Practice Questions

Q72.A point on the ellipse, 4x2 + 9y2 = 36 , where the normal is parallel to the line, 4x −2y −5 = 0 , is : (1) ( 95 , 85 ) (2) ( 85 , −95 ) (3) (−95 , 85 ) (4) ( 85 , 95 )

Q72.Statement-1: The line x −2y = 2 meets the parabola, y2 + 2x = 0 only at the point (−2, −2). Statement-2: The line y = mx − 2m1 (m ≠0) is tangent to the parabola, y2 = −2x at the point (− 2m21 , −1m ) JEE Main 2013 (22 Apr Online) JEE Main Previous Year Paper (1) Statement-1 is true; Statement- 2 is false. (2) Statement-1 is true; Statement-2 is true; Statement-2 is a correct explanation for statement-1. (3) Statement-1 is false; Statement-2 is true. (4) Statement-1 a true; Statement-2 is true; Statement-2 is not a correct explanation for statement-1.

Q72.Equation of the line passing through the points of intersection of the parabola x2 = 8y and the ellipse x2 3 + y2 = 1 is : (1) y −3 = 0 (2) y + 3 = 0 (3) 3y + 1 = 0 (4) 3y −1 = 0

Q73.If the median and the range of four numbers {x, y, 2x + y, x −y}, where 0 < y < x < 2y, are 10 and 28 respectively, then the mean of the numbers is : (1) 18 (2) 10 (3) 5 (4) 14

Q73.The equation of the circle passing through the foci of the ellipse x216 + y29 = 1 , and having centre at (0, 3) is (1) x2 + y2 −6y −5 = 0 (2) x2 + y2 −6y + 5 = 0 (3) x2 + y2 −6y −7 = 0 (4) x2 + y2 −6y + 7 = 0

Q73.Let the equations of two ellipses be x2 y2 x2 y2 E1 : + = 1 and E2 : + = 1, 3 2 16 b2 If the product of their eccentricities is 1 , then the length of the minor axis of ellipse E2 is : 2 (1) 8 (2) 9 (3) 4 (4) 2

Q73.Consider the system of equations : x + ay = 0, y + az = 0 and z + ax = 0 . Then the set of all real values of ' a ' for which the system has a unique solution is: (1) R −{1} (2) R −{−1} (3) {1, −1} (4) {1, 0, −1}

Q74.The value of lim (1−cosx2x)(3+costan 4x x) is equal to x→0 (1) 1 (2) 2 (3) −14 (4) 21

Q74.The value of limx→0 x1 [tan−1 ( 2x+1x+1 ) −π4 ] is : (1) 1 (2) −12 (3) 2 (4) 0

Q75.Mean of 5 observations is 7 . If four of these observations are 6, 7, 8, 10 and one is missing then the variance of all the five observations is : (1) 4 (2) 6 (3) 8 (4) 2

Q75.Statement-1: The statement A →(B →A) is equivalent to A →(A ∨B). Statement-2: The statement ∼[(A ∧B) →(∼A ∨B)] is a Tautology. (1) Statement- 1 is false; Statement- 2 is true. (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 false. (4) Statement-1 is true; Statement-2 is true; Statement- 2 is the correct explanation for Statement-1.

Q75.In a set of 2n observations, half of them are equal to ' a ' and the remaining hall are equal to ' −a′ '. If the standard deviation of all the observations is 2 ; then the value of |a| is : (1) 2 (2) √2 (3) 4 (4) 2√2

Q75.On the sides AB, BC, CA of a △ABC, 3, 4, 5 distinct points (excluding vertices A, B, C ) are respectively chosen. The number of triangles that can be constructed using these chosen points as vertices are : (1) 210 (2) 205 (3) 215 (4) 220

Q75.Consider : Statement - I : (p ∧~q) ∧(~p ∧q) is a fallacy. Statement - II : (p →q) ↔(~q →~p) is a tautology. (1) Statement - I is true; statement - II is false. (2) Statement - I is false; Statement - II is true. (3) Statement - I true; Statement - II is true; (4) Statement - I is true; Statement - II is true; Statement - II is a correct explanation for Statement - II is not a correct explanation for Statement - I. Statement - I.

Q76.If two vertices of an equilateral triangle are A(−a, 0) and B(a, 0), a > 0, and the third vertex C lies above x- axis then the equation of the circumcircle of △ABC is : (1) 3x2 + 3y2 −2√3ay = 3a2 (2) 3x2 + 3y2 −2ay = 3a2 (3) x2 + y2 −2ay = a2 (4) x2 + y2 −√3ay = a2

Q76.Let R = {(x, y) : x, y ∈N and x2 −4xy + 3y2 = 0}, where N is the set of all natural numbers. Then the relation R is : (1) reflexive but neither symmetric nor transitive. (2) symmetric and transitive. (3) reflexive and symmetric, (4) reflexive and transitive. JEE Main 2013 (23 Apr Online) JEE Main Previous Year Paper

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

Q77.Let A , other than I or −I, be a 2 × 2 real matrix such that A2 = I, I being the unit matrix. Let Tr(A) be the sum of diagonal elements of A. Statement-1: Tr(A) = 0 Statement-2: det(A) = −1 (1) Statement-1 is true; Statement- 2 is false. (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 true; Statement-2 is a correct explanation for Statement-1. (4) Statement-1 is false; Statement- 2 is true.

Q77.Let S = {( a11a21 a12a22 ) (1) 27 (2) 24 (3) 10 (4) 20

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.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.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 :

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

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