Practice Questions

Q71.The number of words, with or without meaning, that can be formed by taking 4 letters at a time from the letters of the word 'SYLLABUS' such that two letters are distinct and two letters are alike, is

Q71.The coefficient of x4 in the expansion of (1 + x + x2 + x3)6 in powers of x, is … . .

Q71.The number of terms common to the two A.P.’s 3, 7, 11, … , 407 and 2, 9, 16, … , 709 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.

Q72.Let A = {a, b, c} and B = {1, 2, 3, 4}. Then the number of elements in the set C = {f : A →B ∣2 ∈f(A) and f is not one-one } is …

Q72.If Cr ≡25Cr and C0 + 5 ∙C1 + 9 ∙C2 + … + (101) ∙C25 = 225 ∙k, then k is equal to ____________.

Q72.The sum, ∑7n=1 n(n+1)(2n+1)4 , is equal to √2sinα

Q72.An urn contains 5 red marbles, 4 black marbles and 3 white marbles. Then, the number of ways in which 4 marbles can be drawn so that at the most three of them are red is ___________.

Q72.Let PQ be a diameter of the circle x2 + y2 = 9. If α and β are the lengths of the perpendiculars from P and Q on the straight line, x + y = 2 respectively, then the maximum value of αβ is _______

Q72.Consider the data on x taking the values 0, 2, 4, 8, . . . . . , 2n with frequencies nC0, nC1, nC2, . . . . , nCn respectively. If the mean of this data is 728 , then n is equal to ....... . 2n

Q72.If m arithmetic means (A.Ms) and three geometric means (G.Ms) are inserted between 3 and 243 such that 4th A.M. is equal to 2nd G.M., then m is equal to:

Q72.The natural number m, for which the coefficient of x in the binomial expansion of (xm + x21 ) 22 is 1540, is

Q72.Let A(1, 0), B(6, 2) and C( 32 , 6) be the vertices of a triangle ABC. If P is a point inside the triangle ABC such that the triangles APC, APB and BPC have equal areas, then the length of the line segment PQ, where Q is the point (−76 , −13 ), is

Q72.If the system of equations x −2 y + 3z = 9 2x + y + z = b x −7y + az = 24, has infinitely many solutions, then a −b is equal to ______

Q72.If the variance of the terms in an increasing A. P. b1b2, b3, … … . . , b11 is 90 then the common difference of this A. P. is

Q72.The value of 0. 16 log2.5( 1

Q72.The coefficient of x4 in the expansion of (1 + x + x2) 10 is ________

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.The numbers of integral values of k for which the line, 3x + 4y = k intersects the circle, x2 + y2 −2x −4y + 4 = 0 at two distinct points is.... x+x2+x3+...+xn−n

Q73.If the variance of the following frequency distribution: JEE Main 2020 (04 Sep Shift 2) JEE Main Previous Year Paper Class: 10 −20 20 −30 30 −40 Frequency: 2 x 2 is 50, then x is equal to _______

Q73.The diameter of the circle, whose Centre lies on the line x + y = 2 in the first quadrant and which touches both the lines x = 3 and y = 2 is x2 x2 x2 x2 lim −cos = 2−k then the value of k is 2 −cos 4 + cos 2 cos x8 1 (1 4 )}

Q73.Suppose a differentiable function f(x) satisfies the identity f(x + y) = f(x) + f(y) + xy2 + x2y, for all real x and y. If lim f(x)x = 1, then f ′(3) is equal to : x→0

Q73. sin( x1 ) + 5x2 , x < 0 ⎧ x5 Let f : R →R be defined as f(x) = 0 , x = 0 . The value of λ for which f ′′(0) exists, ⎨ 1 ) + λx2 , x > 0 ⎩x5 cos( x is___.

Q73. lim 3x+33−x−12 is equal to x→2 3−x2 −31−x

Q73.If y = ∑6k=1 k cos−1{ 53 cos kx −45 sin kx} then dxdy at x = 0 is