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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.
| 251. |
The shaded area of figure is best described by ? |
| A. | A‘ (Complement of A) |
| B. | A U B -B |
| C. | A ∩ B |
| D. | B |
| Answer» C. A ∩ B | |
| 252. |
The shaded area of figure is best described by? |
| A. | A‘ (Complement of A) |
| B. | A U B – (A ∩ B) |
| C. | A – B |
| D. | B |
| Answer» C. A – B | |
| 253. |
In the given figure the if n(A)=20,n(U)=50,n(C)=10 and n(A∩B)=5 then n(B)=? |
| A. | 35 |
| B. | 20 |
| C. | 30 |
| D. | 10 |
| Answer» B. 20 | |
| 254. |
A function is defined by mapping f : A → B such that A contains m elements and B contains n elements and 1≤n≤m then number of onto functions are ________ |
| A. | a |
| B. | b |
| C. | c |
| D. | d |
| Answer» B. b | |
| 255. |
Express {x: x= n/ (n+1), n is a natural number less than 7} in roster form. |
| A. | {1⁄2, 2⁄3, 4⁄5, 6⁄7} |
| B. | {1⁄2, 2⁄3, 3⁄4, 4⁄5, 5⁄6, 6⁄7, 7⁄8} |
| C. | {1⁄2, 2⁄3, 3⁄4, 4⁄5, 5⁄6, 6⁄7} |
| D. | Infinite set |
| Answer» D. Infinite set | |
| 256. |
{x: x is a real number between 1 and 2} is an ________ |
| A. | Infinite set |
| B. | Finite set |
| C. | Empty set |
| D. | None of the mentioned |
| Answer» B. Finite set | |
| 257. |
Write set {1, 5, 15, 25,…} in set-builder form. |
| A. | {x: either x=1 or x=5n, where n is a real number} |
| B. | {x: either x=1 or x=5n, where n is a integer} |
| C. | {x: either x=1 or x=5n, where n is an odd natural number} |
| D. | {x: x=5n, where n is a natural number} |
| Answer» D. {x: x=5n, where n is a natural number} | |
| 258. |
If R = {(1, 2),(2, 3),(3, 3)} be a relation defined on A= {1, 2, 3} then R . R( = R2) is |
| A. | R itself |
| B. | {(1, 2),(1, 3),(3, 3)} |
| C. | {(1, 3),(2, 3),(3, 3)} |
| D. | {(2, 1),(1, 3),(2, 3)} |
| Answer» D. {(2, 1),(1, 3),(2, 3)} | |
| 259. |
If A = (1, 2, 3, 4). Let ~ = ((1, 2), (1, 3), (4, 2). Then ~ is |
| A. | reflexive |
| B. | transitive |
| C. | symmetric |
| D. | not anti-symmetric |
| Answer» C. symmetric | |
| 260. |
If the binary operation * is deined on a set of ordered pairs of real numbers as (a, b) * (c, d) = (ad + bc, bd) and is associative, then (1, 2) * (3, 5) * (3, 4) equals |
| A. | (7,11) |
| B. | (23,11) |
| C. | (32,40) |
| D. | (74,40) |
| Answer» E. | |
| 261. |
If (G, .) is a group such that a2 = e, ∀ a ∈ G, then G is |
| A. | semi group |
| B. | abelian group |
| C. | non-abelian group |
| D. | none of these |
| Answer» C. non-abelian group | |
| 262. |
If * is defined on R* as a * b = (ab/2) then identity element in the group (R*, *) is |
| A. | 1 |
| B. | 2 |
| C. | 1/2 |
| D. | 1/3 |
| Answer» C. 1/2 | |
| 263. |
If (G, .) is a group such that (ab)- 1 = b-1 a-1, ∀ a, b ∈ G, then G is a/an |
| A. | abelian group |
| B. | non-abelian group |
| C. | commutative semi group |
| D. | None of these |
| Answer» B. non-abelian group | |
| 264. |
If f : A ---> B is a bijective function, then f -1 of f = |
| A. | f |
| B. | f -1 |
| C. | f o f -1 |
| D. | IA(Identity map of the set A) |
| Answer» E. | |
| 265. |
Let R be a relation "(x -y) is divisible by m", where x, y, m are integers and m > 1, then R is |
