Practice Questions

Q59.A xenon compound A upon partial hydrolysis gives XeO2 F2 . The number of lone pair of electrons present in compound A is ___ (Round off to the Nearest integer)

Q60.The total number of negative charge in the tetrapeptide, Gly-Glu-Asp-Tyr, at pH 12. 5 will be_______ (Integer answer)

Q60.Gaseous cyclobutene isomerizes to butadiene in a first order process which has a 'K' value of 3 . 3 × 10-4 s-1 at 153°C . The time in minutes it takes for the isomerization to proceed 40% to completion at this temperature is_____. (Rounded off to the nearest integer)

Q60.In the electrolytic refining of blister copper, the total number of main impurities, from the following, removed as anode mud is ___________ . Pb, Sb, Se, Te, Ru, Ag, Au and Pt

Q61.The set of all values of k > −1, for which the equation + + 4x + 3)(3x2 + 4x + 2)+ k(3x2 + 4x + 2) = 0 has real roots, is: (3x2 + 4x + 3) 2 −(k 2 1)(3x2 (1) [−12 , 1) (2) (1, 25 ] (3) ( 12 , 32 ] −{1} (4) [2, 3)

Q81.Let z1, z2 be the roots of the equation z2 + az + 12 = 0 and z1, z2 form an equilateral triangle with origin. Then, the value of |a| is

Q81.The total number of numbers, lying between 100 and 1000 that can be formed with the digits 1, 2, 3, 4, 5, if the repetition of digits is not allowed and numbers are divisible by either 3 or 5, is

Q81.Let z1 and z2 be two complex numbers such that arg(z1 −z2) = π4 and z1, z2 satisfy the equation |z −3| =Re (z). Then the imaginary part z1 + z2 is equal to

Q81.If the least and the largest real values of 𝛼, for which the equation 𝑧+ 𝛼𝑧- 1 + 2𝑖= 0 𝑧∈𝐶 and 𝑖= √-1 has a solution, are 𝑝 and 𝑞 respectively; then 4𝑝2 + 𝑞2 is equal to_______.

Q81.Let z and w be two complex numbers such that w = zz −2z + 2, z−3iz+i = 1 and Re (w) has minimum value. Then, the minimum value of n ∈N for which wn is real, is equal to _______.

Q82.Consider an arithmetic series and a geometric series having four initial terms from the set {11, 8, 21, 16, 26, 32, 4}. If the last terms of these series are the maximum possible four digit numbers, then the number of common terms in these two series is equal to _______.

Q82.A number is called a palindrome if it reads the same backward as well as forward. For example 285582 is a six digit palindrome. The number of six digit palindromes, which are divisible by 55, is ________.

Q82.Let z be those complex numbers which satisfy |z + 5| ≤4 and z(1 + i) + z(1 −i) ⩾−10, i = √−1. If the maximum value of |z + 1|2 is α + β√2 , then the value of (α + β) is

Q82.Let S = {1, 2, 3, 4, 5, 6, 9} . Then the number of elements in the set T = {A ⊆S : A ≠ϕ and the sum of all the elements of A is not a multiple of 3} is Q83. 3 × 722 + 2 × 1022 −44 when divided by 18 leaves the remainder

Q82.Let {an}∞n=1 be a sequence such that a1 = 1, a2 = 1 and an+2 = 2an+1 + an for all n ≥1. Then the value of 47 ∑∞n=1( 23nan ) is equal to ________.

Q82.The sum of all the elements in the set {n ∈{1, 2, … … , 100} ∣ H.C.F. of n and 2040 is 1} is equal to __________.

Q82.There are 5 students in class 10, 6 students in class 11 and 8 students in class 12 . If the number of ways, in which 10 students can be selected from them so as to include at least 2 students from each class and at most 5 students from the total 11 students of class 10 and 11 is 100𝑘, then 𝑘 is equal to + … . upto ∞ 2 + 2 6 10 log0 . 25 3 + 3 33

Q82.All the arrangements, with or without meaning, of the word FARMER are written excluding any word that has two 𝑅 appearing together. The arrangements are listed serially in the alphabetic order as in the English dictionary. Then the serial number of the word FARMER in this list is _____ .

Q82.Let Sn(x) = loga1/2 x + loga1/3 x + loga1/6 x + loga1/11 x + loga1/18 x + loga1/27 x + … up to n-terms, where a > 1 . If S24(x) = 1093 and S12(2x) = 265, then value of a is equal to _____ . k )

Q83.For k ∈N, let α(α+1)(α+2)…….(α+20) 2 1 = ∑20K=0 α+kAk , where α > 0. Then the value of 100( A14+A15A13 ) is equal to ____________.

Q83.Let n ∈N and [x] denote the greatest integer less than or equal to x. If the sum of (n + 1) terms of nC0, 3 ⋅nC1, 5 ⋅nC2, 7 ⋅nC3, … is equal to 2100 ⋅101, then 2[ n−12 ] is equal to n is equal to :

Q83.The sum of all 3 -digit numbers less than or equal to 500, that are formed without using the digit 1 and they all are multiple of 11, is ______.

Q83.Let ABCD be a square of side of unit length. Let a circle C1 centered at A with unit radius is drawn. Another circle C2 which touches C1 and the lines AD and AB are tangent to it, is also drawn. Let a tangent line from the point C to the circle C2 meet the side AB at E . If the length of EB is α + √3β, where α, β are integers, then α + β is equal to ________. JEE Main 2021 (16 Mar Shift 1) JEE Main Previous Year Paper aex−b cos x+ce−x

Q83.The total number of 4 -digit numbers whose greatest common divisor with 18 is 3 is _____.

Q83.The locus of the point of intersection of the lines (√3)kx + ky −4√3 = 0 and √3x −y −4(√3)k conic, whose eccentricity is a −b −tan( 2θ )