Practice Questions

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

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.All the students of a class performed poorly in Mathematics. The teacher decided to give grace marks of 10 to each of the students. Which of the following statistical measures will not change even after the grace marks were given ? (1) mode (2) variance (3) mean (4) median

Q76.The mean of a data set consisting of 20 observations is 40 . If one observation 53 was wrongly recorded as 33 , then the correct mean will be: (1) 41 (2) 49 (3) 40.5 (4) 42.5

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

Q76.A common tangent to the conics x2 = 6y and 2x2 −4y2 = 9 is: (1) x −y = 32 (2) x + y = 1 (3) x + y = 92 (4) x −y = 1 Then the number of non-singular matrices in the set S is : : aij ∈{0, 1, 2}, a11 = a22}

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

Q77.Let R = {(3, 3)(5, 5), (9, 9), (12, 12), (5, 12), (3, 9) , (3, 12), (3, 5)} be a relation on the set A = {3, 5, 9, 12} . Then, R is : (1) reflexive, symmetric but not transitive. (2) symmetric, transitive but not reflexive. (3) an equivalence relation. (4) reflexive, transitive but not symmetric. Q78. ⎡3 4 1 ⎤ If p, q, r are 3 real numbers satisfying the matrix equation, [pqr] 3 2 3 = [3 0 1 ] then 2p + q −r ⎣2 0 2 ⎦ equals : (1) −3 (2) −1 (3) 4 (4) 2

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.The matrix A2 + 4A −5I , where I is identity matrix and A = [14 −32 ], equals : (1) 2 1 (2) 0 −1 4 4 [2 0 ] [2 2 ] (3) 2 1 (4) 1 1 32 32 [2 0 ] [1 0 ]

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.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.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.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

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

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) = −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

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.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.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

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.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 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 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