List of top Mathematics Questions asked in KEAM

Let \( A = (a_{ij}) \) be a square matrix of order 3 and let \( M_{ij} \) be the minors of \( a_{ij} \). If \( M_{11} = -40, M_{12} = -10, M_{13} = 35 \), and \( a_{11} = 1, a_{12} = 3, a_{13} = -2 \), then the value of \( |A| \) is equal to:
If the points \( (2, -3), (\lambda, -1) \) and \( (0, 4) \) are collinear, then the value of \( \lambda \) is equal to:
If \( B = \begin{bmatrix} 1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4 \end{bmatrix} \) is the adjoint of a \( 3 \times 3 \) matrix \( A \) and \( |A| = 4 \), then the value of \( \alpha \) is:
The minimum value of \( f(x) = 7x^4 + 28x^3 + 31 \) is:
The numbers \( a, b, c, d \) are in G.P. with common ratio \( r \). If \( \frac{1}{a^3 + b^3} + \frac{1}{b^3 + c^3} + \frac{1}{c^3 + d^3} \) are also in G.P., then the common ratio is:
Evaluate \( \binom{10}{1} + \binom{10}{2} + \dots + \binom{10}{10} \):
The coefficient of \( x^3 \) in the binomial expansion of \( \left( \frac{1}{\sqrt{x}} - x \right)^6 \) is:
If three distinct numbers are chosen randomly from the first 50 natural numbers, then the probability that all of them are divisible by 2 and 3 is:
The mean deviation of the numbers 3, 10, 10, 4, 7, 10 and 5 from the mean is:
The second term of a G.P. is 4, then the product of the first three terms is:
If \( \left( \frac{1 - i}{1 + i} \right)^{10} = a + ib \), then the values of \( a \) and \( b \) are, respectively:
If \( _nP_r = 480 \) and \( _nC_r = 20 \), then the value of \( r \) is equal to:
The common ratio of a G.P. is \( \frac{1}{2} \). If the product of the first three terms is 64, then the sum of the first 10 terms is:
Let a relation \( R \) on the set of natural numbers be defined by \( (x, y) \in R \) if and only if \( x^2 - 4xy + 3y^2 = 0 \) for all \( x, y \in \mathbb{N} \). Then the relation is:
If \( f(x) = \begin{cases} x^2 & \text{for } x < 0 \\ 5x - 3 & \text{for } 0 \leq x \leq 2 \\ x^2 + 1 & \text{for } x > 2 \end{cases} \), then the positive value of \( x \) for which \( f(x) = 2 \) is:
Let \( z \) be a complex number satisfying \( |z + 16| = 4|z + 1| \). Then:
The angle between the lines \( \frac{x}{1} = \frac{y}{1} = \frac{z}{1} \) and \( \frac{x}{0} = \frac{y}{1} = \frac{z}{-1} \) is:
The constant term in the expansion of \( \left( x^3 + \frac{1}{x^2} \right)^{10} \) is:
If \( 2z = 7 + i\sqrt{3} \), then the value of \( z^2 - 7z + 4 \) is:
The degree of the differential equation \( (y^m)^2 + (\sin y')^4 + y = 0 \) is:
The general solution of \( \frac{dy}{dx} + y = 5 \) is:
Evaluate \( \int_0^1 \log \left( \frac{1}{x - 1} \right) \, dx \):
Evaluate \( \int_{-\pi/2}^{\pi/2} \sin^9 x \cos^2 x \, dx \):
If one end of a diameter of the circle \( x^2 + y^2 - 4x - 6y + 11 = 0 \) is \( (3, 4) \), then the coordinate of the other end of the diameter is:
Find the area bounded by the curves \( y = 2x \) and \( y = x^2 \):