbol{n}+mathbf{1}}}{boldsymbol{a}}+frac{boldsymbol{y}^{boldsymbol{n}+mathbf{1}}}{boldsymbol{b}}= )
( left(frac{a b}{a+b}right)^{n} )
10
372Solve equations using substitution method:
( 5 x-2 y=10 ) and ( 4 x-6 y=3 )
A ( cdot frac{-27}{11} ) and ( frac{25}{22} )
B. ( frac{27}{11} ) and ( frac{-25}{22} )
c. ( frac{27}{11} ) and ( frac{25}{22} )
D. ( frac{-27}{11} ) and ( frac{-25}{22} )
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373Solve the following pair of equations by reducing them to a pair of linear equations
( frac{5}{x-1}+frac{1}{y-2}=2 ) and ( frac{6}{x-1}- )
( frac{3}{y-2}=1 )
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374Solve the following systems of equations by the method of crossmultiplication:
( boldsymbol{x}+mathbf{2} boldsymbol{y}+mathbf{1}=mathbf{0} )
( 2 x-3 y-12=0 )
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375Solve the following pair of linear equations by cross miltiplication
method
( 0.3 x+0.4 y=2.5 ) and ( 0.5 x-0.3 y= )
( mathbf{0 . 3} )
A. ( x=-3 ) and ( y=4 )
в. ( x=3 ) and ( y=4 )
c. ( x=4 ) and ( y=-4 )
D. None of these
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376Based on equations reducible to linear
equations, solve for ( x ) and ( y ) ( frac{boldsymbol{x}-boldsymbol{y}}{boldsymbol{x} boldsymbol{y}}=mathbf{9} ; frac{boldsymbol{x}+boldsymbol{y}}{boldsymbol{x} boldsymbol{y}}=mathbf{5} )
A ( cdot x=-frac{1}{2}, y=frac{1}{7} )
B. ( _{x}=-frac{1}{5}, y=frac{1}{2} )
c. ( _{x=-frac{1}{5}, y}=frac{1}{7} )
D. None of these
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377Check if (2,3) will lie on the graph of ( (y-2 x)=-3, ) without drawing the
graph.
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378Solve ( : frac{9}{x}-frac{4}{y}=8 ) and ( frac{13}{x}+frac{7}{y}= )
( mathbf{1 0 1} )
A ( cdot x=frac{1}{7} y=frac{1}{6} )
В. ( x=frac{3}{4} y=frac{1}{6} )
c. ( x=frac{1}{4} y=frac{1}{7} )
D. ( x=frac{2}{7} y=frac{1}{7} )
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379The line passes through ( left(-1, frac{pi}{2}right) ) and perpendicular to the line ( sqrt{3} sin theta+ ) ( 2 cos theta=frac{4}{r} ) is:
A ( .2=sqrt{3} r cos theta-2 r sin theta )
в. ( 5=2 sqrt{3} r sin theta+4 r cos theta )
c. ( 2=sqrt{3} r cos theta+2 r sin theta )
D. ( 8=2 sqrt{3} r sin theta-4 r cos theta )
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380The difference between a two digit number and the number obtained by
the interchanging the digits is ( 27 . ) What is the difference between the two digits of the number?
( A cdot 9 )
B. 6
c. 12
D. 3
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381Reduce the equation ( x+2 y-5=0 ) to
slope-intercept form and find its slope
and ( boldsymbol{y}- ) intercept.
10
382Draw the graph of the following linear
equation
( -boldsymbol{x}+boldsymbol{y}=boldsymbol{6} )
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383Solve: ( a x+b y-c=0 )
( b x+a y=1+c )
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384Solve the following systems of linear equations by using the method of elimination by equating the coefficients:
(i) ( 3 x+2 y=11 )
(ii)2 ( boldsymbol{x}+mathbf{3} boldsymbol{y}=mathbf{4} )
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385Solve the following pair of an equation by elimination the coefficient method:
( x+2 y=11 )
( 2 x-y=2 )
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386Find the common solution:
( boldsymbol{y}=mathbf{3} boldsymbol{x}+mathbf{1} )
( boldsymbol{x}+boldsymbol{y}=mathbf{9} )
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387The father’s age is six times his son’s age. Four years hence, the age of the father will be four times his son’s age.
The present ages, in years, of the son and the father are respectively,
A. 4 and 24
B. 5 and 30
c. 6 and 36
D. 3 and 24
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388In the system of equations ( frac{12}{x+y}+ ) ( frac{8}{x-y}=8 ) and ( frac{27}{x+y}-frac{12}{x-y}=3, ) the
values of ( x ) and ( y ) will be
A ( cdot frac{5}{3} ) and ( frac{1}{3} )
B. ( frac{5}{2} ) and ( frac{1}{2} )
c. 2 and ( frac{1}{3} )
D. ( frac{5}{4} ) and ( frac{1}{4} )
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389Solve by cross multiplication method:
( 6 x+7 y-11=0 )
( 5 x+2 y=13 )
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390For the following system of equation
determine the value of ( k ) for which the
given system of the equation has a unique solution. ( boldsymbol{x}-boldsymbol{k} boldsymbol{y}=mathbf{2} )
( mathbf{3} boldsymbol{x}+mathbf{2} boldsymbol{y}=-mathbf{5} )
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391Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:
The sum of the digits of a two-dlgit number is ( 9 . ) Also, nine times this
number is twice the number obtained
by reversing the order of the digits. Find
the number
A. Number is 18
B. Number is 36
c. Number is 81
D. None of these
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392Solve graphically, the following pairs of equations:
( 2 x+y=23 )
( 4 x-y=19 )
A. ( x=1, y=4 )
B. ( x=9, y=2 )
c. ( x=5, y=0 )
D. ( x=7, y=9 )
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393Find the equation of the line passing
through the point (-4,-3) and perpendicular to the straight line joining (1,3) and (2,7)
10

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