Q.9235·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.9236·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.9237·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 area of the parallelogram?View question
Q.9238·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.9239·Miscellaneous·2016·EasyConsider a triangle ABC in which cos A + cos B + cos C = √3 sin(π/3) What is the value of sin(A/2) sin(B/2) sin(C/2)?View question
Q.9240·Miscellaneous·2016·EasyConsider a triangle ABC in which cos A + cos B + cos C = √3 sin(π/3) What is the value of: cos((A + B)/2) cos((B + C)/2) cos((C + A)/2)?View question
Q.9241·Miscellaneous·2016·EasyConsider the two circles (x - 1)² + (y - 3)² = r² and x² + y² - 8x + 2y + 8 = 0 What is the distance between the centres of the two circles?View question
Q.9242·Miscellaneous·2016·EasyConsider the two circles (x - 1)² + (y - 3)² = r² and x² + y² - 8x + 2y + 8 = 0 If the circles intersect at two distinct points, then which one of the following is correct?View question
Q.9243·Miscellaneous·2016·EasyConsider the two lines x + y + 1 = 0 and 3x + 2y + 1 = 0 What is the equation of the line passing through the point of intersection of the given lines and parallel to x-axis?View question
Q.9244·Miscellaneous·2016·EasyConsider the two lines x + y + 1 = 0 and 3x + 2y + 1 = 0 What is the equation of the line passing through the point of intersection of the given lines and parallel to y-axis?View question
Q.9245·Miscellaneous·2016·EasyConsider the equation k sin x + cos2x = 2k - 7 If the equation possesses solution, then what is the maximum value of k?View question
Q.9246·Miscellaneous·2016·EasyLet z₁, z₂ and z₃ be non-zero complex numbers satisfying z² = i z̅, where i = √−1. Consider the following statements: 1. z₁z₂z₃ is purely imaginary. 2. z₁z₂ + z₂z₃ + z₃z₁ is purely real. Which of the above statements is/are correct?View question
Q.9247·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
Q.9248·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.9249·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.9250·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.9251·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.9252·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