List of top Mathematics Questions asked in AP ECET

Let $M$ and $m$ respectively denote the maximum and the minimum values of $[f(\theta)]^{2}$, where $f(\theta)=\sqrt{a^{2} \cos ^{2} \theta+b^{2} \sin ^{2} \theta}$ $+\sqrt{a^{2} \sin ^{2} \theta+b^{2} \cos ^{2} \theta}$. Then $M-m=$

If $I_{n} = \int \frac{\sin nx}{\sin x} dx $ for $n = 1, 2 , 3,...,$ then $I_6$ =

Let $A, G, H$ and $S$ respectively denote the arithmetic mean, geometric mean, harmonic mean and the sum of the numbers $a_1 , a_2 , a_3 ....., a_n$ . Then the value of at which the function $f(x) =\displaystyle \sum^n_{k =1} (x -a_k)^2$ has minimum is

If $I(x)=\int x^{2}(\log x)^{2} d x$ and $I( 1)=0$, then $I(x)$

Number of ways of forming a committee of $6$ members out of $5$ Indians, $5$ Americans and $5$ Australians such that there will be atleast one member from each country in the committee is

Let $f(x) = x^2 + 2x + 2, g(x) = - x^2 + 2x - 1 $ and $a, b$ be the extreme values of $f(x), g(x)$ respectively. If $c$ is the extreme value of $\frac{f}{g} (x)$ (for x $\neq$ 1), then $a + 2b + 5c + 4$ =

The sum of the four digit even numbers that can be formed with the digits 0,3,5,4 with out repetition is

If $f: R \rightarrow[-1,1]$ and $g: R \rightarrow A$ are two surjective mappings and $\sin \left(g(x)-\frac{\pi}{3}\right)=\frac{f(x)}{2} \sqrt{4-f^{2}(x)}$, then $A=$

Option : No Option Orientation : Vertical If the angle between the tangents drawn to the circle $x^2 + y^2 -12 x - 16y = 0$ at the points w here the line $5y = 5x + k$ cut the circle is $60^{\circ}$ , then the value of $k$ is

If $A = \begin{bmatrix}k/2&0&0\\ 0&1/3&0\\ 0&0&m/4\end{bmatrix} $ and $A^{-1} = \begin{bmatrix}1/2&0&0\\ 0&1/3&0\\ 0&0&1/4\end{bmatrix}$ then $ k + l + m = $

For the matrix $A = \begin{pmatrix}3&-3&4\\ 2&-3&4\\ 0&-1&1\end{pmatrix}, A^{-1} = $

A random variable X has the following probability distribution The variance of this random variable is

If $x^{2}+\alpha y^{2}+2 \beta y=a^{2} \quad$ represents a pair of perpendicular lines, then $\beta$ equals to

The condition for the lines $l x+m y+n=0$ and $l_{1} x+m_{1} y+n_{1}=0$ to be conjugate with respect to the circle $x^{2}+y^{2}=r^{2}$, is

The slopes of the focal chords of the parabola $y^{2}=32 x$, which are tangents to the circle $x^{2}+y^{2}=4$, are

The point at which the circles $x^{2}+y^{2}-4 x-4 y+7=0 $ and $x^{2}+y^{2}-12 x -10 y+45=0$ touch each other, is

If a normal chord at a point $t$ on the parabola $y^{2}=4 \,a \,x$ subtends a right angle at the vertex, then $t$ equals to

The length of the common chord of the two circles $x^{2}+y^{2}-4 y=0 $ and $x^{2}+y^{2}-8 x - 4 y+11=0$, is

A circle with centre at $(2,4)$ is such that the line $x+y+2=0$ cuts a chord of length $6$ . The radius of the circle is

The locus of the centre of the circle, which cuts the circle $x^{2}+y^{2}-20 x+4=0$ orthogonally and touches the line $x=2$, is

The area (in s units) of the triangle formed by the lines $x^{2}-3 x y+y^{2}=0$ and $x+y+1=0$, is

The shortest distance between the skew lines $\bar{r}=(i+2\bar{j}+3\bar{k})+t(i+3\bar{j}+2\bar{k}) $ and $\bar{r}=(4i+5\bar{j}+6\bar{k})+t(2i+3\bar{j}+\bar{k})$ is

If a line $l$ passes through $(k, 2 k),(3 k, 3 k)$ and $(3,1), k \neq 0$, then the distance from the origin to the line $l$ is