Practice questions
88551 published questions with worked solutions.
- If the shortest distance between the lines L₁ : r = (2 + λ)î + (1 − 3λ)ĵ + (3 + 4λ)k̂, λ ∈ R, L₂ : r = 2(1 + μ)î + 3(1 + μ)ĵ + (5...
- If sin x = − 35, where π < x < 3 2 , then 80(tan²x − cos x) is equal to:
- Let I(x) = 6 ^2x(1 - x)^2 dx. If I(0) = 3, then I ( 12 ) is equal to:
- The equations of two sides AB and AC of a triangle ABC are 4x + y = 14 and 3x − 2y = 5, respectively. The point (2, - 43 )...
- Let [t] be the greatest integer less than or equal to t. Let A be the set of all prime factors of 2310 and f : A → ℤ be the...
- Let z be a complex number such that |z + 2| = 1 and Im ( z + 1 z + 2 ) = 15. Then the value of |Re( z + 2 )| is:
- For the function f(x) = (cos x) − x + 1, x ∈ R, between the following two statements (S1) f(x) = 0 for only one value of x in [0,...
- The set of all α, for which the vector a = t i + 6 j - 3 k and b = t i - 2 j - 2 t k are inclined at an obtuse angle for all t ∈...
- Let H : -x^2 a^2 + y^2 b^2 = 1 be the hyperbola, whose eccentricity is √3 and the length of the latus rectum is 4√3. Suppose the...
- Let A = bmatrix 2 & -1 1 & 1 bmatrix . If the sum of the diagonal elements of A¹³ is 3ⁿ, then n is equal to ______.
- If the orthocentre of the triangle formed by the lines 2x + 3y − 1 = 0, x + 2y − 1 = 0 and ax + by − 1 = 0, is the centroid of...
- Three balls are drawn at random from a bag containing 5 blue and 4 yellow balls. Let the random variables X and Y respectively...
- The number of 3-digit numbers, formed using the digits 2, 3, 4, 5 and 7, when the repetition of digits is not allowed, and which...
- If the range of f( ) = ^4 + 3 ^2 ^4 + ^2 , θ ∈ R is [α, β], then the sum of the infinite G.P., whose first term is 64 and the...
- Let = _ r=0 ^ n (4r^2 + 2r + 1) nr and = ( _ r=0 ^ n nr r + 1 ) + 1 n + 1 . If 140 < 2 < 281, then the value of n is ______.
- Let a = 9 i - 13 j + 25 k, b = 3 i + 7 j - 13 k and c = 17 i - 2 j + k be three given vectors. If r is a vector such that r a = (...
- Let the area of the region enclosed by the curve y = min sin x, cos x and the x-axis between x = −π to x = π be A. Then A² is...
- The value of _ x 0 2 ( 1 - x 2x [3] 3x [10] 10x x^2 ) is ________.
- In a hypothetical fission reaction ^ 236 _ 92 X → ^ 141 _ 56 Y + ^ 92 _ 36 Z + 3R. The identity of emitted particles (R) is:
- If ε₀ is the permittivity of free space and E is the electric field, then ε₀E² has the dimensions: