List of top Questions asked in KEAM

Let $t_n$ denote the $n^{th}$ term in a binomial expansion. If $ \frac{t_{6}}{t_{5}}$ in the expansion of $(a+ b)^{n+4}$ and $ \frac{t_{5}}{t_{4}}$ in the expansion of $(a + b)^n$ are equal, then $n$ is

If $\left|z-\frac{3}{2}\right|=2$ , then the greatest value of $\left|z\right|$ is

If $x_1$ and $x_2$ are the roots of $3x^2 - 2x - 6 = 0$, then $x_1^2 + x_2^2$ is equal to

The value of the determinant $\begin{vmatrix}\sin ^{2} 36^{\circ} & \cos ^{2} 36^{\circ} & \cot 135^{\circ} \\ \sin ^{2} 53^{\circ} & \cot 135^{\circ} & \cos ^{2} 53^{\circ} \\ \cot 135^{\circ} & \cos ^{2} 25^{\circ} & \cos ^{2} 65^{\circ}\end{vmatrix}$ is

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 solution set of the in equation $ \frac{x+11}{x-3}>0 $ is

There are $10$ persons including $3$ ladies. A committee of $4$ persons including at least one lady is to be formed. The number of ways of forming such a committee is

Which one of the following is not a statement?

If the combined mean of two groups is $\frac{40}{3}$ and if the mean of one group with $10$ observations is $15$, then the mean of the other group with $8$ observations is equal to

If $ A=\left[ \begin{matrix} 1 & 2 \\ 3 & 5 \\ \end{matrix} \right], $ then the value of the determinant $ |{{A}^{2009}}-5{{A}^{2008}}| $ is

$ ^{15}{{C}_{0}}{{.}^{5}}{{C}_{5}}{{+}^{15}}{{C}_{1}}{{.}^{5}}{{C}_{4}}{{+}^{15}}{{C}_{2}}{{.}^{5}}{{C}_{3}}{{+}^{15}}{{C}_{3}}{{.}^{5}}{{C}_{2}} $ $ {{+}^{15}}{{C}_{4}}{{.}^{5}}{{C}_{1}} $ is equal to

If $ x={{\sin }^{-1}}(3t-4{{t}^{3}}) $ and $ y={{\cos }^{-1}}(\sqrt{1-{{t}^{2}}}), $ then $ \frac{dy}{dx} $ is equal to

The total revenue in rupees received from the sale of x units of a product is given by $ R(x)=13{{x}^{2}}+26x+15 $ . Then, the marginal revolution rupees, when $ x=15 $ is

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

The coefficient of $x^2$ in the expansion of the determinant $\begin{vmatrix}x^{2}&x^{3}+1&x^{5}+2\\ x^{2}+3&x^{3}+x&x^{3}+x^{4}\\ x+4&x^{3}+x^{5}&2^{3}\end{vmatrix}$ is

$\int\limits_{0}^{1} x e^{-5x} \, dx$ is equal to

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

Let $S_n$ denote the sum of first n terms of an $A.P.$ If $S_4 = -3 4 , S_5 = -60$ and $S_6 = -93$, then the common difference and the first term of the $A.P.$ are respectively

If $A$ and $B$ are square matrices of the same order and if $A=A^{T},B=B^{T},$ then $\left(ABA\right)^{T}=$

The coefficient of $x^5$ in the expansion of $(1 + x^2)^5(1 + x)^4$ is

The order of the differential equation $\left(\frac{d^{3}\, y }{dx^{3}}\right)^{2} + \left(\frac{d^{2}\,y}{dx}\right)^{2} + \left(\frac{dy}{dx}\right)^{5} = 0 $ is

The output of the circuit is

Vitamin A is called