782 + Mcqs in Algebra in Aptitude Page 1 McqOptions

1.	If x = 11, the value of x⁵ 12x⁴ + 12x 12x + 12x - 1 is
A.	11
B.	10
C.	12
D.	10
Answer» C. 12

Discussion

2.

If x = 999, y = 1000, z = 1001, then the value of
x + y + z - 3xyz is :
x - y + z

A.

1000

B.

9000

C.

1

D.

9

Answer» E.

Discussion

3.	If x = a + a + b + a - a + b , then x + 3bx is equal to
A.	0
B.	a
C.	2 a
D.	1
Answer» D. 1

Discussion

4.	The expression x⁴ 2x + k will be a perfect square when the value of k is
A.	2
B.	1
C.	1
D.	2
Answer» C. 1

Discussion

5.

If the line x - y = 1
a b

passes through the points (2, 3) and (4, 5) then (a, b) is

A.

(1, 1)

B.

( 1, 1)

C.

(1, 1)

D.

( 1, 1)

Answer» E.

Discussion

6.

If p + 1 = 1 then the value of (p + 2) + 1 - 3 is :
p + 2 (p + 2)

A.

12

B.

16

C.

18

D.

15

Answer» E.

Discussion

7.	The third proportional of the following numbers (x y) , (x y ) is :
A.	(x + y) (x y)
B.	(x + y)
C.	(x y)
D.	(x + y) (x y)
E.	(x + y) (x y)
Answer» C. (x y)

Discussion

8.	The distance between the lines y = mx + c₁ and y = mx + c₁ is
A.
B.	0
Answer» C.

Discussion

9.	When x^m is multiplied by xⁿ, product is 1. The relation between m and n is
A.	mn = 1
B.	m = n
C.	m + n = 1
D.	m = n
Answer» E.

Discussion

10.	If x xy + y = 2 and x⁴ + x y + y⁴ = 6, then the value of (x + xy + y ) is :
A.	1
B.	12
C.	3
D.	36
Answer» D. 36

Discussion

11.	If 4r = h + r² + h² then r : h is ? (r 0)
A.	17:8
B.	8:17
C.	8:15
D.	15:8
Answer» D. 15:8

Discussion

12.	The graph of the linear equation 3x + 4y = 24 is a straight line intersecting x-axis and y-axis at the points A and B respectively. P(2, 0) and Q(0,(³/₂)) are two points on the sides OA and OB respectively of OAB, where O is the origin of the co-ordinate system. Given that AB = 10 cm, then PQ =
A.	20 cm
B.	2.5 cm
C.	40 cm
D.	5 cm
Answer» C. 40 cm

Discussion

13.	If (2^x)(2^y) = 8 and (9^x) (3^y) = 81, then (x, y) is :
A.	(1,2)
B.	(2, 1)
C.	(1,1)
D.	(2, 2)
Answer» B. (2, 1)

Discussion

14.

If A : B : C = 2 : 3 : 4,
A : B : C is equal to :
B C A

A.

8 : 9 : 16

B.

8 : 9 : 12

C.

8 : 9 : 24

D.

