Q.5779·Miscellaneous·2019·EasyA curve y = me^mx where m > 0 intersects y-axis at a point P. What is the slope of the curve at the point of intersection P ?View question
Q.5780·Miscellaneous·2019·EasyWhich one of the following is the second degree polynomial function f(x) where f(0) = 5, f(–1) = 10 and f(1) = 6 ?View question
Q.5781·Miscellaneous·2019·EasyWhat is the area of the region bounded by |x| < 5, y = 0 and y = 8?View question
Q.5784·Miscellaneous·2019·EasyIf angle C of a triangle ABC is a right angle, then what is tanA + tanB equal to?View question
Q.5785·Miscellaneous·2019·EasyFor what value of k is the function ⎧ 2x + 1/4 , x < 0 f(x) = ⎨ k , x = 0 continuous ? ⎩ (x + 1/2)^2 , x > 0View question
Q.5786·Miscellaneous·2019·EasyLet f(x) = x² + 2x – 5 and g(x) = 5x + 30 If h(x) = 5f(x) – xg(x), then what is the derivative of h(x) ?View question
Q.5787·Miscellaneous·2019·EasyLet f(x) = x² + 2x – 5 and g(x) = 5x + 30 Consider the following statements : 1. f[g(x)] is a polynomial of degree 3. 2. g[f(x)] is a polynomial of degree 2. Which of the above statements is/are correct ?View question
Q.5788·Miscellaneous·2019·EasyLet f(x) = x² + 2x – 5 and g(x) = 5x + 30 What are the roots of the equation g[f(x)] = 0 ?View question
Q.5790·Miscellaneous·2019·EasyA straight line passes through the point (1, 1, 1) makes an angle 60° with the positive direction of z-axis, and the cosine of the angles made by it with the positive directions of the y-axis and the x-axis are in the ratio √3 : 1. What is the acute angle between the two possible positions of the line ?View question
Q.5793·Miscellaneous·2019·EasyConsider the function f(x) = 3x⁴ - 20x³ - 12x² + 288x + 1 In which one of the following intervals is the function decreasing ?View question
Q.5794·Miscellaneous·2019·EasyA ladder 9 m long reaches a point 9 m below the top of a vertical flagstaff. From the foot of the ladder, the elevation of the flagstaff is 60°. What is the height of the flagstaff?View question
Q.5795·Miscellaneous·2019·EasyIf the magnitude of the sum of two non-zero vectors is equal to the magnitude of their difference, then which one of the following is correct?View question
Q.5796·Miscellaneous·2019·EasyConsider the following equations for two vectors a and b : 1. ( a + b ) · ( a − b ) = | a |² − | b |² 2. [( a + b )] [( a − b )] = | a |² − | b |² 3. | a · b |² + | a × b |² = | a |² | b |² Which of the above statements are correct?View question