782 + Mcqs in Algebra in Aptitude Page 3 McqOptions

101.

If (x 3)² + (y 5)² + (z 4)² = 0, then the value of
x² + y² + z² is :
9 25 16

A.

12

B.

9

C.

3

D.

1

Answer» D. 1

Discussion

102.	If a³b = abc = 180, a, b, c are positive integers, then the value of c is
A.	110
B.	1
C.	4
D.	25
Answer» C. 4

Discussion

103.	Let a = 6 5 , b = 5 2, c = 2 3 Then point out the correct alternative among the four alternatives given below.
A.	b < a < c
B.	a < c < b
C.	b < c < a
D.	a < b < c
Answer» E.

Discussion

104.	For a > b, if a + b = 5 and ab = 6, then the value of (a² b²) is
A.	1
B.	3
C.	5
D.	7
Answer» D. 7

Discussion

105.	If a² + b² = 2 and c² + d² = 1, then the value of (ad bc)² + (ac + bd)² is
A.	1
B.	2
Answer» E.

Discussion

106.

If x² = y + z, y² = z + x, z² = x + y,
then the value of 1 + 1 + 1 is;
x + 1 x + 1 z + 1

A.

1

B.

1

C.

2

D.

4

Answer» C. 2

Discussion

107.	If a^1/3 =11, then the value of a² 331a is
A.	1331331
B.	1331000
C.	1334331
D.	1330030
Answer» C. 1334331

Discussion

108.	If x = 3 5 , then the value of x² 16x + 6 is
A.	0
B.	2
C.	2
D.	4
Answer» D. 4

Discussion

109.	If a = 0.1039, then the value of 4a² 4a + 1 + 3a is
A.	0.1039
B.	0.2078
C.	1.1039
D.	2.1039
Answer» D. 2.1039

Discussion

110.	If a + b + c = 9 (where a, b, c are real numbers), then the minimum value of a² + b² + c² is
A.	100
B.	9
C.	27
D.	81
Answer» D. 81

Discussion

111.

If a² + b² + c² = ab + bc + ca, where a, b, c are non zero real numbers,
then the value of a + b is
c

A.

2

B.

1

C.

0

D.

1

Answer» B. 1

Discussion

112.	If a = x + y, b = x y, c = x + 2y, then a² + b² + c² ab bc ca is
A.	4y
B.	5y
C.	6y
D.	7y
Answer» E.

Discussion

113.	If x y = 2, xy = 24, then the value of (x² + y²) is :
A.	25
B.	36
C.	63
D.	52
Answer» E.

Discussion

114.

If x 0, y 0 and z 0 and 1 + 1 + 1 + 1 + 1 + 1 + 1 ,
x² y² z² 16 xy yz zx
then the relation among x, y, z is

A.

x + y + z = 0

B.

x + y = z

C.

x = y = z

Answer» E.

Discussion

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

Discussion

116.	The expression x⁴ 2x² + k will be a perfect square if the value of k is
A.	1
B.	0
Answer» B. 0

Discussion

117.	The term to be added to 121a² +64b to make a perfect square is
A.	176 ab
B.	276 a
C.	178 ab
D.	188 b
E.	a
Answer» B. 276 a

Discussion

118.	If x = b + c 2a, y = c + a 2b, z = a + b 2c, then the value of x² + y² z² + 2xy is
A.	0
B.	a + b + c
C.	a b + c
D.	a + b c
Answer» B. a + b + c

Discussion

119.	If x² + y² 4x 4y + 8 = 0, then the value of x y is
A.	4
B.	4
C.	0
D.	8
Answer» D. 8

Discussion

120.	If x y = 2 and x² + y² = 20, then value of (x + y)² is
A.	38
B.	36
C.	16
D.	12
Answer» C. 16

Discussion

121.	If a = 23 and b = 29 then the value of 25a² + 40ab + 16b² is :
A.	1
B.	1
C.	0
D.	2
Answer» B. 1

Discussion

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

Discussion

123.	If x² y² = 80 and x y = 8, then the average of x and y is
A.	2
B.	3
C.	4
D.	5
Answer» E.

Discussion

124.	The value of (x^{b + c})^{b c} (x^{c + a})^{c a} (x^{a + b})^{a b} (x 0) is
A.	1
B.	2
C.	1
D.	0
Answer» B. 2

Discussion

125.	If (a 1)² + (b + 2)² + (c + 1)² = 0, then the value of 2a 3b + 7c is
A.	12
B.	3
C.	11
D.	1
Answer» E.

Discussion

126.	If x, y and z are real numbers such that (x 3)² + (y 4)² + (z 5)² = 0 then (x + y + z) is equal to
A.	12
B.	0
C.	8
D.	12
Answer» E.

