Practice Questions

Q67.Consider the following statements: A: Rishi is a judge. B: Rishi is honest. C : Rishi is not arrogant. The negation of the statement "if Rishi is a judge and he is not arrogant, then he is honest" is (1) B →(A ∨C) (2) (~B) ∧(A ∧C) (3) B →((~A) ∨(~C)) (4) B →(A ∧C)

Q67.Which of the following statements is a tautology? (1) ~𝑝∨𝑞⇒𝑝 (2) 𝑝⇒~𝑝∨𝑞 (3) ~𝑝∨𝑞⇒𝑞 (4) 𝑞⇒~𝑝∨𝑞

Q68.The statement 𝑝⇒𝑞∨𝑝⇒𝑟 is NOT equivalent to: (1) 𝑝∧~𝑟⇒𝑞 (2) ~𝑞⇒~𝑟∨𝑝 (3) 𝑝⇒𝑞∨𝑟 (4) 𝑝∧~𝑞⇒𝑟

Q68. (p ∧r) ⇔(p ∧(~q)) is equivalent to (~p) when r is (1) p (2) ~p (3) q (4) ~q

Q68.If the truth value of the statement (P ∧(~R)) →((~R) ∧Q) is F , then the truth value of which of the following is F ? (1) P ∨Q →~R (2) R ∨Q →~P (3) ~(P ∨Q) →~R (4) ~(R ∨Q) →~P

Q68.Let f(x) = ax2 + bx + c be such that f(1) = 3, f(−2) = λ and f(3) = 4. If f(0) + f(1) + f(−2) + f(3) = 14 , then λ is equal to JEE Main 2022 (28 Jul Shift 2) JEE Main Previous Year Paper (1) −4 (2) 132 (3) 23 (4) 4 2

Q69.Negation of the Boolean statement (p ∨q) ⇒((~r) ∨p) is equivalent to: (1) p ∧(~q) ∧r (2) (~p) ∧(~q) ∧r (3) (~p) ∧q ∧r (4) p ∧q ∧(~r)

Q69.Which of the following matrices can NOT be obtained from the matrix -1 2 by a single elementary row 1 -1 operation? (1) 0 1 (2) 1 -1 1 -1 -1 2 (3) -1 2 (4) -1 2 -2 7 -1 3

Q69.The mean and variance of the data 4, 5, 6, 6, 7, 8, x, y where x < y are 6 and 49 respectively. Then x4 + y2 is equal to (1) 320 (2) 420 (3) 162 (4) 674

Q72.The value of tan-1cos15𝜋 is equal to sin𝜋 4 𝜋 𝜋 (1) - (2) - 4 8 (3) -5𝜋 (4) -4𝜋 12 9

Q74.The value of the integral ∫2−2 (ex|x|+1)x3+x (1) 5e2 (2) 3e−2 (3) 4 (4) 6 dy ax−by+a

Q75.The odd natural number a, such that the area of the region bounded by y = 1, y = 3, x = 0, x = ya is 3643 , equal to: (1) 3 (2) 5 (3) 7 (4) 9

Q80.A random variable X has the following probability distribution: X 0 1 2 3 4 P(X) k 2k 4k 6k 8k The value of P( 1<x<4x≤2 )is equal to (1) 4 (2) 2 7 3 (3) 3 (4) 4 7 5 ¯

Q81.Let S = {z ∈C : z2 + z = 0}. Then ∑z∈S(Re (z)+ Im (z)) is equal to _______.

Q82.A class contains b boys and g girls. If the number of ways of selecting 3 boys and 2 girls from the class is 168 , then b + 3g is equal to

Q90.The sum and product of the mean and variance of a binomial distribution are 82 . 5 and 1350 respectively. They the number of trials in the binomial distribution is JEE Main 2022 (29 Jul Shift 2) JEE Main Previous Year Paper

Q61.Let n denote the number of solutions of the equation z2 + 3z = 0, where z is a complex number. Then the value of ∑∞k=0 nk1 is equal to (1) 1 (2) 34 (3) 32 (4) 2

Q62.If α, β ∈R are such that 1 −2i (here i2 = −1) is a root of z2 + αz + β = 0, then (α −β) is equal to: (1) −7 (2) 7 (3) −3 (4) 3

Q63.The value of ∑6r=0(6Cr ⋅6C6−r) is equal to : (1) 1124 (2) 1324 (3) 1024 (4) 924

Q64.The negation of the statement ~p ∧(p ∨q) is: (1) ~p ∨q (2) ~p ∧q (3) p ∨~q (4) p ∧~q

Q64.If two tangents drawn from a point P to the parabola y2 = 16(x −3) are at right angles, then the locus of point P is: (1) x + 4 = 0 (2) x + 2 = 0 (3) x + 3 = 0 (4) x + 1 = 0 = b, then the ordered pair (a, b) is: lim −x + 1 −ax)

Q65.The length of the latus rectum of a parabola, whose vertex and focus are on the positive x-axis at a distance R and S(> R) respectively from the origin, is : (1) 2( S −R) (2) 2(S + R) (3) 4(S −R) (4) 4(S + R)

Q65.If nP r = nP r+1 and nCr = nCr−1, then the value of r is equal to: (1) 1 (2) 4 (3) 2 (4) 3

Q66.Consider the following three statements: (A) If 3 + 3 = 7 then 4 + 3 = 8 (B) If 5 + 3 = 8 then earth is flat. (C) If both (A) and (B) are true then 5 + 6 = 17. Then, which of the following statements is correct? (1) (A) is false, but (B) and (C) are true (2) (A) and (C) are true while (B) is false (3) (A) is true while (B) and (C) are false (4) (A) and (B) are false while (C) is true

Q66.The Boolean expression (p ∧~q) ⇒(q ∨~p) is equivalent to: (1) q ⇒p (2) p ⇒q (3) ~q ⇒p (4) p ⇒~q