Q.5779·Miscellaneous·2019·EasyArithmetic mean of 10 observations is 60 and sum of squares of deviations from 50 is 5000. What is the standard deviation of the observations?View question
Q.5780·Miscellaneous·2019·EasyThe median of the observations 22, 24, 33, 37, x + 1, x + 3, 46, 47, 57, 58 in ascending order is 42. What are the values of 5th and 6th observations respectively ?View question
Q.5781·Miscellaneous·2019·EasyA bag contains 20 books out of which 5 are defective. If 3 of the books are selected at random and removed from the bag in succession without replacement, then what is the probability that all three books are defective?View question
Q.5782·Miscellaneous·2019·EasyA coin is biased so that heads comes up thrice as likely as tails. For three independent tosses of a coin, what is the probability of getting at most two tails?View question
Q.5783·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.5785·Miscellaneous·2019·EasyConsider the following statements : 1. The magnitude of a × b is same as the area of a triangle with sides a and b 2. If a × b = 0 where a ≠ 0, b ≠ 0, then a = λb Which of the above statements is/are correct ?View question
Q.5786·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
Q.5787·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.5789·Miscellaneous·2019·EasyIf angle C of a triangle ABC is a right angle, then what is tanA + tanB equal to?View question
Q.5791·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.5792·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.5795·Miscellaneous·2019·EasyConsider the function f(x) = g(x) + h(x) where g(x) = sin(x/4) and h(x) = cos(4x/5) What is the period of the function f(x) ?View question
Q.5796·Miscellaneous·2019·EasyConsider the function f(x) = g(x) + h(x) where g(x) = sin(x/4) and h(x) = cos(4x/5) What is the period of the function h(x) ?View question