Practice Questions

Q60.Let θ = and A = . If B = A + A4 , then det (B) : 5 [−sinθcosθ cosθsinθ ] (1) is one (2) lies in (2, 3) (3) is zero (4) lies in (1, 2)

Q60.The mean and variance of 7 observations are 8 and 16, respectively. If five observations are 2, 4, 10, 12, 14 then the absolute difference of the remaining two observations is : (1) 1 (2) 4 (3) 2 (4) 3 JEE Main 2020 (05 Sep Shift 1) JEE Main Previous Year Paper

Q60.If the system of linear equations 2x + 2ay + az = 0 2x + 3by + bz = 0 2x + 4cy + cz = 0, where a, b, c ∈R are non-zero and distinct; has a non-zero solution, then (1) a 1 , 1b , 1c are in A. P. (2) a, b, c are in G. P. (3) a + b + c = 0 (4) a, b, c are in A. P.

Q60.Let xi(1 ≤i ≤10) be ten observation of a random variable X . If ∑10i=1(xi −p) = 3 and ∑10i=1 (xi −p)2 = 9 where 0 ≠p ∈R, then the standard deviation of these observations is: (1) 4 (2) 5 √35 (3) 9 (4) 7 10 10

Q60.Let A be a 2 × 2 real matrix with entries from {0, 1} and |A| ≠0 . Consider the following two statements; (P) If A ≠l2 , then |A| = −1 (Q) If |A| = 1 , then tr(A) = 2 Where l2 denotes 2 × 2 identity matrix and tr(A) denotes the sum of the diagonal entries of A . Then (1) (P) is false and (Q) is true (2) Both (P) and (Q) are false (3) (P) is true and (Q) is false (4) Both (P) and (Q) are true

Q60.If Σ −a) = n and Σ −a)2 = na, (n, a > 1), then the standard deviation of n observations i=1(xi i=1(xi x1, x2, … , xn is JEE Main 2020 (06 Sep Shift 1) JEE Main Previous Year Paper (1) a −1 (2) n√(a −1) (3) √n(a −1) (4) √(a −1)

Q60.The following system of linear equations 7x + 6y −2z = 0 3x + 4y + 2z = 0 x −2y −6z = 0, has (1) infinitely many solutions, (x, y, z) satisfying (2) no solution y = 2z (3) infinitely many solutions, (x, y, z) satisfying (4) only the trivial solution x = 2z

Q60.The statement (p →(q →p)) →(p →(p ∨q)) is : (1) equivalent to (p ∧q) ∨(~q) (2) a contradiction (3) equivalent to (p ∨q) ∧(~p) (4) a tautology

Q60. lim (tan( π4 + x))1/x is equal to x→0 (1) e (2) 2 (3) 1 (4) e2

Q60.The system of linear equations λx + 2y + 2z = 5 2λx + 3y + 5z = 8 4x + λy + 6z = 10 has (1) no solution when λ = 8 (2) a unique solution when λ = −8 (3) no solution when λ = 2 (4) infinitely many solutions when λ = 2

Q60.Let A, B, C and D be four non-empty sets. The contrapositive statement of “If A ⊆B and B ⊆D , then A ⊆C ” is (1) If A ⊈C , then A ⊆B and B ⊆D (2) If A ⊆C , then B ⊂A and D ⊂B (3) If A ⊈C , then A ⊈B and B ⊆D (4) If A ⊈C , then A ⊈B or B ⊈D

Q60.For the frequency distribution: Variate (x) : x1, x2, x3, … , x15 Frequency (f) : f1, f2, f3, … , f15 where 0 < x1 < x2 < x3 < … < x15 = 10 and ∑15i=1 fi > 0, the standard deviation cannot be (1) 4 (2) 1 (3) 6 (4) 2

Q60.The mean and variance of 8 observations are 10 and 13. 5, respectively. If 6 of these observations are 5, 7, 10, 12, 14, 15, then the absolute difference of the remaining two observations is : (1) 9 (2) 5 (3) 3 (4) 7

Q60.Let 50∪ = ∪n = T , where each Xi contains 10 elements and each Yi contains 5 elements. If each element i=1Xi i=1Yi of the set T is an element of exactly 20 of sets Xi 's and exactly 6 of sets Yi 's then n is equal to : (1) 15 (2) 50 (3) 45 (4) 30

Q61.Let S be the set of all λ ∈R for which the system of linear equations 2x −y + 2z = 2 x −2y + λz = −4 x + λy + z = 4 has no solution. Then the set S (1) Contains more than two elements (2) Is an empty set (3) Is a singleton (4) Contains exactly two elements

Q61.If g(x) = x2 + x −1 and (gof)(x) = 4x2 −10x + 5, then f( 54 ) is equal to (1) 3 2 (2) −12 (3) 2 1 (4) −32 tanα+cotα 1 3π dy 5π + sin2α , α ∈( 4 , π), then dα at α = 6 is 1+tan2α )

Q61.If for some α and β in R , the intersection of the following three planes x + 4y −2z = 1 x + 7y −5z = β x + 5y + αz = 5 is a line in R3 , then α + β is equal to: (1) 0 (2) 10 (3) 2 (4) −10 Q62. ; x < 0 ⎧ sin(a+2)x+sinxx If f(x) = is continuous at x = 0 , then a + 2b is equal to: ⎨ b ; x = 0 ; x > 0 ⎩ (x+3x2)1/3−x1/3x1/3 (1) 1 (2) −1 (3) 0 (4) −2

Q61.Let R1 and R2 be two relations defined as follows : R1 = {(a, b) ∈R2 : a2 + b2 ∈Q} and R2 = {(a, b) ∈R2 : a2 + b2 ∉Q} , where Q is the set of all rational numbers, then (1) R1 is transitive but R2 is not transitive. (2) R2 is transitive but R1 is not transitive. (3) Neither R1 nor R2 is transitive. (4) R1 and R2 are both transitive. Q62. ⎡ 2 −1 1 ⎤ Let A be a 3 × 3 matrix such that adj A = −1 0 2 and B =adj (adjA). If |A| = λ and ⎣ 1 −2 −1 ⎦ (B−1) ⊤= μ, then the ordered pair (|λ|, μ) is equal to (1) (3, 811 ) (2) (9, 91 ) (3) (3, 81) (4) (9, 811 )

Q61. x −2 2x −3 3x −4 If Δ = 2x −3 3x −4 4x −5 = Ax3 + Bx2 + Cx + D , then B + C is equal to : 3x −5 5x −8 10x −17 (1) −1 (2) 1 (3) −3 (4) 9 Q62. 2π −(sin−1 45 + sin−1 135 + sin−1 1665 ) is equal to : (1) π (2) 5π 2 4 (3) 3π (4) 7π 2 4

Q61.If the system of equations x + y + z = 2 2 x + 4 y −z = 6 3x + 2y + λz = μ has infinitely many solutions, then : (1) λ + 2μ = 14 (2) 2λ −μ = 5 (3) λ −2μ = −5 (4) 2λ + μ = 14

Q61.Let a −2b + c = 1. x + a x + 2 x + 1 If f(x) = x + b x + 3 x + 2 , then: x + c x + 4 x + 3 (1) f(−50) = 501 (2) f(−50) = −1 (3) f(50) = −501 (4) f(50) = 1 4 ] = A. Then the function, f(x) = [x2] sin(πx) is x

Q61. cos2 x 1 + sin2 x sin 2x Let m and M be respectively the minimum and maximum value values of 1 + cos2 x sin2 x sin 2x cos2 x sin2 x 1 + sin 2x Then the ordered pair (m, M) is equal to: (1) (3, 3) (2) (−3, −1) (3) (4, 1) (4) (1, 3)

Q61.For which of the following ordered pairs (μ, δ), the system of linear equations x + 2y + 3z = 1 3x + 4y + 5z = μ 4x + 4y + 4z = δ is inconsistent? (1) (4, 3) (2) (4, 6) (3) (1, 0) (4) (3, 4)

Q61.If the mean and the standard deviation of the data 3, 5, 7, a, b are 5and 2 respectively, then a and b are the roots of the equation: (1) x2 −10x + 18 = 0 (2) 2x2 −20x + 19 = 0 (3) x2 −10x + 19 = 0 (4) x2 −20x + 18 = 0

Q61.For a suitably chosen real constant a, let a function, f : R −{−a} →R be defined by f(x) = a+xa−x . Further supposed that for any real number x ≠−a,and f(x) ≠−a, (fof)(x) = x. Then f(−12 ) is equal to : (1) 3 1 (2) −13 (3) −3 (4) 3