Practice Questions

Q64. If three positive numbers a , b and c are in A.P. such that abc = 8, then the minimum possible value of b is: (1) 4 23 (2) 2 (3) 4 31 (4) 4

Q65.If the sum of the first n terms of the series √3 + √75 + √243 + √507 + … is 435√3, then n equals: (1) 13 (2) 15 (3) 29 (4) 18

Q65.The value of 21𝐶1-10𝐶1 + 21𝐶2-10𝐶2 + 21𝐶3-10𝐶3 + 21𝐶4-10𝐶4 + … + 21𝐶10-10𝐶10 is (1) 221 - 211 (2) 221 - 210 (3) 220 - 29 (4) 220 - 210

Q65.Let Sn = 131 + 13+231+2 + 13+23+331+2+3 + … + 13+23+…n31+2+…,+n . If 100 Sn = n, then n is equal to: (1) 200 (2) 199 (3) 99 (4) 19 10 x+1 x−1

Q67.The lengths of two adjacent sides of a cyclic quadrilateral are 2 units and 5 units and the angle between them is 60o . If the area of the quadrilateral is 4√3 sq. units, then the perimeter of the quadrilateral is (1) 12.5 units (2) 13 units (3) 13.2 units (4) 12 units

Q67.The locus of the point of intersection of the straight lines, tx −2y −3t = 0 and x −2ty + 3 = 0 (t ∈R), is: (1) A hyperbola with the length of conjugate axis 3 (2) A hyperbola with eccentricity √5 (3) An ellipse with the length of major axis 6 (4) An ellipse with eccentricity 2 √5

Q68.If two parallel chords of a circle, having diameter 4 units, lie on the opposite sides of the center and subtend angles cos−1( 71 ) and sec−1(7) at the center respectively, then the distance between these chords is: (1) 8 (2) 16 √7 7 (3) 4 (4) 8 √7 7

Q68.A square, of each side 2 , lies above the x -axis and has one vertex at the origin. If one of the sides passing through the origin makes an angle 30° with the positive direction of the x-axis , then the sum of the x- JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper coordinates of the vertices of the square is : (1) 2√3 −2 (2) √3 −2 (3) 2√3 −1 (4) √3 −1

Q69.The eccentricity of an ellipse whose centre is at the origin is . If one of its directrices is 𝑥= - 4 , then the 2 equation of the normal to it at 1, 3 is: 2 (1) 2𝑦- 𝑥= 2 (2) 4𝑥- 2𝑦= 1 (3) 4𝑥+ 2𝑦= 7 (4) 𝑥+ 2𝑦= 4

Q70.A hyperbola passes through the point 𝑃√2, √3 and has foci at ± 2, 0. Then the tangent to this hyperbola at 𝑃 also passes through the point (1) 3√2, 2√3 (2) 2√2, 3√3 (3) √3, √2 (4) -√2, - √3 JEE Main 2017 (02 Apr) JEE Main Previous Year Paper cot𝑥- cos𝑥

Q70.If a point P(0, −2) and Q is any point on the circle, x2 + y2 −5x −y + 5 = 0 , then the maximum value of (PQ)2 is (1) 8 + 5√3 (2) 47+10√6 2 (3) 14 + 5√3 (4) 25+ √6 2

Q70.If y = mx + c is the normal at a point on the parabola y2 = 8x whose focal distance is 8 units, then |c| is equal to: (1) 8√3 (2) 10√3 (3) 2√3 (4) 16√3

Q71. lim equals 𝑥→𝜋 𝜋- 2𝑥3 2 1 1 (1) (2) 24 16 (3) 1 (4) 1 8 4

Q71. The eccentricity of an ellipse having centre at the origin, axes along the co-ordinate axes and passing through the points (4, −1) and (−2, 2) is (1) √3 (2) √3 2 4 (3) 2 (4) 1 √5 2

Q72. lim √3x−3 is equal to x→3 √2x−4− √2 (1) 1 (2) 1 √2 2√2 (3) √3 (4) √3 2

Q72.The statement 𝑝→𝑞→~𝑝→𝑞→𝑞 is (1) A tautology (2) Equivalent to ~𝑝→𝑞 (3) Equivalent to 𝑝→~𝑞 (4) A fallacy

Q73.A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the variance of the number of green balls drawn is: 12 (1) (2) 6 5 (3) 4 (4) 6 25

Q73.The sum of 100 observations and the sum of their squares are 400 & 2475, respectively. Later on, three observations 3, 4 & 5 were found to be incorrect. If the incorrect observations are omitted, then the variance of the remaining observations is (1) 8. 25 (2) 8. 50 (3) 9. 00 (4) 8. 00

Q74.Let a vertical tower 𝐴𝐵 have its end 𝐴 on the level ground. Let 𝐶 be the mid-point of 𝐴𝐵 and 𝑃 be a point on the ground such that 𝐴𝑃= 2𝐴𝐵. If ∠𝐵𝑃𝐶= 𝛽, then tan𝛽 is equal to: (1) 6 (2) 1 7 4 2 4 (3) (4) 9 9

Q74.For two 3 × 3 matrices A and B , let A + B = 2B′ and 3A + 2B = I3, where B′ is the transpose of B and I3 is 3 × 3 identity matrix. Then : (1) 10A + 5B = 3I3 (2) 3A + 6B = 2I3 (3) 5A + 10B=2I3 (4) B + 2A = I3

Q75.If x = a, y = b, z = c is a solution of the system of linear equations x + 8y + 7z = 0 9x + 2y + 3z = 0 x + y + z = 0 Such that the point (a, b, c) lies on the plane x + 2y + z = 6 , then 2a + b + c equals: (1) 2 (2) −1 (3) 1 (4) 0

Q75.If 𝐴= 2 -3 , then Adj3𝐴2 + 12𝐴 is equal to: -4 1 (1) 72 -84 (2) 51 63 -63 51 84 72 (3) 51 84 (4) 72 -63 63 72 -84 51

Q75.Let A be any 3 × 3 invertible matrix. Then which one of the following is not always true? (1) adj (adj (A)) = |A|2. (adj (A))−1 (2) adj (adj (A)) = |A|. (adj (A))−1 (3) adj (adj (A)) = |A| . A (4) adj (A) = |A|. A−1

Q76.If 𝑆 is the set of distinct values of 𝑏 for which the following system of linear equations 𝑥+ 𝑦+ 𝑧= 1 𝑥+ 𝑎𝑦+ 𝑧= 1 𝑎𝑥+ 𝑏𝑦+ 𝑧= 0 has no solution, then 𝑆 is: (1) An empty set (2) An infinite set (3) A finite set containing two or more elements (4) A singleton

Q76.A value of x satisfying the equation sin[cot−1(1 + x)] = cos[tan−1x], is: JEE Main 2017 (09 Apr Online) JEE Main Previous Year Paper (1) −12 (2) 0 (3) −1 (4) 21