Practice Questions

Q58.Negation of the statement: √5 is an integer or 5 is irrational is: (1) √5 is not an integer 5 is not irrational (2) √5 is not an integer and 5 is not irrational (3) √5 is irrational or 5 is an integer (4) √5 is an integer and 5 irrational JEE Main 2020 (09 Jan Shift 1) JEE Main Previous Year Paper

Q58.Consider the statement: "For an integer n, if n3 −1 is even, then n is odd". The contrapositive statement of this statement is: (1) For an integer n, if n is even, then n3 −1 is odd. (2) For an integer n, if n3 −1 is not even, then n is not odd. (3) For an integer n, if n is even, then n3 −1 is even.(4) For an integer n , if n is odd, then n3 −1 is even.

Q58.For two statements p and q , the logical statement (p →q) ∧(q →~p) is equivalent to (1) p (2) q (3) ~p (4) ~q JEE Main 2020 (07 Jan Shift 1) JEE Main Previous Year Paper Q59. ⎡ 1 1 1 ⎤ Let α be a root of the equation x2 + x + 1 = 0 and the matrix A = 1 1 α α2 , then the matrix A31 is √3 ⎣ 1 α2 α4 ⎦ equal to (1) A3 (2) I3 (3) A2 (4) A

Q59.If p →(p ∧~q) is false, then the truth values of p and q are respectively (1) F, F (2) T, F (3) T, T (4) F, T JEE Main 2020 (09 Jan Shift 2) JEE Main Previous Year Paper

Q59.The negation of the Boolean expression p ∨(~p ∧q) is equivalent to : (1) p ∧~q (2) ~p ∧~q (3) ~p ∨~q (4) ~p ∨q n n

Q59.Let p, q, r be three statements such that the truth value of (p ∧q) →(~q ∨r) is F . Then the truth values of p, q, r are respectively : (1) T, T, F (2) T, T, T (3) T, F, T (4) F, T, F

Q59.The proposition p →~(p ∧~q) is equivalent to : (1) q (2) (~p) ∨q (3) (~p) ∧q (4) (~p) ∨(~q)

Q61.Let A = [aij] and B = [bij] be two 3 × 3 real matrices such that bij = (3)(i+j−2)aij , where i, j = 1,2, 3 . If the determinant of B is 81 , then determinant of A is (1) 1 (2) 3 3 (3) 1 (4) 1 81 9

Q62.Let S , be the set of all functions f : [0, 1] →R, which are continuous on [0, 1], and differentiable on (0, 1). Then for every f in S , there exists c ∈(0, 1), depending on f , such that. f '(c) (1) |f(c) −f(1)| < (1 −c) f '(c) (2) f(1)−f(c)1−c = (3) |f(c) + f(1)| < (1 + c) f '(c) (4) |f(c) −f(1)| < f '(c)

Q62.A survey shows that 63% of the people in a city read newspaper A whereas 76% read news paper B. If x% of the people read both the newspapers, then a possible value of x can be: (1) 29 (2) 37 (3) 65 (4) 55 where i = √−1, then which one of the following is not (θ = 24π ) and A5 = [ ac bd ],

Q63.The value of c, in the Lagrange’s mean value theorem for the function f(x) = x3 −4x2 + 8x + 11, when x ∈[0,1], is (1) 4−√5 (2) 4−√7 3 3 (3) 2 (4) √7−2 3 3

Q64.Let f and g be differentiable functions on R such that fog is the identity function. If for some a, b ∈R, g'(a) = 5 and g(a) = b, then f '(b) is equal to: (1) 1 (2) 1 5 (3) 5 (4) 52

Q66.The area (in sq. units) of the region {(x, y) ∈R2 : x2 ≤y ≤3 −2x}, is. (1) 32 (2) 34 3 3 (3) 29 (4) 31 3 3 JEE Main 2020 (08 Jan Shift 2) JEE Main Previous Year Paper

Q67.The area (in sq. units) of the region enclosed by the curves y = x2 −1 and y = 1 −x2 is equal to: (1) 4 (2) 8 3 3 (3) 7 (4) 16 2 3 x cosec x is the solution of the differential equation, dxdy + p(x)y = −2π cosec x, 0 < x < 2π ,

Q70.A random variable X has the following probability distribution: X : 1 2 3 4 5 P(X) : k2 2k k 2k 5k2 Then, P(X > 2) is equal to: (1) 7 (2) 1 12 36 (3) 1 (4) 23 6 36

Q70.Let A and B be two independent events such that P(A) = 13 and P(B) = 16 . Then, which of the following is true? (1) P( BA ) = 32 (2) P( B'A ) = 13 = 14 (3) P( B'A' ) = 13 (4) P( (A∪B) A )

Q72.Set A has melements and set B has nelements. If the total number of subsets of A is 112 more than the total number of subsets of B, then the value of m ⋅n is___.

Q72.Let X = {n ∈N : 1 ≤n ≤50}. If A = {n ∈X : n is a multiple of 2} and B = {n ∈X : n is a multiple of 7}, then the number of elements in the smallest subset of X , containing both A and B , is.

Q73.The sum ∑20k=1(1 + 2 + 3 + … + k) is ___________.

Q61.The value of λ such that sum of the squares of the roots of the quadratic equation, x2 + (3 −λ) x + 2 = λ has the least value is: (1) 2 (2) 49 (3) 15 (4) 1 8

Q62.The equation |𝑧- 𝑖| = | 𝑧- 1 | , 𝑖= √-1, represents: 1 (1) a circle of radius (2) a circle of radius 1 2 (3) the line through the origin with slope 1 (4) the line through the origin with slope -1 JEE Main 2019 (12 Apr Shift 1) JEE Main Previous Year Paper

Q62.Let z = 5 5 + . If R(z) and I(z) respectively denote the real and imaginary parts of z, ( √32 + 2i ) ( √32 −i2 ) then (1) I(z) = 0 (2) R(z) < 0 and I(z) > 0 (3) R(z) > 0 and I(z) > 0 (4) R(z) = −3

Q62.Let z1 and z2 be any two non-zero complex numbers such that 3|z1| = 4|z2|. If z = 3z1 + 2z2 then maximum 2z2 3z1 value of |z| is Note: In actual paper value of |z| was asked. Hence, none of the options given were correct. So we have modified the question as well as options. (1) 7 (2) 9 2 2 (3) 5 (4) 1 2 2 √172

Q63.Let a1, a2, … , a10 be a G.P. If a1a3 = 25, then a5a9 equals : (1) 54 (2) 4 (52) (3) 53 (4) 2 (52)

Q63.If 19 th term of a non-zero A.P. is zero, then its (49th term): (29th term) is: (1) 4: 1 (2) 1: 3 (3) 3: 1 (4) 2: 1 2 n where q is a real number + + … +