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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.
| 101. |
Let X be the set of all persons living in a city. Persons x, y in X are said to be related as x < y if y at least 5 years older than x. which one of the following is correct? |
| A. | The relation is an equivalence relation on X. |
| B. | The relation is transitive but neither reflexive nor symmetric. |
| C. | The relation is reflexive but neither transitive nor symmetric. |
| D. | The relation is symmetric but neither transitive nor reflexive. |
| Answer» C. The relation is reflexive but neither transitive nor symmetric. | |
| 102. |
How many students like to play exactly only one game? |
| A. | 196 |
| B. | 228 |
| C. | 254 |
| D. | 268 |
| Answer» D. 268 | |
| 103. |
If log x = 1.25 and y = xlog x, then what is log y equal to? |
| A. | 4.25 |
| B. | 2.5625 |
| C. | 1.5625 |
| D. | 1.25 |
| Answer» D. 1.25 | |
| 104. |
If n = (2017)! then what is \(\frac{1}{{{{\log }_2}n}} + \frac{1}{{{{\log }_3}n}} + \frac{1}{{{{\log }_4}n}} + \ldots + \frac{1}{{{{\log }_{2017}}n}}\) equal to? |
| A. | 0 |
| B. | 1 |
| C. | n/2 |
| D. | n |
| Answer» C. n/2 | |
| 105. |
If log101995 = 3.3000, then what is the value of (0.001995)1/8? |
| A. | \(\frac{1}{{{{10}^{0.3475}}}}\) |
| B. | \(\frac{1}{{{{10}^{0.3375}}}}\) |
| C. | \(\frac{1}{{{{10}^{0.3275}}}}\) |
| D. | \(\frac{1}{{{{10}^{0.3735}}}}\) |
| Answer» C. \(\frac{1}{{{{10}^{0.3275}}}}\) | |
| 106. |
On the set Q+ of all positive rational numbers, the operation O is defined by the formula a O \(\rm b = \frac{{ab}}{2}\), then the inverse of 8 is |
| A. | 1/8 |
| B. | 8 |
| C. | 2 |
| D. | 1/2 |
| Answer» E. | |
| 107. |
A binary number is represented by (cdccddcccddd)2, where c > d. What is its decimal equivalent? |
| A. | 1848 |
| B. | 2048 |
| C. | 2842 |
| D. | 2872 |
| Answer» E. | |
| 108. |
If 3x = 4x - 1, then x = |
| A. | \(\frac {2 - \log_3 2}{2\log_3 2 - 1}\) |
| B. | \(\frac {2}{2\log_3 2 - 1}\) |
| C. | \(\frac {2 - \log_3 2}{2\log_3 2 + 1}\) |
| D. | \(\frac {2 - \log_3 2}{2\log_2 3 - 1}\) |
| Answer» C. \(\frac {2 - \log_3 2}{2\log_3 2 + 1}\) | |
| 109. |
If P(n): 2n < n!, n ϵ N then P(n) is true for n |
| A. | > 2 |
| B. | > 3 |
| C. | < 4 |
| D. | None of these |
| Answer» C. < 4 | |
| 110. |
In the binary equation (1p101)2 + (10q1)2 = (100r00)2Where p, q and r are binary digits, what are the possible values of p, q and r respectively? |
| A. | 0, 1, 0 |
| B. | 1, 1, 0 |
| C. | 0, 0, 1 |
| D. | 1, 0, 1 |
| Answer» B. 1, 1, 0 | |
| 111. |
Consider the following functions:1. f(x) = x3, x ϵ R2. f(x) = sin x, 0 < x < 2π3. f(x) = ex, x ϵ RWhich of the above functions have inverse defined on their ranges? |
| A. | 1 and 2 only |
| B. | 2 and 3 only |
| C. | 1 and 3 only |
| D. | 1, 2 and 3 |
| Answer» B. 2 and 3 only | |
| 112. |
Let R be a relation from A = {1, 2, 3, 4} to B = {1, 3, 5} such thatR = {(a, b) : a < b, where a ∈ A and b ∈ B}.What is RoR-1 equal to? |
| A. | {(1, 3), (1, 5), (2, 3), (2, 5), (3, 5), (4, 5)} |
| B. | {(3, 1), (5, 1), (3, 2), (5, 2), (5, 3), (5, 4)} |
| C. | {(3, 3), (3, 5), (5, 3), (5, 5)} |
| D. | {(3, 3), (3, 4), (4, 5)} |
| Answer» D. {(3, 3), (3, 4), (4, 5)} | |
| 113. |
If m is the minimum value of k for which the function \(f\left( x \right)=x\sqrt{kx-{{x}^{2}}}\) is increasing in the interval [0, 3] and M is the maximum value of f in [0, 3] when k = m, then the ordered pair (m, M) is equal to: |
| A. | \(\left( 4,\text{ }\!\!~\!\!\text{ }3\sqrt{2} \right)\) |
| B. | \(\left( 4,\text{ }\!\!~\!\!\text{ }3\sqrt{3} \right)\) |
| C. | \(\left( 3,\text{ }\!\!~\!\!\text{ }3\sqrt{3} \right)\) |
| D. | \(\left( 5,\text{ }\!\!~\!\!\text{ }3\sqrt{6} \right)\) |
| Answer» C. \(\left( 3,\text{ }\!\!~\!\!\text{ }3\sqrt{3} \right)\) | |
| 114. |
Let X be the set of all persons living in Delhi. The persons a and b in X are said to be related if the difference in their ages is at most 5 years. The relation is |
| A. | an equivalence relation |
| B. | reflexive and transitive but not symmetric |
| C. | symmetric and transitive but not reflexive |
| D. | reflexive and symmetric but not transitive |
| Answer» E. | |
| 115. |
If f(x) + f(-x) = 0, then \(\int_a^x {f(t)dt} \) is |
| A. | An odd function |
| B. | An even function |
| C. | A periodic function |
| D. | None of these |
| Answer» B. An even function | |
| 116. |
If the function, \(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}}{a\left| {\pi - x} \right| + 1,x \le 5}\\{b\left| {x - \pi } \right| + 3,x > 5}\end{array}} \right.\) is continuous at x = 5, then the value of a – b is: |
| A. | \(\frac{2}{{\pi + 5}}\) |
| B. | \({\rm{\;}}\frac{{ - 2}}{{\pi + 5}}\) |
| C. | \(\frac{2}{{\pi - 5}}\) |
| D. | \(\frac{2}{{5 - \pi }}\) |
| Answer» E. | |
| 117. |
Consider the following statements:1. f[g(x)] is a polynomial of degree 3.2. g[g(x)] is a polynomial of degree 2.Which of the above statements is/are correct? |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 nor 2 |
| Answer» E. | |
| 118. |
Let R be a relation defined as xRy if and only if 2x + 3y = 20, where x, y ∈ N. How many elements of the form (x, y) are there in R? |
| A. | 2 |
| B. | 3 |
| C. | 4 |
| D. | 6 |
| Answer» C. 4 | |
| 119. |
Find the range of the function \(\frac{{\left| {x - 1} \right|}}{{x - 1}}\)for {x: x ∈ R | x ≠ 1}? |
| A. | {-1, 1} |
| B. | (-∞, 1) |
| C. | (1, ∞) |
| D. | (-∞, -1) ⋃ (1, ∞) |
| Answer» B. (-∞, 1) | |
| 120. |
If A, B and C are subsets of a Universal set, then which one of the following is not correct? Where A’ is the complement of A. |
| A. | A ∪ (B ∩ C) = (A ∪ B) ∩ (A ∪ C) |
| B. | A’ ∪ (A ∪ B) = (B’ ∩ B)’ ∪ A’ |
| C. | A’ ∪ (B ∪ C) = (C’ ∩ B)’ ∩ A’ |
| D. | (A ∩ B) ∪ C = (A ∪ C) ∩ (B ∪ C) |
| Answer» D. (A ∩ B) ∪ C = (A ∪ C) ∩ (B ∪ C) | |
| 121. |
In an examination, 70% students passed in physics, 80% student passed in Chemistry, 75% students passed in Mathematics and 85% students passed in Biology, and x% students failed in all the four subjects. What is the minimum value of x? |
| A. | 10 |
| B. | 12 |
| C. | 15 |
| D. | None of the above |
| Answer» E. | |
| 122. |
Let , A = {1, 2, 3, 4, 5, 6} and B = {1, 3, 5, 7, 9, 11}. Then find the set which represents the shaded portion in the figure given below? |
| A. | {2, 4, 7, 9, 11} |
