Practice Questions

Q73. (n+1) (n+2)….3n n1 is equal to lim n2n ) n→∞( (1) 9 (2) 3 log 3 −2 e2 (3) 18 (4) 27 e4 e2 1 2x

Q73.A hyperbola whose transverse axis is along the major axis of the conic x2 3 + 4 = 4 and has vertices at the foci of the conic. If the eccentricity of the hyperbola is 3 , then which of the following points does not lie on 2 the hyperbola ? (1) (√5, 2√2) (2) (0, 2) (3) (5, 2√3) (4) (√10, 2√3) is

Q73.Let a and b respectively be the semi-transverse and semi-conjugate axes of a standard hyperbola whose eccentricity satisfies the equation 9e2 −18e + 5 = 0 . If S(5, 0) is a focus and 5x = 9 is the corresponding directrix of this hyperbola, then a2 −b2 is equal to (1) −7 (2) −5 (3) 5 (4) 7 t2 f(x)−x2f(t)

Q74.If f(x) is a differentiable function in the interval (0, ∞) such that f(1) = 1 and lim t−x = 1,for each t→x x > 0, then f( 23 ) is equal to JEE Main 2016 (09 Apr Online) JEE Main Previous Year Paper (1) 23 (2) 13 18 6 (3) 25 (4) 31 9 18 a − 4 ) 2x = e3 , then a is equal to x x2

Q74. lim 2x tan(1−cosx−x2x)2tan 2x x→0 (1) 2 (2) −12 (3) −2 (4) 12

Q74.Let P = lim (1 + tan2 √x ) , then log P is equal to x→0+ (1) 1 (2) 1 2 4 (3) 2 (4) 1

Q75.The Boolean Expression (p∧∼q) ∨q ∨(∼p ∧q) is equivalent to (1) p ∨q (2) p ∨∼q (3) ∼p ∧q (4) p ∧q

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

Q75.The contrapositive of the following statement, "If the side of a square doubles, then its area increases four times", is (1) if the area of a square increases four times, then (2) if the area of a square increases four times, then its side is not doubled. its side is doubled. (3) if the area of a square does not increase four (4) if the side of a square is not doubled, then its area times, then its side is not doubled. does not increase four times.

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.

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

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.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.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

Q78.Let A, be a 3 × 3 matrix, such that A2 −5A + 7I = O. Statement - I : A−1 = 71 (5I −A). Statement - II : The polynomial A3 −2A2 −3A + I ,can be reduced to 5(A −4I). Then : (1) Both the statements are true (2) Both the statements are false (3) Statement - I is true, but Statement - II is false (4) Statement - I is false, but Statement - II is true , then the determinant of the matrix (A2016 −2A2015 −A2014) is :

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.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

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