List of top Mathematics Questions asked in KEAM

The mean deviation about the mean for the data: $5, 6, 14, 15$ is

If $|\vec{a}| = \sqrt{26}, \; |\vec{b}| = \sqrt{3}$ and $\vec{a} \times \vec{b} = 5\hat{i} + \hat{j} - 4\hat{k}$, then $\vec{a} \cdot \vec{b} =$:

Consider the straight line $\vec{r} = (5\hat{i} + 2\hat{j} - 3\hat{k}) + t(4\hat{i} + 6\hat{j} - 7\hat{k}), \; t \in \mathbb{R}$. Which one of the following points is a point on the straight line?

A straight line passes through the point whose position vector is $\hat{k}$. The straight line also passes through the point of intersection of the lines $\vec{r} = \hat{j} + \lambda \hat{i}, \lambda \in \mathbb{R}$ and $\vec{r} = \hat{i} + s\hat{j}, s \in \mathbb{R}$. Then the equation of the straight line is:

The equation of a line passing through $(-1,2,-4)$ and parallel to the straight line $\dfrac{-x-1}{4} = \dfrac{2y+1}{-1} = \dfrac{-z+4}{3}$, is:

Let $\vec{a} = 2\hat{i} - 2\hat{j} + 4\hat{k}$, $\vec{b} = -5\hat{i} - \hat{j} + 8\hat{k}$ and $\vec{c} = 3\hat{i} + \hat{j} - \lambda \hat{k}$. If $\vec{a} + \vec{b} + \vec{c}$ and $\vec{a} - \vec{b} + \vec{c}$ are perpendicular, then the values of $\lambda$ are:

Let $O$ be the origin. Let $\overrightarrow{OA} = \vec{a}$ and $\overrightarrow{OB} = \vec{b}$ be the position vectors of the points $A$ and $B$ respectively. A point $P$ divides the line segment $AB$ internally in the ratio $m:n$. Then $\overrightarrow{AP}$ is equal to:

If $2\hat{i} - \hat{j} + \hat{k} = s(3\hat{i} - 4\hat{j} - 4\hat{k}) + t(\hat{i} - 3\hat{j} - 5\hat{k})$, where $s$ and $t$ are scalars, then $3s + 5t$ is equal to:

Let $R(-2,-2)$ be a point and let $\dfrac{(x-3)^2}{25} + \dfrac{(y+2)^2}{16} = 1$ be an ellipse. If $S$ and $T$ are the foci of the ellipse, then $RS + RT$ is equal to:

The equation of the latus rectum of the parabola $y^2 + 8x + 4y + 12 = 0$ is

If the one end of a diameter of the circle $x^2 + y^2 + 3x + y - 6 = 0$ is at $(-4,-2)$, then the other end of the diameter is at

The value of $\sin\left(2\sin^{-1}\frac{3}{5}\right)$ is equal to

The vertex of a parabola is at $(2,-5)$ and the focus is at $(5,-5)$. The equation of the parabola is

Given that $i^2 = -1$. Then $i^{13} + i^{14} + i^{15} + \ldots + i^{2026}$ is equal to:

The number of terms in the sequence $2, 6, 18, \ldots, 1458$ is:

A straight line makes $y$-intercept of 5. If the angle made by the line with $y$-axis is $60^\circ$ and the line intersects $x$-axis in the negative direction, then the equation of the line is

Let $P = \left(\frac{15}{2}(\csc \theta + \sin \theta), \; 8(\csc \theta - \sin \theta)\right)$, where $\theta$ is a variable parameter. Then the locus of $P$ is

The value of $\sin^{-1}\left(\sin \dfrac{5\pi}{9} \cos \dfrac{\pi}{9} + \sin \dfrac{\pi}{9} \cos \dfrac{5\pi}{9}\right)$ is equal to:

The domain of the function $f(x) = 2\sin^{-1}(2x-1) - \dfrac{\pi}{4}$ is:

If $\tan \alpha = \dfrac{5}{6}$ and $\tan \beta = \dfrac{1}{11}$, where $0<\alpha,\beta<\dfrac{\pi}{2}$ then $\alpha + \beta =$:

The value of $\sin6^\circ \cos36^\circ \sin66^\circ + \cos12^\circ \sin42^\circ \sin18^\circ$ is equal to:

Let $f(x) = \dfrac{2x+3}{x-2}, \, x \in \mathbb{R}, \, x \neq 2$ and $h(x) = f(f(x))$. Then $h(h(10))$ is equal to:

The first and last term of a G.P. are 7 and 448 respectively. If the sum is 889, then the common ratio is

The inverse of the function $f(x) = x^2 + 4x + 4, \, x \leq -2$ is $f^{-1}(x) =$

The value of $\dfrac{(1+i)^n}{(1-i)^{n-4}}$, where $i=\sqrt{-1}$ and $n$ is an integer, is: