

MCQOPTIONS
This section includes 123 Mcqs, each offering curated multiple-choice questions to sharpen your Maths knowledge and support exam preparation. Choose a topic below to get started.
51. |
If a+b = 1 and a3+b3+3ab=k, then the value of k is : |
A. | 5 |
B. | 7 |
C. | 1 |
D. | 3 |
Answer» D. 3 | |
52. |
If $$64^{x+1}={64 over 4^x}$$, then the value of x |
A. | $$1 over 2$$ |
B. | 2 |
C. | 1 |
D. | 0 |
Answer» E. | |
53. |
If a, b are rational number and (a-1) 2+3=b 2+a, the value of (a+b) is : |
A. | -3 |
B. | 5 |
C. | -5 |
D. | 3 |
Answer» C. -5 | |
54. |
if a3b = abc = 180, a, b, c are positive integers, then the value of c is |
A. | 4 |
B. | 25 |
C. | 110 |
D. | 1 |
Answer» E. | |
55. |
If for two real constants a and b the expression ax3+3x2-8x+b is exactly divisible by (x+2) and (x-2), then |
A. | a = 2, b = -12 |
B. | a = -2, b = 12 |
C. | a = 2, b = 12 |
D. | a = 12, b = 12 |
Answer» B. a = -2, b = 12 | |
56. |
If x = b+c -2a, y=c+a-2b, z=a+b-2c, then the value of x2+y2-z2+2xy is : |
A. | a-b+c |
B. | a+b-c |
C. | 0 |
D. | a+b+c |
Answer» D. a+b+c | |
57. |
If x2+y2-4x-4y+8=0, then the value of x-y is: |
A. | 0 |
B. | 8 |
C. | 4 |
D. | -4 |
Answer» B. 8 | |
58. |
If $$ {xy over x+y}= a, $$ $${xz over x+z}=b $$ and $$ {yz over y+z} =c $$ where a, b, c are all non zero numbers, then x equals to |
A. | $$ 2abc over {ab+bc-ac} $$ |
B. | $$ 2abc over {ab+ac-ac} $$ |
C. | $$ 2abc over {ac+bc-ab} $$ |
D. | $$ 2abc over {ac+bc-ac} $$ |
Answer» D. $$ 2abc over {ac+bc-ac} $$ | |
59. |
If $$p q=p+q+{p over q}$$, the value of 8 2 is : |
A. | 14 |
B. | 16 |
C. | 6 |
D. | 10 |
Answer» B. 16 | |
60. |
If a b, then which of the following statement is true ? |
A. | $${a+b over 2}= sqrt{ab} $$ |
B. | $${a+b over 2}> sqrt{ab} $$ |
C. | $${a+b over 2}< sqrt{ab} $$ |
D. | All of the above |
Answer» C. $${a+b over 2}< sqrt{ab} $$ | |
61. |
If $$n+{2 over 3}n+{1 over2}n+{1 over7}n=97$$ then the value of n is : |
A. | 44 |
B. | 46 |
C. | 40 |
D. | 42 |
Answer» E. | |
62. |
If 5 x + 12 x = 13 x, then x is equal to: |
A. | 9 |
B. | 16 |
C. | $${25 over4}$$ |
D. | 4 |
Answer» E. | |
63. |
If $${ sqrt{7-2} over sqrt{7+2}}=a sqrt{7}+b$$, then the value of a is : |
A. | $${4 over3}$$ |
B. | $${-4 7 over3}$$ |
C. | $${11 over2}$$ |
D. | $$-{4 over3}$$ |
Answer» E. | |
64. |
If x is real then the minimum value of (x2-x-1) is : |
A. | 1 |
B. | $$-{5 over 4}$$ |
C. | $$3 over 4 $$ |
D. | 0 |
Answer» C. $$3 over 4 $$ | |
65. |
If a2x+2=1, where a is a positive real number other than 1, then x is equal to |
A. | 0 |
B. | 1 |
C. | 2 |
D. | 1 |
Answer» E. | |
66. |
If x, y are two positive real number and $$x^{1/3}=y^{1/4}$$, then which of the following relations is true? |
A. | $$x=y^3$$ |
B. | $$x^{20}=y^{15}$$ |
C. | $$x^3=y^4$$ |
D. | $$x^3=y$$ |
Answer» C. $$x^3=y^4$$ | |
67. |
If a = 7, b = 5 and c = 3, then the value of $$a^2+b^2+c^2-ab-bc-ca$$ is |
A. | 0 |
B. | 8 |
C. | 12 |
D. | -12 |
Answer» D. -12 | |
68. |
Two numbers x and y (x>y) such that their sum is equal to three times their difference. Then value of $$3xy over 2(x^2-y^2$$ will be |
A. | $$1{1 over 2} $$ |
B. | $$1{1 over 3} $$ |
C. | $$ {2 over 3}$$ |
D. | 1 |
Answer» E. | |
69. |
Out of the given responses one of the factors of (a2-b2)3+(b2-c2)3+(c2-a2)3 is |
A. | (a+b) (a-b) |
B. | (a+b) (a+b) |
C. | (a b) (a b) |
D. | (b c) (b c) |
Answer» B. (a+b) (a+b) | |
70. |
x = y = 333 and z = 334, then value of x3 + y3 + z3 3xyz is |
A. | 0 |
B. | 667 |
C. | 1000 |
D. | 2334 |
Answer» D. 2334 | |
71. |
If a + b + c = 0, then a3+b3+c3 is equal to |
A. | a + b + c |
B. | abc |
C. | 2abc |
D. | 3abc |
Answer» E. | |
72. |
If a2+b2+c2 = 2(a b c) 3 then the value of 4a 3b + 5c is |
A. | 2 |
B. | 3 |
C. | 5 |
D. | 6 |
Answer» B. 3 | |
73. |
If $$ {t^{2}-4t+1=0}$$ then what is the value of $${t^{3}+{1 over {t^{3}}}}$$ ? |
A. | 44 |
B. | 48 |
C. | 52 |
D. | 64 |
Answer» D. 64 | |
74. |
If 0.13 x p2 = 13, then p is equal to |
A. | 10 |
B. | 0.01 |
C. | 0.1 |
D. | 100 |
Answer» B. 0.01 | |
75. |
If $${144 over0.144}={14.4 over x}$$, then the value of x is |
A. | 144 |
B. | 14.4 |
C. | 1.44 |
D. | 0.0144 |
Answer» E. | |
76. |
If x2+y2+z2 = xy + yz + zx, then the value of $${3x^4+7y^4+5z^4} over{5x^2y^2+7y^2z^2+3z^2x^2} $$ is |
A. | 2 |
B. | 1 |
C. | 0 |
D. | -1 |
Answer» C. 0 | |
77. |
If $${3-5x over 2x}+{3-5y over 2y}+{3-5z over 2z}=0$$ then the value of $${2 over x}+{2 over y}+{2 over z}$$ is: |
A. | 20 |
B. | 10 |
C. | 5 |
D. | 15 |
Answer» C. 5 | |
78. |
$$ {x+{1 over{x}}}$$, then the value of $$ {x^2}+{1 over{x^2}}$$ is |
A. | 9 |
B. | 7 |
C. | 11 |
D. | 14 |
Answer» C. 11 | |
79. |
If a2=b+c, b2=c+a and c2=a+b then the value of $$ {1 over{1+a}}+{1 over{1+b}}+{1 over{1+c}}$$ is |
A. | abc |
B. | 1 |
C. | 0 |
D. | 2 |
Answer» C. 0 | |
80. |
If xy(x+y)=1, then $$ {1 over x^3 y^3}-{x^3-y^3}$$ is equal to- |
A. | 0 |
B. | 1 |
C. | 3 |
D. | -2 |
Answer» D. -2 | |
81. |
$$ {a^2-b^2-2bc-c^2} over{a^2+b^2+2ab-c^2}$$ is equal to |
A. | $$ {a-b-c} over{a+b-c}$$ |
B. | $$ {a-b+c} over{a+b-c}$$ |
C. | $$ {a-b-c} over{a+b+c}$$ |
D. | $$ {a-b-c} over{a+b-c}$$ |
Answer» B. $$ {a-b+c} over{a+b-c}$$ | |
82. |
If a-b=10 and ab=-21, then what is the value of a3-b3? |
A. | 316 |
B. | 370 |
C. | 185 |
D. | 158 |
Answer» C. 185 | |
83. |
If $$ {x+{1 over x}}=2$$ then find out the value of $${2x^2+2} over{3x^2+5x+3}$$ |
A. | $${4 over 11}$$ |
B. | $${5 over 11}$$ |
C. | $${7 over 5}$$ |
D. | $${4 over 9}$$ |
Answer» B. $${5 over 11}$$ | |
84. |
The ratio of two unequal sides of a rectangle is 1 : 2. If its perimeter is 24 cm, then the length of diagonal in cm is: |
A. | $$ {2 over { sqrt {5}}}$$ |
B. | $$ {4 over { sqrt {5}}}$$ |
C. | $$ {2 { sqrt {5}}}$$ |
D. | $$ {4 { sqrt {5}}}$$ |
Answer» E. | |
85. |
If x y + z = 15, xyz = -216 and xz xy yz = 18, then the value of $$ {x^3}-{y^3}+{z^3}=$$ |
A. | 2613 |
B. | 2813 |
C. | 3013 |
D. | 3213 |
Answer» E. | |
86. |
If 0.4 m + 0.8 n = 2.2 and 0.8 m + 0.4 n = 1.4, then the value of $$ {m^2}+{n^2}$$ is equal to |
A. | 8.5 |
B. | 6.5 |
C. | 16 |
D. | 9 |
Answer» C. 16 | |
87. |
If $$ {x^2} -4x-1 $$ then the value of $$ {{x^6} -{x^4}+{x^2}-1} over {x^3}$$ will be |
A. | 72 |
B. | 76 |
C. | 80 |
D. | 84 |
Answer» B. 76 | |
88. |
If $$ {{x+1} over4x}={5 over 2}$$ then what is the value of $$ 64x^6+1 over 8x^3 $$ |
A. | 110 |
B. | 115 |
C. | 125 |
D. | 120 |
Answer» C. 125 | |
89. |
If (a-b)2 + (b-c)2 + (c-a)2 = 0, then find the value of (a3+b3+c3-3abc) ? |
A. | 2 |
B. | -1 |
C. | 0 |
D. | 1 |
Answer» D. 1 | |
90. |
If $$ {x+{1 over x}= sqrt{3}}$$ then $$ {x^{48}+x^{378 over7}+x^{726 over11}+x^{60}}$$ is equal to |
A. | 1 |
B. | 0 |
C. | -1 |
D. | 2 |
Answer» C. -1 | |
91. |
If $$ {x+{1 over {x}}=1}$$, then find the value of $$ {x^{208}+{x^{205}+x^{204}+x^{201}}}$$. |
A. | 0 |
B. | 1 |
C. | 1 |
D. | 2 |
Answer» B. 1 | |
92. |
Find the value of. 672 332. |
A. | 3200 |
B. | 3400 |
C. | 3146 |
D. | 3143 |
Answer» C. 3146 | |
93. |
Value of $$ sqrt{6+ sqrt {6+ sqrt {6+....}}}$$ |
A. | 5 |
B. | 4 |
C. | 3 |
D. | 2 |
Answer» D. 2 | |
94. |
Three positive numbers are in the ratio of 11 : 12 : 15. If the sum of the squares of those numbers is 1960, then the sum of the numbers is |
A. | 38 |
B. | 76 |
C. | 114 |
D. | 152 |
Answer» C. 114 | |
95. |
If x - y = 3, then what is the value of x3 - y3-9xy? |
A. | 18 |
B. | 27 |
C. | 3 |
D. | 9 |
Answer» C. 3 | |
96. |
If x - y = 6 and xy = 40, then nd $$ {x^2+y^2}$$ |
A. | 146 |
B. | 80 |
C. | 89 |
D. | 116 |
Answer» E. | |
97. |
If bc+ab+ca=abc, then the value of $$ {b+c over {bc(a-1)}}+{a-c over {ac(b-1)}}+{a+b over {ab(c-1)}}$$ is |
A. | 2 |
B. | 1 |
C. | 0 |
D. | $$ {-1 over {2}}$$ |
Answer» C. 0 | |
98. |
If $$ {3x+}{2 over { sqrt{x}}}=1$$ then $$ {x-{ sqrt{x}}}=?$$ |
A. | $$ {-2 over { sqrt{3}}}$$ |
B. | $$ {-3 over { sqrt{3}}}$$ |
C. | $$ {2 over { sqrt{3}}}$$ |
D. | $$ {-1 over { sqrt{3}}}$$ |
Answer» B. $$ {-3 over { sqrt{3}}}$$ | |
99. |
If x + y + z=1, xy+yz+zx=-26 and x3 + y3+z3=151, then what will be the value of xyz? |
A. | -18 |
B. | 32 |
C. | 24 |
D. | 30 |
Answer» D. 30 | |
100. |
If $$ ({x+y over z})=2$$ , then what is the value of $$ [{ {y over {y-z}}}] +[{ {x over {x-z}}}]$$. |
A. | 0 |
B. | 1 |
C. | 2 |
D. | -1 |
Answer» D. -1 | |