Practice Questions

Q75.If x→∞(1lim + (1) 2 (2) 32 (3) 1 (4) 2 2 3

Q76.Consider the following two statements: P : If 7 is an odd number, then 7 is divisible by 2 . Q : If 7 is a prime number, then 7 is an odd number. If V1 is the truth value of the contrapositive of P and V2 is the truth value of contrapositive of Q, then the ordered pair (V1, V2) equals (1) (F, T) (2) (F, F) (3) (T, F) (4) (T, T)

Q76.The mean of 5 observations is 5 and their variance is 12. 4. If three of the observations are 1, 2 & 6; then the value of the remaining two is : (1) 1, 11 (2) 5, 5 (3) 5, 11 (4) None of these

Q76.If the standard deviation of the numbers 2, 3, a and 11 is 3. 5, then which of the following is true ? (1) 3a2 −34a + 91 = 0. (2) 3a2 −23a + 44 = 0. (3) 3a2 −26a + 55 = 0. (4) 3a2 −32a + 84 = 0.

Q77.The angle of elevation of the top of a vertical tower from a point A, due east of it is 45o . The angle of elevation of the top of the same tower from a point B, due south of A is 30o . If the distance between A and B is 54√2m , then the height of the tower (in meters), is: (1) 108 (2) 36√3 (3) 54√3 (4) 54

Q77.A man is walking towards a vertical pillar in a straight path, at a uniform speed. At a certain point A on the path, he observes that the angle of elevation of the top of the pillar is 30° . After walking for 10 minutes from JEE Main 2016 (03 Apr) JEE Main Previous Year Paper A in the same direction, at a point B, he observes that the angle of elevation of the top of the pillar is 60° . Then the time taken (in minutes) by him, from B to reach the pillar, is (1) 20 (2) 5 (3) 6 (4) 10

Q77.If the mean deviation of the numbers 1, 1 + d, … , 1 + 100d from their mean is 255 , then a value of d is : (1) 10. 1 (2) 5. 05 (3) 20. 2 (4) 10 Q78. ⎡ √32 21 ⎤ 1 1 T If P = , A = and Q = PAP T, then P Q2015 P is : √3 [0 1 ] ⎣−12 2 ⎦ (1) [00 20150 ] (2) [20151 20150 ] (3) [10 20151 ] (4) [20150 20151 ]

Q78.If A = [ 5a3 −b2 ] and A. adjA = A AT , then 5a + b is equal to (1) 4 (2) 13 (3) −1 (4) 5

Q79.If A = [ −43 −11 ] JEE Main 2016 (10 Apr Online) JEE Main Previous Year Paper (1) −175 (2) 2014 (3) 2016 (4) −25

Q79.The system of linear equations x + λy −z = 0 λx −y −z = 0 x + y −λz = 0 has a non -trivial solution for (1) Exactly two values of λ (2) Exactly three values of λ (3) Infinitely many values of λ (4) Exactly one value of λ

Q79. cos x sin x sin x The number of distinct real roots of the equation, sin x cos x sin x = 0 in the interval [−π4 , π4 ] is : sin x sin x cos x (1) 1 (2) 4 (3) 2 (4) 3

Q80.Let a, b ∈R, (a ≠0). If the function f , defined as , 0 ≤x < 1 ⎧ 2x2a f(x) = a, 1 ≤x < √2 ,is continuous in the interval [0, ∞), then an ordered pair (a, b) can be ⎨ 2b2−4b ⎩ x3 , √2 ≤x < 8 1 −1 + −√3) (2) (√2, √3) (1) (−√2, 1 1 + −√3) (4) (−√2, √3) (3) (√2,

Q80.If f(x) + 2f( x1 ) = 3x, x ≠0, and S = {x ∈R : f(x) = f(−x)}, then S (1) Contains exactly two elements (2) Contains more than two elements (3) Is an empty set (4) Contains exactly one element

Q80.For x ∈R, x ≠0, x ≠1, let f0(x) = 1−x1 and fn+1(x) = f0(fn(x)), n = 0, 1, 2, … . . Then the value of f100(3) + f1( 32 ) + f2( 32 ) is equal to : (1) 8 (2) 4 3 3 (3) 5 (4) 1 3 3 is differentiable at x = 1 , then ab is equal to

Q81.For x ∈R, f(x) = |log 2 −sin x| and g(x) = f(f(x)), then (1) g′(0) = −cos(log 2) (2) g is differentiable at x = 0 and g′(0) = −sin(log 2) (3) g is not differentiable at x = 0 (4) g′(0) = cos(log 2) x π π 1−sin x x ∈(0, 2 ). A normal to y = f(x) at x = 6 also passes through the

Q81.Let C be a curve given by y(x) = 1 + √4x −3 , x > 43 . If P is a point on C, such that the tangent at P has slope 2 , then a point through which the normal at P passes, is : 3 (1) (1, 7) (2) (3, −4) (3) (4, −3) (4) (2, 3)

Q81.If the function f(x) = { a + cos−1(x−x, + b), 1 ≤xx < 1≤2 (1) π+2 (2) π−2 2 2 (3) −π−2 (4) −1 −cos−1 (2) 2

Q82.The minimum distance of a point on the curve y = x2 −4 from the origin is (1) √15 units 2 units (2) √192 (4) √19 units units 2 (3) √152 JEE Main 2016 (09 Apr Online) JEE Main Previous Year Paper

Q82.Consider f(x) = tan−1(√1+sin ), point (1) ( π6 , 0) (2) ( π4 , 0) (3) (0, 0) (4) (0, 2π3 )

Q82.Let f(x) = sin4x + cos4x. Then, f is an increasing function in the interval: (1) ] 5π8 , 3π4 [ (2) ] π2 , 5π8 [ (3) ] π4 , π2 [ (4) ]0, π4 [

Q83.If the tangent at a point P, with parameter t, on the curve x = 4t2 + 3, y = 8t3 −1, t ∈R, meets the curve again at a point Q, then the coordinates of Q are : (1) (16t2 + 3, −64t3 −1) (2) (4t2 + 3, −8t3 −1) (3) (t2 + 3, t3 −1) (4) (t2 + 3, −t3 −1)

Q83.The integral ∫ dx is equal to (1+√x)√x−x2 (1) (2) + c + c −2√1+√x1−√x −√1−√x1+√x (3) (4) −2 + c + c √1−√x1+√x √1+√x1−√x

Q83.A wire of length 2 units is cut into two parts which are bent respectively to form a square of side = x units and a circle of radius = r units. If the sum of the areas of the square and the circle so formed is minimum, then (1) x = 2r (2) 2x = r (3) 2x = (π + 4)r (4) (4 −π)x = πr

Q84.If ∫ dx = (tan x)A + C(tan x)B + k, where k is a constant of integration, then A + B + C equals cos3 x √2 sin 2x (1) 16 (2) 27 5 10 (3) 7 (4) 21 10 5

Q84.The integral ∫ 2x12+5x9 dx, is equal to (x5+x3+1)3 (1) x5 + c (2) −x10 + c 2(x5+x3+1)2 2(x5+x3+1)2 (3) −x5 + c (4) x10 + c (x5+x3+1)2 2(x5+x3+1)2