| B. | {2, 3, 6, 7, 9, 11} |
| C. | {2, 4, 6, 7, 9, 11} |
| D. | {2, 4, 6, 7, 9} |
| Answer» D. {2, 4, 6, 7, 9} | |
| 123. |
For r > 0, f(r) is the ratio of perimeter to area of a circle of radius r. Then f(1) + f(2) is equal to |
| A. | 1 |
| B. | 2 |
| C. | 3 |
| D. | 4 |
| Answer» D. 4 | |
| 124. |
Let f(x) = x2, x ∈ R. For any A ⊆ R, define g(A) = {x ∈ R : f(x) ∈ A}. If S = [0, 4], then which one of the following statements is not true? |
| A. | g(f(S)) ≠ S |
| B. | f(g(S)) = S |
| C. | g(f(S)) = g(S) |
| D. | f(g(S)) ≠ f(S) |
| Answer» D. f(g(S)) ≠ f(S) | |
| 125. |
If a = log12 18, b = log24 54, then ab + 5(a - b) is |
| A. | 1 |
| B. | 0 |
| C. | 2 |
| D. | \(\dfrac{3}{2}\) |
| Answer» B. 0 | |
| 126. |
If f(x + 1) = x2 - 3x + 2, then what is f(x) equal to? |
| A. | x2 - 5x + 4 |
| B. | x2 - 5x + 6 |
| C. | x2 + 3x + 3 |
| D. | x2 - 3x + 1 |
| Answer» C. x2 + 3x + 3 | |
| 127. |
If \({\rm{g}}\left( {\rm{x}} \right) = \frac{1}{{{\rm{f}}\left( {\rm{x}} \right)}}\) and f(x) = x, x ≠ 0, then which one of the following is correct? |
| A. | f(f(f(g(g(f(x)))))) = g(g(f(g(f(x))))) |
| B. | f(f(g(g(g(f(x)))))) = g(g(f(g(f(x))))) |
| C. | f(g(f(g(g(f(g(x))))))) = g(g(f(g(f(x))))) |
| D. | f(f(f(g(g(f(x)))))) = f(f(f(g(f(x))))) |
| Answer» C. f(g(f(g(g(f(g(x))))))) = g(g(f(g(f(x))))) | |
| 128. |
Let f: R → R be a function defined as\(f\left( x \right) = \left\{ {\begin{array}{*{20}{c}} {5,\;{\rm{if\;}}x \le 1}\\ {a + bx,\;{\rm{if\;}}1 < x < 3}\\ {b + 5x,\;{\rm{if\;}}3 \le x < 5}\\ {30,\;{\rm{if\;}}x \ge 5} \end{array}} \right.\)Then, f is: |
| A. | Continuous if a = 5 and b = 5 |
| B. | Continuous if a = -5 and b = 10 |
| C. | Continuous if a = 0 and b = 5 |
| D. | Not continuous for any values of a and b |
| Answer» E. | |
| 129. |
Let f(x) = loge (sin x), (0 < x < π) and g(x) = sin-1 (e-x), (x ≥ 0). If α is a positive real number such that a = fog' α and b = fog α, then:" |
| A. | aα2 + bα + a = 0 |
| B. | aα2 - bα - a = 1 |
| C. | aα2 - bα - a = 0 |
| D. | aα2 + bα - a = - 2α2 |
| Answer» C. aα2 - bα - a = 0 | |
| 130. |
If h(x) = 5f(x) – xg(x), then what is the derivative of h(x)? |
| A. | -40 |
| B. | -20 |
| C. | -10 |
| D. | 0 |
| Answer» C. -10 | |
| 131. |
Consider the following statements:1. A function f : Z → Z, defined by f(x) = x + 1, is one-one as well as onto.2. A function f : N → N, defined by f(x) = x + 1, is one-one but not onto.Which of the above statements 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 | |
| 132. |
For an onto function range is equivalent to codomain. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» B. False | |
| 133. |
A function is defined by mapping f : A -> B such that A contains m elements and B contains n elements and m>n then number of one one functions are ________ |
| A. | ⁿCₘ x m! |
| B. | ⁿCₘ x n! |
| C. | 0 |
| D. | none of the mentioned |
| Answer» D. none of the mentioned | |
| 134. |
Let f(x)=sin²(x) + log(x) then domain of f(x) is (-∞, ∞). |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» C. May be True or False | |
| 135. |
An injection is a function which is? |
| A. | many-one |
| B. | one-one |
| C. | onto |
