Practice Questions

Q81.If ∫3 m n2 1 |loge x|dx = n loge( e ), where 3 _____ .

Q81.The value of the integral ∫21 ( t4+1t6+1 )dt is : (1) tan−1 12 + 31 tan−1 8 −π3 (2) tan−1 2 −13 tan−1 8 + π3 (3) tan−1 2 + 13 tan−1 8 −π3 (4) tan−1 21 −13 tan−1 8 + π3 dx is equal to

Q81.The number of ways of giving 20 distinct oranges to 3 children such that each child gets at least one orange is _____ 1 15

Q81.A person forgets his 4-digit ATM pin code. But he remembers that in the code all the digits are different, the greatest digit is 7 and the sum of the first two digits is equal to the sum of the last two digits. Then the maximum number of trials necessary to obtain the correct code is________.

Q82.If the sum of the series + − 1 + 1 − + − 1 + 1 − 1 + . . . . . is αβ 22⋅3 2⋅32 33 23⋅3 22⋅32 2⋅33 34 ( 21 −13 ) + ( 221 − 2⋅31 + 321 ) ( 231 1 ) ( 241 1 )+. , where α and β are co-prime, then α + 3β is equal to ________.

Q82.In an examination, 5 students have been allotted their seats as per their roll numbers. The number of ways, in which none of the students sits on the allotted seat, is

Q82.Suppose 𝑎1, 𝑎2, 2, 𝑎3, 𝑎4 be in an arithmetico-geometric progression. If the common ratio of the corresponding geometric progression is 2 and the sum of all 5 terms of the arithmetico-geometric progression is 49 , then 𝑎4 is 2 equal to ______________

Q82.Number of 4-digit numbers (the repetition of digits is allowed) which are made using the digits 1, 2, 3 and 5 , and are divisible by 15 , is equal to Q83. ∞ 𝑛3 ( (2𝑛)!) + (2𝑛- 1) (𝑛!) 𝑏 ∞ 1 ∑𝑛= 0 ( 𝑛! ) ( ( 2𝑛) ! ) = 𝑎𝑒+ 𝑒+ 𝑐 where 𝑎, 𝑏, 𝑐 ∈ℤ and 𝑒= ∑𝑛= 0 𝑛! Then 𝑎2 - 𝑏+ 𝑐 is equal to _______ JEE Main 2023 (30 Jan Shift 1) JEE Main Previous Year Paper

Q82.Let 𝑎1, 𝑎2, … … , 𝑎𝑛 be in A.P. If 𝑎5 = 2𝑎7 and 𝑎11 = 18, then 12 + + + + … . . + √𝑎10 √𝑎11 √𝑎11 √𝑎12 √𝑎17 √𝑎18 is equal to _____ .

Q82.A boy needs to select five courses from 12 available courses, out of which 5 courses are language courses. If he can choose at most two language courses, then the number of ways he can choose five courses is

Q82.Let for x ∈R, S0(x) = x, Sk(x) = Ckx + k ∫x0 Sk−1(t)dt where k = 1, 2, 3, … Then S2(3) + 6C3 is equal to _______. C0 = 1, Ck = 1 −∫10 Sk−1(x)dx,

Q82.The number of permutations, of the digits 1, 2, 3, … , 7 without repetition, which neither contain the string 153 nor the string 2467, is _______ .

Q82.The coefficient of 𝑥18 in the expansion of 𝑥4 - is ____________ 𝑥3

Q82.Let [t] denote the greatest integer ≤t. Then π 5π 6

Q82.If ∫π0 5cos x(1+cos x cos 3x+cos21+5cos xx+cos3 x cos 3x)dx = JEE Main 2023 (01 Feb Shift 2) JEE Main Previous Year Paper

Q82.Let 𝑎1 = 8, 𝑎2, 𝑎3, … . 𝑎𝑛 be an A.P. If the sum of its first four terms is 50 and the sum of its last four terms is 170 , then the product of its middle two terms is _____ .

Q82.Let [t] denote the greatest integer function. If α + β√2 + γ√3 + δ√5, then α + β + γ + δ is equal to ∫2.40 [x2]dx =

Q82.Let f be a differentiable function defined on [0, π2 ] 2 e ∀x f(x) + ∫x0 f(t)√1 −(loge(f(t)))2dt = ∈[0, π2 ], then {6 loge(f( π6 ))} is equal to

Q83.Let 𝑆= 109 + 108 + 107 + … . + 2 + 1 Then the value of 16𝑆- ( 25 -54 is equal to 5 52 5107 5108. ) 1 1 680 4 is equal to

Q83.Let the area enclosed by the lines x + y = 2, y = 0 , x = 0 and the curve f(x) = min{x2 + 43 , 1 + [x]} where [x] denotes the greatest integer ≤x, be A . Then the value of 12A is

Q83.Number of 4-digit numbers that are less than or equal to 2800 and either divisible by 3 or by 11 , is equal to _____ . JEE Main 2023 (31 Jan Shift 1) JEE Main Previous Year Paper 2 30

Q83.Let the equations of two adjacent sides of a parallelogram 𝐴𝐵𝐶𝐷 be 2𝑥- 3𝑦= - 23 and 5𝑥+ 4𝑦= 23. If the equation of its one diagonal 𝐴𝐶 is 3𝑥+ 7𝑦= 23 and the distance of 𝐴 from the other diagonal is 𝑑, then 50𝑑2 is equal to ______________

Q83.Let A be the area of the region {(x, y) : y ≥x2, y ≥(1 −x)2, y ≤2x(1 −x)}. Then 540A is equal to y(1) = 0 is

Q83.The number of 3-digit numbers, that are divisible by either 2 or 3 but not divisible by 7 is _____ .

Q83.The number of 9 digit numbers, that can be formed using all the digits of the number 123412341 so that the even digits occupy only even places, is ______ 1