List of top Mathematics Questions asked in KEAM

Let A and B be two events such that $P(A)=\frac{1}{8}$ and $P(A/B)=\frac{1}{4}$, $P(B/A)=\frac{2}{5}$. Then $P(B)$ is equal to

Let $x_{1},x_{2},\dots,x_{n}$ be the data with respective frequencies $f_{1},f_{2},\dots,f_{n}$. If $\sum_{i=1}^{n}f_{i}(|x_{i}-\overline{x}|)=400$ and the mean deviation from the mean $\overline{x}$ is 10, then $\sum_{i=1}^{n}f_{i}$ is equal to

Consider the data $x_{1},x_{2},\dots,x_{10}$. If $\sum_{i=1}^{10}(|x_{i}-\overline{x}|)^{2}=662,$ where $\overline{x}$ is the mean, then the standard deviation is approximately, equal to

Let $|\vec{a}|=2,|\vec{b}|=\sqrt{13+6\sqrt{3}}$ and $|\vec{c}|=3$. If $\vec{a}-\vec{b}+\vec{c}=0$, then the angle between $\vec{a}$ and $\vec{c}$ is

The position vectors of the vertices of a triangle are $\hat{i}+2\hat{j}-4\hat{k}$, $-\hat{i}-2\hat{j}-4\hat{k}$ and $2\hat{i}+3\hat{j}+5\hat{k}$. The perimeter of the triangle is

Let $\vec{a}, \vec{b}, \vec{c}$ be three vectors such that $|\vec{a}|=2, |\vec{b}|=3, |\vec{c}|=4$ and $\vec{a}\cdot\vec{b}=\vec{a}\cdot\vec{c}=0$. If the angle between $\vec{b}$ and $\vec{c}$ is $\frac{\pi}{3}$, then $\vec{a}$ is equal to

The straight line $\vec{r}=(2-3t)(\hat{i}+\hat{j})+(6t+1)(\hat{j}+\hat{k})+(12t-11)(\hat{k}+\hat{i}), t\in\mathbb{R}$, is parallel to the vector

If $\alpha,\beta,\gamma$ are the angles made by the straight line $\frac{x-5}{2}=\frac{y+1}{3}=\frac{z-2}{\sqrt{7}}$ with the x-axis, y-axis and z-axis respectively, then $\cos\alpha, \cos\beta, \cos\gamma$ are respectively,

The equation of a line passing through (-1,6,5) and (-2,4,3), is

The vectors $2\vec{a}+6\vec{b}$ and $3\vec{a}-7\vec{b}$ are position vectors of the points A and B respectively. A point P divides the line segment AB internally in the ratio 3:5. Then $\vec{PB}=$

The equation of a chord to the circle $x^{2}+y^{2}=25$ is $x+y-5=0$. The equation of a circle whose diameter is $x+y-5=0$, is}

Let the eccentricity of an ellipse be $\frac{1}{2}$. If $S(3,2)$ is a focus and $x-9=0$ is the corresponding directrix of the ellipse, then the equation of the ellipse is}

The nearest point on the line $x+2y=5$ from the point $P(7,9)$ is equal to

The length of the latus rectum of the ellipse $225x^{2}+125y^{2}=28125$ is}

The eccentricity of the hyperbola $25x^{2}-36y^{2}-50x-72y-911=0$, is

If $A\le2\sin^{-1}x+\cos^{-1}x\le B$, then A and B respectively, are

A straight line has y -intercept -5. If it makes $120^{\circ}$ with the x-axis, then the equation of the line is

The domain of the function $f(x)=\sin^{-1}(5-4x^{2})+\cos^{-1}(5-4x^{2})$ is

Let O be the origin and R be any point on $y^{2}=2x$. The locus of the midpoint of the line segment OR, is

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

If $\frac{2x-10}{x+2}\ge x-5$ then $x$ lies in

The value of $\sin 5^{\circ}\sin 10^{\circ}\sin 15^{\circ}\sin 20^{\circ}\dots\sin 240^{\circ}$ is equal to

$2^{11}\sin(\frac{x}{2^{10}})\cos(\frac{x}{2})\cos(\frac{x}{2^{2}})\cos(\frac{x}{2^{3}})\dots\cos(\frac{x}{2^{10}})$ is equal to

$\sin(\frac{3\pi}{4}+x)+\cos(\frac{3\pi}{4}+x)-\sin(\frac{3\pi}{4}-x)-\cos(\frac{3\pi}{4}-x)=$

The value of $3\cot(-405^{\circ})\tan315^{\circ}-5\cot495^{\circ}\tan(-585^{\circ})$ is equal to