Practice Questions

Q71.The number of words (with or without meaning) that can be formed from all the letters of the word ′′LETTER′′ in which vowels never come together is.....

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

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 number of 4 letter words (with or without meaning) that can be formed from the eleven letters of the word EXAMINATION is

Q71.If the letters of the word ′ MOTHER′ be permuted and all the words so formed (with or without meaning) be listed as in a dictionary, then the position of the word ′ MOTHER′ is.....

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

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 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 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

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

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

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

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.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.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 _______

Q73.If the lines x + y = a and x −y = b touch the curve y = x2 −3x + 2 at the points where the curve intersects the x−axis, then ab is equal to … → → →

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

Q73.If the system of linear equations, x + y + z = 6 x + 2y + 3z = 10 3x + 2y + λz = μ has more than two solutions, then μ −λ2 , is equal to. JEE Main 2020 (07 Jan Shift 2) JEE Main Previous Year Paper 1 loge( 1−2x1+3x ), when x ≠0 , is continuous, then k is by f(x) = x

Q73.If for x ≥0, y = y(x) is the solution of the differential equation, (x + 1)dy = y(2) = 0 then y(3) is equal to ________ ((x + 1)2 + y −3)dx, →

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.If the curves, x2 −6x + y2 + 8 = 0 and x2 −8y + y2 + 16 −k = 0, (k > 0) touch each other at a point, then the largest value of k is ____________. → → → → π If →a

Q73.If the line, 2 x −y + 3 = 0 is at a distance 1 and 2 from the lines 4x −2y + α = 0 and 6x −3y + β = 0 √5 √5 respectively, then the sum of all possible values of α and β is ____________.

Q73.The sum of distinct values of λ for which the system of equations : (λ −1) x + (3λ + 1) y + 2λz = 0 (λ −1) x + (4λ −2) y + (λ + 3) z = 0 2x + (3λ + 1) y + 3 (λ −1) z = 0 , Has non-zero solutions, is ....... .