| A. | partial order |
| B. | equivalence relation |
| C. | symmetric but not transitive |
| D. | anti symmetric and not transitive |
| Answer» C. symmetric but not transitive | |
| 266. |
Let Z denote the set of all integers. Define f : Z —> Z by f(x) = {x / 2 (x is even) 0 (x is odd) then f is |
| A. | one-one and onto |
| B. | one-one but not onto |
| C. | onto but not one-one |
| D. | neither one-one nor-onto |
| Answer» D. neither one-one nor-onto | |
| 267. |
The set of all Equivalence classes of a set A of cardinality C |
| A. | forms a partition of A |
| B. | is of cardinality 2C |
| C. | has the same cardinality as A |
| D. | none of these |
| Answer» B. is of cardinality 2C | |
| 268. |
Let n(A) denotes the number of elements in set A. If n(A) =p and n(B) = q, then how many ordered pairs (a, b) are there with a ∈ A and b ∈ B ? |
| A. | p x q |
| B. | p + q |
| C. | 2 pq |
| D. | 4 pq |
| Answer» B. p + q | |
| 269. |
In a beauty contest, half the number of experts voted for Mr. A and two thirds voted for Mr. B. 10 voted for both and 6 did not vote for either. How many experts were there in all ? |
| A. | 18 |
| B. | 24 |
| C. | 36 |
| D. | 44 |
| Answer» C. 36 | |
| 270. |
G(e, a, b, c} is an abelian group with 'e' as identity element. The order of the other elements are |
| A. | 2,2,4 |
| B. | 2,2,3 |
| C. | 2,3,4 |
| D. | 3,3,3 |
| Answer» C. 2,3,4 | |
| 271. |
Let A = {1, 2, .....3 } Define ~ by x ~ y ⇔ x divides y. Then ~ is |
| A. | symmetric |
| B. | an equivalence relation |
| C. | a partial-ordering relation |
| D. | relexive, but not a partial-ordering |
| Answer» D. relexive, but not a partial-ordering | |
| 272. |
If A = {1, 2, 3} then relation S = {(1, 1), (2, 2)} is |
| A. | symmetric only |
| B. | anti-symmetric only |
| C. | an equivalence relation |
| D. | both symmetric and anti-symmetric |
| Answer» E. | |
| 273. |
A subset H of a group(G,*) is a group if |
| A. | a,b ∈ H ⇒ a * b ∈ H |
| B. | a ∈ H⇒ a-1 ∈ H |
| C. | a,b ∈ H ⇒ a * b-1 ∈ H |
| D. | H contains the identity element |
| Answer» D. H contains the identity element | |
| 274. |
Let s(w) denote the set of all the letters in w where w is an English word. Let us denote set equality, subset and union relations by =, ⊂ and ∪ respectively. Which of the following is NOT true? |
| A. | s(ten) ⊂ s(twenty) |
| B. | s(stored) = s(sorted) |
| C. | s(sixty) ⊂ (s(six) ∪ s(twenty) |
| D. | None of these |
| Answer» E. | |
| 275. |
A partition of {1, 2, 3, 4, 5} is the family |
| A. | {(1, 2, 3),(5)} |
| B. | {(1, 2,), (3, 4, 5)} |
| C. | {φ(1, 2),(3, 4),(5)} |
| D. | {(1, 2),(3, 4),(3, 5)} |
| Answer» C. {φ(1, 2),(3, 4),(5)} | |
| 276. |
Total number of diferent partitions of a set having four elements is |
| A. | 5 |
| B. | 10 |
| C. | 15 |
| D. | 20 |
| Answer» D. 20 | |
| 277. |
The universal relation A x A on A is |
| A. | anti-symmetric |
| B. | an equivalence relation |
| C. | a partial ordering relation |
| D. | not symmetric and not anti-symmetric |
| Answer» C. a partial ordering relation | |
| 278. |
If every element of a group G is its own inverse, then G is |
| A. | abeian |
| B. | cyclic |
| C. | finite |
| D. | infinite |
