Practice Questions

Q63.If P is a point on the parabola y = x2 + 4 which is closest to the straight line y = 4x −1, then the co- ordinates of P are: (1) (−2, 8) (2) (1, 5) (3) (2, 8) (4) (3, 13)

Q63.The sum of all the 4-digit distinct numbers that can be formed with the digits 1, 2, 2 and 3 is: (1) 26664 (2) 122664 (3) 122234 (4) 22264

Q63.If 𝑧 is a complex number such that is purely imaginary, then the minimum value of |𝑧- ( 3 + 3 𝑖) | is : 𝑧- 1 (1) 3√2 (2) 2√2 (3) 2√2 - 1 (4) 6√2

Q63.If n is the number of irrational terms in the expansion of (31/4 + 51/8) 60 , then (n −1) is divisible by : (1) 26 (2) 30 (3) 8 (4) 7

Q63.The value of ∑6r=0(6Cr ⋅6C6−r) is equal to : (1) 1124 (2) 1324 (3) 1024 (4) 924

Q63.If tan( π9 ), x, tan( 7π18 ) are in arithmetic progression and tan( π9 ), y, tan( 5π18 ) are also in arithmetic progression, then |x −2y| is equal to : (1) 4 (2) 3 (3) 0 (4) 1 Q64. 10 + 3(−18 ) log3(5x−1+1)} in A possible value of x, for which the ninth term in the expansion of {3log3 √25x−1+7 the increasing powers of 3(−18 ) log3(5x−1+1) is equal to 180, is : (1) 0 (2) −1 (3) 2 (4) 1

Q63.The minimum value of f(x) = aax + a1−ax , where a, x ∈R and a > 0, is equal to: (1) a + 1 (2) 2a (3) a + a1 (4) 2√a

Q63.Let A(a, 0), B(b, 2b + 1) and C(0, b), b ≠0, |b| ≠1 , be points such that the area of triangle ABC is 1 sq. unit, then the sum of all possible values of a is: (1) −2b (2) 2b2 b+1 b+1 (3) −2b2 (4) 2b b+1 b+1

Q63.The number of solutions of sin7 x + cos7 x = 1, x ∈[0, 4π] is equal to (1) 11 (2) 7 (3) 5 (4) 9

Q63.Team ′A′ consists of 7 boys and n girls and Team ′B′ has 4 boys and 6 girls. If a total of 52 single matches can be arranged between these two teams when a boy plays against a boy and a girl plays against a girl, then n is equal to: (1) 5 (2) 2 (3) 4 (4) 6

Q63.In an increasing geometric series, the sum of the second and the sixth term is 252 and the product of the third and fifth term is 25. Then, the sum of 4th, 6th and 8th terms is equal to: (1) 35 (2) 32 (3) 26 (4) 30 1 10 1 (1−x) 10 where x ∈(0, 1) is: 5 + t )

Q63.The total number of positive integral solutions (x, y, z) such that xyz = 24 is : (1) 45 (2) 30 (3) 36 (4) 24

Q63.If the sum of an infinite GP, a, ar, ar2, ar3, … is 15 and the sum of the squares of its each term is 150, then the sum of ar2, ar4, ar6, … is: (1) 25 (2) 9 2 2 (3) 1 (4) 5 2 2

Q63.If the greatest value of the term independent of x in the expansion of (x sin α + a cosx α )10 is (5!)210! value of a is equal to: (1) −1 (2) 1 (3) −2 (4) 2 10100 1

Q63.The value of 2 sin( 8π ) sin( 2π8 ) sin( 3π8 ) sin( 5π8 ) sin( 6π8 ) sin( 7π8 ) is : (1) 1 (2) 1 4√2 8 (3) 1 (4) 1 8√2 4 JEE Main 2021 (26 Aug Shift 2) JEE Main Previous Year Paper

Q63.If the coefficients of x7 in (x2 + bx1 )11 and x−7 in (x − bx21 )11, to: (1) 2 (2) −1 (3) 1 (4) −2

Q63.If z and ω are two complex numbers such that |zω| = 1 and arg(z) −arg(ω) = 3π2 , then arg( 1+3¯zω1−2¯zω ) is: (Here arg(z) denotes the principal argument of complex number z) (1) π 4 (2) −3π4 (3) −π4 (4) 3π4

Q64.The number of solutions of the equation x + 2 tan x = π2 in the interval [0, 2π] is (1) 3 (2) 4 (3) 2 (4) 5

Q64.If 20Cr is the co-efficient of xr in the expansion of (1 + x)20 , then the value of ∑20r=0 r2(20Cr) is equal to: (1) 420 × 218 (2) 380 × 218 (3) 380 × 219 (4) 420 × 219 cos x

Q64.If two tangents drawn from a point P to the parabola y2 = 16(x −3) are at right angles, then the locus of point P is: (1) x + 4 = 0 (2) x + 2 = 0 (3) x + 3 = 0 (4) x + 1 = 0 = b, then the ordered pair (a, b) is: lim −x + 1 −ax)

Q64.Let [x] denote greatest integer less than or equal to x . If for n ∈N, (1 −x + x3) n = ∑3nj=0 ajxj , then [ 3n2 ] [ 3n−12 ] ∑ j=0 a2j + 4 ∑ j=0 a2j+1 is equal to : (1) 2 (2) 2n−1 (3) 1 (4) n

Q64.The coefficient of x256 in the expansion of (1 −x)101(x2 + x + 1)100 is: (1) 100C16 (2) 100C15 (3) −100C16 (4) −100C15

Q64.The lowest integer which is greater than + is (1 10100 ) (1) 3 (2) 4 (3) 2 (4) 1

Q64.The maximum value of the term independent of t in the expansion of (tx (1) 10! (2) 10! √3(5!)2 3(5!)2 (3) 2.10! (4) 2.10! 3√3(5!)2 3(5!)2

Q64.If p and q are the lengths of the perpendiculars from the origin on the lines, x cosec α −y sec α = k cot 2α and x sin α + y cos α = k sin 2α respectively, then k2 is equal to : (1) 2p2 + q2 (2) p2 + 2q2 (3) 4q2 + p2 (4) 4p2 + q2