Practice Questions

Q74.The minimum number of elements that must be added to relation R = {(a, b), (b, c), (b, d)} on the set {a, b, c, d}, so that it is an equivalence relation is

Q74.Let the mean and variance of 12 observations be 29 and 4 respectively. Later on, it was observed that two observations were considered as 9 and 10 instead of 7 and 14 respectively. If the correct variance is mn , where m and n are coprime, then m + n are coprime, then m + n is equal to (1) 315 (2) 316 (3) 314 (4) 317

Q74.If the mean and variance of the frequency distribution xi 2 4 6 8 10 12 14 16 fi 4 4 α 15 8 β 4 5 are 9 and 15. 08 respectively, then the value of α2 + β2 −αβ is _____.

Q74.Let the mean and variance of 8 numbers x, y, 10, 12, 6, 12, 4, 8 be 9 and 9. 25 respectively. If x > y, then 3x −2y is equal to _______

Q75.Let A = ⌊aˆiˆj⌋⋅aij prime number p ∈(2, 13) is _____ .

Q75.If S = {x ∈R sin−1( √x2+2x+2x+1 ) −sin−1( √x2+1x ) ∑x∈S(sin((x2 + x + 5) π2 ) −cos((x2 + x + 5)π)) is equal to _________.

Q76.If the sum of all the solutions of + cot−1( 1−x22x ) tan−1( 1−x22x ) = π3 , −1 < x < 1, x ≠0, is α − √34 , then α is equal to _____ .

Q76.Let A = {0, 3, 4, 6, 7, 8, 9, 10} and R be the relation defined on A such that R{(x, y) ∈A × A : x −y is odd positive integer or x −y = 2}. The minimum number of elements that must be added to the relation R, so that it is a symmetric relation, is equal to _________ Q77. ⎡2 1 0 ⎤ Let 1 2 −1 . If |adj(adj(adj2A))| = (16)n , then n is equal to ⎣0 −1 2 ⎦ (1) 8 (2) 10 (3) 9 (4) 12 Q78. ⎡ √32 12 ⎤ 1 1 T a b Let P = , A = and Q = PAP . If P TQ2007 P = then 2a + b −3c −4d is equal √3 [0 1] [ c d ] ⎣−12 2 ⎦ to (1) 2004 (2) 2005 (3) 2007 (4) 2006

Q76.Let A be a n × n matrix such that |A| = 2 . If the determinant of the matrix Adj (2. Adj (2 A−1)) is 284 , then n is equal to _____ . Q77. ⎛ 2 10 8⎞ If a point P(α, β, γ) satisfying (α β γ ) 9 3 8 = (0 0 0) lies on the plane 2x + 4y + 3z = 5, then ⎝ 8 4 8⎠ 6α + 9β + 7γ is equal to (1) 5 (2) −1 4 (3) 11 (4) 115

Q78.Let A = {1, 2, 3, 5, 8, 9} . Then the number of possible functions f : A →A such that f(m ⋅n) = f(m) ⋅f(n) for every m, n ∈A with m ⋅n ∈A is equal to ax + bx2, a ≠2b have a common extreme point,

Q78.Let f : R →R be a differentiable function that satisfies the relation f(x + y) = f(x) + f(y) −1, ∀ x, y ∈R. If f ′(0) = 2 , then |f(−2)| is equal to

Q78.Let [x] be the greatest integer ≤x . Then the number of points in the interval (–2, 1) where the function f(x) = |[x]| + √x −[x] is discontinuous, is _____. sin2 x √3e is , x ∈(0, π2 ), is ke , then ( ke ) 8 + k8e5 + k8 sin x )

Q78.Consider a function f : N →R, satisfying f(1) + 2f(2) + 3f(3) + … + xf(x) = x(x + 1)f(x) ; x ≥2 with f(1) = 1 . Then f(2022)1 + f(2028)1 is equal to JEE Main 2023 (29 Jan Shift 2) JEE Main Previous Year Paper (1) 8200 (2) 8000 (3) 8400 (4) 8100

Q78.For some a, b, c ∈N, let f(x) = ax −3 and g(x) = xb + c, x ∈R. If (fog)−1 (x) = ( 1 2 ) 3 , then (f ∘g)(ac) + (g ∘f)(b) is equal to _____ .

Q78.If domain of the function loge( 6x2+5x+12x−1 ) cos−1( 2x2−3x+43x−5 ) is is equal to JEE Main 2023 (08 Apr Shift 2) JEE Main Previous Year Paper

Q79.Let a curve y = f(x), x ∈(0, ∞) pass through the points P(1, 32 ) and Q(a, 12 ). If the tangent at any point R(b, f(b)) to the given curve cuts the y-axis at the point S(0, c) such that bc = 3, then (PQ)2 is equal to JEE Main 2023 (06 Apr Shift 2) JEE Main Previous Year Paper _____.

Q79.Let A = {1, 2, 3, 4, 5} and B = {1, 2, 3, 4, 5, 6} . Then the number of functions f : A →B satisfying f(1) + f(2) = f(4) −1 is equal to........ .Then and g(x) =

Q79.Suppose f is a function satisfying f(x + y) = f(x) + f(y) for all x, y ∈N and f(1) = 51 . If ∑mn=1 n(n+1)(n+2)f(n) = 121 then m is equal to ______.

Q79.Let y(x) = (1 + x)(1 + x2)(1 + x4)(1 + x8)(1 + x16) . Then y′ −y′′ at x = −1 is equal to (1) 976 (2) 464 (3) 496 (4) 944

Q79.Let R = {a, b, c, d, e} and S = {1, 2, 3, 4} . Total number of onto functions f : R →S such that f(a) ≠1, is equal to ________.

Q80.Let I(x) = ∫√x+7x dx and I(9) = 12 + 7 loge 7. If I(1) = α + 7 loge(1 2√2), then α4 is equal to _____. dx = 3000k , then k is equal to _____.

Q80.Let k and m be positive real numbers such that the function f(x) = {3x2mx2+ k√x+ k2,+ 1, 0 <x ≥1x < 1 8f ′(8) is differentiable for all x > 0 . Then 1 is equal to f ′( 8 ) x dx is equal to

Q80.If aα is the greatest term in the sequence an = n3 , n = 1, 2, 3. . . . , then α is equal to ______ n4+147

Q80.The number of points, where the curve y = x5 −20x3 + 50x + 2 crosses the x-axis, is _____. x dx is equal to

Q80.If ∫√sec 2x −1dx = α loge cos 2x + β + √cos 2x(1 ______.