Practice questions
88551 published questions with worked solutions.
- If three letters can be posted to any one of the 5 different addresses, then the probability that the three letters are posted to...
- Suppose the solution of the differential equation dy dx = (2 + )x - y + 2 x - 2 y - ( - 4 ) represents a circle passing through...
- If the locus of the point, whose distances from the point (2, 1) and (1, 3) are in the ratio 5 : 4, is ax² + by² + cxy + dx + ey...
- _ n (1^2 - 1)(n - 1) + (2^2 - 2)(n - 2) + + ((n - 1)^2 - (n - 1)) 1 (1^3 + 2^3 + + n^3) - (1^2 + 2^2 + + n^2) is equal to
- A software company sets up m number of computer systems to finish an assignment in 17 days. If 4 computer systems crashed on the...
- If z₁, z₂ are two distinct complex number such that | z_1 - 2z_2 12 - z_1 z_2 | = 2, then
- If the function f(x) = ( 1x )^ 2x ; x > 0 attains the maximum value at x = 1e then:
- Let a = 6 i + j - k and b = i + j. If c is a vector such that | c| ≥ 6, a c = 6| c|, | c - a| = 2√2 and the angle between a b and...
- If all the words with or without meaning made using all the letters of the word "NAGPUR" are arranged as in a dictionary, then...
- Suppose for a differentiable function h, h(0) = 0, h(1) = 1 and h′(0) = h′(1) = 2. If g(x) = h(eˣ)e^ h(x) , then g′(0) is equal...
- Let P(α, β, γ) be the image of the point Q(3, −3, 1) in the line x - 0 1 = y - 3 1 = z - 1 -1 and R be the point (2, 5, −1). If...
- If P(6, 1) be the orthocentre of the triangle whose vertices are A(5, −2), B(8, 3) and C(h, k), then the point C lies on the...
- Let f(x) = 1 7 - 5x be a function defined on R. Then the range of the function f(x) is equal to:
- Let a = 2 i + j - k, b = (( a ( i + j)) i) i. Then the square of the projection of a on b is:
- If the area of region (x, y) : a x^2 y 1x, 1 ≤ x ≤ 2, 0 < a < 1 is (log_e2) − 17 then the value of 7a − 3 is equal to:
- If 1 a^2 ^2x + b^2 ^2x dx = 1 12 ^ -1 (3 x) + constant, then the maximum value of a sin x + b cos x, is:
- If A is a square matrix of order 3 such that det(A) = 3 and det(adj(−4 adj(−3 adj(3 adj((2A)⁻¹))))) = 2ᵐ3ⁿ, then m + 2n is equal...
- Let [t] denotes the greatest less than or equal to t. Let f : [0, ∞) → R be a function defined by f(x) = [ x2 + 3 ] - [ x]. Let S...
- Let [t] denote the largest integer less than or equal to t. If _0^3 ([x^2] + [ x^2 2 ] )dx = a + b 2 - 3 - 5 + c 6 - 7, where a,...
- In a triangle ABC, BC = 7, AC = 8, AB = α ∈ N and cosA = 23. If 49cos(3C) + 42 = mn, where gcd(m, n) = 1, then m + n is equal to...Not in JEE syllabus