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·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.9237·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.9238·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.9239·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.9240·Miscellaneous·2016·EasyWhich of the following is/are the component/components of the Integrated Power Development Scheme launched by the Government of India recently? 1. Strengthening of sub-transmission and distribution networks in the urban areas 2. Metering of distribution transformers/feeders/consumers in the rural areas Select the correct answer using the code given below:View question
Q.9241·Miscellaneous·2016·EasyWhich of the following statements relating to the Comptroller and Auditor General (CAG) of India is/are correct? 1. The CAG can attend the sittings of the Committee on Public Accounts. 2. The CAG can attend the sittings of Lok Sabha and Rajya Sabha. 3. The jurisdiction of CAG is co-extensive with powers of the Union Government. Select the correct answer using the code given below:View question
Q.9242·Miscellaneous·2016·EasyConsider the function f(x) = (x² + (x - 2)²) What is the number of points of local maxima of the function f(x)?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·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.9249·Miscellaneous·2016·EasyConsider the function f(x) = |x - 1| + x² where x ∈ R. What is the area of the region bounded by x-axis, the curve y = f(x) and the two ordinates x = 1 and x = 3/2?View question
Q.9250·Miscellaneous·2016·EasyConsider the function f(x) = |x - 1| + x² where x ∈ R. What is the area of the region bounded by x-axis, the curve y = f(x) and the two ordinates x = 1/2 and x = 1?View question
Q.9251·Miscellaneous·2016·EasyConsider the function f(x) = |x - 1| + x² where x ∈ R. Which one of the following statements is correct?View question
Q.9252·Miscellaneous·2016·EasyConsider the function f(x) = |x - 1| + x² where x ∈ R. Which one of the following statements is correct?View question