Q.685·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.686·Miscellaneous·2024·EasyThe product of 5 consecutive terms of an AP is 229635. The first, second and fifth terms are in GP. What is the sum of all five terms?View question
Q.687·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.688·Miscellaneous·2024·EasyLet 2x^2 + 2y^2 + 2z^2 + 3x + 3y + 3z - 6 = 0 be a sphere. What is the diameter of the sphere?View question
Q.689·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 is the point of intersection of the diagonals of the trapezium?View question
Q.690·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.691·Miscellaneous·2024·EasyLet ABCDEF be a regular hexagon. If AD̄ = m BC̄ and CF̄ = n AB̄ , then what is m equal to?View question
Q.692·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.694·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
Q.695·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.696·Miscellaneous·2024·EasyThree different numbers are selected at random from the first 15 natural numbers. What is the probability that the product of two of the numbers is equal to third number?View question
Q.697·Miscellaneous·2024·EasyLet A and B be two events such that P(AUB) ≥ 0-75 and 0-125 < P(ANB) 0-375. What is the minimum value of P(A) + P(B)?View question
Q.698·Miscellaneous·2024·EasyLet A and B be two events such that P(AUB) ≥ 0-75 and 0-125 < P(ANB) 0-375. What is the maximum value of P(A) + P(B)?View question
Q.699·Miscellaneous·2024·EasyA, B and C are three events such that P(A) = 0-6, P(B) = 0-4, P(C) = 0-5, P(AUB) = 0-8, P(ANC) = 0-3 and P(ANBNC) = 0-2 and P(AUBUC) > 0-85. What is the minimum value of P(B|C)?View question
Q.700·Miscellaneous·2024·EasyA, B and C are three events such that P(A) = 0-6, P(B) = 0-4, P(C) = 0-5, P(AUB) = 0-8, P(ANC) = 0-3 and P(ANBNC) = 0-2 and P(AUBUC) > 0-85. What is the maximum value of P(B|C)?View question
Q.701·Miscellaneous·2024·EasyFrom data (-4, 1), (-1, 2), (2, 7) and (3, 1), the regression line of y on x is obtained as y = a + bx, then what is the value of 2a + 15b?View question
Q.702·Miscellaneous·2024·EasyIf two random variables X and Y are connected by relation 2X - 3Y = 4 and X follows Binomial distribution with parameters n = 10 and p = 1/2, then what is the variance of Y?View question