Q.9235·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.9236·Miscellaneous·2016·EasyConsider the curves y = |x − 1| and |x| = 2 What is the area of the region bounded by the curves and x-axis?View question
Q.9237·Miscellaneous·2016·EasyConsider the curves y = |x − 1| and |x| = 2 What is/are the point(s) of intersection of the curves?View question
Q.9238·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.9239·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.9240·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.9241·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.9242·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.9243·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.9244·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.9245·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.9246·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.9247·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.9248·Miscellaneous·2016·EasyWhich of the following rivers flow through Himachal Pradesh? 1. Beas 2. Chenab 3. Ravi 4. Sutlej Select the correct answer using the code given below:View question
Q.9249·Miscellaneous·2016·EasyConsider the following statements about Rashtrakuta kings: 1. They were ardent patrons of Shaivism and did not support other religions. 2. They built the famous Kailasa temple at Ellora. Which of the statements given above is/are correct?View question
Q.9250·Miscellaneous·2016·EasyWhich one among the following Acts for the first time allowed Indians, at least theoretically, entry to higher posts in British Indian administration?View question
Q.9251·Miscellaneous·2016·EasyThe citizens of India do not have which one of the following Fundamental Rights?View question
Q.9252·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