Practice questions
88551 published questions with worked solutions.
- Let a unit vector which makes an angle of 60º with 2 i + 2 j - k and an angle of 45º with i - k be C. Then C + (- 12 i + 1 3 2 j...
- Let the first three terms 2, p and q, with q ≠ 2, of a G.P. be respectively the 7th, 8th and 13th terms of an A.P. If the 5th...
- Let a, b ∈ R. Let the mean and the variance of 6 observations −3, 4, 7, −6, a, b be 2 and 23, respectively. The mean deviation...
- If 2 and 6 are the roots of the equation ax² + bx + 1 = 0, then the quadratic equation, whose roots are 1 2a + b and 1 6a + b ,...
- Let α and β be the sum and the product of all the non-zero solutions of the equation ( z)^2 + |z| = 0, z ∈ C. Then 4(α² + β²) is...
- Let the point, on the line passing through the points P(1, −2, 3) and Q(5, −4, 7), farther from the origin and at a distance of 9...
- A square is inscribed in the circle x² + y² − 10x − 6y + 30 = 0. One side of this square is parallel to y = x + 3. If (x_i, y_i)...
- If the domain of the function ^ -1 ( 3x - 22 2x - 19 ) + _e ( 3x^2 - 8x + 5 x^2 - 3x - 10 ) is (α, β], then 3α + 10β is equal to-
- Let f(x) = x⁵ + 2e^ x/4 for all x ∈ R. Consider a function g(x) such that (gof)(x) = x for all x ∈ R. Then the value of 8g′(2) is:
- Let α ∈ (0, ∞) and A = bmatrix 1 & 2 & 1 & 0 & 1 0 & 1 & 2 bmatrix . If det(adj(2A − Aᵀ) · adj(A − 2Aᵀ)) = 2⁸, then (det(A))² is...
- In a survey of 220 students of a higher secondary school, it was found that at least 125 and at most 130 students studied...
- Let the solution y = y(x) of the differential equation dy dx - y = 1 + 4 x satisfy y(π) = 1. Then y ( 2 ) + 10 is equal to ______...
- If the shortest distance between the lines x + 2 2 = y + 3 3 = z - 5 4 and x - 3 1 = y - 2 -3 = z + 4 2 is 38 3 5 k and...
- Let a = 1 + ^2C_2 3! + ^3C_2 4! + ^4C_2 5! + , b = 1 + ^1C_0 + ^1C_1 1! + ^2C_0 + ^2C_1 + ^2C_2 2! + ^3C_0 + ^3C_1 + ^3C_2 +...
- Let A be a 3 × 3 matrix of non-negative real elements such that A bmatrix 1 1 1 bmatrix = 3 bmatrix 1 1 1 bmatrix . Then the...
- Let the length of the focal chord PQ of the parabola y² = 12x be 15 units. If the distance of PQ from the origin is p, then 10p²...
- Let ABC be a triangle of area 15√2 and the vectors AB = i + 2 j - 7 k, BC = a i + b j + c k and AC = 6 i + d j - 2 k, d > 0. Then...
- Light emerges out of a convex lens when a source of light kept at its focus. The shape of wavefront of the light is:
- If G be the gravitational constant and u be the energy density then which of the following quantity have the dimension as that...
- Given below are two statements: Statement-I: When a capillary tube is dipped into a liquid, the liquid neither rises nor falls in...