Practice Questions

Q21.If →a and →b makes an angle cos−1 ( 9 ) with each other, then |→a + →b| = √2|→a −→b| value of n is ____

Q81.Let α, β ∈ be roots of equation x2 −70x + λ = 0, where λ2 , λ3 ∉ . If λ assumes the minimum possible value, (√α−1+√β−1)(λ+35) then is equal to : |α−β|

Q81.The lines 𝐿1, 𝐿2, . .. , 𝐿20 are distinct. For 𝑛= 1, 2, 3, . .. , 10 all the lines 𝐿2𝑛−1 are parallel to each other and all the lines 𝐿2𝑛 pass through a given point 𝑃. The maximum number of points of intersection of pairs of lines from the set 𝐿1, 𝐿2, . .. , 𝐿20 is equal to:

Q81.Let α, β be roots of x2 + √2x −8 = 0. If Un = αn + βn , then U10+√2U9 is equal to______ 2U8

Q81.The number of real solutions of the equation \(x\left(x^2+3|x|+5|x-1|+6|x-2|\right)=0\) is ______.

Q81.Let the complex numbers α and lie on the circles z - z02 = 4 and z - z02 = 16 respectively, where z0 = 1 + i. ¯α Then, the value of 100 | α| 2 is__________.

Q81.The number of ways of getting a sum 16 on throwing a dice four times is______

Q81.There are 4 men and 5 women in Group A, and 5 men and 4 women in Group B. If 4 persons are selected from each group, then the number of ways of selecting 4 men and 4 women is _____

Q81.Let 𝑎, 𝑏, 𝑐 be the length of three sides of a triangle satisfying the condition 𝑎2 + 𝑏2𝑥2 −2𝑏𝑎+ 𝑐 𝑥+ 𝑏2 + 𝑐2 = 0. If the set of all possible values of 𝑥 is in the interval 𝛼, 𝛽, then 12𝛼2 + 𝛽2 is equal to _______.

Q81.Let the set C = {(x, y) ∣x2 −2y = 2023, x, y ∈N}. Then ∑(x,y)∈C(x y)

Q81.Let x1, x2, x3, x4 be the solution of the equation 4x4 + 8x3 −17x2 −12x + 9 = 0 and (4 + x21) (4 + x22) (4 + x23) (4 + x24) = 12516 m. Then the value of m is

Q81.If α satisfies the equation x2 + x + 1 = 0 and (1 + α)7 = A + Bα + Cα2, A, B, C ≥0 , then 5(3 A −2 B −C) is equal to

Q81.The number of distinct real roots of the equation |x + 1||x + 3| −4|x + 2| + 5 = 0, is JEE Main 2024 (08 Apr Shift 2) JEE Main Previous Year Paper

Q81.Let a = 1 + 2C23! + 3C24! + 4C25! + … 1! + 2! + 3! + … Then 2b is equal to a2

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.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

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

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.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.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.The coefficient of x2012 in the expansion of 1 - x20081 + x + x22007 is equal to _____.

Q82.Let α = 12 + 42 + 82 + 132 + 192 + 262 + … … . upto 10 terms and β = ∑10n=1 n4 . If 4α −β = 55k + 40, then k is equal to _______. 6

Q82.The remainder when 4282024 is divided by 21 is__________

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.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