Q.667·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.668·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.669·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.670·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.671·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.672·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.673·Miscellaneous·2024·EasyA die has two faces with number 4, three faces with number 5 and one face with number 6. If the die is rolled once, then what is the probability of getting 4 or 5?View question
Q.674·Miscellaneous·2024·EasyA box contains 2 black, 4 yellow and 6 white balls. Three balls are drawn in succession with replacement. What is the probability that all three are of the same colour?View question
Q.675·Miscellaneous·2024·EasyA can hit a target 5 times in 6 shots, B can hit 4 times in 5 shots and C can hit 3 times in 4 shots. What is the probability that A and C may hit but B may lose?View question
Q.676·Miscellaneous·2024·EasyThe letters of the word ZOOLOGY are arranged in all possible ways. What is the probability that the consonants and vowels occur alternatively?View question
Q.677·Miscellaneous·2024·EasyWhat is the mean deviation of the first 10 natural numbers?View question
Q.678·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.679·Miscellaneous·2024·EasyLet S be the line of intersection of two planes x + y + z = 1 and 2x + 3y - 4z = 8. Which of the following are the direction ratios of S?View question
Q.680·Miscellaneous·2024·EasyLet 2x^2 + 2y^2 + 2z^2 + 3x + 3y + 3z - 6 = 0 be a sphere. The centre of the sphere lies on the planeView question
Q.681·Miscellaneous·2024·EasyLet S be the line of intersection of two planes x + y + z = 1 and 2x + 3y - 4z = 8. If (l, m, n) are direction cosines of S, then what is the value of 43(l^2 + m^2 + n^2)?View question
Q.682·Miscellaneous·2024·EasyABCD is an isosceles trapezium and AB is parallel to DC . Let A(2, 3), B(4, 3), C(5, 1) be the vertices. What are the coordinates of vertex D?View question
Q.683·Miscellaneous·2024·EasyThe diagonals of a quadrilateral ABCD are along the lines x – 2y = 1 and 4x + 2y = 3 . The quadrilateral ABCD may be aView question
Q.684·Miscellaneous·2024·EasyIf P(2, 4), Q(8, 12), R(10, 14) and S(x, y) are vertices of a parallelogram, then what is (x + y) equal to?View question