With respect to the roots of x2 - x - 2 = 0, we can say that :

the latter of the two is negative

both of them are natural numbers

the latter of the two is negative

If x = y or relation cannot be established

142 + Mcqs in Quadratic Equation in Aptitude Page 2 McqOptions

51.	. x² 6x = 7 . 2y² + 13y + 15 = 0
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» C. 3

Discussion

52.	. 16x² + 20x + 6 = 0 . 10y² + 38y + 24 = 0
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» C. 3

Discussion

53.	. 18x² + 18x + 4 = 0 . 12y² + 29y + 14 =0
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» E. 5

Discussion

54.	. 4x + 7y = 209 . 12x 14y = 38
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» F.

Discussion

55.	. 17x² + 48x = 9 . 13y² = 32y 12
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» B. 2

Discussion

56.	6 + 6 + 6 +........ is equal to
A.	2
B.	5
C.	4
D.	3
Answer» E.

Discussion

57.	Determine p so that the equation x² + 5px + 16 = 0 has on real root.
A.	None of these
Answer» C.

Discussion

58.

. 2 4 - 3 4 = x^10/7
x^4/7 x^4/7

. y³ + 783 = 999

A.

1

B.

2

C.

3

D.

4

E.

5

Answer» E. 5

Discussion

59.	. x³ 13 = x² 247 . y^1/3 14 = 294 y^2/3
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» D. 4

Discussion

60.	. x² 11x + 24 = 0 . 2y² 9y + 9 = 0
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» C. 3

Discussion

61.	. ( 17 )² + 144 18 = x . ( 26 )² - 18 21 = y
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» D. 4

Discussion

62.	. 500x + 402 = 0 . 360y + ( 200 )^1/2 = 0
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» D. 4

Discussion

63.	In the following determine the set of value of P for which the given quadratic equation has real roots. Px² + 4x + 1 = 0
A.	P 4
B.	P > 4
C.	P 4
D.	P 4
Answer» D. P 4

Discussion

64.	The roots of the equation 7x² - 6x - 13 7 = 0 are
A.
B.	None of these
Answer» D.

Discussion

65.	With respect to the roots of x² - x - 2 = 0, we can say that :
A.	both of them are natural numbers
B.	both of them are integers
C.	the latter of the two is negative
D.	None of these
Answer» C. the latter of the two is negative

Discussion

66.	If , are the roots of the quadratic equation x² - 8x + k = 0, find the value of k such the ² + ² = 40
A.	12
B.	14
C.	10
D.	16
Answer» B. 14

Discussion

67.	. x² 4 = 0 . y² + 6y + 9 = 0
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» B. 2

Discussion

68.	. x² = 729 . y = 729
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» E. 5

Discussion

69.	. x² - 7x + 12 = 0 . y² - 12y + 32 = 0
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» E. 5

Discussion

70.	. 2x² + 11x + 14 = 0 . 4y² + 12y + 9 = 0
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» D. 4

Discussion

71.	The factors of ( a² + 4b² + 4b 4ab 2a 8 ) are :
A.	(a 2b 4) (a 2b + 2)
B.	(a b + 2) (a + 4b + 4)
C.	(a + 2b 4) (a + 2b + 2)
D.	(a + 2b 1) (a 2b + 1)
Answer» B. (a b + 2) (a + 4b + 4)

Discussion

72.	Find the value of 30 + 30 + 30 +........
A.	5
B.	3
C.	6
D.	7
Answer» D. 7

Discussion

73.	. 5x + 2y = 31 . 3x + 7y = 36
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» B. 2

Discussion

74.	The roots of the equation a²x² - 3abx + 2b² = 0 are
A.	None of these
Answer» C.

Discussion

75.	If and are the roots of the quadratic equation ax²+ bx + c = 0, the value of ³ + ³ is
A.	None of these
Answer» C.

Discussion

76.	Divide 16 into 2 parts such the twice the square of the larger part exceeds the square of the smaller part by 164.
A.	10, 6
B.	8, 8
C.	12, 4
D.	None of these
Answer» B. 8, 8

Discussion

77.	. 4x + 7y = 209 . 12x 14y = 38
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» F.

