Q.649·Miscellaneous·2024·EasyIf f(2x) = 4x^2 + 1, then for how many real values of x will f(2x) be the GM of f(x) and f(4x)?View question
Q.650·Miscellaneous·2024·EasyLet L: x + y + z + 4 = 0 = 2x - y - z + 8 be a line and P: x + 2y + 3z + 1 = 0 be a plane. What is the point of intersection of L and P?View question
Q.651·Miscellaneous·2024·EasyThree perfect dice are rolled. Under the condition that no two show the same face, what is the probability that one of the faces shown is an ace (one)?View question
Q.653·Miscellaneous·2024·EasyWhat is the minimum value of the function f(x) = log10(x^2 + 2x + 1)?View question
Q.654·Miscellaneous·2024·EasyIf f(x) = 4x + 1 and g(x) = kx + 2 such that f o g(x) = g o f(x), then what is the value of k?View question
Q.655·Miscellaneous·2024·EasyLet z = [y] and y = [x] - x, where [.] is the greatest integer function. If x is not an integer but positive, then what is the value of z?View question
Q.656·Miscellaneous·2024·EasyLet 2 ∫[(x² – 1)/(x² + 1)] dx = U(x) V(x) – 3ln |U(x) + V(x)| + V(x) + c What is U(x) V(x) equal to?View question
Q.657·Miscellaneous·2024·EasyLet y dx + (x – y^3) dy = 0 be a differential equation. What are the order and degree respectively of the differential equation?View question
Q.658·Miscellaneous·2024·EasyThe area bounded by the parabola y^2 = kx and the line x = k, where k > 0, is 4/3 square units What is the area of the parabola bounded by the latus rectum?View question
Q.659·Miscellaneous·2024·EasyFor two events A and B, P(A) = P(A|B) = 0.25 and P(B|A) = 0.5. Which of the following are correct? I. A and B are independent. II. P(Aᶜ ∪ Bᶜ) = 0.875 III. P(Aᶜ ∩ Bᶜ) = 0.375 Select the answer using the code given below:View question
Q.660·Miscellaneous·2024·EasyUrn A contains 2 white and 2 black balls while urn B contains 3 white and 2 black balls. One ball is transferred from urn A to urn B and then a ball is drawn out of urn B. What is the probability that the ball is white?View question
Q.661·Miscellaneous·2024·EasyThe area bounded by the parabola y^2 = kx and the line x = k, where k > 0, is 4/3 square units. What is the value of k?View question
Q.662·Miscellaneous·2024·EasyA fair coin is tossed till two heads occur in succession. What is the probability that the number of tosses required is less than 6?View question
Q.663·Miscellaneous·2024·EasyWhat is the mean deviation of the first 10 natural numbers?View question
Q.664·Miscellaneous·2024·EasyTwo perfect dice are thrown. What is the probability that the sum of the numbers on the faces is neither 9 nor 10?View question
Q.665·Miscellaneous·2024·EasyThe occurrence of a disease in an industry is such that the workers have 20% chance of suffering from it. What is the probability that out of 6 workers chosen at random, 4 or more will suffer from the disease?View question
Q.666·Miscellaneous·2024·EasyLet f(x) = [x]^2 – [x^2]. Consider the following statements: I. f(x) is continuous at x = 0. II. f(x) is continuous at x = 1. Which of the statements given above is/are correct?View question