Quadratic Equations Questions

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

List of quadratic equations Questions

Question No Questions Class
1 If ( alpha ) and ( beta ) are the roots of ( a x^{2}+b x+ )
( c=0 ) then find the roots of the equation
( a x^{2}-b x(x-1)+c(x-1)^{2}=0 )
10
2 75. A boat goes 40 km upstream in 8
hours and 36 km downstream in
6 hours. The speed of the boat
in still water is
(1) 6.5 km/hour
(2) 5.5 km/hour
(3) 6 km/hour
(4) 5 km/hour
10
3 If the one of the roots of the equation is zero find ‘a’
( boldsymbol{x}^{2}-2 boldsymbol{a} boldsymbol{x}+boldsymbol{a}^{2}+boldsymbol{a}-boldsymbol{2}=mathbf{0} )
Selective the positive answer.
10
4 Find the roots of the equation ( x ) ( frac{1}{3 x}=frac{1}{6},(x neq 0) ) 10
5 Solve the following equations:
( boldsymbol{x} boldsymbol{y}+boldsymbol{x}+boldsymbol{y}=boldsymbol{2} boldsymbol{3} )
( boldsymbol{x} boldsymbol{z}+boldsymbol{x}+boldsymbol{z}=boldsymbol{4} mathbf{1} )
( boldsymbol{y} boldsymbol{z}+boldsymbol{y}+boldsymbol{z}=mathbf{2 7} )
A. ( x=4,-2 ; y=2 ; 6 ; z=6,-5 )
в. ( x=2,-4 ; y=2,4 ; z=2,-6 )
c. ( x=5,-7 ; y=3,-5 ; z=6,-8 )
D. ( x=3,4 ; y=2,-5 ; z=2,-7 )
10
6 If ( boldsymbol{a}(boldsymbol{p}+boldsymbol{q})^{2}+2 boldsymbol{b} boldsymbol{p} boldsymbol{q}+boldsymbol{c}=boldsymbol{0} ) and ( boldsymbol{a}(boldsymbol{p}+ )
( r)^{2}+2 p b r+c=0(a neq 0), ) then
A ( cdot q r=p^{2} )
B ( cdot q r=p^{2}+frac{c}{a} )
c. ( q r=-p^{2} )
D. None of the above
10
7 6.
(3x – 8)(3x+2)-(4x-11)(2x+1)=(x-3)(x + 7)
10
8 Solve
( 3 x^{2}+20 x+8 )
10
9 >
is
62. The difference of two factors for
the expression a4 + –
(1) -4 12) – 2
(3) 2
(4) 4
10
10 Solve ( : 3^{4 x+1}-2 times 3^{2 x+2}-81=0 )
A. ( x=-3 )
B. ( x=9 )
c. ( x=-1 )
D. ( x=1 )
10
11 The roots of the equation ( sqrt{3 x+1} ) ( mathbf{1}=sqrt{boldsymbol{x}} ) are
( mathbf{A} cdot mathbf{0} )
B.
c. ( 0, )
D. None
10
12 The graph of an equation is given
above. What is the degree of the
polynomial?
( A )
B.
( c )
( D )
10
13 The value of ( m ) for which one of the roots
of ( x^{2}-3 x+2 m=0 ) is double of one of
the roots of ( x^{2}-x+m=0 ) is
A . -2
B.
( c cdot 2 )
D. None of the above
10
14 Add the following ( mathbf{2} p^{2} boldsymbol{q}^{2}-mathbf{3} boldsymbol{p} boldsymbol{q}+boldsymbol{4}=mathbf{0}, mathbf{5}+mathbf{7} boldsymbol{p} boldsymbol{q} )
( 3 p^{2} q^{2}=0 )
10
15 Solve :
[
boldsymbol{x}^{2}-boldsymbol{8} boldsymbol{x}+mathbf{1 2}=mathbf{0}
]
10
16 If ( a-b=1 ) and ( a b=12, ) find the value
of ( left(a^{2}+b^{2}right) )
10
17 If the roots of the equation ( x^{2}+p x- )
( 6=0 ) are 6 and -1 then the value of ( p )
is
A . 2
B. 3
( c .-5 )
D. 5
10
18 Determine the nature of roots of the
given quadratic equation ( 3 x^{2}+ ) ( mathbf{2} sqrt{mathbf{5}} boldsymbol{x}-mathbf{5}=mathbf{0} )
10
19 Factorise
( 63 a^{2}-112 b^{2} )
10
20 Find ( k, ) so that ( (k-12) x^{2}+2(k- )
12) ( x+2=0 ) has equal roots, where
( k neq 12 )
( mathbf{A} cdot k=4 )
B. ( k=12 )
c. ( k=14 )
D. none of these
10
21 7. If y = x2 + 2x – 3, y-x graph is
X
(6)
(c)
-3
-X
(d)

1-3
10
22 Find the exact position solution of the
equation ( x^{2}+x=30 )
10
23 If ( 4 y^{2}+4 y+1=0, ) then ( y=0 )
A. Yes
B. No
c. Ambiguous
D. Data insufficient
10
24 24.
Let a, b, c be real numbers with a 70 and let a, ß be the roots
of the equation ax? + bx + c = 0. Express the roots of
aºx2 + abex + c = 0 in terms of a, B. (2001 – 4 Marks)
10
25 The quadratic polynomial whose sum of
zeroes is 3 and product of zeroes is -2 is:
A ( cdot x^{2}+3 x-2=0 )
B . ( x^{2}-2 x+3=0 )
c. ( x^{2}-3 x+2=0 )
D. ( x^{2}-3 x-2=0 )
10
26 The values of k for which the roots are
real and equal of the following equation ( 3 x^{2}-5 x+2 k=0 ) is
( k=frac{25}{24} )
A. True
B. False
10
27 Find the values of ( K ) so that the
quadratic equations ( x^{2}+2(K-1) x+ )
( K+5=0 ) has atleast one positive root
A. ( k leq-1 )
B. ( k leq 1 )
c. ( k geq-1 )
D. ( -1 leq k leq 1 )
10
28 The number of values ( k ) for which ( left[x^{2}-right. )
( left.(k-2) x+k^{2}right]left[x^{2}+k x+(2 k-1)right] ) is a
perfect square is
( A cdot 2 )
B.
( c cdot 0 )
D. None of these
10
29 Let ( x=2 ) be a root of ( y=4 x^{2}-14 x+ )
( boldsymbol{q}=mathbf{0} . ) Then ( boldsymbol{y} ) is equal to
A ( cdot(x-2)(4 x-6) )
В. ( (x-2)(4 x+6) )
c. ( (x-2)(-4 x-6) )
D. ( (x-2)(-4 x+6) )
10
30 Factorize:
( 2 m^{2}+39 m+19 )
10
31 By increasing the speed of a car by 10 ( k m / h r, ) the time of journey for a distance of ( 72 k m ) is reduced by 36
minutes. Write an equation for the given information and check if it is a
Quadratic Equation?
10
32 If 2,8 are the roots of ( x^{2}+a x+beta=0 )
and 3,3 are the roots of ( x^{2}+alpha x+b= )
0 then find the roots of ( x^{2}+a x+b=0 )
A . -1,-9
в. 1,9
c. -2,-8
D. 2,8
10
33 If ( 3 x^{2}+10=11 x, ) then ( x=2, frac{5}{3} )
A. Yes
B. No
c. Ambiguous
D. Data insufficient
10
34 Solve the given quadratic equation by using the formula method, ( (2 x+ )
( mathbf{3})(mathbf{2} boldsymbol{x}-mathbf{2})+mathbf{2}=mathbf{0} )
10
35 71. There is a square field whose side
is 44 m. A square flowerbed is
prepared in its centre, leaving a
gravel path of uniform width all
around the flowerbed. The total
cost of laying the flowerbed and
gravelling the path at Rs. 2 and
Re. 1 per square metre respec-
tively is Rs. 3536. Find the width
of the gravelled path.
(1) 1 metre (2) 1.5 metre
(3) 2 metre (4) 2.5 metre
10
36 Find the discriminant of the following quadratic equations and hence determine the nature of the roots of the
equation:
( frac{1}{4} x^{2}-2 x+1=0 )
10
37 If the following quadratic equation has two equal and real roots then find the
value of ( mathrm{k}: )
( 4 x^{2}-5 x+k=0 )
10
38 If ( (3-2 x) ) and ( (5 x+8) ) are factors of
( left(-10 x^{2}+h x-kright), ) then the values of ( h )
and ( k ) are respectively
A. -1 and 24
B. 1 and 24
c. -1 and -24
D. 1 and -24
10
39 if ( alpha ) and ( beta ) are sum and product of roots of the given equation respectively, then
( (-boldsymbol{alpha} boldsymbol{beta}) ) is
A. always a prime number
B. always an odd integer
c. always an irrational number
D. dependent on value of a
10
40 Determine the set of values of ( k ) for
which the given quadratic equation has
real roots:
( mathbf{2} boldsymbol{x}^{2}+boldsymbol{k} boldsymbol{x}-boldsymbol{4}=mathbf{0} )
10
41 Find the value of ( p ) such that quadratic
equation ( (boldsymbol{p}-mathbf{1 2}) boldsymbol{x}^{2}-boldsymbol{2}(boldsymbol{p}-mathbf{1 2}) boldsymbol{x}+ )
( 2=0 ) has equal
10
42 The positive root ( x^{2}+b x+8=0 ) is
twice the other root then ( b= )
A. 6
B. – –
c. 12
D. -12
10
43 By selling an article for Rs.24, a trader
loses as much percent as the cost price of the article. Write an equation to express this information and check if it is convertible to a Quadratic Equation.
10
44 ( x^{2}+6 x+9=0 )
( x=? )
10
45 If ( 6 x-x^{2}=1, ) then the value of ( (sqrt{x}- )
( left.frac{1}{sqrt{x}}right) ) is
( A cdot 2 )
B. 3
c. 1
D. –
10
46 For the equation ( boldsymbol{x}^{2}-(boldsymbol{k}+mathbf{1}) boldsymbol{x}+left(boldsymbol{k}^{2}+right. )
( k-8)=0 ) if one root is greater then 2
and other is less than 2 , then ( k ) lies
between
A . ( -2 & 3 )
B. 2 & – 2
c. ( 2 &-3 )
D. None of these
10
47 Solve for ( x: x^{5}+242=frac{243}{x^{5}}, ) where ( x ) is
real number.
10
48 Find the discriminant for the given quadratic equation:
( boldsymbol{x}^{2}+boldsymbol{x}+mathbf{1}=mathbf{0} )
A . -3
B. – 5
( c .-7 )
D. – –
10
49 If ( boldsymbol{h}=mathbf{5}, boldsymbol{k}=mathbf{3} ) then find the value of
( frac{k^{3}}{9}+frac{h k}{10} )
10
50 Find the product of the roots of equation ( left(frac{x}{sqrt{2}}-2right)(x-sqrt{2})=0 )
( mathbf{A} cdot mathbf{4} )
B. 3
c. 2
( D )
10
51 21. Let p,q e{1,2,3,4}. The number of equations of the form 3
px2 + qx+1=0 having real roots is
(1994)
(a) 15 (b) 9 (C) 7 let, (d) 8
10
52 Check whether ( boldsymbol{x}^{2}+frac{1}{2} boldsymbol{x}=mathbf{0} ) is
a quadratic equation.
10
53 Which of the following is not a quadratic equation
A ( cdot x-frac{3}{2 x}=5 )
в. ( 4 x-frac{5}{8}=x^{2} )
c. ( _{x+frac{1}{x}=9} )
D. ( 4 x-frac{2}{3 x}=4 x^{2} )
10
54 Assertion
Let equations ( a x^{2}+b x+c= )
( mathbf{0}(boldsymbol{a}, boldsymbol{b}, boldsymbol{c} in boldsymbol{R}) & boldsymbol{x}^{2}+mathbf{2} boldsymbol{x}+mathbf{5}=mathbf{0} ) have
common root, then ( frac{boldsymbol{a}+boldsymbol{c}}{boldsymbol{b}}=frac{mathbf{1}}{mathbf{3}} )
Reason
If both roots of ( A x^{2}+B x+K_{1}=0 & )
( boldsymbol{A}^{prime} boldsymbol{x}^{2}+boldsymbol{B}^{prime} boldsymbol{x}+boldsymbol{K}_{2}=mathbf{0} ) are identical
( operatorname{then} frac{boldsymbol{A}}{boldsymbol{A}_{1}}=frac{boldsymbol{B}}{boldsymbol{B}_{1}}=frac{boldsymbol{K}_{1}}{boldsymbol{K}_{2}}left(text { where } boldsymbol{A}, boldsymbol{B}, boldsymbol{K}_{1}right. )
and ( left.A^{prime}, B,^{prime} K_{2} in Rright) )
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect, Reason is correct
10
55 Roots of quadratic equation ( 5 x^{2}- ) ( 22 x-15=0 ) are
A ( cdot_{-5,} frac{-3}{5} )
в. ( _{5,} frac{3}{5} )
c. ( _{5}, frac{-3}{5} )
D. None of these
10
56 If the roots of the equation ( 5 x^{2}-7 x+ )
( k=0 ) are mutually reciprocal then ( k= )
A . 5
B. 2
( c cdot frac{1}{5} )
D. None of these
10
57 Find a two-digit number which exceeds
by 12 the sum of the squares of its digits and by 16 the doubled product of its digits.
10
58 Find the value of ( K ), If the roots of the
following quadratic equation are equal ( : x^{2}+K x^{2}+1=0 )
10
59 When will the quadratic equation
( boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{b} boldsymbol{x}+boldsymbol{c}=boldsymbol{0} ) NOT have Real Roots?
A. ( b^{2}-4 a c geq 0 )
B . ( b^{2}-4 a c>0 )
c. ( b^{2}-4 a c<0 )
D. None of these
10
60 If ( a, b, c ) are real and ( b^{2}-4 a c ) is perfect
square then the roots of the equation
( boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{b} boldsymbol{x}+boldsymbol{c}=mathbf{0}, ) will be:
A. Rational & distinct
B. Real & equal
C. Irrational & distanct
D. Imaginary & distinct
10
61 Given that ( z^{2}-10 z+25=9, ) what is ( z )
( ? )
A .3,4
в. 1,6
( c .2,6 )
D. 2,
10
62 Find the roots using factorisation
( 9 x-x^{2}=0 )
A . 1,9
B. 0,9
( c .9,9 )
D.
10
63 A two digit number is such that the product of its digits is ( 18 . ) When 63 is subtracted from the number, the digits interchange their places. Find the number 10
64 State the following statement is True or
False
The digit at ten’s place of a two digit number exceeds the square of digit at units place ( (x) ) by 5 and the number formed is ( 61, ) then the equation is
( mathbf{1 0}left(boldsymbol{x}^{2}+mathbf{5}right)+boldsymbol{x}=mathbf{6 1} )
A. True
B. False
10
65 The two sides of a right-angled triangle are ( boldsymbol{x}, boldsymbol{x}+mathbf{1} ) and hypotenuse, the longest
side is ( sqrt{1} 3 . ) Find the area of the
triangle.
A ( cdot 1 mathrm{m}^{2} )
B. ( 2 mathrm{m}^{2} )
( c cdot 3 m^{2} )
D. ( 4 mathrm{m}^{2} )
10
66 From ( 2012-2016, ) the amount (in crores)
spent on natural gas ( mathrm{N} ) and electricity ( mathrm{E} ) by Indian residents can be described by the following expressions, where t is the number of years since 2012 Gas spending model, ( mathrm{N}=2.13 t^{2}-4.21 t+37.40 )
Electricity spending model, ( mathrm{E}=-0.209 t^{2}+5.393 t+307.735 )
What is the total amount A spent on
natural gas and electricity by Indian residents from 2012 to 2016?
A. ( 1.467 t^{2}+7.423+121.721 )
1
B. ( 1.339 t^{2}-8.729 t+76.245 )
c. ( 1.01 t^{2}+7.083+97.83 )
D. ( 1.921 t^{2}+1.183 t+345.135 )
10
67 If the roots of the equation ( x^{2}+p x+ )
( c=0 ) are (2,-2) and the roots of the
equation ( boldsymbol{x}^{2}+boldsymbol{b} boldsymbol{x}+boldsymbol{q}=mathbf{0} ) are ( (-mathbf{1},-mathbf{2}) )
then the roots of the equation ( x^{2}+ )
( b x+c=0 ) are
A ( .-3,-2 )
в. -3,2
c. 1,-4
D. -5,1
10
68 For what values of ( k, ) the roots of the
quadratic equation ( (boldsymbol{k}+mathbf{4}) boldsymbol{x}^{2}+(boldsymbol{k}+ )
1) ( x+1=0 ) are equal?
10
69 32. Let a, b, c be the sides of a triangle where a #bec and 2
R. If the roots of the equation
x2 +2(a+b+c)x +32 (ab + bc+ca)= 0 are real, then
(2006 – 3M, -1)
(6) and
10
70 If the equation ( k x^{2}+4 x+1=0 ) has
real and distinct roots, then:
( mathbf{A} cdot k4 )
( mathbf{c} cdot k leqslant 4 )
D. ( k geqslant 4 )
10
71 A train travels a distance of ( 480 k m ) at a
uniform speed. If the speed had been ( 8 k m / h r ) less, then it would have taken
3 hours more to cover the same
distance. Formulate the quadratic equation in terms of the speed of the train.
10
72 Find the value ( frac{left(x^{2}-4right)}{(x+2)} )
A ( .2 x-2 )
B. ( x-2 )
c. ( x+2 )
D. None of these
10
73 Find the nature of the roots of the
following quadratic equations. If the real roots exist, find them:
(i) ( 2 x^{2}-3 x+5=0 )
(ii) ( 3 x^{2}-4 sqrt{3} x+4=0 )
(iii) ( 2 x^{2}-6 x+3=0 )
10
74 ( sqrt{2} sec x+tan x=1 ) 10
75 Check whether ( 3 x-10=0 ) is
a quadratic equation.
10
76 For what value of ( k ) does ( (k-12) x^{2}+ )
( mathbf{2}=mathbf{0} ) have equal roots?
10
77 Consider quadratic equation ( a x^{2}+ ) ( (2-a) x-2=0, ) where ( a in R )
If exactly one root is negative, then the
range of ( a^{2}+2 a+5 ) is
( A cdot[4, infty) )
B ( cdot[-2, infty) )
c. ( (-infty, 4] )
( D cdot(5, infty) )
10
78 21. Let a, b, c be real. If ax2+bx+c=0 has two real roots a. and
B, where a 1, then show that 1++ <0.
a al
(1995 – 5 Marks)
where 24-1 med p21. then she was release
10
79 If one of the roots of ( a x^{2}+b x+c=0 ) is
( mathbf{7}+sqrt{mathbf{2}} ) then find the other root
A. ( -7+sqrt{2} )
B. ( 7-sqrt{2} )
c. ( -7-sqrt{2} )
D. Cannot be determined
10
80 Roots of the equation ( boldsymbol{x}^{3}-(boldsymbol{a}+boldsymbol{b}+ )
( c) x^{2}+(a b+b c+c a) x-a b c=0 )
( x^{2}+2 x+7=0 ) and ( a x^{2}+b x+c=0 )
have a common root, where ( a, b, c in R, ) can
be
A .4,8,28
В. 1,2,7
c. 1,4,36
D. None of the above
10
81 Check whether ( 6 x^{3}+x^{2}=2 ) is
a quadratic equations
10
82 The roots of ( x^{2}+k x+k=0 ) are real
and equal, find ( k )
10
83 If ( x^{2}-b x+c=0 ) has equal integral
roots, then
This question has multiple correct options
A. ( b ) and ( c ) are integers
B. ( b ) and ( c ) are even integers
( mathrm{c} . b ) is an even integer and ( c ) is a perfect square of an integer
D. none of these
10
84 Determine the nature of the roots of the
given equation from their discriminants.
( 2 y^{2}+11 y-7=0 )
A. Real and equal
B. Real and unequal
c. one real and one imaginary
D. Both imaginary
10
85 Find ( p in R ) for ( x^{2}-p x+p+3=0 ) has
A. One positive and one negative root.
B. Both roots are negative
c. one root ( >2 ) and the other root ( <2 )
D. None of the above
10
86 Find the value of ( k ) for which the given
equations has real and equal roots:
(i) ( (k-12) x^{2}+2(k-12) x+2=0 )
(ii) ( k^{2} x^{2}-2(k-1) x+4=0 )
10
87 Find the discriminant of the equation and the nature of roots. Also find the
roots.
( 6 x^{2}+x-2=0 )
A ( cdot D=49, ) Real and distinct roots: ( frac{1}{5}, frac{-2}{3} )
B. ( D=39 ), Real and distinct roots: ( frac{1}{2}, frac{-2}{3} )
C. ( D=49 ), Real and distinct roots: ( frac{1}{3}, frac{-7}{3} )
D. ( D=49 ), Real and distinct roots: ( frac{1}{2}, frac{-2}{3} )
10
88 The roots of the equation ( x^{2}-2 sqrt{2} x+ )
( mathbf{1}=mathbf{0} ) are-
A. Real and distinct
B. Imaginary and different
c. Real and equal
D. Rational and different
10
89 The given quadratic equations have real roots and the roots are ( -sqrt{2}, frac{-5}{sqrt{2}} ) ( sqrt{2} x^{2}+7 x+5 sqrt{2}=0 )
A. True
B. False
10
90 Amy is 5 years older than her sister Julie. If the product of their ages is 6 Find the age of Julie.
A. 1 year
B. 2 years
c. 3 years
D. 4 years
10
91 Solve:6 ( +7 b-3 b^{2} ) 10
92 6. Ifx—2-2—2, then x is equal to?
x-2
10
93 If ( x^{2}+a x+b ) is an integer for every
integer ( boldsymbol{x} ) then
A. ( a ) is always an integer but b need not be an integer
B. ( b ) is always an integer but a need not be an integer
( mathrm{c} cdot a+b ) is always an integer
D. none of these
10
94 If the roots of the equation ( p x^{2}+q x+ )
( r=0 ) are in the ratio ( =l: m )
( left(l^{2}+m^{2}right) p r+l mleft(2 p r-q^{2}right)=0 )
10
95 If the equation ( 16 x^{2}+6 k x+4=0 ) has
equal roots, then the value of ( k ) is
( mathbf{A} cdot pm 8 )
в. ( pm frac{8}{3} )
( c cdot_{pm frac{3}{8}} )
D. 0
10
96 If ( x=2+2^{frac{1}{3}}+2^{frac{2}{3}}, ) then the values of
( boldsymbol{x}^{3}-mathbf{6} boldsymbol{x}^{2}+boldsymbol{6} boldsymbol{x} ) is
( mathbf{A} cdot mathbf{3} )
B. 4
( c cdot-2 )
D.
10
97 If the equation ( x^{2}+4+3 cos (a x+ )
( b)=2 x ) has at least one solution where
( boldsymbol{a}, boldsymbol{b} in[mathbf{0}, mathbf{5}], ) then the value of ( (boldsymbol{a}+boldsymbol{b}) )
equal to
This question has multiple correct options
A ( .5 pi )
в. ( 3 pi )
c. ( 2 pi )
D.
10
98 Write the Quadratic equation to find two consecutive odd positive integers, whose product is 323 10
99 Roots of the equations ( x^{2}-3 x+2=0 )
are
A. 1,-2
B . -1,2
c. -1,-2
D. 1,2
10
100 If the roots of the equation
( (x-a)(x-b)+(x-b)(x-c)+ )
( (x-c)(x-a)=0 ) are equal, then
( a^{2}+b^{2}+c^{2} ) is equal to
( mathbf{A} cdot a+b+c )
B . ( 2 a+b+c )
c. ( 3 a b c )
D. ( a b+b c+c a )
E ( . a b c )
10
101 The roots of the equation ( x^{2}+2 sqrt{3} x+ )
( mathbf{3}=mathbf{0} ) are
A . real and unequal
B. rational and equal
c. irrational and equal
D. irrational and unequal
10
102 68. If p2 += 47, then the nu-
merical value of P+
will be
(1) 6
(2) 7
13) Ž
(4)
3
10
103 Find the roots of each of the
following quadratic equations by the method of completing the squares
( 2 x^{2}-5 x+3=0 )
A. ( x=2, x=-7 )
В. ( x=-1, x=3 )
c. ( x=1, x=frac{3}{2} )
D. ( x=1, x=frac{1}{2} )
10
104 If ( a<b<c<d, ) then for any real non-
zero ( lambda ), the quadratic equation ( (x- )
( a)(x-c)+lambda(x-b)(x-d)=0 ) has
This question has multiple correct options
A. Non-real roots
B. One real root between ( a ) and ( c ).
c. one real root between ( b ) and ( d )
D. Irrational roots.
10
105 If the equation ( a x^{2}+2 b x+c=0 ) has
real roots, ( a, b, c ) being real numbers
and if ( m ) and ( n ) are real number such
that ( m^{2}>n>0 ) then show that the
equation ( a x^{2}+2 m b x+n c=0 ) has
real roots.
10
106 expand:
( 9(x-y)^{2}+6(y-x) )
10
107 The average weight of 15 Oarsmen in a
boat is increased by ( 1.6 mathrm{kg} ) when one of the crew, who weigh ( 42 mathrm{kg} ) is replaced
by a new man. Find the weight of the new man (in kg).
A . 65
B. 66
c. 43
D. 67
10
108 The product of two consecutive integers is ( 600 . ) Find the second integer.
A .24
B . 23
c. 25
D. 26
10
109 Is the following equation quadratic? ( mathbf{1 3}=-mathbf{5} boldsymbol{y}^{2}-boldsymbol{y}^{boldsymbol{3}} )
A. Yes
B. No
c. Ambiguous
D. Data insufficient
10
110 The value of ( a ) for which the equation ( a^{2}+2 a+csc ^{2} pi(a+x)=0 ) has a
solution, is/are
( mathbf{A} cdot mathbf{0} )
B.
( c cdot-1 )
D.
10
111 Solve for ( a, b )
( boldsymbol{a}^{2}+boldsymbol{b}^{2}-mathbf{4} boldsymbol{a}+mathbf{1 6} boldsymbol{b}+mathbf{6 8}=mathbf{0} )
10
112 The values of ( k ) for which the equation
( 2 x^{2}+k x+x+8=0 ) will have real and
equal roots are
( A cdot 10 ) and -6
B. 7 and -9
( c cdot 6 ) and -10
D. -7 and 9
10
113 If the roots of ( frac{1}{x+a}+frac{a}{x+b}=frac{1}{c}, ) are equal in magnitude and opposite in sign, then the product of the roots is :
A ( cdot-frac{1}{2}left(a^{2}+b^{2}right) )
B. ( frac{1}{2}left(a^{2}+b^{2}right) )
c. ( -frac{3}{2}left(a^{2}+b^{2}right) )
D. None
10
114 If ( alpha ) and ( beta ) are two zeroes of the
polynomial ( boldsymbol{x}^{2}-mathbf{7} boldsymbol{x}+boldsymbol{k} ) where ( boldsymbol{alpha}-boldsymbol{beta}= )
( 5, ) find value of ( k )
10
115 Divide:-
( boldsymbol{X}^{2}+mathbf{5} boldsymbol{X}+mathbf{6} boldsymbol{b} boldsymbol{y} boldsymbol{X}+mathbf{2} )
10
116 For ( a, b, c in Q ) and ( b+c neq a, ) the roots of
( boldsymbol{a} boldsymbol{x}^{2}-(boldsymbol{a}+boldsymbol{b}+boldsymbol{c}) boldsymbol{x}+(boldsymbol{b}+boldsymbol{c})=mathbf{0} ) are
A. Rational and unequal
B. rational and equal
c. complex numbers
D. none
10
117 Area enclosed by curves ( y=2^{x} ) and
( boldsymbol{y}=|boldsymbol{x}+mathbf{1}| ) in the first quadrant is?
A ( cdot frac{1}{2}-frac{1}{log 2} )
B. ( frac{3}{2}-frac{1}{2 log 2} )
c. ( frac{3}{2}-frac{1}{log 2} )
D. ( frac{1}{2}+frac{3}{log 2} )
10
118 State the following statement is True or False

The length of a rectangle ( (x) ) exceeds its
breadth by ( 3 mathrm{cm} . ) The area of a rectangle is 70 sq.cm, then the equation is
( x(x-3)=70 )
A. True
B. False

10
119 Solve the following equations:
( sqrt{4 x^{2}-7 x-15}-sqrt{x^{2}-3 x}= )
( sqrt{x^{2}-9} )
10
120 If ( a x^{2}+b x+6=0 ) does not have two
distinct real roots, where ( boldsymbol{a} in boldsymbol{R}, boldsymbol{b} in boldsymbol{R} )
then the least value of ( 3 a+b ) is
A .4
B. – 1
( c .1 )
D. – 2
10
121 If ( left(p^{2}-2 p+1right) x^{2}-left(p^{2}-3 p+2right) x+ )
( p^{2}-1=0 ) has more then two roots
then ( p= )
10
122 The product of two consecutive integers is ( 156 . ) Find the integers.
A. 10 and 13
B. 12 and 13
c. 12 and 11
D. 1 and 13
10
123 Three consecutive natural numbers are
such that the square of the middle number exceeds the difference of
squares of the other, two by ( 60 . ) Find the numbers.
10
124 Find the roots
( 4 x^{2}+4 sqrt{3 x}+3=0 )
10
125 Find the value of ( k ) for which the
equation ( 2 x^{2}-k x+3=0 ) will have
two real and equal roots.
10
126 If ( a, b, c ) are non-zero, unequal rational
numbers, then the roots of the equation ( a b c^{2} x^{2}+left(3 a^{2}+b^{2}right) c x-6 a^{2}-a b+ )
( 2 b^{2}=0 ) are
A . rational
B. imaginary
C. irrational
D. none of these
10
127 if sum=1 product ( =-6 ) then find the 2 numbers. 10
128 The length of a rectangle is ( 3 mathrm{cm} ) more than its width and area is ( 54 mathrm{cm}^{2} ). Find
the perimeter of the rectangle.
( mathbf{A} cdot 25 mathrm{cm} )
B. ( 30 mathrm{cm} )
c. ( 35 mathrm{cm} )
D. ( 40 mathrm{cm} )
10
129 If ( r ) be the ratio of the roots of the
equation ( a x^{2}+b x+c=0, ) then ( frac{(r+1)^{2}}{r}= )
A ( cdot frac{a^{2}}{b c} )
в. ( frac{b^{2}}{c a} )
c. ( frac{c^{2}}{a b} )
D. None of these
10
130 1
7.
4x +17
Solve: 18
13x – 2
17x-32
-=

x
3
=-
7x
12
x+16
36
10
131 Check whether the given equation is a
quadratic equation or not. ( x^{2}+2 sqrt{x}-3 )
A. True
B. False
10
132 Which of the following is not a quadratic equation?
A ( cdot x^{2}+6 y+2 )
B. ( (x-2)+(x+2)^{2}+3 )
c. ( (3 x-2)^{3}+frac{1}{2} x-4 )
D. ( 3 x^{2}-6 x+frac{1}{2} )
10
133 If the roots of the equation ( x^{2}-2 a x+ )
( a^{2}+a-3=0 ) are real and less than 3
then
A ( . a<2 )
в. ( 2 leq a leq 3 )
c. ( 34 )
10
134 Check whether the following is quadratic equation.
( boldsymbol{x}^{2}-mathbf{2} boldsymbol{x}=(-mathbf{2})(boldsymbol{3}-boldsymbol{x}) )
10
135 Let ( boldsymbol{alpha}, boldsymbol{beta} ) be the roots of ( boldsymbol{a x}^{2}+boldsymbol{b x}+boldsymbol{c}= )
( 0 ; gamma, delta ) be the roots of ( p x^{2}+q x+r=0 )
and ( D_{1}, D_{2} ) are the respective
discriminants of these equations. If the
( boldsymbol{alpha}, boldsymbol{beta}, boldsymbol{gamma}, boldsymbol{delta} ) are in AP, then ( boldsymbol{D}_{1}: boldsymbol{D}_{2} ) is
equal to
( mathbf{A} cdot frac{a^{2}}{b^{2}} )
B. ( frac{a^{2}}{p^{2}} )
( ^{mathbf{C}} cdot frac{b^{2}}{q^{2}} )
D. ( frac{c^{2}}{r^{2}} )
10
136 If ( alpha, beta ) are zeroes of polynomial ( f(x)= ) ( x^{2}+p x+q ) then polynomial having ( frac{1}{alpha} ) and ( frac{1}{beta} ) as its zeroes is:
A ( cdot x^{2}+q x+p )
B. ( x^{2}-p x+q )
c. ( q x^{2}+p x+1 )
D. ( p x^{2}+q x+1 )
10
137 Sum of a number and its reciprocal is ( mathbf{5} frac{1}{mathbf{5}} . ) Then the required equation is
A ( cdot y^{2}+frac{1}{y}=frac{26}{5} )
B. ( 5 y^{2}-26 y+5=0 )
c. ( y^{2}+frac{1}{y}+frac{26}{5}=0 )
D. ( 5 y^{2}+26 y+5=0 )
10
138 State the nature of the given quadratic
equation ( 3 x^{2}+4 x+1=0 )
A. Real and Distinct Roots
B. Real and Equal Roots
c. Imaginary Roots
D. None of the above
10
139 For what value of ( mathrm{k} ), does the equation ( left[k x^{2}+(2 k+6) x+16=0right] ) have equal
roots?
A. 1 and 9
B. -9 and -1
c. -1 and 9
D. -1 and -9
10
140 f ( x+y+z=0 ) then what is the value
of
( frac{1}{x^{2}+y^{2}-z^{2}}+frac{1}{y^{2}+z^{2}-x^{2}}+ )
( frac{1}{z^{2}+x^{2}-y^{2}} )
A ( cdot frac{1}{x^{2}+y^{2}+z^{2}} )
в.
c. -1
D.
10
141 Solve the following quadratic equation by factorization, the roots are: ( 0, a+b ) ( frac{x-a}{x-b}+frac{x-b}{x-a}=frac{a}{b}+frac{b}{a} )
A. True
B. False
10
142 If 8 is a root of the equation ( x^{2}-10 x+ )
( k=0, ) then the value of ( k ) is :
A . 2
B. 8
( c .-8 )
D. 16
10
143 Find the nature of the roots of ( 3 x^{2}- )
( 4 sqrt{3} x+4=0 )
10
144 The roots of the equation ( 2 x^{2}+x- )
( 4=0 ) are
( mathbf{A} cdot 1,-4 )
в. ( -3, frac{1}{sqrt{3}} )
c. ( frac{sqrt{33}-1}{4}, frac{-sqrt{33}-1}{4} )
D. None
10
145 Solve ( frac{2 x+3}{2 x-3}+frac{2 x-3}{2 x+3}=frac{17}{4} ) 10
146 The ( _{text {一一一一一一 }} ) product rule says that when the product of two terms is zero,
then either of the terms is equal to zero.
A. one
B. two
c. three
D. zero
10
147 Given reason whether the following is an equation or not:
( (x-2)^{2}=x^{2}-4 x+4 )
10
148 Solve :-
[
x^{2}-2 cos alpha+cos 2 alpha=0
]
10
149 If the roots of ( left(a^{2}+b^{2}right) x^{2}-2 b(a+ )
( c) x+left(b^{2}+c^{2}right)=0 ) are equal, then
( a, b, c ) are in
A. A.P
в. G.P.
c. н.P.
D. none of these
10
150 The roots of the following quadratic equation are not real ( 2 x^{2}-3 x+5=0 )
A . True
B. False
10
151 I: If ( a, b, c ) are real, the roots of ( (b- )
( c) x^{2}+(c-a) x+(a-b)=0 ) are real
and equal, then ( a, b, c ) are in A.P.
Il: If ( a, b, c ) are real and the roots of ( left(a^{2}+right. )
( left.boldsymbol{b}^{2}right) boldsymbol{x}^{2}-boldsymbol{2} boldsymbol{b}(boldsymbol{a}+boldsymbol{c}) boldsymbol{x}+boldsymbol{b}^{2}+boldsymbol{c}^{2}=boldsymbol{0} ) are
real and equal, then ( a, b, c ) are in H.P.
Which of the above statement(s) is(are)
true?
A. only।
B. only II
c. both I and II
10
152 Find the root of ( x^{2}-20 x+100 ) 10
153 The roots of the equation ( x^{sqrt{x}}=(sqrt{x})^{x} )
are
A. 0 and 1
B. 0 and 4
c. 1 and 4
D. 0,1 and 4
10
154 Solve the following quadratic equations by factorization method:
( mathbf{3}left(x^{2}-6right)=x(x+7)-3 )
A ( cdotleft{-frac{3}{2}, 5right} )
в. ( left{frac{3}{2}, 5right} )
( ^{c} cdotleft{-frac{3}{2},-5right} )
D. None of these
10
155 Solve for ( x: sqrt{7 x^{2}}-6 x-13 sqrt{7}=0 ) 10
156 Write the suitable quantifier for all
values of ( x ) there is no real number such
that ( x^{2}+2 x+2=0 )
A. Universal quantifier (forall)
B. Existential quantifier
c. Both
D. None
10
157 If ( boldsymbol{alpha} neq boldsymbol{beta}, boldsymbol{alpha}^{2}=mathbf{5} boldsymbol{alpha}-mathbf{3}, boldsymbol{beta}^{2}=mathbf{5} boldsymbol{beta}-mathbf{3} )
then the equation whose roots are ( boldsymbol{alpha} / boldsymbol{beta} )
( & boldsymbol{beta} / boldsymbol{alpha} ) is
A ( cdot x^{2}+5 x-3=0 )
B. ( 3 x^{2}+12 x+3=0 )
c. ( 3 x^{2}-19 x+3=0 )
D. None of these
10
158 Solve :
[
boldsymbol{x}^{2}+4 boldsymbol{x}+boldsymbol{4}=mathbf{0}
]
10
159 Solve the equation obtained ( x^{2}-x- )
( 6=0 ) and hence find the dimensions of
the verandah. Verandah is in
rectangular shape having area and perimeter equal.
A. ( x=3 ; ) length ( =6 mathrm{m} ) and breadth ( =3 mathrm{m} )
B. ( x=3 ; ) length ( =6 mathrm{m} ) and breadth ( =4 mathrm{m} )
c. ( x=3 ; ) length ( =4 mathrm{m} ) and breadth ( =3 mathrm{m} )
D. ( x=4 ; ) length ( =6 mathrm{m} ) and breadth ( =3 mathrm{m} )
10
160 Find the least positive value of ( k ) for
which the equation ( x^{2}+k x+4=0 )
has real roots.
10
161 12. Which of the following is not the quadratic equation
whose roots are cosecand sec-e?
a. x2 – 6x + 6 = 0 b. x2 – 7x + 7 = 0
c. x2 – 4x + 4 = 0 d. none of these
10
162 Find the roots of the equations by the method of completing the square. ( boldsymbol{x}^{2}+mathbf{7} boldsymbol{x}-mathbf{6}=mathbf{0} ) 10
163 Determine whether the equation ( 5 x^{2}= )
( 5 x ) is quadratic or not.
A. Yes
B. No
c. complex equation
D. None
10
164 fsum ( =-12, ) product ( =-28 . ) Then find the 2 numbers. 10
165 58. Two runners cover the samed
tance at the rate of 15 km a
16 km per hour respectively. Find
the distance travelled when one
takes 32 minutes longer than the
other.
(1) 128 km
(2) 64 km
(3) 96 km
(4) 108 km
10
166 Solve ( 6 x^{2}-5 x-25=0 ) 10
167 The following equation is a qudratic equation.
( 16 x^{2}-3=(2 x+5)(5 x-3) )
A. True
B. False
10
168 If the roots of the equation ( p x^{2}+q x+ )
( boldsymbol{r}=mathbf{0} ) are in the ratio ( l: boldsymbol{m} ) prove that
( (l+m)^{2} p r=l m q^{2} )
10
169 If ( n^{2}=(n+6), ) then find the value of ( n )
A. ( n=-2,-3 )
в. ( n=3,2 )
c. ( n=-3,2 )
D. ( n=-2,3 )
10
170 A family is going to a theme park having ( t ) members in the family. Each ticket costs ( $ 80, ) and the number of
tickets needs to be bought can be
calculated from the expression ( t^{2}- )
( 4 t-90=6 ) when ( t>0 . ) What is the
total cost of the theme park tickets that
the family paid?
A. ( $ 640 )
B. ( $ 800 )
c. ( $ 960 )
D. ( $ 1,120 )
10
171 The mentioned equation is in which form?
( mathbf{3} boldsymbol{y}^{2}-mathbf{7}=sqrt{mathbf{3}} boldsymbol{y} )
A. linear
B. Quadratic
c. Cubic
D. None
10
172 The real values of ( a ) for which the
quadratic equation ( 2 x^{2}-left(a^{3}+8 a-right. )
1) ( x+a^{2}-4 a=0 ) possesses roots of opposite signs are given by :
( mathbf{A} cdot a>6 )
B . ( a>9 )
c. ( 0<a<4 )
D. ( a<0 )
10
173 Which of the following is a Quadratic Equation?
A ( .5 x+8=0 )
B ( cdot 6 x^{2}+7 x=19 )
( mathbf{c} cdot x+1 )
D. None of these
10
174 Solve ( x^{2}-6 x+2=0 ) 10
175 13. If cosec -cot 0=, then the value of cosec O is
a. q+
1980
b. q- –
q
1
+ –
d. none of these
10
176 Which of the following equations are not
quadratic?
( mathbf{A} cdot x(2 x+3)=x+2 )
B ( cdot(x-2)^{2}+1=2 x-3 )
( mathbf{c} cdot y(8 y+5)=y^{2}+3 )
D. ( y(2 y+15)=2left(y^{2}+y+8right) )
10
177 John and jivanti together have 45 marbles. Both of them lost 5 marbles
each , and the product of the number of
marbles they now have is ( 128 . ) Form the quadratic equation.
10
178 Solve the following. ( 3 a^{2} x^{2}+8 a b x+4 b^{2}=0,(a neq 0) ) 10
179 Solve
( 4 x^{2}-7 x+5 )
10
180 Say true or false.
f ( x(x-4)=0, ) then ( x=0 ) or ( x=4 )
A. True
B. False
10
181 Check whether ( 2 x^{2}-3 x+5=0 ) has
real roots or no.
A. The equation has real roots.
B. The equation has no real roots.
c. Data insufficient
D. None of these
10
182 The value ( (s) ) of ( k ) for which the
quadratic equation ( k x^{2}-k x+1=0 )
has equal roots is
( mathbf{A} cdot k=0 )
B. ( k=4 )
c. ( k=0,4 )
D. ( k=-4 )
10
183 Say true or false.
( x^{2}+6=5 x, ) then ( x=3 ) or ( x=2 )
A. True
B. False
10
184 Find the discriminant for the given equation:
( mathbf{3} boldsymbol{x}^{2}+mathbf{2} boldsymbol{x}-mathbf{1}=mathbf{0} )
A . 11
B. 13
c. 15
D. 16
10
185 The roots of the equation ( a x^{2}+b x+ )
( c=0 ) will be in reciprocal if
( mathbf{A} cdot a=b )
B . ( a=b c )
( mathbf{c} cdot c=a )
D. ( c=b )
10
186 Choose the quadratic equation in ( boldsymbol{p} )
whose solutions are 1 and 7
A ( cdot p^{3}-p x+6=0 )
B . ( p^{2}-p x+6=0 )
c. ( p^{2}-8 p+7=0 )
D. ( p^{2}-5 p+7=0 )
10
187 Which of the following is a quadratic
equation?
( mathbf{A} cdot x^{frac{1}{2}}+2 x+3=0 )
B. ( left(x^{2}-1right)(x+4)=x^{2}+1 )
C ( cdot x^{2}-3 x+5=0 )
D. ( left(2 x^{2}+1right)(3 x-4)=6 x^{2}+3 )
10
188 An equation whose maximum degree of variable is two is called ( ldots ). equation. 10
189 Let there be two integers such that one integer is 3 more than the other and
their product is ( 70 . ) Find the two integers.
A. 7 and 10
B. 6 and 9
c. 10 and 13
D. 12 and 14
10
190 John and Jivanti together have 45 marbles. Both of them lost 5 marbles
each, and the product of the number of
marbles they now have is ( 124 . ) Form the quadratic equation we can find that John had 36 or 9 marbles.
A. True
B. False
10
191 Solve ( 7 x^{2}-5 x-3=0 ) 10
192 If ( alpha ) and ( beta ) are the roots of the equation
( x^{2}-p x+q=0, ) then find the equation whose roots are ( frac{boldsymbol{q}}{boldsymbol{p}-boldsymbol{alpha}} ) and ( frac{boldsymbol{q}}{boldsymbol{p}-boldsymbol{beta}} )
10
193 Find a quadratic polynomial with ( frac{1}{4},-1 ) as the sum and product of its zeroes respectively. 10
194 Find ( a ) so that roots of ( x^{2}+2(3 a+ )
5) ( x+2left(9 a^{2}+25right)=0 ) are real.
10
195 Determine the values of ‘ ( a^{prime} ) for which
both roots of the quadratic equation ( left(a^{2}+a-2right) x^{2}-(a+5) x-2=0 )
exceed the number minus one.
10
196 Obtains all other zeroes of ( x^{4}-3 x^{3}- )
( x^{2}+9 x-6, ) if two of its zeroes are ( sqrt{3} )
and ( -sqrt{3} )
10
197 If the value of ( b^{2}-4 a c^{prime} ) is greater than
zero, the quadratic equation ( a x^{2}+b x+ )
( c=0 ) will have
A. Two Equal Real Roots.
B. Two Distinct Real Roots.
c. No Real Roots.
D. No Roots or Solutions.
10
198 The roots of the equation ( 2 y^{2}+y- )
( mathbf{2}=mathbf{0} ) are
A. ( frac{-1-sqrt{17}}{2}, frac{-1-sqrt{17}}{2} )
B. ( frac{-1-sqrt{17}}{4}, frac{-1+sqrt{17}}{4} )
c. ( -1-sqrt{17},-1+sqrt{17} )
D. None
10
199 If the roots of the equation ( x^{2}-8 x+ )
( a^{2}-6 a=0 ) are real, then the value of ( a )
will be
A ( .-2<a<8 )
в. ( -2 leq a leq 8 )
( mathbf{c} cdot 2<a<8 )
D. ( 2 leq a leq 8 )
10
200 The mentioned equation is in which form?
( (y-2)(y+2)=0 )
A. cubic
B. quadratic
c. linear
D. none of these
10
201 STATEMENT -1: Roots of the quadratic equation ( 3 x^{2}-2 sqrt{6}+2=0 ) are same
STATEMENT -2: A quadratic equation
( a x^{2}+b x=c=0 ) has two distinct real
roots, if ( b^{2}-4 a c>0 )
A. Statement – 1 is True, Statement- – 2 is True, Statement 2 is a correct explanation for Statement – 1
B. Statement – 1 is True, Statement – 2 is True : Statement 2 is NOT a correct explanation for Statement- –
c. statement- 1 is True, Statement – 2 is False
D. Statement-1 is False, Statement- – 2 is True
10
202 A root of the equation ( (x-1)(x- )
2) ( =frac{30}{49} ) is
A ( -frac{17}{7} )
B. ( frac{15}{7} )
c. ( frac{13}{7} )
D. ( frac{11}{7} )
10
203 Solve
[
boldsymbol{x}^{2}+mathbf{5}=-mathbf{6} boldsymbol{x}
]
10
204 Assertion (A): The roots of ( (x-a)(x- )
( b)+(x-b)(x-c)+(x-c)(x-a)= )
0 are real
Reason (R): A quadratic equation with non-negative discriminant has real
roots
A. Both (A) and (R) are true and (R) is the correct explanation of (A)
B. Both (A) and (R) are true and (R) is not the correct explanation of ( (A) )
( c cdot(A) ) is true but (R) is false
D. (A) is false but (R) is true
10
205 Find the roots of the following quadratic equation, if they exist, using the quadratic formula of Shridhar Acharya. ( 2 x^{2}-2 sqrt{2} x+1=0 ) 10
206 If ( a+b+c=2 s, ) then the value of ( (s- )
( a)^{2}+(s-b)^{2}+(s-c)^{2} ) will be
A ( cdot s^{2}+a^{2}+b^{2}+c^{2} )
B. ( a^{2}+b^{2}+c^{2}-s^{2} )
c. ( s^{2}-a^{2}-b^{2}-c^{2} )
D. ( 4 s^{2}-a^{2}-b^{2}-c^{2} )
10
207 If the product of all solution of the equation ( frac{(2009) x}{2010}=(2009)^{log _{x}(2010)} ) can
be expressed in the lowest form as ( frac{m}{n} ) then the value of ( (boldsymbol{m}+boldsymbol{n}) ) is
10
208 Factorise ( : boldsymbol{m}^{2}-mathbf{1 0 m}-mathbf{1 4 4} ) 10
209 Thrice the square of a natural number decreased by 4 times the number is
equal to 50 more than the number. The number is
( A cdot 4 )
B. 5
( c cdot 6 )
D. 10
10
210 Which of the following equations has two distinct real roots ?
A ( cdot 2 x^{2}-3 sqrt{2} x+frac{9}{4}=0 )
В. ( x^{2}+x-5=0 )
c. ( x^{2}+3 x+2 sqrt{2}=0 )
D. ( 5 x^{2}-3 x+1=0 )
10
211 Solve ( : a^{2}-(b+5) a+5 b=0 ) 10
212 In solving a problem, one student makes a mistake in the coefficient of
the first degree term and obtains -9
and -1 for the roots. Another student
makes a mistake in the constant term
of the equation and obtains 8 and 2 for the roots. The correct equation was?
A. ( x^{2}+10 x+9=0 )
B . ( x^{2}-10 x+16=0 )
c. ( x^{2}-10 x+9=0 )
D. None of the above
10
213 If ( a=frac{1}{3-2 sqrt{2}}, b=frac{1}{3+2 sqrt{2}} ) then the value
of ( boldsymbol{a}^{mathbf{3}}+boldsymbol{b}^{mathbf{3}} ) is:
A ( cdot 194 )
B. 200
c. 198
D. 196
10
214 For what positive values of ‘ ( m ) ‘ roots of given equation
is equal, distinct, imaginary ( boldsymbol{x}^{2}- )
( boldsymbol{m} boldsymbol{x}+boldsymbol{9}=mathbf{0} )
10
215 Let ( f(x)=x^{2}-3 x+4, ) then the value
of ( boldsymbol{x} ) which satisfies ( boldsymbol{f}(mathbf{1})+boldsymbol{f}(boldsymbol{x})= )
( boldsymbol{f}(mathbf{1}) boldsymbol{f}(boldsymbol{x}) ) is
A .
B.
c. 1 or 2
D. 1 and 0
10
216 The sum of the values of k for which the
roots are real and equal of the following equation ( 4 x^{2}-2(k+1) x+(k+4)=0 ) is
10
217 Is the given equation quadratic? Enter 1 for True and 0 for False.
( boldsymbol{x}^{2}+boldsymbol{4} boldsymbol{x}=mathbf{1 1} )
10
218 Find the value of ( k ) for which the
equation ( boldsymbol{x}^{2}+boldsymbol{k}(boldsymbol{2} boldsymbol{x}+boldsymbol{k}-mathbf{1})+boldsymbol{2}=mathbf{0} )
has real and equal roots.
10
219 The product of two consecutive natural
numbers is ( 12 . ) The equation form of this statement is
A. ( x^{2}+2 x-12=0 )
B . ( x^{2}+1 x-12=0 )
c. ( x^{2}+1 x+12=0 )
D. ( x^{2}+2 x+12 )
10
220 The value of ( a ) for which one root of the
quadratic equation ( left(a^{2}-5 a+3right) x^{2}+ )
( (3 a-1) x+2=0 ) is twice as large as the other is
A ( cdot-frac{2}{3} )
в. ( frac{1}{3} )
( c cdot-frac{1}{3} )
D. ( frac{2}{3} )
10
221 Find the discriminant of the equation
and the nature of roots. Also find the
roots, if they are real:
( 3 x^{2}-2 x+frac{1}{3}=0 )
A. Roots are imaginary
B. ( mathrm{D}=0, ) Roots are real and equal ( frac{1}{3}, frac{1}{3} )
( mathrm{c} cdot_{mathrm{D}=} frac{2}{5}, ) Roots are real and unequal ( frac{1}{5}, frac{1}{2} )
D. Cannot be determined
10
222 Find the roots of each of the
following quadratic equations by the method of completing the squares ( sqrt{5} x^{2}+9 x+4 sqrt{5}=0 )
A. ( -sqrt{7}, frac{-17}{sqrt{3}} )
в. ( -sqrt{5}, frac{-4}{sqrt{5}} )
c. ( -sqrt{5}, frac{-14}{sqrt{3}} )
D. ( -sqrt{7}, frac{-13}{sqrt{5}} )
10
223 1 U0 WUL LUI DU
16. Let a, b, c be real numbers, a = 0.
o, c be real numbers, a = 0. If a is a root of
+bx+c = 0. B is the root of a2x2 – bx -c= 0 and
0<a<B, then the equation a2x2 +2bx +2c=0 has a root y
that always satisfies
(1989- 2 Marks)
(a)
=
(b) y = a +5
(d) a <y<B.
(c) yra
10
224 Check whether ( x^{2}-frac{29}{4} x+5=0 ) is
a quadratic equation
10
225 Let ( p, q in{1,2,3,4} . ) The number of
equation of the form ( p x^{2}+q x+1=0 )
having real roots, is
A . 15
B. 9
c. 8
D. 7
10
226 The number of real roots of the
equation ( (x-1)^{2}+(x-2)^{2}+(x- )
( mathbf{3})^{2}=mathbf{0} ) is :
( mathbf{A} cdot mathbf{1} )
B . 2
( c .3 )
D. None of these
10
227 f ( p ) and ( q ) are positive then the roots of the equation ( x^{2}-p x-q=0 ) are
A. imaginary
B. real & both positive
c. real & both negative
D. real & of opposite sign
10
228 5. Find the solution for
5.
Find the solution for
10
229 The graph of ( boldsymbol{p}(boldsymbol{x})=boldsymbol{x}^{2}-boldsymbol{4} boldsymbol{x}+boldsymbol{3} )
represents
A. a line segment
B. parabola
c. a line
D. a ray
10
230 If ( 3 x^{2}+4 k x+1>0 ) for all real values
of ( x, ) then ( k ) lies in the interval.
A ( cdotleft(frac{-sqrt{3}}{2}, frac{sqrt{3}}{2}right) )
в. ( left(frac{-1}{4}, frac{1}{4}right) )
( ^{c} cdotleft[frac{-sqrt{3}}{2}, frac{sqrt{3}}{2}right] )
D. ( left(frac{-1}{2}, frac{1}{2}right) )
10
231 Which of the following is quadratic polynomial
( mathbf{A} cdot x+2 )
B. ( x^{2}+2 )
c. ( x^{3}+2 )
D. ( 2 x+2 )
10
232 The formula of discriminant of
quadratic equation ( a x^{2}+b x+c=0 ) is
( D= )
10
233 In a square box, a glass is to be surrounded by a ( 2 mathrm{cm} ) glass border. If
the total area of the square is ( 121 mathrm{cm}^{2} ) Find the dimension of the glass box.
A. ( 5 mathrm{cm} )
в. ( 6 mathrm{cm} )
( c cdot 7 mathrm{cm} )
D. ( 8 mathrm{cm} )
10
234 Verify:
( (a+b)^{2}-(a-b)^{2}=4 a b, ) for ( a= )
( mathbf{4}, boldsymbol{b}=mathbf{3} )
10
235 For what value of ( ^{prime} boldsymbol{k}^{prime},left(boldsymbol{k}^{2}-mathbf{4}right) boldsymbol{x}^{2}+ )
( 2 x-9=0 ) can not be quadratic
equation?
10
236 Solve the following quadratic equation
for ( x )
( 4 x^{2}+4 b x-left(a^{2}-b^{2}right)=0 )
10
237 Solve the equation ( mathbf{5}^{x^{2}+3 x+2}=mathbf{1} )
find the difference between the roots of
the equation.
10
238 If the area of rectangle is given by ( x^{2}+ ) ( 5 x+6 ) then write the possible length
and breadth.
10
239 The Discriminant value of equation ( mathbf{5} boldsymbol{x}^{2}-mathbf{6} boldsymbol{x}+mathbf{1}=mathbf{0} ) is
A . 16
B. ( sqrt{56} )
( c cdot 4 )
D. 56
10
240 Determine the nature of roots of the
equation ( x^{2}+2 x sqrt{3}+3=0 )
A. Real and distinct
B. Non-real and distinct
c. Real and equal
D. Non-real and equal
10
241 Check whether the given equation is a quadratic equation
( x+frac{3}{x}=x^{2} )
10
242 Determine the nature of the roots of the
follwoing quadratic equation:
( 2 x^{2}-6 x+3=0 )
10
243 ( frac{1}{(x-1)(x-2)}+frac{1}{(x-2)(x-3)}= )
( frac{2}{3}, x neq 1,2,3 . ) Find sum of values of ( x )
10
244 Solve the given quadratic equation by
factorization method
( boldsymbol{x}^{2}-mathbf{9}=mathbf{0} )
10
245 Find the roots of the quadratics equation ( 3 x^{2}-4 sqrt{3} x+4=0 ) 10
246 Solve
( 6 m^{2}-11 m+6=0 )
10
247 If ( a<c<b ) then the roots of the
equation ( (a-b)^{2} x^{2}+2(a+b- )
( 2 c) x+1=0 ) are
A. Imaginary
B. Real
c. one real and one Imaginary
D. Equal and Imaginary
10
248 If the roots of ( a x^{2}-b x-c=0 ) change
by the same quantity, then the expression in ( a, b, c ) that does not
change is
A ( cdot frac{b^{2}-4 a c}{a^{2}} )
в. ( frac{b-4 c}{a} )
c. ( frac{b^{2}+4 a c}{a^{2}} )
D. none of these
10
249 Find the value of ( k ) for which the
equation ( x^{2}-6 x+k=0 ) has distinct
roots.
( mathbf{A} cdot k>9 )
B. ( k=6,7 ) only
c. ( k<9 )
( mathbf{D} cdot k=9 )
10
250 Solve by factorization ( sqrt{mathbf{3}} boldsymbol{x}^{2}+mathbf{1 1} boldsymbol{x}+ )
( mathbf{6} sqrt{mathbf{3}}=mathbf{0} )
10
251 The number of points ( (p, q) ) such that
( boldsymbol{p}, boldsymbol{q} in{1,2,3,4} ) and the equation
( p x^{2}+q x+1=0 ) has real roots is
( A cdot 7 )
B. 8
c. 9
D. none of these
10
252 State the following statement is True or
False

The sum of a natural number ( x ) and its
eciprocal is ( frac{37}{6}, ) then the equation is ( boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}=frac{mathbf{3 7}}{mathbf{6}} )
A. True
B. False

10
253 Solve
( 12 x^{2}-27=0 )
10
254 Calculate ( frac{1}{x_{1}^{3}}+frac{1}{x_{2}^{3}}, ) where ( x_{1} ) and ( x_{2} )
are roots of the equation ( 2 x^{2}-3 a x- )
( mathbf{2}=mathbf{0} )
10
255 For what value of ( k,(4-k) x^{2}+ )
( (2 k+4) x+(8 k+1)=0 ) is a perfect
square:
10
256 18. Let a, ß be the roots of the equation (x-a)(x-6)=c,c*0.-
Then the roots of the equation
(x-a) (x-B)+c=0 are
(1992 – 2 Marks)
(a) a,
(b) b,c
(c) a b
(d) at c,b+c
10
257 Find the value ( (s) ) of ( k ) so that the
equation ( x^{2}-11 x+k=0 ) and ( x^{2}- )
( 14 x+2 k=0 ) may have a common root.
10
258 Figure shows a square with total area of
121 square units. Calculate the value of
( boldsymbol{x} )
begin{tabular}{|c|c|}
hline & \
( 7 x ) & 49 \
hline( x^{2} ) & ( 7 x ) \
hline
end{tabular}
( A )
B.
( c )
D. 1
( E )
10
259 Solve ( 2 cos ^{2} theta-sqrt{3} sin theta+1=0 ) 10
260 I: The roots of ( a(b-c) x^{2}+b(c-a) x+ )
( c(a-b)=0 ) are real and equal, then
( a, b, c ) are in G.P.
II: The number of solutions of ( mid x^{2}- ) ( 2 x+2 mid=3 x-2 ) is 4
Which of the above statement(s) is/are
true?
A. only।
B. only II
c. both I and II
D. neither I nor II
10
261 If the roots of a quadratic expression
( a x^{2}+b x+c ) are complex, then
A ( cdot b^{2}4 a c )
c. ( b^{2}=4 a c )
( mathbf{D} cdot a=0 )
10
262 Solve: ( sqrt{7 sqrt{7 sqrt{7 sqrt{7 sqrt{7 ldots ldots}}}}}=k . ) Find k. 10
263 If
( a, b, c ) are real numbers such that ac
( neq 0, ) then show that at least one of the
equations ( a x^{2}+b x+c=0 ) and ( -a x^{2}+b x )
( +c=0 ) has real roots.
10
264 Factorise: ( 5 x^{2}-x-4 ) 10
265 71.
1+2 72 + 73 73+ 74
will be equal to
(1) 1
(2) -3
(3) Both of above
(4) None of the above
10
266 Solve: ( boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}=mathbf{5} ) 10
267 The values of he equation afor which
both the roots of the equation ( (a- )
6)( x^{2}=a(x-3) ) are positive are given
by
в. ( left(0, frac{72}{11}right) )
c. ( left(6, frac{72}{11}right) )
D. ( left(frac{72}{13}, 6right) )
10
268 The number of point of intersection of the two curves ( y=2 sin x ) and ( y= )
( 5 x^{2}+2 x+3 ) is ( ? )
( A cdot infty )
B. 0
c. 1
D. less than two
10
269 If ( a ) and ( b ) are the roots of ( x^{2}-p x+q= )
( 0, ) then ( a^{2}+b^{2} ) is
A ( cdot p^{2}+q^{2} )
B . ( p^{2}+2 q )
c. ( p^{2}-q^{2} )
D. ( p^{2}-2 q )
10
270 if ( [mathrm{x}] ) is the integral part of ( mathrm{x} ), then solve ( left[mathbf{4}-[boldsymbol{x}]^{2}right]-[boldsymbol{x}]^{2}=mathbf{2} )
find the number of integers satisfying
the equation.
10
271 Which of the following statements has
the truth value ( ^{prime} F^{prime} ? )
A. A quadratic equation has always a real root
B. The number of ways of seating 2 persons in two chairs out of ( n ) persons in ( P(n, 2) )
C. The cube roots of unity are in GP
D. None of the above
10
272 Determine ( k ) for which the quadratic
equation has equal roots ( k x^{2}-5 x+ )
( boldsymbol{k}=mathbf{0} )
10
273 If ( frac{1}{a}+frac{1}{b}+frac{1}{c}=frac{1}{a+b+c} ) where ( (a+ )
( b+c) neq 0 ) and ( a b c neq 0 . ) What is the
value of ( (boldsymbol{a}+boldsymbol{b})(boldsymbol{b}+boldsymbol{c})(boldsymbol{c}+boldsymbol{a}) ? )
( mathbf{A} cdot mathbf{0} )
B.
( c cdot-1 )
( D )
10
274 Find the value of ‘p’ for which the
quadratic equatio has equal roots, ( (p+1) n^{2}+2(p+3) n+(p+8)=0 )
10
275 Simplify ( frac{a}{x-a}+frac{b}{x-b}=frac{2 c}{x-c} ) 10
276 2.
A number which satisfies the given equation is called
solutions or root of the equation.
10
277 18. For a s 0, determine all real roots of the equation
x2 – 2a x – al-3a2 = 0
(1986 – 5 Marks)
10
278 If the roots of the equation ( x^{2}-15- )
( boldsymbol{m}(mathbf{2} boldsymbol{x}-mathbf{8})=mathbf{0} ) are equal, then ( boldsymbol{m}= )
A. 3,-5
в. 3,5
c. -3,5
D. -3,-5
10
279 For ( a>0, ) all the real roots of the
equation ( boldsymbol{x}^{2}-mathbf{3} boldsymbol{a}|boldsymbol{x}-boldsymbol{a}|-mathbf{7} boldsymbol{a}^{2}=mathbf{0} ) are
( mathbf{A} cdot 4 a, 5 a )
в. ( -4 a, 5 a )
( mathbf{c} .-4 a,-5 a )
D. ( 4 a,-5 a )
10
280 If one root of ( x^{2}-x-k=0 ) is square of
the other, then ( k= )
A ( .2 pm sqrt{5} )
B . ( 2 pm sqrt{3} )
( c cdot 3 pm sqrt{2} )
D. ( 5 pm sqrt{2} )
10
281 For what value of ( k ) will the quadratic
equation: ( k x^{2}+4 x+1=0 ) have real
and equal roots?
A .2
B. 3
( c cdot 4 )
( D )
10
282 71. Which one of the following is a
root of equation x + x + 1 = 0?
(1) x=0 (2) x= 1
(3) Both of above
(4) none of the above
10
283 If ( A ) and ( B ) are whole numbers such that
( 9 A^{2}=12 A+96 ) and ( B^{2}=2 B+3, ) find
the value of ( 5 A+7 B )
A . 31
B. 37
c. 41
D. 43
10
284 Find the quadratic equation in ( x, ) whose
solutions are 3 and 2
A ( cdot x^{3}-5 x+6=0 )
B. ( x^{2}-5 x+6=0 )
c. ( x^{2}-3 x+6=0 )
D. ( x^{2}-5 x+7=0 )
10
285 The product of two consecutive even
numbers is ( 120 . ) Can you express this information in the form of a Quadratic
Equation? If yes, what would be the resulting Quadratic Equation?
10
286 Show that the equation ( 2left(a^{2}+b^{2}right) x^{2}+ )
( 2(a+b) x+1=0 ) has no real roots,
when ( a neq b )
10
287 The area of a rectangular field is given
as 300 square metres. It is also given that the breadth of the field is 3 metres
more than its length. Can this
information be expressed mathematically as a Quadratic
Equation. If yes, what would be the resulting Quadratic Equation?
10
288 f ( a, b, c in R^{+} ) and ( 2 b=a+c, ) then
check the nature of roots of equation ( boldsymbol{a} boldsymbol{x}^{2}+boldsymbol{2} boldsymbol{b} boldsymbol{x}+boldsymbol{c}=mathbf{0} )
10
289 One year ago a man was eight times old as his son. Now his age is equal to the square of his son’s age. Represent this situation in form of a quadratic equation 10
290 Solve:
( 28-31 x-5 x^{2}=0 )
10
291 All the values of ‘a’ for which the
quadratic expression ( a x^{2}+(a- )
2) ( x-2 ) is negative for exactly two
integral values of ( x ) may lie in
A. ( (1,3 / 2) )
B. ( (3,2 / 2) )
c. (1,2)
(i) 5
D. (-1,2)
10
292 f ( a(a+2)=24 ) and ( b(b+2)=24 )
where ( a neq b, ) then ( a+b= )
A . – 48
B . – –
( c cdot 2 )
D. 46
E. 48
10
293 1.
If l, m, n are real, em, then the roots by the equation:
(l-mx2–5 (+ m)x-2 (1-m)=0 are (1979)
(a) Real and equal
(6) Complex
(c) Real and unequal
(d) None of these.
10
294 Solve the following quadratic equation by factorization, the roots are ( boldsymbol{x}^{2}-(sqrt{mathbf{3}}+mathbf{1}) boldsymbol{x}+sqrt{mathbf{3}}=mathbf{0} )
A . 3,1
в. ( sqrt{2}, )
c. ( sqrt{3}, 1 )
D. ( sqrt{5}, )
10
295 If ( frac{5 x-7 y+10}{1}=frac{3 x+2 y+1}{8}= )
( frac{11 x+4 y-10}{9}, ) then what is the ( x+y )
equal to?
A . 1
B. 2
( c cdot 3 )
D. –
10
296 Find the value of ‘k’ so that the equation
( boldsymbol{x}^{2}+mathbf{4} boldsymbol{x}+(boldsymbol{k}+mathbf{2})=mathbf{0} ) has one root
equal to zero.
10
297 The value of k for which the quadratic
equation, ( k x^{2}+1=k x+3 x-11 x^{2} )
has real and equal roots are
A. ( -11 .-3 )
3 ( 3.31-31-3 )
B. 5,7
c. 5,-7
D. None of these
10
298 4.
If (y – 4)² = 16 then find the value of y.
10
10
299 The rectangular fence is enclosed with an area ( 16 mathrm{cm}^{2} . ) The width of the field is
( 6 mathrm{cm} ) longer than the length of the fields.
What are the dimensions of the field?
A. length ( =2 mathrm{cm}, ) width ( =6 mathrm{cm} )
B. length ( =1 mathrm{cm}, ) width ( =8 mathrm{cm} )
c. length ( =2 mathrm{cm}, ) width ( =8 mathrm{cm} )
D. length ( =3 mathrm{cm}, ) width ( =8 mathrm{cm} )
10
300 If one of the zeroes of the quadratic
polynomial ( (k-1) x^{2}+k x+1 ) is -3
then the value of ( k ) is.
A ( cdot frac{4}{3} )
в. ( frac{-4}{3} )
( c cdot frac{2}{3} )
D. ( frac{-2}{3} )
10
301 What is the absolute value of the difference
between the roots of ( x^{2}+6 x+5=0 ? )
10
302 If the roots of the quadratic equation
( x^{2}+6 x+b=0 ) are real and distinct
and they differ by atmost 4 then the least value of ( b ) is
A . 5
B. 6
( c cdot 7 )
D. 8
10
303 f ( p, q, r ) are real and ( p neq q, ) then roots of
the equation ( (boldsymbol{p}-boldsymbol{q}) boldsymbol{x}^{2}+mathbf{5}(boldsymbol{p}+boldsymbol{q}) boldsymbol{x}- )
( mathbf{2}(boldsymbol{p}-boldsymbol{q})=mathbf{0} ) are
A. Real and equal
B. Complex
c. Real and unequal
D. None of these
10
304 58. I 2×2 +5x+2, value of
1) 2
(3) -2
(4-2
10
305 Check whether the following is Quadratic equations:
( (x+1)^{2}=2(x-3) )
10
306 Find a quadratic equation with real coefficient whose one root is ( 3-2 i ) 10
307 Two candidates attempt to solve a
quadratic equation of the ( a x^{2}+b x+ )
( c=0 ) One starts with a wrong value of ( b )
and find the roots to be 2 and 6 . The
other starts with the wrong values of ( c )
and find the roots to be ( +2,-9 . ) The correct roots of the equation are
10
308 ( sqrt{x^{2}+1} ) 10
309 20. Solve
? +4x+31 +2x + 5 = 0
(1988 – 5 Marks)
10
310 Factorize ( 3 x^{2}+14 x+15 ) 10
311 Solve the equation using formula. ( 2 x^{2}+frac{x-1}{5}=0 )
A ( cdot x=frac{-1 pm sqrt{10}}{4} )
B. ( x=frac{-1 pm sqrt{41}}{20} )
c. ( x=frac{1 pm sqrt{41}}{20} )
D. ( _{x}=frac{1 pm sqrt{10}}{4} )
10
312 Factorise: ( 12 a x-4 a b+18 b x-6 b^{2}= )
0
10
313 Find the values of ( k ) for which the given equation has real and equal roots ( mathbf{2} boldsymbol{x}^{2}-mathbf{1} mathbf{0} boldsymbol{x}+boldsymbol{k}=mathbf{0} ) 10
314 53. If (3a + 1)2 + (b – 1)2 + (20-3)2
= 0, then the value of
(3a + b + 2c) is equal to :
(1) 3 (2)-1
(3) 2
(4)5
10
315 If ( x ) is real, ( x+frac{1}{x} neq 0 ) and ( x^{3}+frac{1}{x^{3}}=0 )
then the value of ( left(boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}right)^{mathbf{4}} ) is
( mathbf{A} cdot mathbf{4} )
B. 9
c. 16
D. 25
10
316 If ( x=5+2 sqrt{6}, ) then the value of
( left(sqrt{boldsymbol{x}}-frac{1}{sqrt{x}}right)^{2} )
A ( .4 sqrt{6} )
B. 8
c. 16
D. 12
E. None of these
10
317 ( mathbf{f} boldsymbol{x}=frac{1}{mathbf{5}+frac{mathbf{1}}{mathbf{5}+frac{mathbf{1}}{mathbf{5}+} cdots cdots}}^{text {then }} )
A ( cdot x^{2}+5 x-1=0 )
B . ( x^{2}-5 x-1=0 )
C ( cdot x^{2}-5 x+1=0 )
D. ( x^{2}+5 x+1=0 )
10
318 ( frac{41 x-12}{x^{2}-16}=frac{4 x+3}{x-4} ) 10
319 63. The value of
20+ V20 + 120+……. is:
(1) 4 (2) 3 h
(3) 5
(4) 0
10
320 A two-digit number is such that the product of its digits is 8. When 18 is subtracted from the number, the digits interchange their places. Find the number. 10
321 If one root of the equation ( x^{2}+p x+ )
( 12=0 ) is 4 while the equation ( x^{2}+ )
( p x+q=0 ) has equal roots, then one
value of ( q ) is
( mathbf{A} cdot mathbf{3} )
в. 12
c. ( frac{49}{4} )
D. 4
10
322 ( x^{2}+(a+b+c) x+a b+b c ) 10
323 If ( a-b=5 ) and ( a^{2}+b^{2}=53, ) find the
value of ( a b )
10
324 ( boldsymbol{x}^{2}+mathbf{5} boldsymbol{x}-left(boldsymbol{a}^{2}+boldsymbol{a}-boldsymbol{6}right)=mathbf{0} ) 10
325 A farmer wishes to start a 100 sq.m
rectangular vegetable garden. since he has only ( 30 mathrm{m} ) barbed wire, he fences the sides of the rectangular garden letting his house compound wall act as the fourth side fence. Find the
dimension of the garden.
A. ( 20 m, 5 m ) or ( 10 m, 10 m )
В. ( 2 m, 5 m ) or ( 10 m, 10 m )
( mathrm{c} .20 mathrm{m}, 5 mathrm{m} ) or ( 1 mathrm{m}, 10 mathrm{m} )
D. None of these
10
326 Is the following equation a quadratic equation?
( 16 x^{2}-3=(2 x+5)(5 x-3) )
A. Yes
B. No
c. Ambiguous
D. Data insufficient
10
327 ( f(m)=2, ) find the value of ( m^{2}-m+1 ) 10
328 The value of ( mathrm{k} ) for which polynomial
( x^{2}-k x+4 ) has equal zeroes is
This question has multiple correct options
A .4
B . 2
( c .-4 )
D. –
10
329 ( frac{1-frac{9}{y^{2}}}{1-frac{3}{y}}-frac{3}{y}, ) where ( (y neq 0)= )
A. ( frac{y-3}{y} )
в. ( frac{y+3}{y} )
( c cdot 3 )
D.
E ( .3 y-1 )
10
330 Solve :
( sqrt{2} x^{2}-sqrt{3} x-3 sqrt{2} )
10
331 Factories:
( x^{2}+6 x+9 )
10
332 If one of the zeroes of the polynomial ( boldsymbol{f}(boldsymbol{z})=boldsymbol{p}^{2} boldsymbol{z}^{2}+boldsymbol{8} boldsymbol{z}+boldsymbol{1} boldsymbol{6} ) is reciprocal of
the other, then the value of ( p ) is:
( A ldots pm 4 )
B. – 5
( c cdot 6 )
D. –
10
333 If the sum of the roots of the equation ( x^{2}-x=k(2 x-1) ) is zero, find ( k ) 10
334 If the equation ( x^{2}+b x+c=0 ) and
( boldsymbol{x}^{2}+boldsymbol{c} boldsymbol{x}+boldsymbol{b}=mathbf{0},(boldsymbol{b} neq boldsymbol{c}) ) have a
common root then
A. ( b+c=0 )
B. ( b+c=1 )
c. ( b+c+1=0 )
D. None of these
10
335 Number of solutions of the equation ( (sqrt{3}+1)^{2 x}+(sqrt{3}-1)^{2 x}=2^{3 x} ) is 10
336 The roots of ( a^{2} x^{2}+a b x=b^{2}, a neq )
( mathbf{0}, boldsymbol{b} neq mathbf{0} ) are:
A. Equal
B. Non- real
c. Unequal
D. None of these
10
337 17. Solve for x; (5+276)+2-3 +(5-216)*2-3 = 10
(1985 – 5 Marks)
10
338 Classify the following polynomials as linear, quadratic, cubic and biquadratic polynomials:
( x+x^{2}-4 )
10
339 If Sum of two numbers ( =-21 ) and
Product ( =-100 )
Then find the two numbers
10
340 State whether the given algebraic expressions are polynomials? Justify. ( x^{2}+7 x+9 ) 10
341 If ( a>0, ) then the expression ( a x^{2}+ )
( b x+c ) is positive for all values of ( x )
provided
A ( . b^{2}-4 a c>0 )
В. ( b^{2}-4 a c<0 )
( mathbf{c} cdot b^{2}-4 a c=0 )
D. ( b^{2}-a c<0 )
10
342 The roots of the equation ( a x^{2}+b x+ )
( c=0 ) will be imaginary if
A. ( a>0, b=0, c0, b=0, c>0 )
c. ( a=0, b>0, c>0 )
D. ( a>0, b>0, c=0 )
10
343 State true or false:
( x^{2}-5 x+6 ) cannot be written as a
product of two linear factors.
A . True
B. False
10
344 The angry Arjun carried some arrows for fighting with Bheeshm. With half the arrows, he cut down the arrows thrown
by Bheeshm on him and with six other
arrows he killed the rath driver of
Bheeshm. With one arrow each, he
knocked down respectively the rath, flag and the bow of Bheeshm. Finally, with one more than four times the square
root of arrows he laid Bheeshm
unconscious on an arrow bed. Find the
total number of arrows Arjun had.
10
345 For what value of ( k ) will ( x^{2}- )
( (3 k-1) x+2 k^{2}+2 k=11 ) have equal
roots?
( mathbf{A} cdot 9,-5 )
В. -9,5
( c .9,5 )
D. -9,-5
10
346 If the equation ( a x^{2}+b x+c=0 )
( a, b, c in R ) have non-real roots, then
This question has multiple correct options
A ( cdot c(a-b+c)>0 )
B. ( c(a+b+c)>0 )
c. ( c(4 a-2 b+c)>0 )
D. None of the above
10
347 Which of the following is a quadratic
equation?
A ( cdot x^{frac{1}{2}}+2 x+3=0 )
B ( cdot(x-1)(x+4)=x^{2}+1 )
( mathbf{c} cdot x^{4}-x+5=0 )
D. ( (2 x+1)(3 x-4)=2 x^{2}+3 )
10
348 Find the roots of the equation ( 2 x^{2}- ) ( boldsymbol{x}+frac{mathbf{1}}{mathbf{8}}=mathbf{0} ) 10
349 If ( a^{2}-5 a-1=0 ) and ( a neq 0 ; ) find:
( (i) a-frac{1}{a} )
( (mathrm{ii}) boldsymbol{a}+frac{mathbf{1}}{boldsymbol{a}} )
10
350 Find the value of ( mu ) for which one root of
the quadratic equation ( mu x^{2}-14 x+ )
( 8=0 ) in 6 times the other.
10
351 Which of the following is not a
quadratic equation?
A ( cdot 2(x-1)^{2}=4 x^{2}-2 x+1 )
B. ( left(x^{2}+1right)^{2}=x^{2}+3 x+9 )
( mathbf{C} cdotleft(x^{2}+2 xright)^{2}=x^{4}+3+4 x^{3} )
D ( cdot x^{2}+9=3 x^{2}-5 x )
10
352 What is a Quadratic Equation? 10
353 Find a quadratic equation whose roots
( operatorname{are} alpha, beta ) such that ( alpha+beta=3 ) and ( alpha^{3}+ )
( boldsymbol{beta}^{mathbf{3}}=mathbf{9} )
10
354 For the expression ( a x^{2}+7 x+2 ) to be
quadratic, the necessary condition is
( mathbf{A} cdot a=0 )
B. ( a neq 0 )
( ^{c} cdot_{a}>frac{7}{2} )
D. ( a<-1 )
10
355 The values of ( k, ) so that the equations
( 2 x^{2}+k x-5=0 ) and ( x^{2}-3 x-4=0 )
have one root in common, are
A ( cdot_{3, frac{27}{2}} )
в. ( 9, frac{27}{4} )
c. ( _{-3, frac{-27}{4}} )
D. ( -3, frac{4}{27} )
10
356 The given equation ( (x+1)^{2}=2(x-3) )
is
A . linear
B. quadratic
c. cubic
D. none of these
10
357 Find the value of ( s, ) if ( 3 s^{2}+8 s+3 ) 10
358 Find the equation whose roots are the
reciprocals of the roots of ( 3 x^{2}-5 x+ )
( mathbf{7}=mathbf{0} )
A ( cdot 7 x^{2}-5 x+3=0 )
B . ( 7 x^{2}+5 x+3=0 )
c. ( 4 x^{2}-5 x+3=0 )
D. ( 7 x^{2}-5 x+7=0 )
10
359 If ( left(2 x^{2}-3 x+1right)left(2 x^{2}+5 x+1right)=9 x^{2} )
A. For real root
B. Two real and two imaginary root
c. Four imaginary roots
D. None of the above
10
360 7.
The solution of the equation
5x^2(2x– 7) = 2(3x-1) +
10
361 If 1 lies between the roots of the
equation ( y^{2}-m y+1=0 ) and ( [x] ) is
the GIF function,
then the value of ( left[left(frac{4|x|}{|x|^{2}+16}right)^{m}right], ) is
( mathbf{A} cdot mathbf{0} )
B.
( c cdot 2 )
D. None of the above
10
362 Solve:
( x+frac{1}{x}=25 frac{1}{25} )
10
363 Choose best possible option. ( left(x+frac{1}{2}right)left(frac{3 x}{2}+1right)= )
( frac{6}{2}(x-1)(x-2) ) is quadratic.
A. Yes
B. No
c. Complex equation
D. None
10
364 Solve the equation ( x^{2}-2 b x+left(b^{2}-right. )
( left.boldsymbol{a}^{2}right)=mathbf{0} )
10
365 62. The speed of the current is 5 km
hour. A motorboat goes 10 km
upstream and back again to the
starting point in 50 minutes. The
speed, in km/hour, of the mo-
torboat in still water is
(1) 20 (2) 26
(3) 25
(4) 28
10
366 Check whether ( 5-6 x=frac{2}{5} x^{2} ) is
a quadratic equation.
10
367 Solve the following by using the method of completing square. ( 6 x^{2}-11 x+3=0 ) 10
368 Which of the following equations have no real roots ?
A ( cdot x^{2}-2 sqrt{3}+5=0 )
B ( cdot 2 x^{2}+6 sqrt{2} x+9=0 )
c. ( x^{2}-2 sqrt{3}-5=0 )
D ( cdot 2 x^{2}-6 sqrt{2} x-9=0 )
10
369 The given quadratic equation have real roots and the roots are ( -2 sqrt{3}, frac{-sqrt{3}}{2} ) ( mathbf{2} boldsymbol{x}^{2}+mathbf{5} sqrt{mathbf{3}} boldsymbol{x}+mathbf{6}=mathbf{0} )
A. True
B. False
10
370 15. If one root of the quadratic equation ax2 + bx+c=0 is
equal to the n-th power of the other, then show that
(ac”)”+1 +(a” c)2+1 +b=0
(1983 – 2 Marks)
10
371 Solve: ( x^{2}+y^{2}-4 x-4 y+8=0 ) 10
372 The nature of the roots of the equation ( x^{2}-5 x+7=0 ) is
A. No real roots
B. 1 real root and 1 imaginary
c. Real and unequal
D. Real and equal
10
373 Two types of boxes ( A, B ) are to be
placed in a truck having capacity of 10
tons. When 150 boxes of type ( A ) and 100 boxes of type ( B ) are loaded in the truck, it weighs 10 tons. But when 260 boxes
of type ( A ) are loaded in the truck, it can
still accommodate 40 boxes of type ( B )
so that it is fully loaded. Find the weight of each type of box.
10
374 If the quadratic equation ( x^{2}+b x+ )
( mathbf{7 2}=mathbf{0} ) has two distinct integer roots,
then the number of all possible values of bis
A . 12
B. 9
c. 15
D. 18
10
375 The set of values of ( p ) for which the roots
of the equation ( 3 x^{2}+2 x+p(p-1)= )
0 are of opposite sign is
( A cdot(-infty, 0) )
B. (0,1)
c. ( (1, infty) )
D. ( (0, infty) )
10
376 If sec ( alpha ) and ( csc alpha ) are the roots of ( x^{2}- )
( boldsymbol{p} boldsymbol{x}+boldsymbol{q}=boldsymbol{0} ) then
A ( cdot p^{2}=q(q-2) )
B . ( p^{2}=q(q+2) )
c. ( p^{2}+q^{2}=2 q )
D・ ( p^{2}+q^{2}=1 )
10
377 Assertion
If the roots of the equations ( x^{2}-b x+ )
( c=0 ) and ( x^{2}-c x+b=0 ) differ by the
same quantity, then ( b+c ) is equal to
-4
Reason
If ( alpha, beta ) are the roots of the equation ( A x^{2}+B x+C=0, ) then ( alpha-beta= )
( frac{sqrt{boldsymbol{B}^{2}-boldsymbol{4} boldsymbol{A} boldsymbol{C}}}{boldsymbol{A}} )
A. Both Assertion and Reason are correct and Reason is the correct explanation for Assertion
B. Both Assertion and Reason are correct but Reason is not the correct explanation for Assertion
c. Assertion is correct but Reason is incorrect
D. Assertion is incorrect but Reason is correct
10
378 The length of a rectangular verandah is
( 3 m ) more than its breadth. The
numerical value of its area is equal to
the numerical value of its
perimeter. Taking ( x ) as the breadth of
the verandah, write an equation in ( x )
that represents the above statement.
A ( cdot x^{2}-x-6=0 )
B. ( x^{2}-x+6=0 )
c. ( x^{2}-x+5=0 )
D. ( x^{2}-x-5=0 )
10
379 Find the number of all real solution to
the quadratic equation ( x^{2}+2 x=-1 )
10
380 Which of the following steps should be
followed to convert a given word problem into a Quadratic Equation?
A. Represent the unknown quantity/ies with variables ( (x ) y etc.
B. Express the information of the problem mathematically in the form of an equation.
c. check if the equation formed is in one variable and the degree of the equation is 2
D. All of the above
10
381 16. Find all real values of x which satisfy x2-3x+2> 0 and
x-2x-450
(1983 – 2 Marks)
10
382 The expression ( 21 x^{2}+a x+21 ) is to be
factored into two linear prime binomial factors with integer coefficients. This
can be done if a is:
A. odd number
B. zero
c. even number
D. None
10
383 Before Robert Norman worked on ‘Dip and Field Concept’, his predecessor thought that the tendency of the magnetic needle to swing towards the
poles was due to a point attractive. However, Norman showed with the help of experiment that nothing like point attractive exists. Instead, he argued that magnetic power lies is lodestone. Which one of the following is the problem on which Norman and others
worked?
A. Existence of point attractive
B. Magnetic power in lodestone
c. Magnetic power in needle
D. swinging of magnetic needle
10
384 Find the value of x for which the
expression 2 – 3x – 4×2 has the
greatest value.
(1)
16
10
385 Is the following equation a quadratic equation? ( (x+2)^{3}=x^{3}-4 )
A. Yes
B. No
c. Ambiguous
D. Data insufficient
10
386 Check whether the following are Quadratic equations
( (x+2)^{3}=2 xleft(x^{2}-1right) )
10
387 The sum of all real values of ( x ) satisfying the equation ( left(x^{2}-5 x+5right)^{x^{2}+4 x-60}=1 )
is?
10
388 If ( a^{2}-a b=0, ) which of the following is
the correct conclusion?
( mathbf{A} cdot a=0 )
B . ( a=b )
( mathbf{c} cdot a^{2}=b )
D. either ( a=0 ) or ( a=b )
10
389 Using the identity ( a^{2}-b^{2}= )
( (a+b)(a-b) ) solve ( left(7 frac{3}{4}right)^{2}-left(2 frac{1}{4}right)^{2} )
10
390 The product of 2 consecutive integers is 20 find them 10
391 63. The current of a stream runs
at the rate of 4 km an hour. A
boat goes 6 km and comes back
to the starting point in 2
hours. The speed of the boat
in still water is
(1) 6 km/hour
(2) 8 km/hour
(3) 7.5 km/hour
(4) 6-8 km/hour
10
392 f ( p=-2, ) find the value of:
( -3 p^{2}+4 p+7 )
10
393 Find the root of the quadratic equation
( x^{2}+2 sqrt{2 x}+6=0 ) by using the
quadratic formula
A . ( x=sqrt{2} pm 2 i )
B. ( x=-sqrt{2} pm 2 i )
c. ( x=-sqrt{4} pm 2 i )
D. ( x=-sqrt{2} pm 4 i )
10
394 The expression ( frac{5-x}{x^{2}-x-20} ) when simplified equals
A ( cdot frac{1}{(x+4)} )
в. ( frac{1}{(x-4)} )
c. ( -frac{1}{(x+4)} )
D. ( frac{1}{(x-5)} )
10
395 For what values of ( m in R, ) both roots of
the equation ( x^{2}-6 m x+9 m^{2}- )
( 2 m+2=0 ) exceed ( 3 ? )
B. ( left(frac{11}{9}, inftyright) )
c. ( [1, infty] )
D. ( [0, infty] )
10
396 If ( x^{4}+frac{1}{x^{4}}=119, ) then the value of ( x- )
( frac{1}{-} ) is
( x )
( A cdot 6 )
B. 12
c. 11
D.
10
397 If the sum of the roots of the quadratic
equation ( a x^{2}+b x+c=0 ) is equal to
the sum of the square of their reciprocals, then ( frac{a}{c}, frac{b}{a} ) and ( frac{c}{b} ) are in
A . GP
в. нР
c. АGР
D. AP
10
398 Check whether the following are
Quadratic equations
( x^{2}+3 x+1=(x-2)^{2} )
10
399 Greatest ratio of roots of ( 4 x^{2}-2left(a^{2}+right. )
( left.b^{2}right) x+a^{2} b^{2}=0 ) if ( a=2 b )
10
400 Find the roots of the equation ( 2 x^{2}+ )
( x-6=0 ) by factorisation.
10
401 The number of roots of the equation ( 2^{x}+2^{x-1}+2^{x-2}=7^{x}+7^{x-1}+7^{x-2} )
is-
10
402 Solve:
( frac{2 x-1}{x+4}-2 x-5 x+3=0 )
10
403 Find the value of ( k ) for which the
equation ( 3 x^{2}-6 x+k=0 ) has distinct
and real root.
10
404 Solve ( boldsymbol{x}+mathbf{2}+boldsymbol{y}+mathbf{3}+ )
( sqrt{(x+2)(y+3)}=39 )
( (x+2)^{2}+(y+3)^{2}+(x+2)(y+ )
3)( =741 )
10
405 A quadratic equation in ( x ) is ( a x^{2}+ )
( boldsymbol{b} boldsymbol{x}+boldsymbol{c}=mathbf{0}, ) where ( boldsymbol{a}, boldsymbol{b}, boldsymbol{c} ) are real
numbers and the other condition is
( mathbf{A} cdot a neq 0 )
в. ( b neq 0 )
c. ( c neq 0 )
( mathbf{D} cdot b=0 )
10
406 Find the quadratic function ( boldsymbol{f}(boldsymbol{x}) boldsymbol{i} boldsymbol{f} boldsymbol{f}(boldsymbol{0})=mathbf{1}, boldsymbol{f}(1)=mathbf{0}, boldsymbol{a} boldsymbol{n} boldsymbol{d} boldsymbol{f}(boldsymbol{3})= )
( mathbf{5} )
10
407 Find the value of discriminant for
( sqrt{3} x^{2}+2 sqrt{2} x-2 sqrt{3}=0 )
10
408 Which of the following is a quadratic polynomial in one variable?
A. ( sqrt{2 x^{3}}+5 )
.
B. ( 2 x^{2}+2 x^{-2} )
c. ( x^{2} )
D. ( 2 x^{2}+y^{2} )
10
409 Ifa, ß are the roots of x2 + px +q=0 and y, 8 are the roots
of r+rx+s=0, evaluate (a-ya-8)(-y)
(B-8) in terms of p, q, r and s.
Deduce the condition that the equations have a common
(1979)
root.
10
410 Equation of the tangent at (4,4) on ( x^{2}= )
4y is
A. ( 2 x+y+4=0 )
В. ( 2 x-y-4=0 )
c. ( 2 x+y-12=0 )
D. ( 2 x+y+12=0 )
10
411 Find the value(s) of ( k ) for which the
equation ( boldsymbol{x}^{2}+mathbf{5} boldsymbol{k} boldsymbol{x}+mathbf{1 6}=mathbf{0} ) has equal
roots.
10
412 63. 11 (*+
+* +- 4 = 0.
then possible of x will be (x+0.
x# 1)
(1) 5485 2 515
(3 3445 (4) – 3415
10
413 In the following, determine the value of
( k ) for which the given value is a solution
of the equation.
( mathbf{3} boldsymbol{x}^{2}+mathbf{2} boldsymbol{k} boldsymbol{x}-mathbf{3}=mathbf{0}, boldsymbol{x}=-frac{mathbf{1}}{mathbf{2}} )
10
414 If the quadratic equation ( k x^{2}-2 k x+ )
( 6=0 ) has equal roots, then find the
value of ( k )
10
415 The sum of the real roots of the
equation ( |boldsymbol{x}-mathbf{2}|^{2}+|boldsymbol{x}-mathbf{2}|-mathbf{2}=mathbf{0} )
( A cdot 2 )
B. 3
( c cdot 4 )
D.
10
416 Divide 18 into 2 parts such that their product is 81
A. 9,-9
в. 3,27
c. ( 9, frac{1}{9} )
D. 9,9
10
417 If ( boldsymbol{A}=boldsymbol{x}^{2}+boldsymbol{x}+mathbf{1}, boldsymbol{B}=boldsymbol{x}^{2}-boldsymbol{x}+mathbf{1} )
then ( boldsymbol{A}-mathbf{2} boldsymbol{B} )
10
418 7.
Find all integers x for which
(5x-1)<(x+1)2 < (Tx-3).
10
419 Discriminant of the equation ( -3 x^{2}+ )
( 2 x-8=0 ) is
A . -92
B. -29
c. 39
D. 49
10
420 Find the value of ( k ) for which the
quadratic equation ( (k-2) x^{2}+ )
( 2(2 k-3) x+5 k-6=0 ) has equal
roots
( A )
B. 3
c. A and B both
D. none of these
10
421 If ( alpha ) and ( beta ) are zeroes of the polynomial ( 2 x^{2}+3 x+7 . ) Find a quadratic
polynomial whose zeroes are ( frac{1}{alpha^{2}} & frac{1}{beta^{2}} )
A ( cdot 49 x^{2}+18 x+4 )
B . ( 49 x^{2}-18 x+4 )
c. ( 49 x^{2}-23 x-4 )
D. ( 49 x^{2}-21 x+4 )
10
422 Determine the nature of roots of the
following quadratic equation:
( 2 x^{2}+5 x+5=0 )
10
423 The solution of the equation ( boldsymbol{x}+frac{mathbf{1}}{boldsymbol{x}}=mathbf{2} )
will be
A .2,-1
в. ( _{0,-1,-frac{1}{5}} )
( mathrm{c} cdot_{-1,-frac{1}{5}} )
D. None of these
10
424 Negetive of Discriminant of the following quadratic equation is :
( x^{2}-x+1=0 )
10
425 If one root of ( x^{2}+a x+8=0 ) is 4 and
the equation ( x^{2}+a x+b=0 ) has equal
roots, then ( b= )
A . 7
B. 9
( c .1 )
D. 3
10
426 Which is a quadratic equation?
A ( cdot x+frac{1}{x}=2 )
B . ( x^{2}+1=(x+3)^{2} )
c. ( x(x+2) )
D. ( _{x+frac{1}{x}} )
10
427 If ( n ) is a positive integer and ( n in[5,100] )
then the number of integral roots of the equation ( x^{2}+2 x-n=0 ) are
A . 4
B. 6
c. 8
D. 10
10
428 If the equation ( 2 x^{2}-6 x+p=0 ) has
real and different roots, then the values
of ( p ) are given by
( ^{A} cdot_{p}frac{9}{2}} )
( mathrm{D} cdot_{p} geq frac{9}{2} )
10
429 Let ( a, b, c ) be the sides of a triangle. No
two of them are equal and ( lambda epsilon R ) If the
roots of the equation ( x^{2}+2(a+b+ )
( c) x+3 lambda(a b+b c+c a)=0 ) are real
then.
10
430 Check whether the following is a quadratic equation or not
( (x+1)^{2}=2(x-3) )
10
431 If both roots of the equation ( a x^{2}+ ) ( 2 x a+1+a^{2}-16=0 ) are opposite in
( operatorname{sign}, ) then the range of ( a ) is
( A cdot(-infty,-4) cup(4, infty) )
B . (-4,4)
( mathbf{c} cdot(-infty,-4) cup(0,4) )
D ( cdot(0,4) )
10
432 The trinomial ( a x^{2}+b x+c ) has no real
roots, ( a+b+c<0 . ) Find the sign of
the number ( c )
10
433 The sign of the quadratic polynomial
( a x^{2}+b x+c ) is always positive, if?
( mathbf{A} cdot ) a is positive and ( b^{2}-4 a c leq 0 )
B. a is positive and ( b^{2}-4 a geq 0 )
( mathrm{C} cdot ) a can be any real number and ( b^{2}-4 a c leq 0 )
D. a can be any real number and ( b^{2}-4 a c geq 0 )
10
434 The roots of ( a x^{2}+b x+c=0, ) where
( a neq 0, b, c epsilon R ) are non real complex and
( a+c2 b )
B . ( 4 a+c<2 b )
c. ( 4 a+c=2 b )
D. None of these
10
435 ( boldsymbol{x}^{2}-(boldsymbol{m}-mathbf{3}) boldsymbol{x}+boldsymbol{m}=mathbf{0}(boldsymbol{m} in boldsymbol{R}) ) be a
quadratic equation. Find the value of ( boldsymbol{m} )
for which both the roots are equal:
A ( cdot{1,9} )
B.
( c .3 )
D. {4,11}
10
436 The value of ( k, ) of the roots of the
equation ( 2 k x^{2}+2 k x+2=0 ) are
equal is
( A cdot frac{4}{5} )
B. 4
c. 1
D.
10
437 ( frac{x-a}{x-b}+frac{x-b}{x-a}= ) 10
438 The given quadratic equations have real roots and roots are Real and equal, ( sqrt{frac{3}{2}} )
( mathbf{2} boldsymbol{x}^{2}-mathbf{2} sqrt{mathbf{6} boldsymbol{x}}+mathbf{3}=mathbf{0} )
A. True
B. False
10
439 If ( boldsymbol{alpha}, boldsymbol{beta} in boldsymbol{C} ) are the distinct roots, of the
equation ( x^{2}-x+1=0, ) then ( alpha^{101}+ )
( beta^{107} ) is equal to
A .
B. 2
( c cdot-1 )
D.
10
440 Identify which of the following is/are
a quadratic polynomial function:
This question has multiple correct options
( mathbf{A} cdot f(x)=(x+1)^{3}-(x+2)^{3} )
( g(x)=left{begin{array}{cc}frac{x^{4}}{x^{2}} & text { if } x neq 0 \ 0 & text { if } x=0end{array}right. )
C ( cdot h(x)=(x+1)^{2}-(x+2)^{2} )
D. All of these
10
441 Solve the equation:
( 4 x^{2}-4 p x+left(p^{2}-q^{2}right)=0 )
10
442 f ( x=3 t, y=1 / 2(t+1), ) then the value
of ( t ) for which ( x=2 y ) is
( A cdot 1 )
B. ( 1 / 2 )
( c .-1 )
D. ( 2 / 3 )
10
443 Is the given equation quadratic? Enter 1 for True and 0 for False.
( boldsymbol{n}-mathbf{3}=mathbf{4} boldsymbol{n}^{2} )
10
444 If the roots of the equation ( frac{alpha}{x-alpha}+ ) ( frac{beta}{boldsymbol{x}-beta}=1 ) be equal in magnitude but
opposite in ( operatorname{sign}, ) then ( alpha+beta ) is equal to:
A.
B. 1
( c cdot 2 )
D.
10
445 Decide whether ( m^{2}+m+2=4 m ) is a
quadratic equation
10
446 The number of solutions of the
equation, ( 2{x}^{2}+5{x}-3=0 ) is
A. No solution
B.
( c cdot 2 )
D. Infinite
10
447 The number of quadratic equation which are unchanged by squaring their roots is 10
448 ( boldsymbol{x}^{2}-(boldsymbol{m}-mathbf{3}) boldsymbol{x}+boldsymbol{m}=mathbf{0}(boldsymbol{m} in boldsymbol{R}) ) be a
quadratic equation. Find the value of ( boldsymbol{m} )
for which, both the roots lie in the
interval of (1,2)
A. ( (10, infty) )
)
в. ( (-infty, 0) )
( c cdot(-infty, infty) )
D. None of the above
10

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