Practice Questions

Q77.If A is a 3 × 3 matrix such that |5 adjA| = 5, then |A| is equal to (1) ± 251 (2) ±5 (3) ± 51 (4) ±1

Q77.In a certain town, 25% of the families own a phone and 15% own a car; 65% families own neither a phone nor a car and 2000 families own both a car and a phone. Consider the following three statements: (i) 5% families own both a car and a phone. (ii) 35% families own either a car or a phone. (iii) 40000 families live in the town. Then, (1) Only (ii) and (iii) are correct (2) Only (i) and (ii) are correct (3) All (i), (ii) and (iii) are correct (4) Only (i) and (iii) are correct

Q78. x2 + x x + 1 x −2 If 2x2 + 3x −1 3x 3x −3 = ax −12 , then a is equal to: x2 + 2x + 3 2x −1 2x −1 (1) −24 (2) 24 (3) −12 (4) 12

Q78.If A = [ 01 −10 ] , then which one of the following statements is not correct? (1) A3 + I = A(A3 − I) (2) A4 −I = A2 + I (3) A2 + I = A(A2 −I) (4) A3 −I = A(A −I) JEE Main 2015 (10 Apr Online) JEE Main Previous Year Paper

Q78.The set of all values of λ for which the system of linear equations: 2x1 −2x2 + x3 = λx1 2x1 −3x2 + 2x3 = λx2 −x1 + 2x2 = λx3 has a non-trivial solution, (1) Contains more than two elements. (2) Is an empty set. (3) Is a singleton. (4) Contains two elements.

Q79. (ex−1)2 , x ≠0 x ⎧ sin ( k ) log (1+ x4 ) Let k be a non - zero real number. If f(x) = is a continuous function at x = 0 ⎨ ⎩12 , x = 0 , then the value of k is (1) 2 (2) 4 (3) 3 (4) 1

Q79.Let tan−1 y = tan−1 x + tan−1( 1−x22x ), where |x| < √31 ,Then a value of y is (1) 3x+x3 (2) 3x−x3 1+3x2 1−3x2 (3) 3x+x3 (4) 3x−x3 1−3x2 1+3x2 is differentiable, then the value of k + m is

Q79.The least value of the product xyz (such that x, y and z are positive real numbers) for which the determinant x 1 1 1 y 1 is non-negative is 1 1 z (1) −1 (2) −16√2 (3) −8 (4) −2√2

Q80.If f(x) = 2 tan−1 x + sin−1( 1+x22x ), x > 1, then f(5) is equal to (1) π 2 (2) tan−1( 15665 ) (3) π (4) 4 tan−1(5)

Q80.The equation of a normal to the curve, sin y = x sin( π3 + y) at x = 0, is: (1) 2x −√3 y = 0 (2) 2y −√3 x = 0 (3) 2y + √3 x = 0 (4) 2x + √3 y = 0

Q80.If the function g (x) = {k√xmx ++21 ,, 30 <≤xx ≤3≤5 (1) 4 (2) 2 (3) 16 (4) 10 5 3

Q81.If Rolle's theorem holds for the function f(x) = 2x3 + bx2 + cx, x ∈[−1, 1] at the point x = 12 , then 2b + c is equal to (1) 2 (2) 1 (3) −1 (4) −3

Q81.The normal to the curve x2 + 2xy −3y2 = 0 , at (1, 1) (1) Meets the curve again in the fourth quadrant (2) Does not meet the curve again (3) Meets the curve again in the second quadrant (4) Meets the curve again in the third quadrant

Q81.Let k and K be the minimum and the maximum values of the function f(x) = (1+x)0.6 in [0, 1], respectively, 1+x0.6 then the ordered pair (k, K) is equal to: (1) (2−0.4, 1) (2) (2−0.6, 1) (3) (2−0.4, 20.6) (4) (1,20.6) JEE Main 2015 (11 Apr Online) JEE Main Previous Year Paper 1

Q82.Let f(x) be a polynomial of degree four and having its extreme values at x = 1 and x = 2. If f(x) lim + = 3, then f(2) is equal to [1 x2 ] x→0 (1) 4 (2) −8 (3) −4 (4) 0 JEE Main 2015 (04 Apr) JEE Main Previous Year Paper

Q82.The distance from the origin, of the normal to the curve, x = 2 cos t + 2t sin t, y = 2 sin t −2t cos t at t = π4 , is : (1) √2 (2) 2√2 (3) 4 (4) 2

Q82.If ∫ log(t+√1+t2) dt = 2 (g(t))2 + c, where c is a constant, then g(2), is equal to √1+t2 (1) 2 + + √5) (2) log(2 √5) 1 log(2 √5 + log + (3) log(2 √5) (4) 12 (2 √5)

Q83.Let f : R →R be a function such that f(2 −x) = f(2 + x) and f(4 −x) = f(4 + x), for all x ∈R and 2 50 ∫ f(x)dx = 5. Then the value of ∫ f(x)dx is 0 10 (1) 100 (2) 125 (3) 80 (4) 200

Q83.The integral ∫ 3dx 5 , is equal to (x+1) 4 (x−2) 4 (1) 1 1 4 + c 4( x+1x−2 ) 4 + c (2) −43 ( x+1x−2 ) (3) 1 1 4 + c 4( x−2x+1 ) 4 + c (4) −43 ( x−2x+1 )

Q83.The integral ∫ dx 3 equals to x2(x4+1) 4 4 (1) x4+1 1 1 4 (2) x4+1 + c + c −( x4 ) ( x4 ) (3) 14 (4) 41 (x4 + 1) + c −(x4 + 1) + c logx2 dx is equal to

Q84.Let f : (−1, 1) →R be a continuous function. If ∫sin0 x f(t) dt = √32 x, then f( √32 ) is equal to: (1) √3 (2) √3 2 (3) 1 (4) 2 √32

Q84.For x > 0, let f(x) = ∫x1 log1+tt dt. Then f(x) + f( x1 ) is equal to (1) 1 (log x)2 (2) log x 2 (3) 1 4 log x2 (4) 14 (log x)2

Q84.The integral ∫4 logx2+log(6−x)2 2 (1) 6 (2) 2 (3) 4 (4) 1

Q85.The area (in square units) of the region bounded by the curves y + 2x2 = 0 and y + 3x2 = 1 , is equal to (1) 4 3 sq. units (2) 13 sq. units (3) 5 3 sq. units (4) 43 sq. units

Q85.The area (in sq. units) of the region described by [(x, y) : y2 ≤2x and y ≥4x −1] is (1) 32 9 sq. units (2) 327 sq. units (3) 64 5 sq. units (4) 6415 sq. units