Practice Questions

Q62.Let S1 be the sum of first 2n terms of an arithmetic progression. Let S2 be the sum of first 4n terms of the same arithmetic progression. If (S2 −S1) is 1000 , then the sum of the first 6n terms of the arithmetic progression is equal to: (1) 1000 (2) 7000 (3) 5000 (4) 3000

Q62.Let C be the set of all complex numbers. Let S1 = {z ∈C |z–3–2i|2 = 8}, S2 = z ∈C| Re(z) ≥5 and ¯S3 = {z ∈C| |z–z| ≥8}. Then the number of elements in S1 ∩S2 ∩S3 is equal to (1) 1 (2) 0 (3) 2 (4) Infinite b ≠0, are equal, then the value of b is equal

Q62.Consider a rectangle ABCD having 5, 6, 7, 9 points in the interior of the line segments AB, BC, CD, DA respectively. Let α be the number of triangles having these points from different sides as vertices and β be the number of quadrilaterals having these points from different sides as vertices. Then (β −α) is equal to (1) 795 (2) 1173 (3) 1890 (4) 717

Q62.The sum of the series ∑∞n=1 n2+6n+10(2n+1)! is equal to (1) 41 8 e + 198 e−1 + 10 (2) 418 e + 198 e−1 −10 (3) −418 e + 198 e−1 −10 (4) 418 e −198 e−1 −10 + + …

Q62.The area of the triangle with vertices P(z), Q(iz) and R(z + iz) is (1) 1 (2) 12 z 2 (3) 1 (4) 1 z + iz 2 2 2

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.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.If 𝑒cos2𝑥+ cos4𝑥+ cos6𝑥+ . . . . ∞log𝑒2 satisfies the equation 𝑡2 - 9𝑡+ 8 = 0, then the value of 2sin𝑥 where sin𝑥+ √3cos𝑥, 0 < 𝑥< 𝜋2, is equal to (1) 3 (2) 1 2 2 (3) √3 (4) 2√3

Q63. cosec 18° is a root of the equation: (1) x2 −2x −4 = 0 (2) 4x2 + 2x −1 = 0 (3) x2 + 2x −4 = 0 (4) x2 −2x + 4 = 0

Q63.The sum of all values of 𝑥 in [0, 2𝜋], for which sin𝑥+ sin2𝑥+ sin3𝑥+ sin4𝑥= 0, is equal to : (1) 8𝜋 (2) 11𝜋 (3) 12𝜋 (4) 9𝜋

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.Let A(−1, 1), B(3, 4) and C(2, 0) be given three points. A line y = mx, m > 0 , intersects lines AC and BC at point P and Q respectively. Let A1 and A2 be the areas of ΔABC and ΔPQC respectively, such that A1 = 3A2 , then the value of m is equal to : (1) 4 (2) 1 15 (3) 2 (4) 3 JEE Main 2021 (16 Mar Shift 2) JEE Main Previous Year Paper

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

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.If for x, y ∈R, x > 0, y = log10 x + log10 x1/3 + log10 x1/9 + … upto ∞ terms and 2+4+6+…+2y3+6+9+…+3y = log104 x , then the ordered pair (x, y) is equal to (1) (106, 6) (2) (106, 9) (3) (102, 3) (4) (104, 6)

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 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.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 0 < a, b < 1 , and tan−1 a + tan−1 b = π4 , then the value of (a + b) −( a2+b22 ) ( a3+b33 ) −( a4+b44 ) is : (1) loge( 2e ) (2) e (3) e2 −1 (4) loge 2

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.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.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. Let 𝑆𝑛= 1 · ( 𝑛- 1 ) + 2 · ( 𝑛- 2 ) + 3 · ( 𝑛- 3 ) + … + ( 𝑛- 1 ) · 1, 𝑛⩾4 . ∞ 2 Sn 1 The sum ∑n = 4 n! - ( n - 2 ) ! is equal to : 𝑒- 2 e - 1 (1) (2) 6 3 (3) e (4) e 6 3 20 1 4 = . If the sum of this 𝐴. 𝑃. is 189, then a6a16