Mathematics questions
18011 published questions with worked solutions.
- 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
- If the shortest distance between the lines x - 3 = y - 2 -1 = z - 1 1 and x + 2 -3 = y + 5 2 = z - 4 4 is 44 30 , then the...
- Let α, β be roots of x² + √2x − 8 = 0. If Uₙ = αⁿ + βⁿ, then U_ 10 + 2U_9 2U_8 is equal to _____.
- If the system of equations 2x + 7y + λz = 3, 3x + 2y + 5z = 4, x + μy + 32z = −1 has infinitely many solutions, then (λ − μ) is...
- If the solution y(x) of the given differential equation (eʸ + 1)cos x dx + eʸ sin x dy = 0 passes through the point ( 2, 0 ),...
- If |x| < 1, |y| < 1 and x ≠ y, then the sum to infinity of the following series (x+y)+(x^2+xy+y^2)+(x^3+x^2y+xy^2+y^3)+
- Let >0, >0 be such that ^3+ ^2=4. If the maximum value of the term independent of x in the binomial expansion of ( x^ 1/9 + x^...
- If a function f(x) defined by f(x)= cases ae^x+be^ -x , & -1 x<1 cx^2, & 1 x 3 ax^2+2cx, & 3<x 4 cases be continuous for some a,...