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
Evaluate \( \int_{0}^{1} (2x + 1) \, dx \).
The equation of the circle with center at $ (2, -3) $ and radius $ 5 $ is:
If $ \log_2(x + 1) = 3 $, what is the value of $ x $?
Let a circle pass through the point \( (1, 2) \) and touch the \( x \)-axis at \( (3, 0) \). Then the equation of the circle is:
If the roots of the quadratic equation \( 2x^2 - 8x + 5 = 0 \) are \( p \) and \( q \), find the value of \( \frac{1}{p} + \frac{1}{q} \).
If the roots of the quadratic equation $ 2x^2 - 3x + 1 = 0 $ are $ \alpha $ and $ \beta $, what is the value of $ \alpha^2 + \beta^2 $?
If the roots of the quadratic equation \( x^2 - 6x + k = 0 \) have a difference of 2, find the value of \( k \).
Let \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), then \( A^2 - 5A + 6I = ? \)
If \( A = \begin{bmatrix} 1 & 2 \\ 3 & 4 \end{bmatrix} \), find the inverse of matrix \( A \).
If \( \tan \theta = \frac{3}{4} \) and \( \theta \) is in the first quadrant, find the value of \( \sin \theta + \cos \theta \).

If \(\sin \theta = \frac{3}{5}\) and $ \theta $ is in the first quadrant, what is $ \tan \theta $?

$D = \left\{x\in\mathbb{R}: f\left(x\right) =\sqrt{\frac{x - \left|x\right|}{x - \left[x\right]}} \text{is defined} \right\}$ and $C$ be the range of the real function $g(x) = \frac{2x}{4 + x^{2}}$. Then $D \cap C$
$f\left(x\right) = \frac{x}{e^{x}-1} + \frac{x}{2} + 2 \cos^{3} \frac{x}{2} $ on $R-\left\{0\right\} $ is
If \( z \) is a complex number such that \( |z| = 5 \) and \( \text{Re}(z) = 3 \), then the value of \( z^2 \) is:
If \( \tan A + \tan B + \tan C = \tan A \tan B \tan C \) and \( A + B + C = \pi \), then which of the following is true?
Evaluate \( \int_{1}^{2} \frac{1}{x^2} \, dx \).
The integral $ \int (3x^2 - 2x + 1) \, dx $ is:
A box contains 4 white and 6 black balls. If 3 balls are drawn at random with replacement, what is the probability that at least one is white?
Two numbers are selected at random (without replacement) from the first 50 natural numbers. The probability that their sum is even is:
A box contains 5 red balls and 3 green balls. Two balls are drawn at random without replacement. What is the probability that both balls are red?
Find the distance between the points \( (3, 4) \) and \( (7, 1) \) in the Cartesian plane.
Investigate the values of $\lambda$ and $\mu$ for the system $x+2 y+3 z=6, x+3 y+5 z=9$, $2 x+5 y+\lambda z=\mu$ and match the values in List - I with the items in List - II.
List I List II
(A) $\lambda=8, \mu \neq 15$ 1. Infinitely many solutions
(B) $\lambda \neq 8, \mu \in R$ 2. No solution
(C) $\lambda=8, \mu=15$ 3. Unique solution
Find the area of the triangle with vertices at (0, 0), (3, 0), and (0, 4).
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}