Q.10297·Miscellaneous·2015·EasyConsider the following statements : 1. f(x) = ln x is an increasing function on (0, ∞). 2. f(x) = e^x - x (ln x) is an increasing function on (1, ∞). Which of the above statements is/are correct ?View question
Q.10298·Miscellaneous·2015·EasyConsider the following statements : Statement 1: The function f : R → R such that f(x) = x³ for all x ∈ R is one-one. Statement 2: f(a) = f(b) ⇒ a = b for all a, b ∈ R if the function f is one-one. Which one of the following is correct in respect of the above statements ?View question
Q.10299·Miscellaneous·2015·EasyConsider the function f(x) = (1/x)^(2x²), where x > 0 At what value of x does the function attain maximum value ?View question
Q.10300·Miscellaneous·2015·EasyConsider the function f(x) = (1/x)^(2x²), where x > 0 The maximum value of the function isView question
Q.10301·Miscellaneous·2015·EasyConsider f′(x) = (x²/2) - kx + 1 such that f(0) = 0 and f(3) = 15 The value of k isView question
Q.10302·Miscellaneous·2015·EasyConsider the function f(x) = -2x³ - 9x² - 12x + 1 The function f(x) is an increasing function in the intervalView question
Q.10303·Miscellaneous·2015·EasyConsider the function f(x) = -2x³ - 9x² - 12x + 1 The function f(x) is a decreasing function in the intervalView question
Q.10304·Miscellaneous·2015·EasyConsider the integrals A = ∫[0 to π] (sin x dx / (sin x + cos x)) and B = ∫[0 to π] (sin x dx / (sin x - cos x)) Which one of the following is correct ?View question
Q.10305·Miscellaneous·2015·EasyConsider the integrals A = ∫[0 to π] (sin x dx / (sin x + cos x)) and B = ∫[0 to π] (sin x dx / (sin x - cos x)) What is the value of B ?View question
Q.10306·Miscellaneous·2015·EasyConsider the function which is continuous everywhere. The value of A isView question
Q.10307·Miscellaneous·2015·EasyConsider the function which is continuous everywhere. The value of B isView question
Q.10308·Miscellaneous·2015·EasyThe degree of the differential equation (dy/dx - x = (y - x(dy/dx))^(-4)) isView question
Q.10309·Miscellaneous·2015·EasyThe differential equation of the family of circles passing through the origin and having centres on the x-axis isView question
Q.10310·Miscellaneous·2015·EasyA brass ball is tied to a thin wire and swung so as to move uniformly in a horizontal circle. Which of the following statements in this regard is/are true? 1.The ball moves with constant velocity 2.The ball moves with constant speed 3.The ball moves with constant acceleration 4.The magnitude of the acceleration of the ball is constant Select the correct answer using the code given below:View question
Q.10311·Miscellaneous·2015·EasyTwo long wires each carrying a d.c. current in the same direction are placed close to each other. Which one of the following statements is correct?View question
Q.10312·Miscellaneous·2015·EasyThe first Indian Satellite, Aryabhatt, was launched in the year:View question
Q.10313·Miscellaneous·2015·EasyWhich one of the following sea routes is the shortest from point to point?View question