List of top Mathematics Questions asked in KEAM

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

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

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

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

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

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

If $ A= \begin{bmatrix} 1 & 0 & 0 \\ x & 1 & 0 \\ x & x & 1 \\ \end{bmatrix} $ and $ I= \begin{bmatrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 1 \\ \end{bmatrix} , $ then $ {{A}^{3}}-4{{A}^{2}}+3A+I $ is equal to

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:

If $p : 2$ plus $3$ is five and $q $ : Delhi is the capital of India < are two statements, then the statement "Delhi is the capital of India and it is not that $2$ plus $3$ is five" is

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

If $tan \left(\frac{\theta}{2}\right)=\frac{2}{3}$, then $sec\,\theta $ is equal to

$ \frac{1}{\cos 80{}^\circ }-\frac{\sqrt{3}}{\sin 80{}^\circ } $ is equal to:

The area of the circle $x^2 - 2x + y^2 - 10\,y + k = 0$ is $25 \pi $ . The value of k is equal to

The angle between the planes $3x + 4y + 5z = 3$ and $4 x-3 y + 5z = 9$ is equal to

A plane makes intercepts $a, b, c$ at $A, B, C$ on the coordinate axes respectively. If the centroid of the $ \Delta ABC $ is at $(3, 2, 1)$, then the equation of the plane is

The position of a particle is given by $ r =\hat{i}+2\hat{j}-\hat{k} $ and its linear momentum is given by $ p = 3\hat{i}+4\hat{j}-2\hat{k} $ . Then its angular momentum, about the origin is perpendicular to