List of top Mathematics Questions asked in AP EAPCET

The equation of the line, passing through the point $(a\cos^3\theta, a\sin^3\theta)$ and perpendicular to the line $x\sec\theta - y\csc\theta = a$, is
If the mean and varian of a binomial variable $X$ are 2 and 1 respectively, then $P(X>1) = $
In triangle $\triangle ABC$, $A=(1,2)$ and the equations of medians through $B$ and $C$ are $x+y=5$ and $x=4$. Find area of triangle ABC.
The probability that a person chosen at random is left handed is 0.1. Then the probability that in a group of 10 people there is exactly one left-handed person is
If A(2,3) and B(2,-3) are two points, then the equation of the locus of a point $P$ such that $PA + PB = 8$ is
Probability that missing card is not a spade, given two drawn cards are spades?
If A speaks truth with probability $\frac{4}{5}$ and B with $\frac{3}{4}$, find probability they contradict.
Given independent events A, B, and C with rtain intersection probabilities, find $P(A)$, $P(B)$, and $P(C)$.
If $\vec{a} = 2\hat{i} - \hat{j} + 3\hat{k}$, $\vec{b} = -3\hat{i} + 5\hat{j} - 4\hat{k}$, $\vec{c} = 6\hat{i} - 4\hat{j} + 5\hat{k}$, then $(\vec{a} \times \vec{b}) \cdot (\vec{b} \times \vec{c}) = $
Planes $\pi_1$ and $\pi_2$ are defined by vectors. If $|\vec{a}| = \sqrt{14}$ and $\vec{a}$ is parallel to their intersection, then $|\vec{a} \cdot (\hat{i} + \hat{j} + \hat{k})| = $
If $\vec{a} = 2\hat{i} - t\hat{j} - 2\hat{k}$ and $\vec{b} = 6\hat{i} + 2\hat{j} - 3\hat{k}$ are two vectors such that $\vec{a} \cdot \vec{b}$ is minimum, then $t=$

Assertion (A): \[ \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{(\sin x)^{\sqrt{2}}}{(\sin x)^{\sqrt{2}} + (\cos x)^{\sqrt{2}}} \, dx = \frac{\pi}{12} \]

Reason (R): \[ \int_{\frac{\pi}{6}}^{\frac{\pi}{3}} \frac{f(x)}{f(x) + f\left(\frac{\pi}{2}-x\right)} \, dx = \frac{\pi}{12} \]

If \( A = \left\{ \frac{x}{9x^2 + 20} \right\} \) and \( f: A \to \mathbb{R} \) is defined by \( f(x) = 2x^3 - 15x^2 + 36x - 48 \), then the maximum value of \( f(x) \) is
Let \( f(x) \) be a differentiable function, \( A(0, \alpha) \) and \( B(8, \beta) \) be two points on the curve \( y = f(x) \). Given \( f(0) = 2 \) and \( f'(4) = -\frac{3}{4} \). If the chord \( AB \) of the curve is parallel to the tangent drawn at the point \( (4, f(4)) \), then \( \beta \) is:

If \( f(x) = \begin{cases} 1 + 6x - 3x^2, & x \leq 1 \\ x + \log_2(b^2 + 7), & x > 1 \end{cases} \) is continuous at all real \( x \), then \( b \) is:

If two subsets \( A \) and \( B \) are selected at random from a set \( S \) containing \( n \) elements, then the probability that \( A \cap B = \emptyset \) and \( A \cup B = S \) is:

If \( \tan \left( \frac{\alpha + \beta}{2} \right) \), \( \cos (\alpha + \beta) \), \( \sin (\alpha + \beta) \), and \( \tan (\alpha + \beta) \) are matched with their values, then the correct matching is:

The number of natural numbers less than 10000 which are divisible by 5 and that no digit is repeated in the same number, is
If \( S = \begin{bmatrix} 0 & 1 \\ 0 & 1 \\ 1 & 0 \end{bmatrix} \) and \( A = \frac{1}{2} \begin{bmatrix} b + c & c - a \\ a + b & b - c \end{bmatrix} \), then \( SAS^{-1} \) is:
If \( f(x) = \int_0^x \frac{5t^8 + 7t^6}{(t^2 + 2t + 1)^2} dt \) and \( f(0) = 0 \), then the value of \( f(1) \) is:
If the angle between the curves \( y = e^{(x+4)} \) and \( x^2 y = 1 \) at the point \( (1, 1) \) is \( \theta \), then \[ \sin \theta + \cos \theta = \dots \]
If \( x^x y^y = e^e \), then \( \left( \frac{d^2 y}{dx^2} \right)_{(e, e)} = \):
Evaluate the integral: \[ \int_0^1 \left( \sqrt{10} \right)^{2x} \, dx \]
The area (in sq. units) of the region bounded by the curves \( y = 4 \cos x \) and \( y = -|\cos x| \) from \( x = -\frac{\pi}{2} \) to \( x = \frac{\pi}{2} \) is:
If \( \alpha \) and \( \beta \) are respectively the order and degree of the differential equation \[ y = e^{\frac{d^2y}{dx^2}}, \] then the value of \( \alpha + \alpha^\beta + \alpha^{2\beta} + \dots + \alpha^{2023\beta} \) is: