List of top Mathematics Questions asked in KEAM

Out of $15$ persons, $10$ can speak Hindi and $8$ can speak English. If two persons are chosen at random, then the probability that one person speaks Hindi only and the other speaks both Hindi and English is

Let $x = 2$ be a root of $y = 4x^2 - 14x + q = 0$. Then $y$ is equal to

If $f \left(z\right)=\frac{1-z^{3}}{1-z} ,$ where $z=x+iy$ with $z\ne1,$ then $Re\left\{\overline{f \left(z\right)}\right\}=0$ reduces to

The $100^{th}$ term of the sequence $1, 2, 2, 3, 3, 3, 4, 4, 4, 4, \dots$, is

Let $ {{(1+x)}^{n}}=1+{{a}_{1}}x+{{a}_{2}}{{x}^{2}}+.....+{{a}_{n}}{{x}^{n}} $ .If $ {{a}_{1}},{{a}_{2}} $ and $ {{a}_{3}} $ are in $AP$, then the value of $n$ is

Let $A (6, -1), B (1, 3)$ and $C (x, 8)$ be three points such that $AB = BC$. The values of $x$ are

If $ n=5, $ then $ {{{{(}^{n}}{{C}_{0}})}^{2}}+{{{{(}^{n}}{{C}_{1}})}^{2}}+{{{{(}^{n}}{{C}_{2}})}^{2}}+..... $ $ +{{{{(}^{n}}{{C}_{5}})}^{2}} $ is equal to

The boolean expression corresponding to the combinational circuit is

If $ y={{\cot }^{-1}}\left( \tan \frac{x}{2} \right), $ then $ \frac{dy}{dx} $ is equal to

If $f\left(x\right) = \int\limits^{sin\,x}_{2x}cos\left(t^{3}\right)dt$, then $f'{x}$ is equal to

$\int_{0}^{1} \frac{1}{\left(x^{2}+16\right)\left(x^{2}+25\right)} \,dx$ is equal to

$\int\frac{2x+\sin2x}{1+\cos2x}\, dx$ is equal to

Let $ z=\frac{11-3i}{1+i}. $ If a is a real number such that $ z-i\alpha $ is real, then the value of $ \alpha $ is

If $z = \cos\left(\frac{\pi}{3} \right) - i \sin \left(\frac{\pi }{3}\right),$ the $z^{2} - z +1 $ is equal to

If tan $\frac{\theta}{2}=\frac{1}{2}$,then the value of sin $\theta$ is

A man of $2\,m$ height walks at a uniform speed of $6 \,km/h$ away from a lamp post of $6 \,m$ height. The rate at which the length of his shadow increases is

If $ \theta $ is semi vertical angle of a cone of maximum volume and given slant height, then $ tan\theta $ is equal to

A plane makes intercepts $a, b, c$ at $A, B, C$ on the coordinate axes respectively. If the centroid of the $ \Delta ABC $ is at $(3, 2, 1)$, then the equation of the plane is

If the plane $ 3x+y+2z+6=0 $ is parallel to the line $ \frac{3x-1}{2b}=3-y=\frac{z-1}{a}, $ then the value of $ 3a+3b $ is

If the distance between the two points $(-1, a )$ and $(-1, -4a )$ is $10$ units, then the values of $a$ are

If $A$ and $B$ are mutually exclusive events and if $ p(B)=\frac{1}{3},p(A\cup B)=\frac{13}{21}, $ then $P(A)$ is equal to

A die has four blank faces and two faces marked $3$. The chance of getting a total of $12$ in $5$ throws is

Out of $15$ persons $10$ can speak Hindi and $8$ can speak English. If two persons are chosen at random, then the probability that one person speaks Hindi only and the other speaks both Hindi and English is

In a certain town $25\%$ families own a cell phone, $15\%$ families own a scooter and $65\%$ families own neither a cell phone nor a scooter. If $1500$ families own both a cell phone and a scooter, then the total number of families in the town is

If $^{n}C_{r-1}=28$, $^{n}C_{r}=56$ and $^{n}C_{r+1}=70$, then the value of $r$ is equal to