List of top Mathematics Questions asked in KEAM

If $ 3\le 3t-18\le 18, $ then which one of the following is true?
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
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?
If the conjugate of a complex number $z$ is $\frac{1}{i - 1}$ , then $z$ is
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
The least integer satisfying $\frac{396}{10}-\frac{19-x}{10} < \frac{376}{10}-\frac{19-9x}{10}$ 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
If $ |2x-3|
The number of diagonals in a hexagon is
$\left(\frac{1+\cos\left(\frac{\pi}{12}\right) + i \sin\left(\frac{\pi}{12}\right)}{1+\cos \left(\frac{\pi}{12}\right) - i \sin\left(\frac{\pi}{12}\right)}\right)^{72}$ is equal to
If A\B = {a, b}, B\A = {c, d} and A\B = {e, f}, then the set B is equal to
If $6^{th}$ term of $G.P.$ is $2$, then the product of first $11$ terms of the $G.P.$ is equal to
The area bounded by the curves $y = - x^2 + 3$ and $y = 0$ is
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
Two numbers $x$ and $y$ have arithmetic mean $9$ and geometric mean $4$. Then $x$ and $y$ are the roots of
The power of $x$ in the term with the greatest coefficient in the expansion of $\left(1+\frac{x}{2}\right)^{10}$ is:
If the two pair of lines $ {{x}^{2}}-2mxy-{{y}^{2}}=0 $ and $ {{x}^{2}}-2nxy-{{y}^{2}}=0 $ are such that one of them represents the bisector of the angles between the other, then:
An integrating factor of the differential equation $xdy - ydx + x^2e^xdx = 0$ is
$ \tan\left(\frac{\pi}{4} +\frac{\theta}{2}\right) + \tan\left(\frac{\pi}{4} - \frac{\theta}{2}\right)$ is equal to
$ \frac{1}{\cos 80{}^\circ }-\frac{\sqrt{3}}{\sin 80{}^\circ } $ is equal to: