MCQOPTIONS
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MCQOPTIONS
This section includes 462 Mcqs, each offering curated multiple-choice questions to sharpen your SRMJEEE knowledge and support exam preparation. Choose a topic below to get started.
| 51. |
Let \(f:\left[ { - 6,\;6} \right] \to R\) be defined by f(x) = x2 – 3. Consider the following:1. (f ∘ f ∘ f) (-1) = (f ∘ f ∘ f) (1)2. (f ∘ f ∘ f) (-1) – 4 (f ∘ f ∘ f) (1) = (f ∘ f) (0)Which of the above is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» D. Neither 1 nor 2 | |
| 52. |
If f ∶ R → R and g ∶ R → R are two mappings defined as f(x) = 2x and g(x) = x2 + 2, then the value of (f + g) (2) is: |
| A. | 8 |
| B. | 10 |
| C. | 12 |
| D. | 24 |
| Answer» C. 12 | |
| 53. |
A relation R is defined on the set N of natural numbers as xRy ⇒ x2 – 4xy + 3y2 = 0. Then which one of the following is correct? |
| A. | R is reflexive and symmetric, but not transitive |
| B. | R is reflexive and transitive, but not symmetric |
| C. | R is reflexive, symmetric and transitive |
| D. | R is reflexive, but neither symmetric nor transitive |
| Answer» E. | |
| 54. |
Let S be the set of all persons living in Delhi. We say that x, y in S are related if they were born in Delhi on the same day. Which one of the following is correct? |
| A. | The relation is an equivalent relation |
| B. | The relation is not reflexive but it is symmetric and transitive |
| C. | The relation is not symmetric but it is reflexive and transitive |
| D. | The relation is not transitive but it is reflexive and symmetric |
| Answer» B. The relation is not reflexive but it is symmetric and transitive | |
| 55. |
If \(x + {\log _{10}}\left( {1 + {2^x}} \right) = x{\log _{10}}5 + {\log _{10}}6\) then x is equal to |
| A. | 2, -3 |
| B. | 2 only |
| C. | 1 |
| D. | 3 |
| Answer» D. 3 | |
| 56. |
For each non-zero real number x, let \({\rm{f}}\left( {\rm{x}} \right) = \frac{{\rm{x}}}{{\left| {\rm{x}} \right|}}{\rm{\;}}\)the range of f is |
| A. | A null set |
| B. | A set consisting of only one element |
| C. | A set consisting of two elements |
| D. | A set consisting of infinitely many elements |
| Answer» D. A set consisting of infinitely many elements | |
| 57. |
If \(f(x)-\dfrac{1}{1+2^{1/x}}\) then at x = 0 the function is: |
| A. | Discontinuous because \(\displaystyle L \lim_{x\rightarrow0}f(x){\ne}R\displaystyle\lim_{x\rightarrow0}f(x)\) |
| B. | Discontinuous because \(\displaystyle \lim_{x\rightarrow0}f(0){\ne}f(0)\) |
| C. | Continuous |
| D. | Discontinuous because \(R\displaystyle\lim_{x\rightarrow0}f(x)\) does not exist |
| Answer» B. Discontinuous because \(\displaystyle \lim_{x\rightarrow0}f(0){\ne}f(0)\) | |
| 58. |
If A = {λ, {λ, μ}}, then the power set of A is |
| A. | {φ, {φ}, {λ}, {λ, μ}} |
| B. | {φ, {λ}, {{λ, μ}}, {λ, {λ, μ}}} |
| C. | {φ, {λ}, {λ, μ}, {λ, {λ, μ}}} |
| D. | {{λ}, {λ, μ}, {λ, {λ, μ}}} |
| Answer» C. {φ, {λ}, {λ, μ}, {λ, {λ, μ}}} | |
| 59. |
If A = {x : x is a multiple of 2}, B = {x : x is a multiple of 5} and C = {x : x is a multiple of 10}, then A ∩ (B ∩ C) is equal to |
| A. | A |
| B. | B |
| C. | C |
| D. | {x : x is a multiple of 100} |
| Answer» D. {x : x is a multiple of 100} | |
| 60. |
Let f : R → R be defined by \(f\left( x \right)=\frac{x}{1+{{x}^{2}}}\), x ∈ R. Then the range of f is: |
| A. | \(\left[ -\frac{1}{2},\frac{1}{2} \right]\) |
| B. | \(\text{R}-\left[ -1,1 \right]\) |
| C. | \(\text{R}-\left[ -\frac{1}{2},\frac{1}{2} \right]\) |
| D. | (-1, 1) - {0} |
| Answer» B. \(\text{R}-\left[ -1,1 \right]\) | |
| 61. |
If we define a relation R on the set N × N as (a, b) R (c, d) ⇔ a + d = b + c for all (a, b), (c, d) ∈ N × N, then the relation is |
| A. | symmetric only |
| B. | symmetric and transitive only |
| C. | equivalence relation |
| D. | reflexive only |
| Answer» D. reflexive only | |
| 62. |
If f(x + y, x - y) = xy, then arithmetic mean of f(x, y) and f(y, x) is: |
| A. | x |
| B. | y |
| C. | 0 |
| D. | xy |
| Answer» D. xy | |
| 63. |
If \({{x}^{{{\log }_{7}}x}}>7\) where x > 0, then which one of the following is correct? |
| A. | xϵ(0, ∞) |
| B. | \(x\epsilon\left( {\frac{1}{7},\;7} \right)\) |
| C. | \(x\epsilon \left( 0,\frac{1}{7} \right)\cup \left( 7,~\infty \right)\) |
| D. | \(x\epsilon \left( \frac{1}{7},~\infty \right)\) |
| Answer» D. \(x\epsilon \left( \frac{1}{7},~\infty \right)\) | |
| 64. |
If 2p + 3q = 18 and 4p2 + 4pq – 3q2 – 36 = 0 then what is (2p + q) equal to? |
| A. | 6 |
| B. | 7 |
| C. | 10 |
| D. | 20 |
| Answer» D. 20 | |
| 65. |
If the mapping f and g are given by f = {(1, 2), {3, 5), (4, 1)}g = {(2, 3), {5, 1), (1, 3)}then gof is |
| A. | {(2, 5), (5, 2), (1, 5)} |
| B. | {(1, 2), (3, 5), (4, 1(} |
| C. | {(1, 3), (3, 1), (4, 3)} |
| D. | {(2, 3), (5, 1), (1, 3)} |
| Answer» D. {(2, 3), (5, 1), (1, 3)} | |
| 66. |
Let f(x) = px + q and g(x) = mx + n. Then f (g(x)) = g (f(x)) is equivalent to |
| A. | f(p) = g(m) |
| B. | f(q) = g(n) |
| C. | f(n) = g(q) |
| D. | f(m) = g(p) |
| Answer» D. f(m) = g(p) | |
| 67. |
If A = {1, 4}, B = {2, 3}, C = {3, 5} then (A × B) ∩ (A × C) is equal to - |
| A. | {(1, 3), (4, 3)} |
| B. | {(1, 3), (2, 5)} |
| C. | {(1, 3), (1, 5), (2, 5)} |
| D. | None of these |
| Answer» B. {(1, 3), (2, 5)} | |
| 68. |
If log8 m + log8 \(\frac{1}{6} = \frac{2}{3}\), then m is equal to |
| A. | 24 |
| B. | 18 |
| C. | 12 |
| D. | 4 |
| Answer» B. 18 | |
| 69. |
Let R be a relation on the set N of natural numbers defined by ‘nRm ⟺ n is a factor of m’. Then which one of the following is correct? |
| A. | R is reflexive, symmetric but not transitive |
| B. | R is reflexive, symmetric but not reflexive |
| C. | R is reflexive, transitive but not symmetric |
| D. | R is an equivalence relation |
| Answer» D. R is an equivalence relation | |
| 70. |
Let S = {1, 2, 3, ...}, A relation R on S × S is defined by xRy if loga x > loga y when a \(\rm = \frac 1 2.\) Then the relation is |
| A. | reflexive only |
| B. | symmetric only |
| C. | transitive only |
| D. | both symmetric and transitive |
| Answer» D. both symmetric and transitive | |
| 71. |
If logx 4 + logx 16 + logx 64 = 12, the value of x is |
| A. | 2 |
| B. | 4 |
| C. | 5 |
| D. | 10 |
| Answer» B. 4 | |
| 72. |
If f(a) = 2, f'(a) = 1, g(a) = -1, g'(a) = 2 then \(\mathop {\lim }\limits_{x \to a} .\frac{{g(x)f(a) - g(a)f(x)}}{{x - a}}\) is |
| A. | -5 |
| B. | \(\frac{1}{5}\) |
| C. | 5 |
| D. | 0 |
| Answer» D. 0 | |
| 73. |
If \(f(x) = \frac{x^2-3x+2}{x^2-2x}, \;x\ne2\) is defined and function f(x) be continuous at x = 2, then the value of f(2) is |
| A. | 0 |
| B. | 1/2 |
| C. | 1 |
| D. | 3/4 |
| Answer» C. 1 | |
| 74. |
If f(x) \(= \frac{{\sqrt {x - 1} }}{{x - 4}}\) defines a function on R, then what is its domain? |
| A. | (-∞, 4) ∪ (4, ∞) |
| B. | (4, ∞) |
| C. | (1, 4) ∪ (4, ∞) |
| D. | [1, 4) ∪ (4, ∞) |
| Answer» E. | |
| 75. |
If A = {x : 0 ≤ x ≤ 2} and B = {y; y is a prime number}, then what is A∩B equal to? |
| A. | Φ |
| B. | {1} |
| C. | {2} |
| D. | {1, 2} |
| Answer» D. {1, 2} | |
| 76. |
Let A and B be subsets of X and C = (A ∩ B’) ∪ (A’ ∩ B), where A’ and B’ are complements of A and B respectively in X. what is C equal to? |
| A. | (A ∪ B’) – (A ∩ B’) |
| B. | (A’∪ B) – (A ∩ B) |
| C. | (A ∪ B) – (A ∩ B) |
| D. | (A’ ∪ B’) – (A’ ∩ B’) |
| Answer» D. (A’ ∪ B’) – (A’ ∩ B’) | |
| 77. |
If \({\rm{f}}\left( {\rm{x}} \right) = \frac{{\rm{x}}}{{{\rm{x}} - 1}},\) then what is \(\frac{{{\rm{f}}\left( {\rm{a}} \right)}}{{{\rm{f}}\left( {{\rm{a}} + 1} \right)}}\) equal to? |
| A. | \({\rm{f}}\left( { - \frac{{\rm{a}}}{{{\rm{a}} + 1}}} \right)\) |
| B. | \({\rm{f}}\left( {{{\rm{a}}^2}} \right)\) |
| C. | \({\rm{f}}\left( {\frac{1}{{\rm{a}}}} \right)\) |
| D. | f(-a) |
| Answer» C. \({\rm{f}}\left( {\frac{1}{{\rm{a}}}} \right)\) | |
| 78. |
If x, y, z are three consecutive positive integers, then log (1 + xz) is |
| A. | log y |
| B. | \(\log \dfrac{y}{2}\) |
| C. | log (2y) |
| D. | 2 log (y) |
| Answer» E. | |
| 79. |
If (11101011)2 is converted to decimal system, then the resulting number is |
| A. | 235 |
| B. | 175 |
| C. | 160 |
| D. | 126 |
| Answer» B. 175 | |
| 80. |
Let S = {(x, y): x2 + y2 = 1, - 1 ≤ x ∈ R ≤ 1 and - 1 ≤ y ∈ R ≤ 1} Which one of the following is correct? |
| A. | S is a one - one function |
| B. | S is a many - one function |
| C. | S is a bijective mapping |
| D. | S is not a function |
| Answer» E. | |
| 81. |