| Answer» B. cyclic | |
| 279. |
If f : R ---->R defined by f(x) = x2 + 1, then values of f -1 (17) and f -1(-3) are respectively |
| A. | {4,-4},Ø |
| B. | {Ø},{3,-3} |
| C. | {3,-3},{Ø} |
| D. | {Ø}, (4, - 4) |
| Answer» B. {Ø},{3,-3} | |
| 280. |
If R = ((1, 1), (3, 1), (2, 3), (4, 2)), then which of the following represents R2, where R2 is R composite R? |
| A. | ((1, 1), (2, 1), (4, 3), (3, 1)) |
| B. | ((1, 1), (3, 1), (2, 3), (4, 2)) |
| C. | 1(1, 3), (3, 3), (3, 4), (3, 2)) |
| D. | f(1, 1), (9, 1), (4, 9), (16, 4)) |
| Answer» B. ((1, 1), (3, 1), (2, 3), (4, 2)) | |
| 281. |
The number of elements in the power set of the set {{a, b}, c} is |
| A. | 2 |
| B. | 4 |
| C. | 6 |
| D. | 8 |
| Answer» C. 6 | |
| 282. |
A Relation R is defined on the set of integers as xRy if (x + y) is even. Which of the following statements is TRUE? |
| A. | R is an equivalence relation having three equivalence classes |
| B. | R is an equivalence relation having two equivalence classes |
| C. | R is an equivalence relation having one equivalence class |
| D. | R is not an equivalence relation |
| Answer» C. R is an equivalence relation having one equivalence class | |
| 283. |
Which of the following sets is a null set ? I. X = {x | x= 9, 2x = 4 } II. Y = {x | x= 2x.x ≠ 0 } III. Z = { x | x-8 = 4 } |
| A. | I and II only |
| B. | I, II and III |
| C. | I and III only |
| D. | II and III only |
| Answer» B. I, II and III | |
| 284. |
Let A = {0, 1} × {0, 1} × {0, 1} and B = {a, b, c} × {a, b, c} × {a, b, c}. Suppose A is listed in lexicographic order based on 0 < 1 and B is listed in lexicographic order based on a < b < c. If A×B |
| A. | ((1, 0, 0),(b, a, a),(0, 0, 0)) |
| B. | ((1, 0, 0),(a, a, a),(0, 0, 1)) |
| C. | ((1, 0, 0),(a, a, a),(1, 0, 0)) |
| D. | ((1, 0, 0),(a, a, a),(0, 0, 0)) |
| Answer» E. | |
| 285. |
Let f : X → Y and g : Y → Z. Let h = g ◦ f : X → Z. Suppose g is one-to-one and onto. Which of the following is FALSE? |
| A. | If f is one-to-one then h is one-to-one and onto |
| B. | If f is not onto then h is not onto |
| C. | If f is not one-to-one then h is not one-to-one |
| D. | If f is one-to-one then h is one-to-one |
| Answer» B. If f is not onto then h is not onto | |
| 286. |
The number of partitions of {1, 2, 3, 4, 5} into three blocks is S(5, 3) = 25. The total number of functions f : {1, 2, 3, 4, 5} → {1, 2, 3, 4} with |Image(f)| = 3 is |
| A. | 4 × 6 |
| B. | 4 × 25 |
| C. | 25 × 6 |
| D. | 4 × 25 × 6 |
| Answer» E. | |
| 287. |
Let f : X → Y . Consider the statement, “For all subsets C and D of Y , f −1 (C∩Dc ) = f −1 (C) ∩ [f −1 (D)]c . This statement is |
| A. | True and equivalent to:For all subsets C and D of Y , f −1 (C − D) = f −1 (C) − f −1 (D). |
| B. | False and equivalent to:For all subsets C and D of Y , f −1 (C − D) = f −1 (C) − f −1 (D). |
| C. | True and equivalent to:For all subsets C and D of Y , f −1 (C − D) = f −1 (C) − [f −1 (D)]c |
| D. | False and equivalent to:For all subsets C and D of Y , f −1 (C − D) = f −1 (C) − [f −1 (D)]c . |
| Answer» B. False and equivalent to:For all subsets C and D of Y , f −1 (C − D) = f −1 (C) − f −1 (D). | |
| 288. |
Let σ = 452631 be a permutation on {1, 2, 3, 4, 5, 6} in one-line notation (based on the usual order on integers). Which of the following is NOT a correct cycle notation for σ? |
| A. | (614)(532) |
| B. | (461)(352) |
| C. | (253)(146) |
| D. | (325)(614) |
| Answer» C. (253)(146) | |
| 289. |
The power set P((A × B) ∪ (B × A)) has the same number of elements as the power set P((A × B) ∪ (A × B)) if and only if |
| A. | A = B |
| B. | A = ∅ or B = ∅ |
| C. | B = ∅ or A = B |
| D. | A = ∅ or B = ∅ or A = B |
| Answer» E. | |
| 290. |
Which of the following statements is TRUE? |
| A. | For all sets A, B, and C, (A − B) ∩ (C − B) = (A ∩ C) − B. |
| B. | For all sets A, B, and C, (A − B) ∩ (C − B) = A − (B ∪ C). |
| C. | For all sets A, B, and C, A − (B − C) = (A − B) − C. |
| D. | For all sets A, B, and C, if A ∪ C = B ∪ C then A = B. |
| Answer» B. For all sets A, B, and C, (A − B) ∩ (C − B) = A − (B ∪ C). | |
| 291. |
Let A = {0, 1} × {0, 1} and B = {a, b, c}. Suppose A is listed in lexicographic order based on 0 < 1 and B is in alphabetic order. If A × B × A is listed in lexicographic order, then the next element |
| A. | ((1, 0), a,(0, 0)) |
| B. | ((1, 1), c,(0, 0)) |
| C. | ((1, 1), a,(0, 0)) |
| D. | ((1, 1), a,(1, 1)) |
| Answer» D. ((1, 1), a,(1, 1)) | |
| 292. |
Let R be na equivalence relation on the set {1,2,3,4,5,6} given by {(1,1),(1,5),(2,2),(2,3),(2,6),(3,2),(3,3),(3,6),(4,4),(5,1),(5,5),(6,2),(6,6),(6,6)}. The partition included by R is |
| A. | {1,2,3,4,5,6} |
| B. | {{1,3,5,6},{2,4}} |
| C. | {{1,2,3,4},{5,6}} |
| D. | {{1,5},{2,3,6},{4}} |
| Answer» E. | |
| 293. |
A relation R is defined on the set of positive integers as xRy if 2x + y ≤ 5. The realation R is |
| A. | reflexive |
| B. | transitive |
| C. | symmetric |
| D. | None of these |
| Answer» C. symmetric | |
| 294. |
Let f : R → R be defined by f(x)= {x+2 (x ≤ -1) { x2 (-1 ≤ x ≤1) {2 - x (x ≥ 1) Then value of f (-1.75) + f (0.5) + f (1.5) is |
| A. | 0 |
| B. | 1 |
| C. | 2 |
| D. | None of these |
| Answer» C. 2 | |
| 295. |
If f : X -> Y and a, b ⊆ X, then f (a ∩ b) is equal to |
| A. | f(a) - f(b) |
| B. | f(a) ∩ f(b) |
| C. | f(b) - f(a) |
| D. | a proper subset of f(a) ∩ f(b) |
| Answer» E. | |
| 296. |
If X and Y are two sets, then X ∩ (Y ∪ X) C equals |
| A. | Ø |
| B. | X |
| C. | Y |
| D. | None of these |
| Answer» B. X | |
| 297. |
Which of the following statements is FALSE? |
| A. | 2 ∈ A ∪ B implies that if 2 ∈/ A then 2 ∈ B. |
| B. | {2, 3} ⊆ A implies that 2 ∈ A and 3 ∈ A. |
| C. | A ∩ B ⊇ {2, 3} implies that {2, 3} ⊆ A and {2, 3} ⊆ B |
| D. | {2} ∈ A and {3} ∈ A implies that {2, 3} ⊆ A. |
| Answer» E. | |
| 298. |
Set of Second element of ordered pair forming a relation is called its |
| A. | Range |
| B. | Domain |
| C. | Relation in A |
| D. | Relation in B |
| Answer» C. Relation in A | |
| 299. |
A declarative statement which may be true or false but not both is called |
| A. | Induction |
| B. | Deduction |
| C. | Knowledge |
| D. | Proposition |
| Answer» E. | |
| 300. |
To draw general conclusions from well known facts is called |
| A. | Induction |
| B. | Deduction |
| C. | Proposition |
| D. | Knowledge |
| Answer» B. Deduction | |