MCQOPTIONS
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MCQOPTIONS
This section includes 108 Mcqs, each offering curated multiple-choice questions to sharpen your Maharashtra CET knowledge and support exam preparation. Choose a topic below to get started.
| 1. |
In every (n + 1) - - elementic subset of the set (1, 2, 3, .......2n) which of the following is correct: |
| A. | There exist at least two natural numbers which are prime to each other |
| B. | exist at least three natural umber which are prime to each other |
| C. | There exist no consecutive natural number |
| D. | There exist more than two natural numbers which are prime to each other |
| Answer» B. exist at least three natural umber which are prime to each other | |
| 2. |
Of the members of three athletic teams in a school, 21 are in the cricket team, 26 are in the hockey team and 29 are in the football team. Among them, 14 play hockey and cricket, 15 play hockey and football, 12 play football and cricket and 8 play all the three games. The total number of members in the three athletic teams is: |
| A. | 76 |
| B. | 49 |
| C. | 43 |
| D. | 41 |
| Answer» D. 41 | |
| 3. |
If x = {4n - 3n - 1: n ϵ N} and Y = {9(n - 1) : n ϵ N}, where N is the set of natural numbers, then |
| A. | X ⊂ Y |
| B. | X \(\subseteq\) Y |
| C. | X \(\supset\) Y |
| D. | X \(\supseteq\) Y |
| Answer» B. X \(\subseteq\) Y | |
| 4. |
Let f(x) = 15 – |x – 10|; x ∈ R. Then the set of all values of x, at which the function, g(x) = f(f(x)) is not differentiable, is: |
| A. | {5, 10, 15} |
| B. | {10, 15} |
| C. | {5, 10, 15, 20} |
| D. | {10} |
| Answer» B. {10, 15} | |
| 5. |
A square is a convex set, its exterior points are |
| A. | vertices of square |
| B. | sides of squares |
| C. | inside of square |
| D. | Outside of square |
| Answer» B. sides of squares | |
| 6. |
In a class of 140 students numbered 1 to 140, all even numbered students opted Mathematics course, those who number is divisible by 3 opted Physics course and those who number is divisible by 5 opted Chemistry course. Then the number of students who did not opt for any of the three courses is: |
| A. | 102 |
| B. | 42 |
| C. | 1 |
| D. | 38 |
| Answer» E. | |
| 7. |
Let A and B be two events. If \(P(A) = \dfrac{1}{2}, P(B) = \dfrac{1}{4}, P(A \cap B) = \dfrac{1}{5}\) then \(P({A'\over B'})\) = |
| A. | 0.8 |
| B. | 0.4 |
| C. | 0.3 |
| D. | 0.6 |
| Answer» E. | |
| 8. |
Let S be a set of all distinct numbers of the form \(\frac{{\rm{p}}}{{\rm{q}}}\), where p, q ∈ {1, 2, 3, 4, 5, 6}. What is the the cardinality of the set S? |
| A. | 21 |
| B. | 23 |
| C. | 32 |
| D. | 36 |
| Answer» C. 32 | |
| 9. |
If P and Q are two sets, then (P - Q) ∪ (Q - P) ∪ (P ∩ Q) will be |
| A. | P |
| B. | Q |
| C. | P ∩ Q |
| D. | P ∪ Q |
| Answer» E. | |
| 10. |
Considering only the principal values of inverse functions, the set \(A = \left\{ {x \ge 0;ta{n^{ - 1}}\left( {2x} \right) + ta{n^{ - 1}}\left( {3x} \right) = \frac{\pi }{4}} \right\}\) |
| A. | Is an empty set |
| B. | Is a singleton |
| C. | Contains more than two elements |
| D. | contains two elements. |
| Answer» C. Contains more than two elements | |
| 11. |
If A is an open set and B is a closed set, then B - A is |
| A. | Open set |
| B. | Closed set |
| C. | Both open and closed set |
| D. | None of these |
| Answer» C. Both open and closed set | |
| 12. |
Let A and B two sets containing four and two elements respectively, The number of subsets of the set A × B, each having at least three elements is: |
| A. | 270 |
| B. | 239 |
| C. | 219 |
| D. | 256 |
| Answer» D. 256 | |
| 13. |
Consider a Takagi - Sugeno - Kanga (TSK) Model consisting of rules of the form :If x1 is Ai1 and ... and xr is AirTHEN y = fi (x1, x2, ...., xr) = bi0 + bi1x1 + birxrassume, αi is the matching degree of rule i, then the total output of the model is given by : |
| A. | \(y = \;\mathop \sum \limits_{i = 1}^L {\alpha _i}{f_i}\left( {{x_1},\;{x_2}, \ldots .,\;{x_r}} \right)\) |
| B. | \(y = \frac{{\mathop \sum \nolimits_{i = 1}^L {\alpha _i}{f_i}\left( {{x_1},\;{x_2}, \ldots .,\;{x_r}} \right)}}{{\mathop \sum \nolimits_{i = 1}^L {\alpha _i}}}\) |
| C. | \(y = \frac{{\mathop \sum \nolimits_{i = 1}^L {f_i}\left( {{x_1},\;{x_2}, \ldots .,\;{x_r}} \right)}}{{\mathop \sum \nolimits_{i = 1}^L {\alpha _i}}}\) |
| D. | y = max[αifi (x1, x2,....xr)] |
| Answer» C. \(y = \frac{{\mathop \sum \nolimits_{i = 1}^L {f_i}\left( {{x_1},\;{x_2}, \ldots .,\;{x_r}} \right)}}{{\mathop \sum \nolimits_{i = 1}^L {\alpha _i}}}\) | |
| 14. |
A, B, C and D are four sets such that A ∩ B = C ∩ D = ϕ. Consider the following:1. A ∪ C and B ∪ D are always disjoint.2. A ∩ C and B ∩ D are always disjoint.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» C. Both 1 and 2 | |
| 15. |
For any two groups A and B, A ∪ (A ∩ B) = ? |
| A. | O |
| B. | B |
| C. | A ∩ B |
| D. | A |
| Answer» E. | |
| 16. |
If the cardinality of a set A is 4 and that of a set B is 3, then what is the cardinality of the set A Δ B? |
| A. | 1 |
| B. | 5 |
| C. | 7 |
| D. | Cannot be determined as the sets A and B are not given |
| Answer» E. | |
| 17. |
Let A be a set having 'p' elements and B be the set having 'q' elements, the number of relations from A to B is |
| A. | 2p |
| B. | 2q |
| C. | 2pq |
| D. | 2pq-q |
| Answer» D. 2pq-q | |
| 18. |
If A = {x ∈ R : x2 + 6x - 7 < 0} and B = {x ∈ R : x2 + 9x + 14 > 0}, then which of the following is/are correct?1. (A ∩ B) = (-2, 1)2. (A - B) = (-7, -2)Select the correct answer using the code given below: |
| A. | 1 only |
| B. | 2 only |
| C. | Both 1 and 2 |
| D. | Neither 1 and 2 |
| Answer» D. Neither 1 and 2 | |
| 19. |
For any two statements p and q, the negation of the expressionp∨(~p ∧ q) is: |
| A. | ~p ∧ ~q |
| B. | p ∧ q |
| C. | p ↔ q |
| D. | ~ p ∨ ~q |
| Answer» B. p ∧ q | |
| 20. |
In a group of athletic teams in a school, 21 are in the basketball team, 26 in the hockey team and 29 in the football team. If 14 play hockey and basketball, 12 play football and basketball, 15 play hockey and football, 8 play all the three games, then how many play football only ? |
| A. | 10 |
| B. | 29 |
| C. | 21 |
| D. | 18 |
| E. | None of the above/More than one of the above |
| Answer» B. 29 | |
| 21. |
Let P̅ and Q̅ denote the complements of two sets P and Q. Then the set (P - Q) ∪ (Q - P) ∪ (P ∩ Q) is |
| A. | P ∪ Q |
| B. | P̅ ∪ Q̅ |
| C. | P ∩ Q |
| D. | P̅ ∩ Q̅ |
| Answer» B. P̅ ∪ Q̅ | |
| 22. |
Consider the following statements:1. A = {1, 3, 5} and B = {2, 4, 7} are equivalent sets.2. A = {1, 5, 9} and B = {1, 5, 5, 9, 9} are equal sets.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 | |
| 23. |
In a city, there are 3 major newspapers A, B and C of which at least two are read by 35% of population. A and B are read by 15%. C is read by 45% and that all the three are read by 10%. Then the percentage of people who read the newspaper C alone is |
| A. | 20 |
| B. | 10 |
| C. | 15 |
| D. | 5 |
| Answer» D. 5 | |
| 24. |
Consider to subsets of R3 given as,S1 = {[2, 3, 1], [1, 0, 5], [0, 1, 0], [0, 0, 1]} and S2 = {[1, 0, 0], [0, 1, 1], [0, 0, 0]}. Which of the following statements is true? |
| A. | 1 is linearly dependent but S2 is linearly independent. |
| B. | Both S1 and S2 are linearly independent. |
| C. | S1 is linearly independent but S2 is linearly dependent. |
| D. | Both S1 and S2 are linearly dependent. |
| Answer» E. | |
| 25. |
Find the number of elements in the union of 4 sets A, B, C and D having 150, 180, 210 and 240 elements respectively, given that each pair of sets has 15 elements in common. Each triple of sets has 3 elements in common and A ∩ B ∩ C ∩ D = ϕ |
| A. | 616 |
| B. | 512 |
| C. | 111 |
| D. | 702 |
| Answer» E. | |
| 26. |
If A = { x : x is a multiple of 3} and B = (x : x is a multiple of 4} and C = {x : x is a multiple of 12}, then which one of the following is a null set? |
| A. | (A \ B) ∪ C |
| B. | (A \ B) \ C |
| C. | (A ∩ B)∩ C |
| D. | (A ∩ B) \ C |
| Answer» E. | |
| 27. |
If P, Q and R are three sets, then which of the following is correct? |
| A. | P ∪ (Q ∩ R) = (P ∪ Q) ∩ (P ∩ R) |
| B. | P ∩ (Q ∪ R) = (P ∪ Q) ∩ (P ∪ R) |
| C. | P ∪ (Q ∩ R) = (P ∪ Q) ∩ (P ∪ R) |
| D. | P ∩ (Q ∪ R) = (P ∩ Q) ∩ (P ∩ R) |
| Answer» D. P ∩ (Q ∪ R) = (P ∩ Q) ∩ (P ∩ R) | |
| 28. |
Let P = {θ∶ sin θ - cos θ = √2 cos θ} and Q = {θ∶ sin θ + cos θ = √2 sin θ} be two sets. Then: |
| A. | P ⊂ Q and Q - P ≠ 0. |
| B. | P ⊄ Q. |
| C. | Q ⊄ P. |
| D. | P = Q. |
| Answer» E. | |
| 29. |
Let S = {1, 2, ..., n}. The number of possible pairs of the form (A, B) with A ⊆ B for subsets A, B of S is |
| A. | 2n |
| B. | 3n |
| C. | n! |
| D. | \({\rm{\Sigma }}_{k = 0}^n\left( {\begin{array}{*{20}{c}} n\\ k \end{array}} \right)\left( {\begin{array}{*{20}{c}} n\\ {n - k} \end{array}} \right)\) |
