Mathematics questions
18011 published questions with worked solutions.
- Let R = pmatrix x&0&0 0&y&0 0&0&z pmatrix be a non-zero 3 × 3 matrix, where x sinθ = y sin(θ + 2π/3) = z sin(θ + 4π/3) ≠ 0, θ ∈...
- Bag A contains 3 white, 7 red balls and Bag B contains 3 white, 2 red balls. One bag is selected at random and a ball is drawn...
- Let L₁ : r⃗ = (î − ĵ + 2k̂) + λ(î − ĵ + 2k̂), λ ∈ ℝ, L₂ : r⃗ = (ĵ − k̂) + μ(3î + ĵ + pk̂), μ ∈ ℝ, and L₃ : r⃗ = δ(ℓî + mĵ + nk̂),...
- Consider the system of linear equations x + y + z = 5, x + 2y + λ²z = 9, x + 3y + λz = μ, where λ, μ ∈ ℝ. Then, which of the...
- Let f(x) = (x + 3)²(x – 2)³, x ∈ [–4, 4]. If M and m are the maximum and minimum values of f, respectively in [–4, 4], then the...
- If x² – y² + 2hxy + 2gx + 2fy + c = 0 is the locus of a point, which moves such that it is always equidistant from the lines x +...
- Let P be a point on the hyperbola H : x²/9 − y²/4 = 1, in the first quadrant such that the area of triangle formed by P and the...
- Let a and b be two distinct real numbers. Let 11ᵗʰ term of a GP, whose first term is a and third term is b, is equal to pᵗʰ term...
- Let f : ℝ → ℝ be defined as f(x) = ae²ˣ + beˣ + cx. If f(0) = −1, f′(log_e 2) = 21 and _0^ _e4 (f(x) - cx)dx = 39 2, then the...
- In an examination of Mathematics paper, there are 20 questions of equal marks and the questions paper is divided into three...
- The number of real solution of the equation x(x² + 3|x| + 5|x – 1| + 6|x – 2|) = 0 is ________.
- Let Sₙ be the sum to n-terms of an arithmetic progression 3, 7, 11, ...... . If 40 < ( 6 n(n+1) _ k=1 ^nS_k ) < 42, then n equals...
- The area of the region enclosed by the parabola (y − 2)² = x − 1, the line x − 2y + 4 = 0 and the positive coordinate axes is...
- The number of symmetric relations defined on the set 1, 2, 3, 4 which are not reflexive is ________.
- Let = _ k=0 ^n nk^2 k+1 and = _ k=0 ^ n-1 nk n k+1 k+2 . If 5α = 6β, then n equals ________.
- Let a line passing through the point (−1, 2, 3) intersect the lines L₁ : (x − 1)/3 = (y − 2)/2 = (z + 1)/(−2) at M(α, β, γ) and...
- The variance σ² of the data | xᵢ | 0 | 1 | 5 | 6 | 10 | 12 | 17 | |---|---|---|---|---|---|---|---| | fᵢ | 3 | 2 | 3 | 2 | 6 | 3...
- Consider two circles C₁ : x² + y² = 25 and C₂ : (x − α)² + y² = 16, where α ∈ (5, 9). Let the angle between the two radii (one to...
- Let Y = Y(X) be a curve lying in the first quadrant such that the area enclosed by the line Y − y = Y′(x)(X − x) and the...
- If f(x) = vmatrix 2 ^4x & 2 ^4x & 3 + ^22x 3 + 2 ^4x & 2 ^4x & ^22x 2 ^4x & 3 + 2 ^4x & ^22x vmatrix , then 15f'(0) is equal to :