Simple Equations Questions

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Simple Equations Questions

List of simple equations Questions

Question No Questions Class
1 A man bought a plot of land for
Rs. 8,47,500 to build a house. He spent Rs. 3,94,252 on building materials and
he paid ( R s .95,846 ) to laboures build
the house. How much money did he spend in all?
7
2 The line represented by ( x=7 ) is parallel
to the ( x ) -axis. Justify whether the statement is true or not.
A . True
B. False
7
3 The sum of ( 15, x, 51,2 x+3 ) is 114 find
( x )
7
4 The linear equation ( (2 x+5 y=7) ) has
A. a unique solution.
B. two solutions.
c. infinitely many solutions
D. no solution
7
5 If we multiply or divide both sides of a linear equation with a non-zero number, then the solution of the linear equation:
A. changes
B. remains the same
c. changes in case of multiplication only
D. changes in case of division only
7
6 A child drank 250 lit. on Sunday. On Monday he drank 650 lit. On Tuesday he drank 100 lit. How much in all did the
child drink?
A. 950 lit
B. 1000 litt
c. 850 lit
D. None of these
7
7 State which of the following are equation (with a variable) given reason and tell your answer. identify the variable from the equation with a variable.
( frac{3 q}{2}<5 )
7
8 Which of the following can be expressed as the sum of square of two positive integers, as well as three positive integers?
A . 75
в. 192
( c cdot 250 )
D. 100
7
9 What is an equation?
A. A statement in which the values of two mathematical
expressions are equal
B. An expression that computes the values of variables.
C. A mathematical expression.
D. None of these
7
10 The average weight of 39 students in a
class is ( 23 mathrm{kgs} ). Among them Sita is the heaviest while Tina is the lightest. If
both of them are excluded from the
class still the average remains same.
The ratio of weight of Sita to Tina is 15:
8, then what is the weight of the Tina?
7
11 Give the geometric representations of
( 2 x+9=0 ) as an equation
(i) in one variable
(ii) in two variable
7
12 The weight of Rahul is ( 5 k g ) more than
Sachin.The weight of Samir is 12 kg less than double the weight of Sachin.lf the total weight of all the three is 93 find the weight of each one of them.
A. Sachin-25 kg, Rahul – 30 kg, Samir 38kg
B. Sachin-25 kg, Rahul -30 kg, Samir 40 kg
c. Sachin- -25 kg, Rahul – 38 kg, Samir -25 kg
D. Sachin- -25 kg, Rahul -38 kg, Samir 38kg
7
13 The product of 2 rational numbers is ( frac{-28}{81} . ) If one of them is ( frac{14}{27} ) then the other one? 7
14 we UI MUTE statements given in LUUMI-A.
1.
Column-II
(p) 2
(q) 13
Find the value of x.
Column-I
(A) 8x +4=3 (x-1)+7
3x-2 2x+3 2
4 3 3
(©) 3 (5x – 7) -2(9x -11)
=4(8x – 13)-17
x+17 3
X +7 2
(r) 0
(s) 0<x<4
7
15 Find the addition of ( -2 x+1 ) and
( -2 x-2 )
7
16 Number of sides of equation in simple equation is/ are
A. Two
B. One
c. Three
D. None of these
7
17 The largest number of the three
consecutive number is ( x+1 ) then the
smallest number is
( mathbf{A} cdot x+2 )
B. ( x+1 )
( c )
D. ( x-1 )
7
18 Solve:
( frac{5 p+2}{8-2 p}=frac{7}{6} )
7
19 If ( boldsymbol{x}+mathbf{1}<mathbf{0} ) then ( |boldsymbol{x}| ) is
( mathbf{A} cdot mathbf{0} )
B. ( x+1 )
( c .-x )
D. ( -x-1 )
( E )
7
20 If ( frac{2 y+5}{3}=3 y-10, ) then the value of ( y )
is-
A . 4
B. 3
( c cdot 2 )
D. None of these
7
21 A man spends ( frac{1}{5} ) of his salary to meet pocket expenses and ( frac{4}{5} ) of the
remainder to meet other expenses If his
monthly savings amount to Rs 1200 his monthly salary is
( A cdot R s 3,750 )
B. Rs 8,500
c. ( R s 7,000 )
D. Rs 7,500
7
22 Solve the equation ( frac{2}{2-x}+frac{1}{2}- ) ( frac{4}{x(2-x)}=0 ) 7
23 The sum of three number is ( 15 . ) If the
second number is subtracted from the
sum of first and third number then we
get 5 an if twice of first number is added to second and if the third number
is subtracted from the sum we get 4
7
24 State which of the following are equations (with a variable ). Give reason
for your answer. Identify the variable from the equations with a variable. ( frac{4}{2}=2 )
7
25 If ( frac{x^{2}+n}{x^{2}+4}=1, ) then ( n= )
A. 4
B. 3
c.
D.
E . -3
7
26 The Inverse expression of ( x+frac{1}{x} ) will be:
A ( frac{x^{2}+1}{x} )
B. ( frac{1}{x}-x )
c. ( frac{x}{x^{2}+1} )
D. ( frac{x}{x^{2}-1} )
7
27 The equation ( _{-}-_{-}-_{-}–_{-}- ) and ( 2 x+ )
( 2=0 ) have the same solution.
A ( . x-1=0 )
B . ( x+1=0 )
c. ( x-2=0 )
D. ( x+2=0 )
7
28 Draw the graph of each of the following equations:
¡) ( boldsymbol{x}=mathbf{5} )
7
29 Show that no triangular number can be
of the form ( 3 n-1 )
7
30 61. Of the three numbers, the first
number is twice of the second
and the second is thrice of the
third number. If the average of
these 3 numbers is 20, then the
sum of the largest and smallest
numbers is
(1) 24
(2) 42
(3) 54 (4) 60
7
31 State which of the following are equation (with a variable) given reason and tell your answer. identify the variable from the equation with a variable.
( mathbf{7}=(mathbf{1 1} times mathbf{2}) div boldsymbol{p} )
7
32 The difference of two numbers is 21 , the
larger number is ( x, ) then smaller number
is
A. 21+x
B. 21-x
c. ( x-21 )
D. -x-21
7
33 Abhishek has Rs.7.45. He bought toffees
for Rs.5.30. Find the balance amount left
with him.
7
34 The value of the variable which satisfies
the equation is called the
A . coefficient
B. degree
c. variable
D. solution of the equation
7
35 Form the expression for: “Sum of number ( a ) and ( b ) subtracted from their
product-
7
36 Solve the equation
[
begin{array}{l}
frac{(x-b)(x-c)}{(a-b)(a-c)}+frac{(x-c)(x-a)}{(b-c)(b-a)}+ \
frac{(x-a)(x-b)}{(c-a)(c-b)}=1
end{array}
]
7
37 What is a linear equation? 7
38 Write L.H.S and R.H.S of the following simple equations:
( 2 a-3=5 )
7
39 State true or false:
If we multiply both sides of an equation by zero, then we can create an
equivalent equation.
A. True
B. False
7
40 64. Two numbers are 30% and 40%
more than the third number re-
spectively. The first number is
x% of the second. Then x=
(1) 105
(3) 105
(2) 140
(492
7
41 If ( 2 x+frac{1}{3 x}=5 ) then the value of
( frac{5 x}{6 x^{2}+20 x+1} ) is
A ( cdot frac{3}{7} )
B. ( frac{2}{7} )
( c cdot frac{1}{7} )
D.
7
42 Find ( mathbf{k} ) if ( frac{mathbf{1}}{mathbf{6} !}+frac{mathbf{1}}{mathbf{7} !}=frac{boldsymbol{k}}{mathbf{8} !} ) 7
43 ( ln frac{2}{3} p-2 frac{1}{2}=3 frac{1}{2}, ) the value of ( p ) is
A . – 9
B. +6
( c cdot+9 )
D.
7
44 Find and correct errors of the following mathematical expressions:
( x+2 x+3 x=6 x )
7
45 The numerator of a fraction is 4
less than its denominator. If the
numerator is decreased by 2 and
the denominator is increased by
1, then the denominator becomes
eight times the numerator. Find
the fraction.
0000
7
46 Express the given linear equation in the form ( a x+b y+c=0 ) and indicate the
values of ( a, b ) and ( c ) in given case:
( boldsymbol{x}-frac{boldsymbol{y}}{mathbf{2}}-mathbf{5}=mathbf{0} )
7
47 Lightning quickly heats the air causing it to expand, which produces the sound
of thunder.

Sound travels approximately 1 mile in 5 seconds. Knowing ( boldsymbol{X}=boldsymbol{r} cdot boldsymbol{t} ) (where ( boldsymbol{D}= )
distance, ( r=text { rate and } t=text { time }), ) how
far away is a thunderstrom when you
notice a 3 -second delay between the
flash of lightning and the sound of
thunder?
( mathbf{A} cdot 1 ) mile away
B. ( 3 / 5 ) mile away
c. ( 1 / 2 ) mile away
D. ( 1 / 5 ) mile away

7
48 Get the algebraic expressions in the following case using variable, constants and arithmetic operations. One-half of the sum of numbers x and y 7
49 ( 9548+7314=8362+(?) )
A .8230
В. 8410
( c .8500 )
D. 8600
E. None of these
7
50 15. Naresh’s age is 4 years less than
twice the age of his brother. Which
of the following represents the
equation to find his age?
(1) 2x + 4 (2) 4x + 2
(3) X-4
(4) 2x – 4
7
51 1. A wall is built with 254 bricks. A
builder has to built 88 such walls.
He has 20,100 bricks and has
ordered for 500 more bricks.
How many bricks still be re-
quired ?
(1) 2352 (2) 1352
(3) 1752 (4) 2052
7
52 Solve:3 ( -2 x geq x-32 ) for ( x in I ) 7
53 Solve: ( -frac{5 x-4}{8}-frac{x-3}{5}=frac{x-6}{4} ) 7
54 ( A, B ) and ( c ) can do a piece of work in 12 days, 15 days and 10 days respectively In what time will they all together finish it?
A. 6 days
B. 4 days
c. 8 days
D. 2 days
7
55 Number of variables in a simple linear equation are
A. Two
B. one
c. 0
D. None
7
56 If ( x ) is an even number then the
consecutive even number is
( A cdot x+1 )
B. x+2
( c cdot 2 x )
D. x-2
7
57 Mohit baked 2000 cookies. He sold 600
of them and gave the rest equally to 20 of his friends. How many cookies did
each of his friends receive?
A . 18
B. 70
c. 80
D. 1400
7
58 The sum of numeretor and deniminator
of a faction 4 more than its numerator If
3 is added to numerator and
denominator, its ratio becomes 2: 3
Find the fraction
7
59 If ( frac{3 x-1}{5}-frac{1+x}{2}=3-frac{x-1}{2}, ) then ( x= )
( A cdot 2 )
B. 3
( c cdot 7 )
D. 12/7
7
60 66. A number xwhen divided by 289
leaves 18 as the remainder. The
same number when divided by
17 leaves y as a remainder. The
value of y is
(1) 5
(2) 2
(3) 3
(4) 1
7
61 The equation ( x-2=0 ) on number line
is represented by
( A ). a line
B. a point
c. infinitely many lines
D. two lines
7
62 Value of ( x ) in ( frac{2}{3} x+6=12 )
A . –
B. +27
( c cdot+9 )
D. -27
7
63 56. A drum of kerosene is full.
When 30 litres of kerosene is
drawn from it, it remains full.
The capacity of the drum is
(1) 1201 (2) 135 1
(3) 1501 (4) 180 1
7
64 Get the algebraic expressions in the
following case using variables, constants and arithmetic operations. One-fourth of the product of numbers p and ( q )
7
65 How are the points (0,1),(3,1) and (1,3) situated with respect to the circle ( x^{2}+y^{2}-2 x-4 y+3=0 ) 7
66 ( 2+frac{1+n}{n}=frac{7}{2} ) find ( n ) 7
67 Solve: for ( x )
( frac{3-2 x}{2 x+5}=-frac{3}{11} )
7
68 The difference of the squares of two
consecutive odd integers is divisible by which of the following integers?
( A cdot 3 )
B. 6
( c cdot 7 )
D. 8
7
69 The substraction of 3 from ( 2 x ) is
represent as
A. ( 2 x-3 )
B. 3-2xx
( c cdot 2 x+3 )
( D cdot frac{2 x}{3} )
7
70 Solve
( boldsymbol{x}-boldsymbol{4}=boldsymbol{9} )
7
71 Write the expression of following
statement:
5 is taken from ( y ) we get ( x )
7
72 Equations with linear expressions in one variable only are called in
one variable.
7
73 Convert the statement into an equation Adding 14 to 9 times ( y ) is 89
A ( .14 y+9=89 )
B. ( 14+9 y=89 )
c. ( 14-9 y=-89 )
D. ( 14+y=89 )
7
74 Find ( x )
i)x-4=3
ii) ( 9 x=81 )
iii)x+6=10
A ( . x=7,9,4 )
( c cdot x=-1,4,5 )
D. ( x=-3,6,7 )
7
75 The value of ( left(1+frac{1}{a}right)left(1+frac{1}{a-1}right)left(1+frac{1}{a-2}right) )
A. ( frac{a-3}{a} )
B. ( frac{a+1}{a-4} )
c. ( frac{a+1}{a-1} )
D. ( frac{a-1}{a-4} )
7
76 A man travelled ( 72 mathrm{km} ) to the North of
Hubballi and then ( 121 mathrm{km} ) to the south
of it. How far from Hubballi was he
finally.
( mathbf{A} cdot 49 mathrm{km} )
B. 9 кт
c. ( 49 mathrm{m} )
D. ( 4 mathrm{km} )
7
77 The parking charges of a vehicle in a
shopping centre is ( R s 40 ) for first 2
hours and ( R s 5 ) for each subsequent
hour. Write an equation for 8 hours.
7
78 Solve in positive integers:
( 5 x+2 y=53 )
A. ( x=1,3,5,7,9 ; y=24,19,14,9,4 )
В. ( x=2,4,6,8,10 ; y=23,20,13,8,3 )
c. ( x=11,13,15,17,19 ; y=1,3,4,6,9 )
D. None of these
7
79 19. Five years ago, the ages of Raju
and Rani were in the ratio 1:
10. Today the sum of their ages
is 32 years. What will be their
ages after 10 years ?
(1) 7, 27 (2) 17, 35
(3) 15, 55 (4) 18, 38
7
80 Find the general solution of the
congruence ( 98 x-1 equiv 0(bmod .139) )
7
81 Simplify ( frac{x}{sqrt{x+4}}, x>0 ) 7
82 If ( a=0.1039, ) then the value of ( sqrt{4 a^{2}-4 a+1}+3 a ) is:
A . 0.1039
B. 0.2078
c. 1.1039
D. 2.1039
7
83 If ( 1400 times x=1050 . ) Then, ( x=? )
A ( cdot frac{1}{4} )
B. 3
( c cdot frac{2}{3} )
D.
E. None of these
7
84 Solve for ( -boldsymbol{x} )
( frac{mathbf{5}}{boldsymbol{x}}=frac{mathbf{7}}{boldsymbol{x}-mathbf{4}} )
7
85 Standard form for linear equation in one variable? 7
86 Identify the variable from the equation, ( (t-7)>5 ? ) 7
87 Fill in the blank:
If a system has at least one solution, it is said to be
A. Consistent
B. Inconsistent
c. Dependent
D. Independent
7

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