Discussion

127.	If 2^{x + 3} = 32, then the value of 3^x+1 is equal to
A.	27
B.	81
C.	72
D.	9
Answer» B. 81

Discussion

128.	The expression x⁴ 2x² + k will be a perfect square when the value of k is
A.	2
B.	1
C.	1
D.	2
Answer» C. 1

Discussion

129.

If 0.04 0.4 a = 0.004 0.4 b, value of a is
b

A.

16 10

B.

16 10

C.

16 10

D.

16 10

Answer» D. 16 10

Discussion

130.	If 9 x = 12 + 147 , then x = ?
A.	2
B.	3
C.	4
D.	5
Answer» C. 4

Discussion

131.	If x * y = (x + 3)² (y 1), then the value of 5 * 4 is
A.	192
B.	182
C.	180
D.	172
Answer» B. 182

Discussion

132.	If a * b = a^b , then the value of 5 * 3 is
A.	125
B.	243
C.	53
D.	15
Answer» B. 243

Discussion

133.	If ( 5)⁷ ÷ ( 5)⁵ = 5^p, then the value of p is
A.	5
B.	2
C.	1
Answer» E.

Discussion

134.	If 2^x = 256 , then the value of x is
A.	14
B.	16
C.	18
D.	20
Answer» C. 18

Discussion

135.

If 47.2506 = 4A + 7 + 2C + 5 + 6E ,
B D
then the value of 5A + 3B + 6C + D + 3E is

A.

53.6003

B.

53.603

C.

153.6003

D.

213.0003

Answer» D. 213.0003

Discussion

136.	If x * y = x² + y² xy, then the value of 9 * 11 is
A.	93
B.	103
C.	113
D.	121
Answer» C. 113

Discussion

137.	Given that 10^0.48 = x, 10^0.70 = y, and x^z = y² , then the value of z is close to
A.	1.45
B.	1.88
C.	2.9
D.	3.7
Answer» D. 3.7

Discussion

138.	If 1 < x < 2, then the value of (x 1)² + (x 3)² is
A.	1
B.	2
C.	3
D.	2x 4
Answer» C. 3

Discussion

139.	If x = 0.5 and y = 0.2, then value of 0.6 (3y)^x is equal to
A.	1.0
B.	0.5
C.	0.6
D.	1.1
Answer» D. 1.1

Discussion

140.	If 0.13 p² = 13, then p is equal to
A.	10
B.	0.01
C.	0.1
D.	100
Answer» D. 100

Discussion

141.	If a = 7, b = 5 and c = 3, then the value of a² + b² + c² ab bc ca is
A.	12
B.	12
C.	0
D.	8
Answer» B. 12

Discussion

142.	If 5^x + 12^x = 13^x , then x is equal to
A.	4
B.	9
C.	16
Answer» C. 16

Discussion

143.	If x is real, then the minimum value of (x² x + 1) is
A.	0
B.	1
Answer» B. 1

Discussion

144.	If a and b be positive integers such that a² b²= 19, then the value of a is
A.	19
B.	20
C.	9
D.	10
Answer» E.

Discussion

145.

Two numbers x and y (x > y) are such that their sum is equal to three times their difference.
Then value of 3xy will be:
2(x² y²)

A.

1

Answer» C.

Discussion

146.	If 3^{x + 3} + 7 = 250, then x is equal to
A.	5
B.	3
C.	2
D.	1
Answer» D. 1

Discussion

147.	If p(x + y)² = 5 and q(x - y)² = 3 , then the simplified value of p² (x + y)² + 4pq xy q² (x - y)² is :
A.	(p + q)
B.	2 (p + q)
C.	p + q
D.	2 (p + q)
Answer» C. p + q

Discussion

148.	If x = 7 + 3 then the vlaue of x³ - 9x² + 27x - 34 is :
A.	0
B.	1
C.	2
D.	1
Answer» B. 1

Discussion

149.

If a, b, c and d satisfy the equations
a + 7b + 3c + 5d = 0,
8a + 4b + 6c + 2d = 4
2a + 6b + 4c + 8d = 4,
5a + 3b + 7c + d = 4,
then (a + d) = ?
(b + c)

A.

0

B.