| Answer» B. 3n | |
| 30. |
If S = {x : x2 + 1 = 0, x is real}, then S is |
| A. | {-1} |
| B. | {0} |
| C. | {1} |
| D. | an empty set |
| Answer» E. | |
| 31. |
Let N denote the set of natural numbers and A = {n2 : n ∈ N} and B = {n3 : n ∈ N}. Which one of the following is not correct? |
| A. | A ∪ B = N |
| B. | The complement of (A ∪ B) is an infinite set |
| C. | A ∩ B must be a finite set |
| D. | A ∩ B must be a proper subset of {m6 : m ∈ N} |
| Answer» B. The complement of (A ∪ B) is an infinite set | |
| 32. |
In a class of 60 students, 45 students like music, 50 students like dancing, 5 students like neither. Then the number of students in the class who like both music and dancing is |
| A. | 35 |
| B. | 40 |
| C. | 50 |
| D. | 55 |
| Answer» C. 50 | |
| 33. |
In a beauty contest, half the number of experts voted for Mr. A and two third voted for Mr. B. 10 voted for both and 6 did not for either. How many experts were there in all? |
| A. | 18 |
| B. | 36 |
| C. | 24 |
| D. | None of these |
| Answer» D. None of these | |
| 34. |
Match List I with List IILet R1 = {(1, 1), (2, 2), (3, 3)} and R2 = {(1, 1), (1, 2), (1, 3), (1, 4)}List IList II(A) R1 ∪ R2(I) {(1, 1), (1, 2), (1, 3), (1, 4), (2, 2), (3, 3)}(B) R1 - R2(II) {1, 1}(C) R1 ∩ R2(III) {(1, 2), (1, 3), (1, 4)}(D) R2 - R1(IV) {(2, 2), (3, 3)} Choose the correct answer from the options given below: |
| A. | A - I, B - II, C - IV, D - III |
| B. | A - I, B - IV, C - III, D - II |
| C. | A - I, B - III, C - II, D - IV |
| D. | A - I, B - IV, C - II, D - III |
| Answer» E. | |
| 35. |
If the number of elements in Y and Z are in the ratio 4 : 5, then what is the value of b? |
| A. | 18 |
| B. | 19 |
| C. | 21 |
| D. | 23 |
| Answer» D. 23 | |
| 36. |
A coin is tossed three times. Consider the following events:A: No head appearsB: Exactly one head appearsC. At least two heads appearWhich one of the following is correct? |
| A. | (A ∪ B) ∩ (A ∪ C) = B ∪ C |
| B. | (A ∩ B’) ∪ (A ∪ C’) = B’ ∪ C’ |
| C. | A ∩ (B’ ∪ C’) = A ∪ B ∪ C |
| D. | A ∩ (B’ ∪ C’) = B’ ∩ C’ |
| Answer» E. | |
| 37. |
If A is a subset of B and B is a subset of C, then the cardinality of A ∪ B ∪ C is equal to: |
| A. | Cardinality of C. |
| B. | Cardinality of B. |
| C. | Cardinality of A. |
| D. | None of the above. |
| Answer» B. Cardinality of B. | |
| 38. |
In a survey where 100 students reported which subjects they like, 32 students in total liked Mathematics, 38 students liked Business and 30 students liked Literature. Moreover 7 students liked both Mathematics and Literature, 10 students liked both Mathematics and Business, 8 students liked both Business and Literature, 5 students liked all three subjects.Then the number of people who liked exactly one subject is |
| A. | 60 |
| B. | 65 |
| C. | 70 |
| D. | 78 |
| Answer» C. 70 | |
| 39. |
Let A = {1, 2, 3, 4, 5, 6, 7, 8, 9, 10}. Then the number of subsets of A containing exactly two elements is |
| A. | 20 |
| B. | 40 |
| C. | 45 |
| D. | 90 |
| Answer» D. 90 | |
| 40. |
In a class of 50 students, it was found that 30 students read "Hitavad", 35 students read "Hindustan" and 10 read neither. How many students read both "Hitavad" and "Hindustan" newpapers? |
| A. | 25 |
| B. | 35 |
| C. | 15 |
| D. | 30 |
| Answer» B. 35 | |
| 41. |
Let S be the set of all points in (-π, π) at which the function, f(x) = min (sin x, cos x) is not differentiable. Then, S is a subset of which of the following |
| A. | \(\left\{ -\frac{\pi }{4},0,\text{ }\!\!~\!\!\text{ }\frac{\pi }{4} \right\}\) |
| B. | \(\left\{ -\frac{\pi }{2},-\frac{\pi }{4},\frac{\pi }{4},\frac{\pi }{2} \right\}\) |
| C. | \(\left\{ -\frac{3\pi }{4},-\frac{\pi }{4},\frac{3\pi }{4},\frac{\pi }{4} \right\}\) |
| D. | \(\left\{ -\frac{3\pi }{4},-\frac{\pi }{2},\frac{\pi }{2},\frac{3\pi }{4} \right\}\) |
| Answer» D. \(\left\{ -\frac{3\pi }{4},-\frac{\pi }{2},\frac{\pi }{2},\frac{3\pi }{4} \right\}\) | |
| 42. |
In a school, out of 50 students, 25 have scooters and 35 have cycles for coming to school. The number of students who have scooter and cycle both are- |
| A. | 15 |
| B. | 18 |
| C. | 10 |
| D. | 12 |
| Answer» D. 12 | |
| 43. |
In n(A) = 20, n(B) = 35 and n(A ∪ B) = 45, then n (A ∩ B) equals |
| A. | 10 |
| B. | 15 |
| C. | 0 |
| D. | None of these |
| Answer» B. 15 | |
| 44. |
A professor has 24 text books on computer science and is concerned about their coverage of the topics (P) compilers, (Q) data structures and (R) Operating systems. The following data gives the number of books that contain material on these topics: n(P) = 8, n(Q) = 13, n(R) = 13, n(P ∩ R) = 3, n(P ∩ R) = 3, n(Q ∩ R) = 3, n(Q ∩ R) = 6, n(P ∩ Q ∩ R) = 2, where n(x) is the cardinality of the set x. Then the number of text books that have no material on compilers is |
| A. | 4 |
| B. | 8 |
| C. | 12 |
| D. | 16 |
| Answer» E. | |
| 45. |
Consider the proper subsets of {1, 2, 3, 4}. How many of these proper subsets are a superset of the set {3}? |
| A. | 5 |
| B. | 6 |
| C. | 7 |
| D. | 8 |
| Answer» C. 7 | |
| 46. |
If A and B are non-empty subsets of a set C, then A ∪ (A ∩ B) is equal to |
| A. | A ∩ B |
| B. | A ∪ B |
| C. | A |
| D. | B |
| Answer» D. B | |
| 47. |
If P and Q be two sets such that P ∪ Q = P, then P ∩ Q will be |
| A. | P |
| B. | Q |
| C. | ϕ |
| D. | None of these |
| Answer» C. ϕ | |
| 48. |
If X = {4n - 3n - 1, n ∈ N} and Y = {9n - 9, n ∈ N}, then X ∪ Y is equal to |
| A. | Y |
| B. | X |
| C. | N |
| D. | None of these |
| Answer» B. X | |
| 49. |
Let S = {1, 2, 3,…, 100}. The number of non-empty subsets A of S such that the product of elements in A is even, is |
| A. | 250 (250 – 1) |
| B. | 250 – 1 |
| C. | 250 + 1 |
| D. | 2100 + 1 |
| Answer» B. 250 – 1 | |
| 50. |
If A and B be any two sets such that A Δ B = A, then A ∩ B is |
| A. | ϕ |
| B. | A |
| C. | B |
| D. | A ∪ B |
| Answer» B. A | |