List of top Mathematics Questions asked in KEAM

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

The argument of the complex number $ \left( \frac{i}{2}-\frac{2}{i} \right) $ is equal to

Let $ \alpha $ and $ \beta $ be the roots of $ a{{x}^{2}}+bx+c=0 $ . Then, $ \underset{x\to \alpha }{\mathop{\lim }}\,\frac{1-\cos (a{{x}^{2}}+bx+c)}{{{(x-\alpha )}^{2}}} $ is equal to

If $ \sqrt{x+iy}=\pm (a+ib), $ then $ \sqrt{-x-iy} $ is equal to

Let $p : 57$ is an odd prime number, $\quad \, q : 4$ is a divisor of $12$ $\quad$ $r : 15$ is the $LCM$ of $3$ and $5$ Be three simple logical statements. Which one of the following is true?

If the mean of six numbers is $41$, then the sum of these numbers is

If $ y={{\tan }^{-1}}\left( \frac{\cos x}{1+\sin x} \right), $ then $ \frac{dy}{dx} $ 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 area of the triangle formed by the points $(2, 2), (5, 5), (6, 7)$ is equal to (in square units)

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

The number of words that can be formed by using all the letters of the word $PROBLEM$ only one is

The value of $\displaystyle \lim_{y \to \infty} \left[y \, sin \left(\frac{1}{y}\right) - \frac{1}{y} \right]$ is equal to

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

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

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 $ |2x-3|

If $ 3\le 3t-18\le 18, $ then which one of the following is true?

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

The domain of the function $f \left(x\right)=\frac{\log_{2}\left(x+3\right)}{x^{2}+3x+2}$ is

Area of the triangle with vertices $(- 2, 2), (1, 5) $and $(6, - 1)$ is

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

If $a , \,b$ and $c$ are three non-zero vectors such that each one of them being perpendicular to the sum of the other two vectors, then the value of $| a + b + c |^{2}$ is

The value of the integral $\displaystyle \int_0^1$ $\frac{x^{3}}{1+x^{8}} dx$ is equal to

The area bounded by the parabola $ {{y}^{2}}=8x $ and its latus rectum in sq unit is