4 : 9 : 16

Answer» D. 4 : 9 : 16

Discussion

15.	If p = 2 a, then a³ + 6 ap + p³ 8 = ?
A.	0
B.	8
C.	6
D.	5
Answer» B. 8

Discussion

16.	If x + y = 1 + xy, then x³ + y³ x³y³ is equal to :
A.	0
B.	1
C.	1
D.	2
Answer» C. 1

Discussion

17.	Given (a b) = 2, (a³ b³) = 26 then (a + b)² is
A.	9
B.	4
C.	16
D.	12
Answer» D. 12

Discussion

18.	If (x 2) is a factor of x² + 3Qx 2Q, then the value of Q is
A.	2
B.	2
C.	1
D.	1
Answer» E.

Discussion

19.	If x + y + z = 13 and x² + y² + z² = 69, then xy + z (x + y) is equal to
A.	70
B.	40
C.	50
D.	60
Answer» D. 60

Discussion

20.	If x = 5 + 2 then the value of x 6x + 12x 13 is
A.	1
B.	1
C.	2
D.	0
Answer» E.

Discussion

21.	If x = y = 333 and z = 334, then the value of x³ + y³ + z³ 3xyz is
A.	0
B.	667
C.	1000
D.	2334
Answer» D. 2334

Discussion

22.	If a² + b² + c² = 2 (a b c) 3, then the value of 4a 3b + 5c is
A.	2
B.	3
C.
D.	5
E.	6
Answer» B. 3

Discussion

23.	If 2^{2x y} = 16 and 2^{x + y} = 32, the value of xy is
A.	2
B.	4
C.	6
D.	8
Answer» D. 8

Discussion

24.	If a^{2x + 2} = 1, where a is a positive real number other than 1, then x is equal to
A.	2
B.	1
C.	0
D.	1
Answer» C. 0

Discussion

25.	If 5^{5x + 5} = 1, then x equals
A.	0
B.	1
C.	1
Answer» C. 1

Discussion

26.	If x = z = 225 and y = 226 then the value of x³ + y³ + z³ - 3xyz is :
A.	765
B.	676
C.	576
D.	674
Answer» C. 576

Discussion

27.	If x = 5 + 3 and y = 5 - 3 then the value of (x⁴ y⁴) is
A.	64
B.
C.	16
D.	544
E.	32
Answer» B.

Discussion

28.	If a, b, c are real and a² + b² + c² = 2 (a b c) 3, then the value of 2a 3b + 4c is
A.	1
B.	0
C.	1
D.	2
Answer» D. 2

Discussion

29.	The value of the expression x⁴ 17x³ + 17x² 17x + 17 at x = 16 is
A.	0
B.	1
C.	2
D.	3
Answer» C. 2

Discussion

30.	One of the factors of the expression 4 3x² + 5x 2 3 is :
A.	4x +
B.	4x + 3
C.	4x 3
D.	4x
Answer» E.

Discussion

31.

If x = 4 15 , the value of x + 20 + x + 12 is
5 + 3 x 20 x 12

A.

1

B.

2

C.

D.

Answer» C.

Discussion

32.

If a = 1 (a > 0), then the value of a + 1 is
a 5 a

A.

B.

C.

D.

Answer» B.

Discussion

33.

If a + b + c + d = 4 then the value of
1 + 1 + 1 + 1 is
(1 a)(1 b)(1 c) (1 b)(1 c)(1 d) (1 c)(1 d)(1 a) (1 d)(1 a)(1 b)

A.

0

B.

1

C.

4

D.

1+ abcd

Answer» B. 1

Discussion

34.	If a + b + c = 15 and a² + b² + c² = 83, then a³ + b³ + c³ 3abc = ?
A.	160
B.	175
C.	180
D.	100
Answer» D. 100

Discussion

35.	For what value of a , the polynomial 2x³ + ax² + 11x + a + 3, is exactly divisible by (2x 1) ?
A.	7
B.	7
C.	5
D.	5
Answer» C. 5

Discussion

36.	For what value of k, the system of equations 5x + 2y = k 10x + 4y = 3 has infinite solutions ?
A.	3/2
B.	1/2
C.	5/2
D.	2
Answer» B. 1/2

Discussion

37.	If 4x² + 4y² + 4z² = 12x + 12y 18 then x + y + z = ?
A.	3
B.	4
C.	3/2
D.	2
Answer» B. 4

Discussion

38.	What will be the value of (x a)³ + (x b)³ + (x c)³ 3 (x a) (x b) (x c) if a + b+c = 3x ?
A.	1
B.	3
C.	0
D.	5
Answer» D. 5

Discussion

39.

If x + 1 = 2 then the vlaue of x^p + x^q is :
x
(where p is an even number and q is an odd number)

A.

2

B.

2

C.

1

D.

0

Answer» E.

Discussion

40.	Equation of line 3x + y 8 = 0 can be represented in normal form as
A.
B.	x + y 4 = 0
C.
D.	x y 8 = 0
Answer» B. x + y 4 = 0

Discussion

41.

What is (x y )³ + (y z )³ + (z x )³
(x y)³ + (y z)³ +(z x)³

A.

(x + y)

B.

(y + z)

C.

(z + x)

D.

(x + y) (y + z) (z + x)

E.

(x + y) (y + z)

Answer» D. (x + y) (y + z) (z + x)

Discussion

42.	What will be the value of x³ + y³ + z³ 3xyz when x + y + z = 9 and x² + y² + z² = 31?
A.	27
B.	3
C.	54
D.	9
Answer» D. 9

Discussion

43.	If a + b + c = 1, ab + bc + ca = 1 and abc = 1, then the value of a³ + b³ + c³ is :
A.	1
B.	1
C.	2
D.	2
Answer» B. 1

Discussion

44.

If (2a 3)² + (3b + 4)² + (6c + 1)² = 0, then the value of
a³ + b³ + c³ 3ac + 3 is :
a² + b² + c²

A.

abc + 3

B.

6

C.

0

D.

3

Answer» E.

Discussion

45.	If a = 2, b = 3 then the value of 27 a³ 54 a²b + 36 ab² 8b³ is
A.	1562
B.	1616
C.	1676
D.	1728
Answer» E.

Discussion

46.	If x + y + z = 9 then the value of (x 4)³ + (y 2)³ + (z 3)³ 3 (x 4) (y 2) (z 3) is
A.	6
B.	9
C.	0
D.	1
Answer» D. 1

Discussion

47.	If m + n = 1, then the value of m³ + n³ + 3mn is equal to
A.	0
B.	1
C.	2
D.	3
Answer» C. 2

Discussion

48.	If a + b = 3, then the value of a³ + b³ + 9ab 27 is
A.	24
B.	25
C.	0
D.	27
Answer» D. 27

Discussion

49.	If x = 12 and y = 4, then the value of (x + y)^x/y is
A.	48
B.	1792
C.	4096
D.	570
Answer» D. 570

Discussion

50.	x² + y² + z² = 14 and xy + yz + zx = 11, then the value of (x + y + z)² is
A.	16
B.	25
C.	36
D.	49
Answer» D. 49

Discussion

Explore topic-wise MCQs in Aptitude.

If x = 11, the value of x5 12x4 + 12x 12x + 12x - 1 is

If x = 999, y = 1000, z = 1001, then the value of x + y + z - 3xyzis :x - y + z

If x = a + a + b + a - a + b , then x + 3bx is equal to

The expression x4 2x + k will be a perfect square when the value of k is

If the linex - y = 1abpasses through the points (2, 3) and (4, 5) then (a, b) is

If p + 1 = 1 then the value of (p + 2) + 1 - 3 is : p + 2(p + 2)

The third proportional of the following numbers (x y) , (x y ) is :

The distance between the lines y = mx + c1 and y = mx + c1 is

When xm is multiplied by xn, product is 1. The relation between m and n is

If x xy + y = 2 and x4 + x y + y4 = 6, then the value of (x + xy + y ) is :

If 4r = h + r2 + h2 then r : h is ? (r 0)

The graph of the linear equation 3x + 4y = 24 is a straight line intersecting x-axis and y-axis at the points A and B respectively.P(2, 0) and Q(0,(3/2)) are two points on the sides OA and OB respectively of OAB, where O is the origin of the co-ordinate system. Given that AB = 10 cm, then PQ =

If (2x)(2y) = 8 and (9x) (3y) = 81, then (x, y) is :

If A : B : C = 2 : 3 : 4, A : B : C is equal to : BCA

If p = 2 a, then a3 + 6 ap + p3 8 = ?

If x + y = 1 + xy, then x3 + y3 x3y3 is equal to :

Given (a b) = 2, (a3 b3) = 26 then (a + b)2 is

If (x 2) is a factor of x2 + 3Qx 2Q, then the value of Q is

If x + y + z = 13 and x2 + y2 + z2 = 69, then xy + z (x + y) is equalto

If x = 5 + 2 then the value of x 6x + 12x 13 is

If x = y = 333 and z = 334, then the value of x3 + y3 + z3 3xyz is

If a2 + b2 + c2 = 2 (a b c) 3, then the value of 4a 3b + 5c is

If 22x y = 16 and 2x + y = 32, the value of xy is

If a2x + 2 = 1, where a is a positive real number other than 1, then x is equal to

If 55x + 5 = 1, then x equals

If x = z = 225 and y = 226 then the value of x3 + y3 + z3 - 3xyz is :

If x = 5 + 3 and y = 5 - 3 then the value of (x4 y4) is

If a, b, c are real and a2 + b2 + c2 = 2 (a b c) 3, then the value of 2a 3b + 4c is

The value of the expression x4 17x3 + 17x2 17x + 17 at x = 16 is

One of the factors of the expression 4 3x2 + 5x 2 3 is :

If x = 4 15, the value of x + 20 + x + 12 is 5 + 3x 20x 12

If a = 1 (a > 0), then the value of a +1 is a 5a

If a + b + c + d = 4 then the value of 1 + 1 + 1 + 1 is (1 a)(1 b)(1 c)(1 b)(1 c)(1 d)(1 c)(1 d)(1 a)(1 d)(1 a)(1 b)

If a + b + c = 15 and a2 + b2 + c2 = 83, then a3 + b3 + c3 3abc = ?

For what value of a , the polynomial 2x3 + ax2 + 11x + a + 3, is exactly divisible by (2x 1) ?

For what value of k, the system of equations 5x + 2y = k10x + 4y = 3 has infinite solutions ?

If 4x2 + 4y2 + 4z2 = 12x + 12y 18 then x + y + z = ?

What will be the value of (x a)3 + (x b)3 + (x c)3 3 (x a) (x b) (x c) if a + b+c = 3x ?

If x +1 = 2 then the vlaue of xp + xq is :x (where p is an even number and q is an odd number)

Equation of line 3x + y 8 = 0 can be represented in normal form as

What is(x y )3 + (y z )3 + (z x )3(x y)3 + (y z)3 +(z x)3

What will be the value of x3 + y3 + z3 3xyz when x + y + z = 9 and x2 + y2 + z2 = 31?

If a + b + c = 1, ab + bc + ca = 1 and abc = 1, then the value of a3 + b3 + c3 is :

If (2a 3)2 + (3b + 4)2 + (6c + 1)2 = 0, then the value ofa3 + b3 + c3 3ac + 3 is :a2 + b2 + c2

If a = 2, b = 3 then the value of 27 a3 54 a2b + 36 ab2 8b3 is

If x + y + z = 9 then the value of (x 4)3 + (y 2)3 + (z 3)3 3 (x 4) (y 2) (z 3) is

If m + n = 1, then the value of m3 + n3 + 3mn is equal to

If a + b = 3, then the value of a3 + b3 + 9ab 27 is

If x = 12 and y = 4, then the value of (x + y)x/y is

x2 + y2 + z2 = 14 and xy + yz + zx = 11, then the value of (x + y + z)2 is

If x = 11, the value of x⁵ 12x⁴ + 12x 12x + 12x - 1 is

If x = 999, y = 1000, z = 1001, then the value of
x + y + z - 3xyz is :
x - y + z

The expression x⁴ 2x + k will be a perfect square when the value of k is

If the line x - y = 1
a b

passes through the points (2, 3) and (4, 5) then (a, b) is

If p + 1 = 1 then the value of (p + 2) + 1 - 3 is :
p + 2 (p + 2)

The distance between the lines y = mx + c₁ and y = mx + c₁ is

When x^m is multiplied by xⁿ, product is 1. The relation between m and n is

If x xy + y = 2 and x⁴ + x y + y⁴ = 6, then the value of (x + xy + y ) is :