Discussion

78.	. 8x² + 6x = 5 . 12y² 22y + 8 = 0
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» D. 4

Discussion

79.	If 2x² - 7xy + 3y² = 0, then the value of x : y is
A.	3 : 2
B.	2 : 3
C.	3 : 1 and 1 : 2
D.	5 : 6
E.	None of the above
Answer» D. 5 : 6

Discussion

80.	If one roots of the equation x²/a = x/b + 1/c = 0 is reciprocal of the other, then which one of the following is correct ?
A.	a = b
B.	b = c
C.	ac = 1
D.	a = c
Answer» E.

Discussion

81.	. 18x² + 18x + 4 = 0 . 12y² + 29y + l4 = 0
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» E. 5

Discussion

82.	One root of the quadratic equation x² - 5x + 6 = 0 is 3. Find the other root.
A.	2
B.	2
C.	1
D.	1
Answer» B. 2

Discussion

83.	If log₁₀ ( x² - 6x + 45 ) = 2, then the values of x are
A.	6, 9
B.	9, 5
C.	10, 5
D.	11, 5
Answer» E.

Discussion

84.	If the equations x² + 2x - 3 = 0 and x² + 3x - k = 0 have a common root, then the non - zero value of k is :
A.	1
B.	2
C.	3
D.	4
Answer» E.

Discussion

85.	. 16x² + 20x + 6 = 0 .10y² + 38y + 24 = 0
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» C. 3

Discussion

86.	. 17x² + 48x = 9 .13y² = 32y 12
A.	1
B.	2
C.	3
D.	4
E.	5
Answer» B. 2

Discussion

87.	The expression x² x + 1 has :
A.	one proper linear factor
B.	two proper linear factors
C.	no proper linear factor
D.	None of these
Answer» D. None of these

Discussion

88.	The length of a rectangular plot is 8 m greater than its breadth. If the area of the plot is 308 m², find the length of the plot.
A.	22 m
B.	18 m
C.	20 m
D.	None of these
Answer» D. None of these

Discussion

89.	Find 2 consecutive positive odd integers whose squares have the sum 290.
A.	11, 13
B.	13, 15
C.	9, 11
D.	None of these
Answer» B. 13, 15

Discussion

90.	x = 3a solution of the equation 3x² + (k 1)x + 9 = 0 if k has value
A.	13
B.	13
C.	11
D.	11
Answer» E.

Discussion

91.	The common root of the equations x² - 7x + 10 = 0 and x² - 10x + 16 = 0 is :
A.	- 2
B.	3
C.	5
D.	2
Answer» E.

Discussion

92.	The sum of the squares of 2 natural consecutive odd numbers is 394. The sum of the numbers is :
A.	24
B.	32
C.	40
D.	28
Answer» E.

Discussion

93.	The roots of the equation ax² + bx + c = 0 will be reciprocal if
A.	a = b
B.	b = c
C.	c = a
D.	None of these
Answer» D. None of these

Discussion

94.	Find the roots of the equation 2x² - 9x - 18 = 0.
A.	3/2 and 6
B.	-3/2 and - 6
C.	-3/2 and 6
D.	3/2 and -6
E.	None of the above
Answer» D. 3/2 and -6

Discussion

95.	If one root of x² - 6kx + 5 = 0 is 5, find the value of k.
A.	-1/2
B.	-1
C.	1
D.	2
Answer» D. 2

Discussion

96.	Find the roots of the equation 2x² - 11x + 15 = 0
A.	3 and 5/2
B.	-3 and -5/2
C.	5 and 3/2
D.	-5 and -3/2
Answer» B. -3 and -5/2

Discussion

97.	If one root of x
A.	-1/2
B.	-1
C.	1
D.	2
Answer» D. 2

Discussion

98.	(4/
A.	if x > y
B.	if x y
C.	if x < y
D.	if x y
E.	If x = y or relation cannot be established
Answer» F.

Discussion

99.	Mr. Arjun is on tour and he has 360 for his expenses. If he exceeds his tour by 4 days, he must cut down his daily expenses by 3. For how many days is Mr. Arjun out on tour ?
A.	40
B.	20
C.	60
D.	15
E.	None of the above
Answer» C. 60

Discussion

100.

The roots of x + 4 + x - 4 = 10 are :
x - 4 x + 4 3

A.

4

B.

6

C.

8

D.

2

E.

Answer» D. 2

Discussion

Explore topic-wise MCQs in Aptitude.

. x2 6x = 7 . 2y2 + 13y + 15 = 0

. 16x2 + 20x + 6 = 0 . 10y2 + 38y + 24 = 0

. 18x2 + 18x + 4 = 0 . 12y2 + 29y + 14 =0

. 4x + 7y = 209 . 12x 14y = 38

. 17x2 + 48x = 9 . 13y2 = 32y 12

6 + 6 + 6 +........ is equal to

Determine p so that the equation x 2 + 5px + 16 = 0 has on real root.

.2 4-3 4= x10/7x4/7x4/7 . y3 + 783 = 999

. x3 13 = x2 247 . y1/3 14 = 294 y2/3

. x2 11x + 24 = 0 . 2y2 9y + 9 = 0

. ( 17 )2 + 144 18 = x . ( 26 )2 - 18 21 = y

. 500x + 402 = 0 . 360y + ( 200 )1/2 = 0

In the following determine the set of value of P for which the given quadratic equation has real roots. Px2 + 4x + 1 = 0

The roots of the equation 7x2 - 6x - 13 7 = 0 are

With respect to the roots of x2 - x - 2 = 0, we can say that :

If , are the roots of the quadratic equation x2 - 8x + k = 0, find the value of k such the 2 + 2 = 40

. x2 4 = 0 . y2 + 6y + 9 = 0

. x2 = 729 . y = 729

. x2 - 7x + 12 = 0 . y2 - 12y + 32 = 0

. 2x2 + 11x + 14 = 0 . 4y2 + 12y + 9 = 0

The factors of ( a2 + 4b2 + 4b 4ab 2a 8 ) are :

Find the value of 30 + 30 + 30 +........

. 5x + 2y = 31 . 3x + 7y = 36

The roots of the equation a2x2 - 3abx + 2b2 = 0 are

If and are the roots of the quadratic equation ax 2 + bx + c = 0, the value of 3 + 3 is

Divide 16 into 2 parts such the twice the square of the larger part exceeds the square of the smaller part by 164.

. 4x + 7y = 209 . 12x 14y = 38

. 8x2 + 6x = 5 . 12y2 22y + 8 = 0

If 2x2 - 7xy + 3y2 = 0, then the value of x : y is

If one roots of the equation x2/a = x/b + 1/c = 0 is reciprocal of the other, then which one of the following is correct ?

. 18x2 + 18x + 4 = 0 . 12y2 + 29y + l4 = 0

One root of the quadratic equation x2 - 5x + 6 = 0 is 3. Find the other root.

If log10 ( x2 - 6x + 45 ) = 2, then the values of x are

If the equations x2 + 2x - 3 = 0 and x2 + 3x - k = 0 have a common root, then the non - zero value of k is :

. 16x2 + 20x + 6 = 0 .10y2 + 38y + 24 = 0

. 17x2 + 48x = 9 .13y2 = 32y 12

The expression x2 x + 1 has :

The length of a rectangular plot is 8 m greater than its breadth. If the area of the plot is 308 m2, find the length of the plot.

Find 2 consecutive positive odd integers whose squares have the sum 290.

x = 3a solution of the equation 3x2 + (k 1)x + 9 = 0 if k has value

The common root of the equations x2 - 7x + 10 = 0 and x2 - 10x + 16 = 0 is :

The sum of the squares of 2 natural consecutive odd numbers is 394. The sum of the numbers is :

The roots of the equation ax2 + bx + c = 0 will be reciprocal if

Find the roots of the equation 2x2 - 9x - 18 = 0.

If one root of x2 - 6kx + 5 = 0 is 5, find the value of k.

Find the roots of the equation 2x2 - 11x + 15 = 0

If one root of x

(4/

Mr. Arjun is on tour and he has 360 for his expenses. If he exceeds his tour by 4 days, he must cut down his daily expenses by 3. For how many days is Mr. Arjun out on tour ?

The roots of x + 4 + x - 4 = 10 are :x - 4 x + 4 3

. x² 6x = 7
. 2y² + 13y + 15 = 0

. 16x² + 20x + 6 = 0
. 10y² + 38y + 24 = 0

. 18x² + 18x + 4 = 0
. 12y² + 29y + 14 =0

. 4x + 7y = 209
. 12x 14y = 38

. 17x² + 48x = 9
. 13y² = 32y 12

Determine p so that the equation x² + 5px + 16 = 0 has on real root.

. 2 4 - 3 4 = x^10/7
x^4/7 x^4/7

. y³ + 783 = 999

. x³ 13 = x² 247
. y^1/3 14 = 294 y^2/3

. x² 11x + 24 = 0
. 2y² 9y + 9 = 0

. ( 17 )² + 144 18 = x
. ( 26 )² - 18 21 = y

. 500x + 402 = 0
. 360y + ( 200 )^1/2 = 0

In the following determine the set of value of P for which the given quadratic equation has real roots. Px² + 4x + 1 = 0

The roots of the equation 7x² - 6x - 13 7 = 0 are

With respect to the roots of x² - x - 2 = 0, we can say that :

If , are the roots of the quadratic equation x² - 8x + k = 0, find the value of k such the ² + ² = 40

. x² 4 = 0
. y² + 6y + 9 = 0

. x² = 729
. y = 729

. x² - 7x + 12 = 0
. y² - 12y + 32 = 0

. 2x² + 11x + 14 = 0
. 4y² + 12y + 9 = 0

The factors of ( a² + 4b² + 4b 4ab 2a 8 ) are :

. 5x + 2y = 31
. 3x + 7y = 36

The roots of the equation a²x² - 3abx + 2b² = 0 are

If and are the roots of the quadratic equation ax²+ bx + c = 0, the value of ³ + ³ is

. 4x + 7y = 209
. 12x 14y = 38

. 8x² + 6x = 5
. 12y² 22y + 8 = 0

If 2x² - 7xy + 3y² = 0, then the value of x : y is

If one roots of the equation x²/a = x/b + 1/c = 0 is reciprocal of the other, then which one of the following is correct ?

. 18x² + 18x + 4 = 0
. 12y² + 29y + l4 = 0

One root of the quadratic equation x² - 5x + 6 = 0 is 3. Find the other root.

If log₁₀ ( x² - 6x + 45 ) = 2, then the values of x are

If the equations x² + 2x - 3 = 0 and x² + 3x - k = 0 have a common root, then the non - zero value of k is :

. 16x² + 20x + 6 = 0
.10y² + 38y + 24 = 0

. 17x² + 48x = 9
.13y² = 32y 12

The expression x² x + 1 has :

The length of a rectangular plot is 8 m greater than its breadth. If the area of the plot is 308 m², find the length of the plot.

x = 3a solution of the equation 3x² + (k 1)x + 9 = 0 if k has value

The common root of the equations x² - 7x + 10 = 0 and x² - 10x + 16 = 0 is :

The roots of the equation ax² + bx + c = 0 will be reciprocal if

Find the roots of the equation 2x² - 9x - 18 = 0.

If one root of x² - 6kx + 5 = 0 is 5, find the value of k.

Find the roots of the equation 2x² - 11x + 15 = 0

The roots of x + 4 + x - 4 = 10 are :
x - 4 x + 4 3