List of top Mathematics Questions asked in KEAM

If $ \omega \ne 1 $ is a cube root of unity, then the value of $ \left| \begin{matrix} 1+2{{\omega }^{100}}+{{\omega }^{200}} \\ 1 \\ \omega \\\end{matrix}\begin{matrix} {{\omega }^{2}} \\ 1+{{\omega }^{100}}+2{{\omega }^{200}} \\ {{\omega }^{2}} \\\end{matrix}\begin{matrix} 1 \\ \omega \\ 1+{{\omega }^{100}}+2{{\omega }^{200}} \\\end{matrix} \right| $ is equal to

If $xy\, = \,A \,sinx \,+ \,B \,cos \,x$ is the solution of the differential equation $x\frac{d^{2}y}{dx^{2}}-5a\frac{dy}{dx}+xy=0$ then the value of $a$ is equal to

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

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

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

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

The locus of a point which is equidistant from the points $(1,1)$ and $(3, 3)$ is

The set $\{(x, y) : x + y =1\}$ in the $xy$ plane represents

The area bounded by $y =x^{2} +3$ and $y =2x+3$ is

The coefficient of $x$ in the expansion of $ (14+x)(1+2x)(1+3x)....(1+100x) $ is

If $A$ and $B$ are non-empty sets such that $A \supset B$, then

If $ |2x-3|

Let $u , v$ and $w$ be vectors such that $u + v + w = 0 .$ If $| u |=3,| v |=4$ and $| w |=5$ then $u \cdot v + v \cdot w + w \cdot u$ is equal to

If $ \overrightarrow{a},\text{ }\overrightarrow{b},\text{ }\overrightarrow{c} $ are non-coplanar and $ (\overrightarrow{a}+\lambda \overrightarrow{b}).[(\overrightarrow{b}+3\overrightarrow{c})\times (\overrightarrow{c}\times 4\overrightarrow{a})]=0, $ then the value of $ \lambda $ is equal to

Standard deviation of first $n$ odd natural numbers is

The angle between the line $ \frac{3x-1}{3}=\frac{y+3}{-1} $ $ =\frac{5-2z}{4} $ and the plane $ 3x-3y-6z=10 $ is equal to

The length of the transverse axis of a hyperbola is $2 \,\cos \,\alpha$ . The foci of the hyperbola are the same as that of the ellipse $9x^{2}+16y^{2}=144$ . The equation of the hyperbola is

If $ l,m $ and $ n $ are real numbers such that $ {{l}^{2}}+{{m}^{2}} $ $ +{{n}^{2}}=0, $ then $ \left| \begin{matrix} 1+{{l}^{2}} & lm & ln \\ lm & 1+{{m}^{2}} & mn \\ ln & mn & 1+{{n}^{2}} \\ \end{matrix} \right| $ is equal to

If $ {{c}_{1}},{{c}_{2}},{{c}_{3}},{{c}_{4}},{{c}_{5}} $ and $ {{c}_{6}} $ are constants, then the order of the differential equation whose general solution is given by $ y={{c}_{1}}cos $ $ (x+{{c}_{2}})+{{c}_{3}}\sin (x+{{c}_{4}})+{{c}_{5}}{{e}^{x}}+{{c}_{6}} $

If f(x)=$ \left(\frac{x}{2}\right)^{10}, then\, f \left(1\right)+\frac{f '\left(1\right)}{\lfloor1}+\frac{f \left(1\right)}{\lfloor2}+\frac{f '\left(1\right)}{\lfloor3}+\ldots+\frac{f ^{\left(10\right)}\left(1\right)}{\lfloor10}$ is equal to

$\left(\frac{1+\cos\left(\frac{\pi}{12}\right) + i \sin\left(\frac{\pi}{12}\right)}{1+\cos \left(\frac{\pi}{12}\right) - i \sin\left(\frac{\pi}{12}\right)}\right)^{72}$ is equal to

Let $S_{n}$ denote the sum of first $n$ terms of an $A.P$. and $S_{2n} = 3S_{n}$. If $S_{3n} =k S_{n}$, then the value of $k$ is equal to

If $ {{a}_{1}},{{a}_{2}},.....,{{a}_{n}} $ are in AP with common difference $ d\ne 0, $ then $ (\sin d) $ $ [\sec {{a}_{1}}\sec {{a}_{2}}+ $ $ \sec {{a}_{2}}\sec {{a}_{3}}+...+\sec {{a}_{n-1}}\sec {{a}_{n}}] $ is equal to