If 4r = h + r² + h² then r : h is ? (r 0)

The graph of the linear equation 3x + 4y = 24 is a straight line intersecting x-axis and y-axis at the points A and B respectively.
P(2, 0) and Q(0,(³/₂)) are two points on the sides OA and OB respectively of OAB, where O is the origin of the co-ordinate system. Given that AB = 10 cm, then PQ =

If (2^x)(2^y) = 8 and (9^x) (3^y) = 81, then (x, y) is :

If A : B : C = 2 : 3 : 4,
A : B : C is equal to :
B C A

If p = 2 a, then a³ + 6 ap + p³ 8 = ?

If x + y = 1 + xy, then x³ + y³ x³y³ is equal to :

Given (a b) = 2, (a³ b³) = 26 then (a + b)² is

If (x 2) is a factor of x² + 3Qx 2Q, then the value of Q is

If x + y + z = 13 and x² + y² + z² = 69, then xy + z (x + y) is equal
to

If x = y = 333 and z = 334, then the value of x³ + y³ + z³ 3xyz is

If a² + b² + c² = 2 (a b c) 3, then the value of 4a 3b + 5c is

If 2^{2x y} = 16 and 2^{x + y} = 32, the value of xy is

If a^{2x + 2} = 1, where a is a positive real number other than 1, then x is equal to

If 5^{5x + 5} = 1, then x equals

If x = z = 225 and y = 226 then the value of x³ + y³ + z³ - 3xyz is :

If x = 5 + 3 and y = 5 - 3 then the value of (x⁴ y⁴) is

If a, b, c are real and a² + b² + c² = 2 (a b c) 3, then the value of 2a 3b + 4c is

The value of the expression x⁴ 17x³ + 17x² 17x + 17 at x = 16 is

One of the factors of the expression 4 3x² + 5x 2 3 is :

If x = 4 15 , the value of x + 20 + x + 12 is
5 + 3 x 20 x 12

If a = 1 (a > 0), then the value of a + 1 is
a 5 a

If a + b + c + d = 4 then the value of
1 + 1 + 1 + 1 is
(1 a)(1 b)(1 c) (1 b)(1 c)(1 d) (1 c)(1 d)(1 a) (1 d)(1 a)(1 b)

If a + b + c = 15 and a² + b² + c² = 83, then a³ + b³ + c³ 3abc = ?

For what value of a , the polynomial 2x³ + ax² + 11x + a + 3, is exactly divisible by (2x 1) ?

For what value of k, the system of equations
5x + 2y = k
10x + 4y = 3 has infinite solutions ?

If 4x² + 4y² + 4z² = 12x + 12y 18 then x + y + z = ?

What will be the value of (x a)³ + (x b)³ + (x c)³ 3 (x a) (x b) (x c) if a + b+c = 3x ?

If x + 1 = 2 then the vlaue of x^p + x^q is :
x
(where p is an even number and q is an odd number)

What is (x y )³ + (y z )³ + (z x )³
(x y)³ + (y z)³ +(z x)³

What will be the value of x³ + y³ + z³ 3xyz when x + y + z = 9 and x² + y² + z² = 31?

If a + b + c = 1, ab + bc + ca = 1 and abc = 1, then the value of a³ + b³ + c³ is :

If (2a 3)² + (3b + 4)² + (6c + 1)² = 0, then the value of
a³ + b³ + c³ 3ac + 3 is :
a² + b² + c²

If a = 2, b = 3 then the value of 27 a³ 54 a²b + 36 ab² 8b³ is

If x + y + z = 9 then the value of (x 4)³ + (y 2)³ + (z 3)³ 3 (x 4) (y 2) (z 3) is

If m + n = 1, then the value of m³ + n³ + 3mn is equal to

If a + b = 3, then the value of a³ + b³ + 9ab 27 is

If x = 12 and y = 4, then the value of (x + y)^x/y is

x² + y² + z² = 14 and xy + yz + zx = 11, then the value of (x + y + z)² is