1

C.

1

D.

4

Answer» D. 4

Discussion

150.	If a² + a + 1 = 0, then the value of a⁹ is
A.	2
B.	3
C.	1
D.	0
Answer» D. 0

Discussion

Explore topic-wise MCQs in Aptitude.

If (x 3)2 + (y 5)2 + (z 4)2 = 0, then the value ofx2 + y2 + z2 is :92516

If a3b = abc = 180, a, b, c are positive integers, then the value of c is

Let a = 6 5 , b = 5 2, c = 2 3Then point out the correct alternative among the four alternatives given below.

For a > b, if a + b = 5 and ab = 6, then the value of (a2 b2) is

If a2 + b2 = 2 and c2 + d2 = 1, then the value of (ad bc)2 + (ac + bd)2 is

If x2 = y + z, y2 = z + x, z2 = x + y, then the value of 1 + 1 + 1 is;x + 1x + 1z + 1

If a1/3 =11, then the value of a2 331a is

If x = 3 5 , then the value of x2 16x + 6 is

If a = 0.1039, then the value of 4a2 4a + 1 + 3a is

If a + b + c = 9 (where a, b, c are real numbers), then the minimum value of a2 + b2 + c2 is

If a2 + b2 + c2 = ab + bc + ca, where a, b, c are non zero real numbers, then the value of a + b is c

If a = x + y, b = x y, c = x + 2y, then a2 + b2 + c2 ab bc ca is

If x y = 2, xy = 24, then the value of (x2 + y2) is :

If x 0, y 0 and z 0 and1 + 1 + 1 + 1 + 1 + 1 + 1,x2y2z216xyyzzx then the relation among x, y, z is

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

The expression x4 2x2 + k will be a perfect square if the value of k is

The term to be added to 121a2 +64b to make a perfect square is

If x = b + c 2a, y = c + a 2b, z = a + b 2c, then the value of x2 + y2 z2 + 2xy is

If x2 + y2 4x 4y + 8 = 0, then the value of x y is

If x y = 2 and x2 + y2 = 20, then value of (x + y)2 is

If a = 23 and b = 29 then the value of 25a2 + 40ab + 16b2 is :

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

If x2 y2 = 80 and x y = 8, then the average of x and y is

The value of (xb + c)b c (xc + a)c a (xa + b)a b (x 0) is

If (a 1)2 + (b + 2)2 + (c + 1)2 = 0, then the value of 2a 3b + 7c is

If x, y and z are real numbers such that (x 3)2 + (y 4)2 + (z 5)2 = 0 then (x + y + z) is equal to

If 2x + 3 = 32, then the value of 3x+1 is equal to

The expression x4 2x2 + k will be a perfect square when the value of k is

If 0.04 0.4 a = 0.004 0.4 b, value of a is b

If 9 x = 12 + 147 , then x = ?

If x * y = (x + 3)2 (y 1), then the value of 5 * 4 is

If a * b = ab , then the value of 5 * 3 is

If ( 5)7 ÷ ( 5)5 = 5p, then the value of p is

If 2x = 256 , then the value of x is

If 47.2506 = 4A + 7 + 2C + 5 + 6E , BD then the value of 5A + 3B + 6C + D + 3E is

If x * y = x2 + y2 xy, then the value of 9 * 11 is

Given that 100.48 = x, 100.70 = y, and xz = y2 , then the value of z is close to

If 1 < x < 2, then the value of (x 1)2 + (x 3)2 is

If x = 0.5 and y = 0.2, then value of 0.6 (3y)x is equal to

If 0.13 p2 = 13, then p is equal to

If a = 7, b = 5 and c = 3, then the value of a2 + b2 + c2 ab bc ca is

If 5 x + 12 x = 13 x , then x is equal to

If x is real, then the minimum value of (x2 x + 1) is

If a and b be positive integers such that a2 b2= 19, then the value of a is

Two numbers x and y (x > y) are such that their sum is equal to three times their difference.Then value of 3xy will be:2(x2 y2)

If 3x + 3 + 7 = 250, then x is equal to

If p(x + y)2 = 5 and q(x - y)2 = 3 , then the simplified value of p2 (x + y)2 + 4pq xy q2 (x - y)2 is :

If x = 7 + 3 then the vlaue of x3 - 9x2 + 27x - 34 is :

If a, b, c and d satisfy the equationsa + 7b + 3c + 5d = 0,8a + 4b + 6c + 2d = 42a + 6b + 4c + 8d = 4,5a + 3b + 7c + d = 4,then (a + d) = ? (b + c)

If a2 + a + 1 = 0, then the value of a9 is

If (x 3)² + (y 5)² + (z 4)² = 0, then the value of
x² + y² + z² is :
9 25 16

If a³b = abc = 180, a, b, c are positive integers, then the value of c is

Let a = 6 5 , b = 5 2, c = 2 3
Then point out the correct alternative among the four alternatives given below.

