List of top Mathematics Questions asked in KEAM

Let \(f(x) = \begin{cases} 5x^2 + ax + 16, & \text{if } x < 2 \\ x^2, & \text{if } x \geq 2 \end{cases}\). If \(f\) is differentiable at \(x = 2\), then the value of \(a\) is equal to

If \(f(x) = \frac{\sqrt{2\sin x}}{\sqrt{1 + \cos 2x}}\), then \(f'\left(\frac{\pi}{6}\right) =\)

Let \(f(x) = \frac{1}{x^2}\) and let \(u = f(x)f''(x)\). Then \(\frac{du}{dx} =\)

If \(y = (x - 1)\log_{e}(x - 1)\), then \(\frac{d^{2}y}{dx^{2}}\) at \(x = 3\) is

\(\int \frac{1}{x(1 + x^{4})} \, dx\) is equal to

Let \(f(x) = e^{x(2x^{2} + ax + 2 - a)}\). If \(f\) has a local minimum at \(x = 2\), the value of \(a\) is equal to

\(\int \frac{\sec^2(\sqrt{2x+5})}{\sqrt{2x+5}} \, dx =\)

\(\int_{0}^{2} \frac{x^{4}}{x^{4} + (2 - x)^{4}} \, dx =\)

\(f(x) = \frac{1}{7 - \cos x},\ x \in \mathbb{R}\). Then the range of \(f\) is

Let \(A\) and \(B\) be two finite sets. If \(n(A) = 7\) and the number of relations from \(A\) into \(B\) is 128, then \(n(B) =\)

The domain of the function \(f(x) = \sqrt{7 - 11x}\) is

The value of \((1 + i)^{10}\) is equal to

Let \(a_{n} = 2^{n - 1}, n = 1, 2, 3, \ldots\) . Then the value of the sum \(\sum_{n = 1}^{20} a_{n}\) is equal to

\(a_{1}, a_{2}, \ldots , a_{10}\) are in G.P., and if \(a_{1} + a_{2} = 6, a_{9} + a_{10} = \frac{3}{128}\) then the common ratio of the G.P. is equal to

The value of \(i^{3} + i^{4} + i^{5} + \ldots i^{93}\) , where \(i = \sqrt{-1}\) , is equal to

Let \(z_{1} = \frac{1}{2} +i\frac{\sqrt{3}}{2}\) and \(z_{2} = -\frac{1}{2} -i\frac{\sqrt{3}}{2}\) . If \(w = z_{1} + \bar{z}_{2}\) , then \(\overline{w} =\)

Imaginary parts of \(\left(\frac{3 - 2i}{2i}\right)^2\) is equal to

If \(\cos\left(2\sin^{-1}\alpha\right) = \frac{47}{72}\), where \(0 < \alpha < 1\), then the value of \(\alpha\) is

\(\frac{3\tan 15^{\circ} - \tan^3 15^{\circ}}{1 - 3\tan^2 15^{\circ}}\)

If \(x \neq 11\) satisfies the inequality \(\frac{2x - 21}{x - 11} \geq 3\), then \(x\) lies in the interval

If the matrix \(A = \left[ \begin{array}{cc}1 & -1 4\lambda & 8 \end{array} \right]\) is singular, then the value of \(\lambda\) is equal to

Let \(A = \begin{bmatrix} a & -1 & -a 0 & 1 & -1 1 & 0 & 4 \end{bmatrix}\). If \(|A| = 26\), then the value of \(a\) is equal to

The set of all \(x\) satisfying the inequality \(|3 - 4x| \leq 11\) is

The numbers \(a_{1},a_{2},a_{3},a_{4},a_{5}\) and \(a_{6}\) are in G.P. If \(a_{1} = 2\) and the common ratio \(r = \frac{1}{2}\), then the value of \(\left| \begin{array}{lll}a_{1} & a_{2} & 1 a_{3} & a_{4} & 1 a_{5} & a_{6} & 1 \end{array} \right|\) is equal to

If \(X = A^{-1}B,\) Where \(A = \left[ \begin{array}{cc}1 & -1 2 & 1 \end{array} \right],B = \left[ \begin{array}{c}3 6 \end{array} \right]\) and \(X = \left[ \begin{array}{c}x_{1} x_{2} \end{array} \right],\) then \(x_{1} + x_{2} =\)