Q.11359·Miscellaneous·2014·EasyThe line 2y = 3x + 12 cuts the parabola 4y = 3x². What is the area enclosed by the parabola, the line and the y-axis in the first quadrant ?View question
Q.11360·Miscellaneous·2014·EasyConsider the function f(x) = { (tan kx)/x , x < 0 3x + 2k² , x ≥ 0 What is the non-zero value of k for which the function is continuous at x = 0 ?View question
Q.11361·Miscellaneous·2014·EasyConsider the following statements : 1.The function f(x) = [x], where [.] is the greatest integer function defined on R, is continuous at all points except at x = 0. 2.The function f(x) = sin|x| is continuous for all x ∈ R. Which of the above statements is/are correct ?View question
Q.11362·Miscellaneous·2014·EasyConsider the curve x = a(cos θ + θ sin θ) and y = a(sin θ - θ cos θ). What is dy/dx equal to ?View question
Q.11363·Miscellaneous·2014·EasyIf y = x ln x + xe^x, then what is the value of dy/dx at x = 1 ?View question
Q.11364·Miscellaneous·2014·EasyConsider I = ∫₀^π (x dx) / (1 + sin x) What is I equal to ?View question
Q.11365·Miscellaneous·2014·EasyConsider ∫ (x tan⁻¹x dx) = A(x² + 1) tan⁻¹x + Bx + C, where C is the constant of integration. What is the value of A ?View question
Q.11366·Miscellaneous·2014·EasyConsider ∫ (x tan⁻¹x dx) = A(x² + 1) tan⁻¹x + Bx + C, where C is the constant of integration. What is the value of B ?View question
Q.11367·Miscellaneous·2014·EasyA rectangular box is to be made from a sheet of 24 inch length and 9 inch width cutting out identical squares of side length x from the four corners and turning up the sides. What is the value of x for which the volume is maximum ?View question
Q.11368·Miscellaneous·2014·EasyA rectangular box is to be made from a sheet of 24 inch length and 9 inch width cutting out identical squares of side length x from the four corners and turning up the sides. What is the maximum volume of the box ?View question
Q.11370·Miscellaneous·2014·EasyEliminating the arbitrary constants B and C in the expression y = (2/3C)(Cx – 1)^(3/2) + B, we getView question
Q.11371·Miscellaneous·2014·EasyLet f(x) = ax² + bx + c such that f(1) = f(-1) and a, b, c are in Arithmetic Progression. What is the value of b ?View question
Q.11372·Miscellaneous·2014·EasyIf |a + b| = |a – b|, then which one of the following is correct ?View question
Q.11373·Miscellaneous·2014·EasyWhat is the area of the triangle OAB where O is the origin, OA = 3i – j + k and OB = 2i + j – 3k ?View question
Q.11374·Miscellaneous·2014·EasyWhich one of the following is the unit vector perpendicular to both a = -i + j + k and b = i – j + k ?View question
Q.11375·Miscellaneous·2014·Easya + b + c = 0 such that |a| = 3, |b| = 5 and |c| = 7. What is the angle between a and b ?View question
Q.11376·Miscellaneous·2014·Easya + b + c = 0 such that |a| = 3, |b| = 5 and |c| = 7. What is cosine of the angle between b and c ?View question