For a > b, if a + b = 5 and ab = 6, then the value of (a² b²) is

If a² + b² = 2 and c² + d² = 1, then the value of (ad bc)² + (ac + bd)² is

If x² = y + z, y² = z + x, z² = x + y,
then the value of 1 + 1 + 1 is;
x + 1 x + 1 z + 1

If a^1/3 =11, then the value of a² 331a is

If x = 3 5 , then the value of x² 16x + 6 is

If a = 0.1039, then the value of 4a² 4a + 1 + 3a is

If a + b + c = 9 (where a, b, c are real numbers), then the minimum value of a² + b² + c² is

If a² + b² + c² = ab + bc + ca, where a, b, c are non zero real numbers,
then the value of a + b is
c

If a = x + y, b = x y, c = x + 2y, then a² + b² + c² ab bc ca is

If x y = 2, xy = 24, then the value of (x² + y²) is :

If x 0, y 0 and z 0 and 1 + 1 + 1 + 1 + 1 + 1 + 1 ,
x² y² z² 16 xy yz zx
then the relation among x, y, z is

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

The expression x⁴ 2x² + k will be a perfect square if the value of k is

The term to be added to 121a² +64b to make a perfect square is

If x = b + c 2a, y = c + a 2b, z = a + b 2c, then the value of x² + y² z² + 2xy is

If x² + y² 4x 4y + 8 = 0, then the value of x y is

If x y = 2 and x² + y² = 20, then value of (x + y)² is

If a = 23 and b = 29 then the value of 25a² + 40ab + 16b² is :

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

If x² y² = 80 and x y = 8, then the average of x and y is

The value of (x^{b + c})^{b c} (x^{c + a})^{c a} (x^{a + b})^{a b} (x 0) is

If (a 1)² + (b + 2)² + (c + 1)² = 0, then the value of 2a 3b + 7c is

If x, y and z are real numbers such that (x 3)² + (y 4)² + (z 5)² = 0 then (x + y + z) is equal to

If 2^{x + 3} = 32, then the value of 3^x+1 is equal to

The expression x⁴ 2x² + k will be a perfect square when the value of k is

If 0.04 0.4 a = 0.004 0.4 b, value of a is
b

If x * y = (x + 3)² (y 1), then the value of 5 * 4 is

If a * b = a^b , then the value of 5 * 3 is

If ( 5)⁷ ÷ ( 5)⁵ = 5^p, then the value of p is

If 2^x = 256 , then the value of x is

If 47.2506 = 4A + 7 + 2C + 5 + 6E ,
B D
then the value of 5A + 3B + 6C + D + 3E is

If x * y = x² + y² xy, then the value of 9 * 11 is

Given that 10^0.48 = x, 10^0.70 = y, and x^z = y² , then the value of z is close to

If 1 < x < 2, then the value of (x 1)² + (x 3)² is

If x = 0.5 and y = 0.2, then value of 0.6 (3y)^x is equal to

If 0.13 p² = 13, then p is equal to

If a = 7, b = 5 and c = 3, then the value of a² + b² + c² ab bc ca is

If 5^x + 12^x = 13^x , then x is equal to

If x is real, then the minimum value of (x² x + 1) is

If a and b be positive integers such that a² b²= 19, then the value of a is

Two numbers x and y (x > y) are such that their sum is equal to three times their difference.
Then value of 3xy will be:
2(x² y²)

If 3^{x + 3} + 7 = 250, then x is equal to

If p(x + y)² = 5 and q(x - y)² = 3 , then the simplified value of p² (x + y)² + 4pq xy q² (x - y)² is :

If x = 7 + 3 then the vlaue of x³ - 9x² + 27x - 34 is :

If a, b, c and d satisfy the equations
a + 7b + 3c + 5d = 0,
8a + 4b + 6c + 2d = 4
2a + 6b + 4c + 8d = 4,
5a + 3b + 7c + d = 4,
then (a + d) = ?
(b + c)

If a² + a + 1 = 0, then the value of a⁹ is