Mathematics questions
18011 published questions with worked solutions.
- Let a circle pass through the origin and its centre be the point of intersection of two mutually perpendicular lines x + (k − 1)y...
- Let O be the origin, and P and Q be two points on the rectangular hyperbola xy = 12 such that the mid point of the line segment...
- Let the parabola y = x² + px + q passing through the point (1, −1) be such that the distance between its vertex and the x-axis is...
- Let P = θ ∈ [0, 4π] : tan²θ ≠ 1 and S = a ∈ ℤ : 2(cos⁸θ − sin⁸θ)sec2θ = a², θ ∈ P . Then n(S) is:Not in JEE Main syllabus
- Let the vectors a = - i + j + 3 k and b = i + 3 j + k. For some λ, μ ∈ ℝ, let c = a + b. If c (3 i - 6 j + 2 k) = 10 and c ( i +...
- Let the point A be the foot of perpendicular drawn from the point P(a, b, 0) on the line x-1 2 = y-2 1 = z- 3 . If the midpoint...
- Two adjacent sides of a parallelogram PQRS are given by PQ = j + k and PS = i - j. If the side PS is rotated about the point P by...
- The value of _0^ 20 ( ^4x + ^4x)dx is equal to:
- Let f(x) be a polynomial of degree 5, and have extrema at x = 1 and x = −1. If _ x 0 ( f(x) x^3 ) = -5, then f(2) − f(−2) is...
- Let f(x) = ( 16x+24 x^2+2x-15 )dx. If f(4) = 14log_e(3) and f(7) = log_e(2^ 3^ )$, α, β ∈ ℕ, then α + β is equal to:
- Let x = x(y) be the solution of the differential equation 2y^2 dx dy - 2xy + x^2 = 0, y > 1, x(e) = e. Then x(e²) is equal to:
- Let A = 2, 3, 4, 5, 6 . Let R be a relation on the set A × A given by (x, y)R(z, w) if and only if x divides z and y ≤ w. Then...
- Consider the matrices A = bmatrix 2 & -2 4 & -2 bmatrix and B = bmatrix 3 & 9 1 & 3 bmatrix . If matrices P and Q are such that...
- Let A be the point (3, 0) and circles with variable diameter AB touch the circle x² + y² = 36 internally. Let the curve C be the...
- If the area of the region bounded by 16x² − 9y² = 144 and 8x − 3y = 24 is A, then 3(A + 6log_e(3)) is equal to _______.
- The number of points in the interval [2, 4], at which the function f(x) = [x^2 - x - 12 ], where [·] denotes the greatest integer...
- Let α, α + 2, α ∈ ℤ, be the roots of the quadratic equation x(x + 2) + (x + 1)(x + 3) + (x + 2)(x + 4) + … + (x + n − 1)(x + n +...
- Let x and y be real numbers such that 50 ( 2x 1 + 3i - y 1 - 2i ) = 31 + 17i, i = √−1. Then the value of 10(x − 3y) is:
- Let α, β ∈ ℝ be such that the system of linear equations x + 2y + z = 5, 2x + y + αz = 5, 8x + 4y + βz = 18 has no solution. Then...
- Let A = bmatrix 1 & 2 1 & bmatrix and B = bmatrix 3 & 3 & 2 bmatrix . If A² − 4A + I = O and B² − 5B − 6I = O, then among the two...