List of top Mathematics Questions asked in KEAM

The velocity is given as \( \mathbf{v} = 3\hat{i} + 3\hat{j} \). Find the acceleration \( \mathbf{a} \).
If \( \sin \alpha = \frac{12}{13} \), and \( \frac{\pi}{6} \leq \alpha \leq \frac{3\pi}{2} \), find \( \tan \alpha \).
Solve for \( a \) and \( b \) given the equations: \[ \sin x + \sin y = a, \quad \cos x + \cos y = b, \quad x + y = \frac{2\pi}{3} \]
Given that \( \vec{a} \parallel \vec{b} \), \( \vec{a} \cdot \vec{b} = \frac{49}{2} \), and \( |\vec{a}| = 7 \), find \( |\vec{b}| \).
Given that \( |\mathbf{a} + \mathbf{b}| = \frac{\sqrt{14}}{2} \), where \( \mathbf{a} \) and \( \mathbf{b} \) are unit vectors, find the value of \( |\mathbf{a} + \mathbf{b}|^2 - |\mathbf{a} - \mathbf{b}|^2 \).
Find the equation of the circle touching the x-axis at \( (9, 0) \) and the line \( y = 14 \).
Given: \[ \sum_{k=0}^{5} \binom{10}{2k} = \alpha \quad \text{and} \quad \sum_{k=0}^{4} \binom{10}{2k+1} = \beta \] \text{Find the value of} \( \alpha - \beta \).
Evaluate the integral: \[ \int \frac{2x^2 + 4x + 3}{x^2 + x + 1} \, dx \]
Find the standard deviation of the numbers: -3, 0, 3, 8.
Find \( \tan 15^\circ + \tan 45^\circ \).
If \( f(x) = \cos x \), find the following expression: \[ \frac{1}{2} \left[ f(x + y) + f(y - x) - f(x) \cdot f(y) \right] \]
Evaluate the integral: \[ \int \frac{\sin^1 x}{\sqrt{1 - x^2}} \, dx \]
Evaluate the integral: \[ \int_{\frac{\pi}{10}}^{\frac{2\pi}{5}} \frac{\cot^3 x}{1 + \cot^3 x} \, dx \]
An unbiased die is tossed until a sum \( S \) is obtained. If \( X \) denotes the number of times tossed, find the ratio \( \frac{P(X = 2)}{P(X = 5)} \).
If \( \cot^{-1} \left( \frac{\sqrt{1 - x}}{\sqrt{1 + x}} \right) \), then find \( \sec^2 \theta \).
What is the value of n when \( t_n = \frac{n(n+6)}{n+4} \) and \( t_n = 5 \)?
The product of the first five terms of a GP is 32. What is the 3rd term?
If \( A \) is a \( 3 \times 3 \) matrix and \( |B| = 3|A| \) and \( |A| = 5 \), then find \( \left| \frac{\text{adj} B}{|A|} \right| \).
If \( Z = \frac{2 - i}{\alpha + i} \) and \( 4 \, \text{Re}(Z) = 3 \, \text{Im}( \overline{Z} ) \), find \( \alpha \).
Find the value of \( Z^2 \) if \( Z = \left( 1 + \frac{1}{i} \right) \).
Equation of parabola having focii (-3, 1) and (3, 1)
Evaluate the integral: $ \int_{-1}^1 |x - 3| \, dx $

The value of $ i^3 + i^4 + i^5 $+ .. + $i^{93}$ is:

Find the domain of the function: $ f(x) = \sqrt{7 - 11x} $
Given the set $ S = \{ a, b, c, d, e, f \} $, find the total number of subsets with an odd number of elements.