Q.9217·Miscellaneous·2016·EasyConsider a circle passing through the origin and the points (a, b) and (−b, −a). What is the sum of the squares of the intercepts cut off by the circle on the axes?View question
Q.9218·Miscellaneous·2016·EasyConsider the following statements : 1. There exists θ ∈ (−π/2, π/2) for which tan⁻¹(tan θ) ≠ θ. 2. sin⁻¹(1/3) − sin⁻¹(1/5) = sin⁻¹ ( 2√2(√3 − 1) / 15 ) Which of the above statements is/are correct?View question
Q.9219·Miscellaneous·2016·EasyConsider the following statements : 1. tan⁻¹ x + tan⁻¹(1/x) = π 2. There exist x, y ∈ [−1, 1], where x ≠ y such that sin⁻¹ x + cos⁻¹ y = π/2. Which of the above statements is/are correct?View question
Q.9220·Miscellaneous·2016·EasyWhat is the number of natural numbers less than or equal to 1000 which are neither divisible by 10 nor 15 nor 25?View question
Q.9221·Miscellaneous·2016·Easy(a, 2b) is the mid-point of the line segment joining the points (10, -6) and (k, 4). If a - 2b = 7, then what is the value of k?View question
Q.9222·Miscellaneous·2016·EasyConsider the following statements : 1. If ABC is an equilateral triangle, then 3 tan (A + B) tan C = 1. 2. If ABC is a triangle in which A = 78°, B = 66°, then tan (B + C)/2 < tan A. 3. If ABC is any triangle, then tan (A + B)/2 = cot (C/2). Which of the above statements is/are correct?View question
Q.9223·Miscellaneous·2016·EasyThree dice are thrown simultaneously. What is the probability that the sum on the three faces is at least 5?View question
Q.9224·Miscellaneous·2016·EasyIf m is the geometric mean of log(yz), log(zx), log(xy), then what is the value of m?View question
Q.9225·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.9226·Miscellaneous·2016·EasyConsider the equation k sin x + cos2x = 2k - 7 If the equation possesses solution, then what is the minimum value of k?View question
Q.9227·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.9228·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.9229·Miscellaneous·2016·EasyConsider the function f(x) = | x³ sin x cos x | | 6 −1 0 | | p p² p³ | where p is a constant. What is the value of p for which f ''(0) = 0?View question
Q.9230·Miscellaneous·2016·EasyConsider the function f(x) = | x³ sin x cos x | | 6 −1 0 | | p p² p³ | where p is a constant. What is the value of f '(0)?View question
Q.9231·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.9232·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.9233·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.9234·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? x, y and z areView question