List of top Mathematics Questions asked in AP EAPCET

A box contains $30$ toys of same size in which $10$ toys are white and all the remaining toys are blue. A toy is drawn at random horn the box and it is replaced in the box after noting down its colour. If $5$ toys are drawn in tills way, then the probability of getting atmost $2$ white toys is

$f\left(x\right) = \frac{x}{e^{x}-1} + \frac{x}{2} + 2 \cos^{3} \frac{x}{2} $ on $R-\left\{0\right\} $ is

$D = \left\{x\in\mathbb{R}: f\left(x\right) =\sqrt{\frac{x - \left|x\right|}{x - \left[x\right]}} \text{is defined} \right\}$ and $C$ be the range of the real function $g(x) = \frac{2x}{4 + x^{2}}$. Then $D \cap C$

If $z= x +iy , x,y \in R , (x,y) \ne (0, -4)$ and $Arg \left( \frac{2z-3}{z+4i}\right) = \frac{\pi}{4}$ , then the locus of $z$ is

Consider the following lists.

List-I		List-II
(A)	$f(x) = \frac{|x+2|}{x+2} , x \ne -2 $	(I)	$[\frac{1}{3} , 1 ]$
(B)	$(x)=|[x]|,x \in [R$	(II)	Z
(C)	$h(x) = |x - [x]| , x \in [R$	(III)	W
(D)	$f(x) = \frac{1}{2 - \sin 3x} , x \in [R$	(IV)	[0, 1)
		(V)	{ -1, 1}

If $[x]$ is the greatest integer less than or equal to $x$ and $|x|$ is the modulus of $x$. then the system of three equations $2x + 3 | y | + 5[z] = 0, x + |y| - 2[z] = 4, x + |y| + |z| = 1$ has

If $A=\begin{bmatrix}1 & 0 \\ 0 & -1\end{bmatrix}, P=\begin{bmatrix}1 & 1 \\ 0 & 1\end{bmatrix}$ and $X=A P A^{T}$, then $A^{T} X^{50} A=$

If \( \vec{a} = 2\hat{i} - \hat{j} + 3\hat{k} \), \( \vec{b} = \hat{i} + 2\hat{j} - \hat{k} \), then the angle \( \theta \) between \( \vec{a} \) and \( \vec{b} \) is:

If \( f(x) = 2x^3 - 3x^2 + 4 \), then the minimum value of \( f(x) \) in the interval \( [0, 3] \) is:

The integral $ \int (3x^2 - 2x + 1) \, dx $ is: