Practice Questions

Q82.An arithmetic progression is written in the following way The sum of all the terms of the 10th row is_______

Q82.If ( α+11 + α+21 + … … + α+10121 ) −( 2⋅11 + 4⋅31 + 6⋅51 + … . . + 2024⋅20231 ) = 20241 , then α is equal to________

Q82.If 8 = 3 + 14 (3 + p) + 421 (3 + 2p) + 431 (3 + 3p) + … ∞, then the value of p is JEE Main 2024 (27 Jan Shift 1) JEE Main Previous Year Paper

Q82.Let 3, 7, 11, 15, . . , 403 and 2, 5, 8, 11, . . . , 404 be two arithmetic progressions. Then the sum, of the common terms in them, is equal to_________ 1 6

Q82.Let the coefficient of 𝑥𝑟 in the expansion of 𝑥+ 3𝑛−1 + 𝑥+ 3𝑛−2𝑥+ 2 + 𝑥+ 3𝑛−3𝑥+ 22 + . ... + 𝑥+ 2𝑛−1 be 𝛼𝑟. If ∑𝑟=𝑛 0 𝛼𝑟= 𝛽𝑛−𝛾𝑛, 𝛽, 𝛾∈𝑁, then the value of 𝛽2 + 𝛾2 equals _______.

Q82.In an examination of Mathematics paper, there are 20 questions of equal marks and the question paper is divided into three sections : A, B and C. A student is required to attempt total 15 questions taking at least 4 questions from each section. If section A has 8 questions, section B has 6 questions and section C has 6 questions, then the total number of ways a student can select 15 questions is _________. 6 𝑛

Q82.Let the length of the focal chord PQ of the parabola y2 = 12x be 15 units. If the distance of PQ from the origin is p, then 10p2 is equal to _______ JEE Main 2024 (04 Apr Shift 1) JEE Main Previous Year Paper

Q82.If 1 + √3−√2 a + loge ( ab ), where a and b are + 49−20√6180 + … upto ∞= 2 + 2√3 + 5−2√618 + 9√3−11√236√3 (√b 1) integers with gcd(a, b) = 1, then 11a + 18 b is equal to ______

Q82.The total number of words (with or without meaning) that can be formed out of the letters of the word "DISTRIBUTION" taken four at a time, is equal to ______. 3 3 1 5

Q82.If three successive terms of a G.P. with common ratio 𝑟𝑟> 1 are the length of the sides of a triangle and 𝑟 denotes the greatest integer less than or equal to r, then 3𝑟+ −𝑟 is equal to: 2𝜋

Q82.All the letters of the word GTWENTY are written in all possible ways with or without meaning and these words are written as in a dictionary. The serial number of the word GTWENTY IS 11C2 11C9

Q82.Let α, β be the roots of the equation x2 −√6x + 3 = 0 such that Im (α) >Im (β). Let a, b be integers not + i = √−1. Then n + a + b is divisible by 3 and n be a natural number such that α99β + α98 = 3n(a ib), equal to ___________.

Q82.If S(x) = (1 + x) + 2(1 + x)2 + 3(1 + x)3 + ⋯+ 60(1 + x)60, x ≠0, and (60)2 S(60) = a(b)b + b, where a, b ∈N , then (a + b) equal to ______

Q82.Let the positive integers be written in the form : If the kth row contains exactly k numbers for every natural number k, then the row in which the number 5310 will be, is _______ + n+11 . If 140 < 2αβ < 281, then the value of n is

Q83.Let 𝐴−2, −1, 𝐵1, 0, 𝐶𝛼, 𝛽 and 𝐷𝛾, 𝛿 be the vertices of a parallelogram 𝐴𝐵𝐶𝐷. If the point 𝐶 lies on 2𝑥−𝑦= 5 and the point 𝐷 lies on 3𝑥−2𝑦= 6, then the value of 𝛼+ 𝛽+ 𝛾+ 𝛿 is equal to ______.

Q83.Number of integral terms in the expansion of 1 1 824 is equal to ______. 2 ) + 11( )} {7(

Q83.Let A, B and C be three points on the parabola y2 = 6x and let the line segment AB meet the line L through C parallel to the x-axis at the point D. Let M and N respectively be the feet of the perpendiculars from A and AM⋅BN 2 B on L. Then ( CD ) is equal to _________

Q83.If the sum of squares of all real values of α, for which the lines 2x - y + 3 = 0, 6x + 3y + 1 = 0 and αx + 2y - 2 = 0 do not form a triangle is p, then the greatest integer less than or equal to p is ________.

Q83.The number of solutions of sin2 x + (2 + 2x −x2) sin x −3(x −1)2 = 0, where −π ≤x ≤π, is________

Q83.If the constant term in the expansion of (1 + 2x −3x3)( 32 x2 − 3x1 ) 9

Q83.In the expansion of 1 + 𝑥1 −𝑥21 + + , 𝑥≠0, the sum of the coefficient of 𝑥3 and 𝑥-13 is equal to 𝑥+ 𝑥2 𝑥3 ______

Q83.If the coefficient of 𝑥30 in the expansion of 1 + 1 + 𝑥271 −𝑥38; 𝑥≠0 is 𝛼, then 𝛼 equals _________. 𝑥 JEE Main 2024 (01 Feb Shift 1) JEE Main Previous Year Paper

Q83.If the second, third and fourth terms in the expansion of (x + y)n are 135,30 and 103 , respectively, then 6 (n3 + x2 + y) is equal to _______

Q83.Let 𝑆𝑛 be the sum to n-terms of an arithmetic progression 3, 7, 11, … … , if 40 < 𝑛( 𝑛+ 1 ) ∑𝑘= 1 𝑆𝑘< 42, then 𝑛 equals ____________. 𝑛C𝑘 𝑛C𝑘+ 1 𝑛 𝑛C𝑘 2

Q83.Let a ray of light passing through the point (3, 10) reflects on the line 2x + y = 6 and the reflected ray passes through the point (7, 2). If the equation of the incident ray is ax + by + 1 = 0, then a2 + b2 + 3ab is equal to_________ , on the positive x-axis. Let C be the circle with its centre at