| D. | none of the mentioned |
| Answer» C. onto | |
| 136. |
The range of function f(x) = sin(x) is (-∞, ∞). |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» C. May be True or False | |
| 137. |
If X = Floor(X) = Ceil(X) then __________ |
| A. | X is a fractional number |
| B. | X is a Integer |
| C. | X is less than 1 |
| D. | none of the mentioned |
| Answer» C. X is less than 1 | |
| 138. |
Let n be some integer greater than 1,then floor((n-1)/n) is 1. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» C. May be True or False | |
| 139. |
If f is a function defined from R to R, is given by f(x) = 3x – 5 then f⁻¹(x) is given by __________ |
| A. | 1/(3x-5) |
| B. | (x+5)/3 |
| C. | does not exist since it is not a bijection |
| D. | none of the mentioned |
| Answer» C. does not exist since it is not a bijection | |
| 140. |
A bijection is a function which is many-one and onto. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» C. May be True or False | |
| 141. |
If f is a function defined from R to R, is given by f(x) = x² then f⁻¹(x) is given by? |
| A. | 1/(3x-5) |
| B. | (x+5)/3 |
| C. | does not exist since it is not a bijection |
| D. | none of the mentioned |
| Answer» D. none of the mentioned | |
| 142. |
If x, and y are positive numbers both are less than one, then maximum value of ceil(x + y) is? |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | -1 |
| Answer» D. -1 | |
| 143. |
A function f(x) is defined from A to B then f⁻¹ is defined __________ |
| A. | from A to B |
| B. | from B to A |
| C. | depends on the inverse of function |
| D. | none of the mentioned |
| Answer» C. depends on the inverse of function | |
| 144. |
What is the domain of a function? |
| A. | the maximal set of numbers for which a function is defined |
| B. | the maximal set of numbers which a function can take values |
| C. | it is a set of natural numbers for which a function is defined |
| D. | none of the mentioned |
| Answer» B. the maximal set of numbers which a function can take values | |
| 145. |
The big-O notation for f(x) = 5logx is? |
| A. | 1 |
| B. | x |
| C. | x² |
| D. | x³ |
| Answer» C. x² | |
| 146. |
A function is defined by mapping f : A → B such that A contains m elements and B contains n elements and m ≤ n then number of one one functions are _________ |
| A. | ⁿCₘ x m! |
| B. | ⁿCₘ x n! |
| C. | 0 |
| D. | none of the mentioned |
| Answer» B. ⁿCₘ x n! | |
| 147. |
Let f(x) = x then number of solution to f(x) = f⁻¹(x) is zero. |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» C. May be True or False | |
| 148. |
A mapping f : X → Y is one one if __________ |
| A. | f(x1) ≠ f(x2) for all x1, x2 in X |
| B. | If f(x1) = f(x2) then x1 = x2 for all x1, x2 in X |
| C. | f(x1) = f(x2) for all x1, x2 in X |
| D. | None of the mentioned |
| Answer» C. f(x1) = f(x2) for all x1, x2 in X | |
| 149. |
If f(x) = y then f⁻¹(y) is equal to __________ |
| A. | y |
| B. | x |
| C. | x² |
| D. | none of the mentioned |
| Answer» C. x² | |
| 150. |
For some number x, Floor(x) |
| A. | True |
| B. | False |
| C. | May be True or False |
| D. | Can't say |
| Answer» B. False | |