If \({\rm{f}}\left( {\rm{x}} \right) = \frac{{4{\rm{x}} + {{\rm{x}}^4}}}{{1 + 4{{\rm{x}}^3}}}\) and \({\rm{g}}\left( {\rm{x}} \right) = {\rm{In\;}}\left( {\frac{{1 + {\rm{x}}}}{{1 - {\rm{x}}}}} \right)\), then what is the value of \({\rm{f\;o\;g\;}}\left( {\frac{{{\rm{e}} - 1}}{{{\rm{e}} + 1}}} \right)\) equal to? |
| A. | 2 |
| B. | 1 |
| C. | 0 |
| D. | \(\frac{1}{2}\) |
| Answer» C. 0 | |
| 82. |
A survey of 850 students in a university yields that 680 students like music and 215 like dance. What is the least number of students who like both music and dance? |
| A. | 40 |
| B. | 45 |
| C. | 50 |
| D. | 55 |
| Answer» C. 50 | |
| 83. |
If a set A contains 3 elements and another set B contains 6 elements, then what is the minimum number of elements that (A∪B) can have? |
| A. | 3 |
| B. | 6 |
| C. | 8 |
| D. | 9 |
| Answer» C. 8 | |
| 84. |
Let A = {x, y, z} and B = {p, q, r, s}. What is the number of distinct relations from B to A? |
| A. | 4096 |
| B. | 4094 |
| C. | 128 |
| D. | 126 |
| Answer» B. 4094 | |
| 85. |
Let f(x) = ax (a > 0) be written as f(x) = f1(x) + f2(x), where, f1(x) is an even function and f2(x) is an odd function. Then f1(x + y) + f1(x – y) equals: |
| A. | 2f1(x)f1(y) |
| B. | 2f1(x + y)f1(x – y) |
| C. | 2f1(x)f2(y) |
| D. | 2f1(x + y)f2(x – y) |
| Answer» B. 2f1(x + y)f1(x – y) | |
| 86. |
Convert 29 into binary.A. 10101B. 11110C. 11101D. 11001 |
| A. | A |
| B. | B |
| C. | D |
| D. | C |
| Answer» E. | |
| 87. |
Consider the following in respect of sets A and B:1. (A - B) ∪ B = A2. (A - B) ∪ A = A3. (A - B) ∩ B = ϕ 4. A ⊆ B ⇒ A ∪ B = BWhich of the above are correct? |
| A. | 1, 2 and 3 |
| B. | 2, 3 and 4 |
| C. | 1, 3 and 4 |
| D. | 1, 2 and 4 |
| Answer» C. 1, 3 and 4 | |
| 88. |
For x ∈ R-{0, 1}. Let \({{\text{f}}_{1}}\left( \text{x} \right)=\frac{1}{\text{x}},\text{ }\!\!~\!\!\text{ }{{\text{f}}_{2}}\left( \text{x} \right)=1-\text{x }\!\!~\!\!\text{ and }\!\!~\!\!\text{ }{{\text{f}}_{3}}\left( \text{x} \right)=\frac{1}{1-\text{x}}\) be three given functions. If a function, J(x) satisfies (f2∘J∘f1)(x) = f3(x) then J(x) is equal to: |
| A. | f3 (x) |
| B. | \(\frac{1}{\text{x}}{{\text{f}}_{3}}\left( \text{x} \right)\) |
| C. | f2 (x) |
| D. | f1 (x) |
| Answer» B. \(\frac{1}{\text{x}}{{\text{f}}_{3}}\left( \text{x} \right)\) | |
| 89. |
Let L denote the set of all straight lines in a plane. Let a relation R be l R m if l is perpendicular to m ∀ l, m ∈ L. Then R is: |
| A. | reflexive |
| B. | symmetric |
| C. | transitive |
| D. | equivalence |
| Answer» C. transitive | |
| 90. |
Let \({\rm{f}}\left( {\rm{a}} \right) = \frac{{{\rm{a}} - 1}}{{{\rm{a}} + 1}}\).Consider the following:1. f(2a) = f(a) + 12. \({\rm{f}}\left( {\frac{1}{{\rm{a}}}} \right) = - {\rm{f}}\left( {\rm{a}} \right)\)Which of the above is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» C. Both 1 and 2 | |
| 91. |
Let \({{f}_{\text{k}}}\left( x \right)=\frac{1}{\text{k}}\left( \text{si}{{\text{n}}^{\text{k}}}x+\text{co}{{\text{s}}^{\text{k}}}x \right)\) for k = 1, 2, 3, … Then for all x ∈ R, the value of f4(x) – f6(x) is equal to: |
| A. | 1/12 |
| B. | 1/4 |
| C. | -1/12 |
| D. | 5/12 |
| Answer» B. 1/4 | |
| 92. |
Let \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{{\rm{max}}\left\{ {\left| x \right|,{x^2}} \right\},}&{\left| x \right| \le 2}\\{8 - 2\left| x \right|,}&{2 < \left| x \right| \le 4}\end{array}} \right.\)Let S be the set of points in the interval (-4, 4) at which f is not differentiable. Then S: |
| A. | Is an empty set |
| B. | Equals {-2, -1, 0, 1, 2} |
| C. | Equals {-2, -1, 1, 2} |
| D. | Equals {-2, 2} |
| Answer» C. Equals {-2, -1, 1, 2} | |
| 93. |
In a school, 50% students play cricket and 40% play football. If 10% of students play both the games, then what per cent of students play neither cricket nor football? |
| A. | 10% |
| B. | 15% |
| C. | 20% |
| D. | 25% |
| Answer» D. 25% | |
| 94. |
If \(f\left( x \right) = lo{g_e}\left( {\frac{{1 - x}}{{1 + x}}} \right)\), |x| < 1, then \(f\left( {\frac{{2x}}{{1 + {x^2}}}} \right)\) is equal to: |
| A. | 2f(x) |
| B. | 2f(x2) |
| C. | (f(x))2 |
| D. | -2f(x) |
| Answer» B. 2f(x2) | |
| 95. |
Find the range of the function, f(x) = |x + 3|- 2, where x ∈ R. |
| A. | R |
| B. | R – {- 3} |
| C. | [- 2, ∞) |
| D. | None of these |
| Answer» D. None of these | |
| 96. |
Let a function f : (0, ∞) → (0, ∞) be defined by \(f\left( x \right) = \left| {1 - \frac{1}{x}} \right|\). Then f is: |
| A. | Not injective but it is surjective |
| B. | Injective only |
| C. | Neither injective nor surjective |
| D. | Both injective as well as surjective |
| Answer» B. Injective only | |
| 97. |
If X = {a, {b}, c}, Y = {{a}, b, c} and Z = {a, b, {c}}, then (X ∩ Y) ∩ Z equals to |
| A. | {a, b, c} |
| B. | {{a}, {b}, {c}} |
| C. | {φ} |
| D. | φ |
| Answer» E. | |
| 98. |
For any real numbers x and y, we write x R y x2 - y2 + √3 is an irrational number. Then the relation R is: |
| A. | reflexive |
| B. | symmetric |
| C. | Transitive |
| D. | None of these |
| Answer» E. | |
| 99. |
Let f : R → R be a differentiable function satisfying f'(3) + f'(2) = 0.Then \(\mathop {{\rm{lim}}}\limits_{x \to 0} {\left( {\frac{{1 + f\left( {3 + x} \right) - f\left( 3 \right)}}{{1 + f\left( {2 - x} \right) - f\left( 2 \right)}}} \right)^{\frac{1}{x}}}\)is equal to: |
| A. | 1 |
| B. | e-1 |
| C. | e |
| D. | e2 |
| Answer» B. e-1 | |
| 100. |
Let R be the set of real numbers and * be the binary operation defined on R as a * b = a + b - ab ∀ a, b ∈ R. Then, the identity element with respect to the binary operation * is: |
| A. | 1/1 - a |
| B. | 1 - a |
| C. | 1 |
| D. | 0 |
| Answer» E. | |