Q.9235·Miscellaneous·2016·EasyGiven that logₓ y, log_z x, log_y z are in GP, xyz = 64 and x³, y³, z³ are in AP. Which one of the following is correct? xy, yz and zx areView question
Q.9236·Miscellaneous·2016·EasyLet z be a complex number satisfying |z - 4| / |z - 8| = 1 and |z / (z - 2)| = 3/2 What is |z| equal to?View question
Q.9237·Miscellaneous·2016·EasyLet z be a complex number satisfying |z - 4| / |z - 8| = 1 and |z / (z - 2)| = 3/2 What is |(z - 6) / (z + 6)| equal to?View question
Q.9238·Miscellaneous·2016·EasyA function f(x) is defined as follows : f(x) = x + π for x ∈ [−π, 0) π cos x for x ∈ [0, π/2] (x − π/2)² for x ∈ (π/2, π] Consider the following statements : 1. The function f(x) is continuous at x = 0. 2. The function f(x) is continuous at x = π/2. Which of the above statements is/are correct?View question
Q.9239·Miscellaneous·2016·Easyf(x) = x + π for x ∈ [−π, 0) π cos x for x ∈ [0, π/2] (x − π/2)² for x ∈ (π/2, π] Consider the following statements : 1. The function f(x) is differentiable at x = 0. 2. The function f(x) is differentiable at x = π/2. Which of the above statements is/are correct?View question
Q.9240·Miscellaneous·2016·EasyLet α and β (α < β) be the roots of the equation x² + bx + c = 0, where b > 0 and c < 0. Consider the following : 1. β < −α 2. β < |α| Which of the above is/are correct?View question
Q.9241·Miscellaneous·2016·EasyLet α and β (α < β) be the roots of the equation x² + bx + c = 0, where b > 0 and c < 0. Consider the following : 1. α + β + αβ > 0 2. α²β + β²α > 0 Which of the above is/are correct?View question
Q.9242·Miscellaneous·2016·EasyConsider a parallelogram whose vertices are A(1, 2), B(4, y), C(x, 6) and D(3, 5) taken in order. What is the point of intersection of the diagonals?View question
Q.9243·Miscellaneous·2016·EasyConsider the function f(x) = (x² + (x - 2)²) What is the number of points of local minima of the function f(x)?View question
Q.9244·Miscellaneous·2016·EasyConsider the lines y = 3x, y = 6x and y = 9 The centroid of the triangle is at which one of the following points?View question
Q.9245·Miscellaneous·2016·EasyConsider the lines y = 3x, y = 6x and y = 9 What is the area of the triangle formed by these lines?View question
Q.9246·Miscellaneous·2016·EasyConsider the equation x + |y| = 2y What is the derivative of y as a function of x with respect to x for x < 0?View question
Q.9247·Miscellaneous·2016·EasyConsider the equation x + |y| = 2y Which of the following statements are not correct? 1. y as a function of x is not defined for all real x. 2. y as a function of x is not continuous at x = 0. 3. y as a function of x is differentiable for all x. Select the correct answer using the code given below.View question
Q.9248·Miscellaneous·2016·EasyA straight line intersects x and y axes at P and Q respectively. If (3, 5) is the middle point of PQ, then what is the area of the triangle OPQ?View question
Q.9249·Miscellaneous·2016·EasyConsider the function f(θ) = 4(sin²θ + cos⁴θ) Consider the following statements: 1. f(θ) = 2 has no solution. 2. f(θ) = 7/2 has a solution. Which of the above statements is/are correct?View question
Q.9250·Miscellaneous·2016·EasyGiven that aₙ = ∫(0 to π) [sin²((n+1)x) / sin 2x] dx Consider the following statements: 1. The sequence {a₂n} is in AP with common difference zero. 2. The sequence {a₂n+1} is in AP with common difference zero. Which of the above statements is/are correct?View question
Q.9251·Miscellaneous·2016·EasyConsider the curves f(x) = x|x| - 1 and g(x) = {3x/2, x > 0; 2x, x ≤ 0} Where do the curves intersect?View question
Q.9252·Miscellaneous·2016·EasyConsider the curves f(x) = x|x| - 1 and g(x) = {3x/2, x > 0; 2x, x ≤ 0} What is the area bounded by the curves?View question