List of top Mathematics Questions

If the sum of the first 2n terms of 2, 5, 8, … is equal to the sum of the first n terms of 57, 59, 61, …, then n is equal to:
The length of the latus-rectum of the parabola whose focus is ((u²)/(2g)\sin2α,-(u²)/(2g)\cos2α) and directrix is y=(u²)/(2g), is:
The equation of the ellipse with focus at (±5,0) and eccentricity =(5)/(6) is:
Which of the following is not a vertex of the positive region bounded by the inequalities 2x + 3y ≤ 6, 3x + 3y ≤ 15 and x, y ≥ 0?
If ²⁰Cᵣ = ²⁰Cᵣ-₁₀, then ¹⁵Cᵣ is equal to:
The term independent of x in the expansion of (9x - 13√(x))¹8, x>0, is a times the corresponding binomial coefficient. Then a is:
For n N, xⁿ⁺¹ + (x+1)²n-1 is divisible by:
If α, β are the roots of the equation ax² + bx + c = 0, then the roots of the equation ax² + bx(x+1) + c(x+1)² = 0 are:
If a > 0, a R, z = a + 2i and |z| = -az + 1, then:
In the binomial (2¹/³+3⁻¹/³)ⁿ, if the ratio of the seventh term from the beginning to the seventh term from the end is 1/6, then n is equal to:
cosθ1-tanθ + sinθ1-cotθ is equal to:
If tan A = (1)/(2) and tan B = (1)/(3), then find the value of A + B.
If sin θ = -(1)/(2) and tan θ = 1√(3), then θ is equal to:
If f(x) is a function that is odd and even simultaneously, then f(3) - f(2) is equal to:
If \[ \mathbf{I} = \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \end{bmatrix}, \quad B = \begin{bmatrix} \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end{bmatrix} \] then \( B \) is equal to:
The order and degree of the differential equation \[ \left( 1 + 4 \frac{dy}{dx} \right)^{2/3} = 4 \frac{d^2 y}{dx^2} \] are respectively:
The solution of the differential equation \[ \frac{dy}{dx} = (4x + y + 1)^2 \] is:
Let \( R: \mathbb{R} \to \mathbb{R} \) be defined as \( f(x) = x^2 + 1 \), find \( f^{-1}(-5) \):
The system of equations \[ 2x + y - 5 = 0, \quad x - 2y + 1 = 0, \quad 2x - 14y - a = 0 \] is consistent. Then, \( a \) is equal to:
If \( X \) is a Poisson variate such that \( P(X = 1) = P(X = 2) \), then \( P(X = 4) \) is equal to:
The area enclosed by \( y = 3x - 5 \), \( y = 0 \), \( x = 3 \), and \( x = 5 \) is:
In how many ways 6 letters can be posted in 5 different letter boxes?
The locus of the mid-points of the focal chord of the parabola \( y^2 = 4ax \) is:
A die is rolled twice and the sum of the numbers appearing on them is observed to be 7. What is the conditional probability that the number 2 has appeared at least once?
If \( A \) and \( B \) are two sets such that \( A \times B \) consists of 6 elements, find \( B \times A \):