Practice Questions

Q77. ABCD is a trapezium such that AB and CD are parallel and BC ⊥CD. If ∠ADB = θ, BC = p and CD = q , then AB is equal to (1) p2+q2 (2) (p2+q2) sin θ p2 cos θ+q2 sin θ (p cos θ+q sin θ)2 (3) (p2+q2) sin θ (4) p2+q2 cos θ p cos θ+q sin θ p cos θ+q sin θ

Q78.Let A and B be two sets containing 2 elements and 4 elements respectively. The number of subsets of A × B having 3 or more elements is : (1) 219 (2) 211 (3) 256 (4) 220 Q79. ⎡1 α 3 ⎤ If P = 1 3 3 is the adjoint of a 3 × 3 matrix A and |A| = 4 , then α is equal to ⎣2 4 4 ⎦ (1) 5 (2) 0 (3) 4 (4) 11

Q78.Consider the function : f(x) = [x] + |1 −x|, −1 ≤x ≤3 where [x] is the greatest integer function. Statement −x, −1 ≤x < 0 1 −x, 0 ≤x < 1 1: f is not continuous at x = 0, 1, 2 and 3 Statement 2:f(x)= = 1 + x, 1 ≤x < 2 2 + x, 2 ≤x ≤3 (1) Statement 1 is true; Statement 2 is false, (2) Statement 1 is true; Statement 2 is true; Statement 2 is not correct explanation for Statement 1. (3) Statement 1 is true; Statement 2 is true; (4) Statement 1 is false; Statement 2 is true. Statement It is a correct explanation for Statement 1.

Q78. a b c If a, b, c are sides of a scalene triangle, then the value of b c a is : c a b (1) non - negative (2) negative (3) positive (4) non-positive JEE Main 2013 (09 Apr Online) JEE Main Previous Year Paper

Q78.Statement-1: The system of linear equations x + (sin α)y + (cos α)z = 0 x + (cos α)y + (sin α)z = 0 x −(sin α)y −(cos α)z = 0 has a non-trivial solution for only one value of α lying in the interval (0, π2 ). Statement-2: The equation in α cos α sin α cos α sin α cos α sin α = 0 cos α −sin α −cos α has only one solution lying in the interval (0, π2 ) (1) Statement-1 is true, Statement-2 is true, (2) Statement-1 is true, Statement-2 is true, Statement-2 is not correct explantion for Statement-2 is a correct explantion for Statement-1. Statement-1. (3) Statement-1 is true, Statement- 2 is false. (4) Statememt-1 is false, Statement-2 is true. , then tan S is equal to :

Q79.A spherical balloon is being inflated at the rate of 35cc/min . The rate of increase in the surface area (in cm2/min.) of the balloon when its diameter is 14 cm, is : JEE Main 2013 (25 Apr Online) JEE Main Previous Year Paper (1) 10 (2) √10 (3) 100 (4) 10√10

Q79.Let A = {1, 2, 3, 4} and R : A →A be the relation defined by R = {(1, 1), (2, 3), (3, 4), (4, 2)} . The correct statement is : (1) R does not have an inverse. (2) R is not a one to one function. (3) R is an onto function. (4) R is not a function. x2−x

Q79. S = tan−1 ( n2+n+11 ) + tan−1 ( n2+3n+31 ) + … + tan−1 ( 1+(n+19)(n+20)1 ) (1) 20 (2) n 401+20n n2+20n+1 (3) 20 (4) n n2+20n+1 401+20n

Q79.If the system of linear equations : x1 + 2x2 + 3x3 = 6 x1 + 3x2 + 5x3 = 9 2x1 + 5x2 + ax3 = b JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper is consistent and has infinite number of solutions, then : (1) a = 8, b can be any real number (2) b = 15, a can be any real number (3) a ∈R −{8} and b ∈R −{15} (4) a = 8, b = 15

Q80.Let f(1) = −2 and f ′(x) ≥4.2 for 1 ≤x ≤6 . The possible value of f(6) lies in the interval : (1) [15, 19) (2) (−∞, 12) (3) [12, 15) (4) [19, ∞)

Q80.Let f(x) = x ≠0, −2. Then dxd [f −1(x)] (wherever it is defined) is equal to: x2+2x (1) −1 (2) 3 (1−x)2 (1−x)2 (3) 1 (4) −3 (1−x)2 (1−x)2

Q80.Let f be a composite function of x defined by f(u) = 1 , u(x) = x−11 . Then the number of points x u2+u−2 where f is discontinuous is : (1) 4 (2) 3 (3) 2 (4) 1

Q80.The number of values of k, for which the system of equations : (k + 1)x + 8y = 4k JEE Main 2013 (07 Apr) JEE Main Previous Year Paper kx + (k + 3)y = 3k −1 has no solution, is : (1) 2 (2) 3 (3) Infinite (4) 1

Q80.Let f(x) = −1 + |x −2|, and g(x) = 1 −|x|; then the set of all points where fog is discontinuous is : (1) {0, 2} (2) {0, 1, 2} (3) {0} (4) an empty set π

Q81.For a > 0, t ∈(0, 2 2 ), let x = √asin−1 t and y = √acos−1 t , Then, 1 + ( dxdy ) equals : (1) x2 (2) y2 y2 x2 (3) x2+y2 (4) x2+y2 y2 x2

Q81.If f(x) = sin(sin x) and f ′′(x) + tan xf ′(x) + g(x) = 0, then g(x) is : (1) cos2 x cos(sin x) (2) sin2 x cos(cos x) (3) sin2 x sin(cos x) (4) cos2 x sin(sin x) y2

Q81.If y = sec(tan−1 x), then dxdy at x = 1 is equal to (1) 1 (2) √2 (3) 1 (4) 1 √2 2 x

Q81.If an equation of a tangent to the curve, y −cos(x + f), −1 −1 ≤x ≤1 + π, is x + 2y = k then k is equal to : (1) 1 (2) 2 (3) π (4) π 4 2

Q81.Statement-1: The equation x log x = 2 −x is satisfied by at least one value of x lying between 1 and 2. Statement-2: The function f(x) = x log x is an increasing function in [1, 2] and g(x) = 2 −x is a decreasing function in [1, 2] and the graphs represented by these functions intersect at a point in [1, 2] (1) Statement-1 is true; Statement-2 is true; (2) Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for Statement-2 is not correct explanation for Statement-1. Statement-1. (3) Statement-1 1 is false, Statement- 2 is true. (4) Statement-1 1 is true, Statement- 2 is false.

Q82.If the surface area of a sphere of radius r is increasing uniformly at the rate 8 cm2/s, then the rate of change of its volume is: (1) constant (2) proportional to √r (3) proportional to r2 (4) proportional to r dx is equal to:

Q82.If the curves x2 α + 4 = 1 and y3 = 16x intersect at right angles, then a value of α is : (1) 2 (2) 4 3 (3) 1 (4) 3 2 4

Q82.The intercepts on the x-axis made by tangents to the curve, y = ∫ |t| dt, x ∈R, which are parallel to the line 0 y = 2x , are equal to (1) ±3 (2) ±4 (3) ±1 (4) ±2

Q82.Statement-1: The function x2 (ex + e−x) is increasing for all x > 0 . Statement-2: The functions x2ex and x2e−x are increasing for all x > 0 and the sum of two increasing functions in any interval (a, b) is an increasing function in (a, b). (1) Statement-1 is false; Statement-2 is true. (2) Statement-1 is true; Statement-2 is true; Statement-2 is not a correct explanation for Statement-1. (3) Statement-1 is true; Statement-2 is false. (4) Statement-1is true; Statement-2 is true; Statement-2 is a correct explanation for statement-1.

Q82.If the integral cos 8x + 1 dx = A cos 8x + k ∫ cot 2x −tan 2x where k is an arbitrary constant, then A is equal to: (1) −116 (2) 161 (3) 8 1 (4) −18

Q83.If ∫ x+x7dx = p(x) then, ∫ x+x7x6 (1) ln |x| −p(x) + c (2) ln |x| + p(x) + c (3) x −p(x) + c (4) x + p(x) + c is equal to :