List of top Mathematics Questions asked in KEAM

If $0< x< \pi$, then $\frac{\sin 8 x+7 \sin 6 x+18 \sin 4 x+12 \sin 2 x}{\sin 7 x+6 \sin 5 x+12 \sin 3 x}$ equal to

The standard deviation of $9, 16, 23, 30, 37, 44, 51$ is

How many numbers with no more than three digits can be formed using only the digits $1$ through $7$ with no digit used more than once in a given number?

If $p :$ The earth is round, $q : 3 + 4 = 7 $ then $\left(\sim p\right)\vee\left(\sim q\right)$ is

If $\frac{\sin x}{\cos x} \times \frac{\sec x}{\operatorname{cosec} x} \times \frac{\tan x}{\cot x}=9, $ where $x \in\left(0, \frac{\pi}{2}\right)$, then the value of $x$ is equal to

$\int\frac{1+log\,x}{\left(1+x\,log\,x\right)^{2}}dx$ is equal to

The solutions set of inequation $\cos^{-1}x < \,\sin^{-1}x$ is

The equation of the line parallel to x-axis and tangent to the curve $ y=\frac{1}{{{x}^{2}}+2x+5} $ is

The equation of the plane containing the lines $ \frac{x-1}{2}=\frac{y+1}{-1}=\frac{z}{3} $ and $ \frac{x}{2}=\frac{y-2}{-1}=\frac{z+1}{3} $ is

The sum of all two digit natural numbers which leave a remainder $5$ when they are divided by $7$ is equal to

In a boolean algebra $B$ with respect to $' +' $ and $'.',$ $ x' $ denotes the negation of $ x\in B $ . Then

The value of $ \cos [{{\tan }^{-1}}\{\sin ({{\cot }^{-1}}x)\}] $ is

The solution of the differential equation $ \frac{dy}{dx}=\frac{1}{x+{{y}^{2}}} $ is

The range of the function $ f(x)\frac{{{x}^{2}}-x+1}{{{x}^{2}}+x+1} $ where $ x\in R, $ is

Triangle $ABC$ has vertices $(0, 0), (11, 60)$ and $(91, 0)$. If the line $ y=kx $ cuts the triangle into $2$ two triangles of equal area, then $k$ is equal to

The standard deviation for the scores $1, 2, 3, 4, 5, 6$ and $7$ is $2$. Then, the standard deviation of $12, 23, 34, 45, 56, 67$ and $78$ is

Let $ {{z}_{1}} $ and $ {{z}_{2}} $ be the roots of the equation $ {{z}^{2}}+pz+q=0 $ where p, q are real. The points represented by $ {{z}_{1}},{{z}_{2}} $ and the origin form an equilateral triangle, if

Given $ tan\text{ }A $ and $ tan\text{ B} $ are the roots of $ {{x}^{2}}-ax+b=0 $ . The value of $ {{\sin }^{2}}(A+B) $ is

On the set $N$ of all natural numbers define the relation $R$ by $a R b$ if and only if the $G.C.D.$ of $a$ and $b$ is $2$, then $R$ is

The $ x- $ axis, $ y- $ axis and a line passing through the point A (6, 0) form a triangle $ABC$. If $ \angle A=30{}^\circ , $ then the area of the triangle, in sunits 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

If $r$ is a real number such that $ |r| < 1 $ and if $ a=5(1-r), $ then

If $C_{0}$, $C_{1}$, $C_{2}$, $C_{3}$, $\cdots$ are binomial coefficients in the expansion of $(1 + x)^n$, then $\frac{C_{0}}{3}- \frac{C_{1}}{4}+ \frac{C_{2}}{5}- \frac{C_{3}}{6}+ \cdots$ is equal to

The coefficient of $ {{a}^{5}}{{b}^{6}}{{c}^{7}} $ in the expansion of $ {{(bc+ca+ab)}^{9}} $ is

Suppose $a, b$ and $c$ are real numbers such that $ \frac{a}{b}>1 $ and $ \frac{a}{c}<0 $ . Which one of the following is true?