List of top Questions asked in KEAM

If $ |2x-3|

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

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

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

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

An anti-aircraft gun can take a maximum of four shots at any plane moving away from it. The probabilities of hitting the plane at the 1 st, 2 nd, 3 rd and 4 th shots are 0.4, 0.3, 0.2 and 0.1 respectively. What is the probability that at least one shot hits the plane?

An $A.P.$ has the property that the sum of first ten terms is half the sum of next ten terms. If the second term is $13$, then the common difference is

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

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

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 the conjugate of a complex number $z$ is $\frac{1}{i - 1}$ , then $z$ is

If the semi-major axis of an ellipse is 3 and the latus rectum is $\frac{16}{9},$ then the standard equation of the ellipse is

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

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

The least integer satisfying $\frac{396}{10}-\frac{19-x}{10} < \frac{376}{10}-\frac{19-9x}{10}$ is

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

The area bounded by the curves $y = - x^2 + 3$ and $y = 0$ is

If $6^{th}$ term of $G.P.$ is $2$, then the product of first $11$ terms of the $G.P.$ is equal to

If A\B = {a, b}, B\A = {c, d} and A\B = {e, f}, then the set B is equal to

If $^n$C$_2$ + $^n$C$_3$ = $^6$C$_3$ and $^n$C$_x$ = $^n$C$_3$, x ? 3, then the value of x is equal to

The number of diagonals in a hexagon is

Two numbers $x$ and $y$ have arithmetic mean $9$ and geometric mean $4$. Then $x$ and $y$ are the roots of

A ground receiver receives a signal at $5\, MHz$, transmitted by a ground transmitter at a height of $320\, m$, which is $110\, km$ away from it. Then it can communicate through (radius of earth $R \,= \,6400 \,km$)

A metallic bar of coefficient of linear expansion $10^{-5} K^{-1}$ is heated from $0^{\circ}C$ to $100^{\circ}C$. The percentage increase in its length is