List of top Questions asked in AP EAPCET- 2022

Evaluate the integral: \[ \int_{-\pi}^{\pi} \frac{2x(1 + \sin x)}{1 + \cos^2 x}\, dx \]

Find the radius of the circle that has the lines: $$ 3x - 4y + 4 = 0 \quad \text{and} \quad 6x - 8y - 7 = 0 $$ as its tangents.

Three points $ A, B, C $ in the plane have: - x-coordinates in G.P. - y-coordinates in the same G.P. Then, the points $ A, B, C $ lie on:

Given 5 different green toys, 4 different blue toys, and 3 different red toys, how many combinations of toys can be chosen taking at least one green and one blue toy?

Let point $ P $ divide the line segment joining $ A(1, 2, -1) $ and $ B(-1, 0, 1) $ externally in the ratio $ 1:2 $. Given point $ Q = (1, 3, -1) $, find $ PQ $.

If \( a^2+b^2+c^2=1, a,b,c \in R \), then the set of extreme values of \(ab+bc+ca\) is

If \( \int \frac{\sin(x-\pi/4)}{2+\sin 2x} dx = -\frac{1}{\sqrt{2}} \tan^{-1}(f(x)) + C \), then \(f(x) = \)

Given \[ \frac{d}{dx} \left( \frac{(x+1)^2 \sqrt{x-1}}{(x+4)^3 e^x} \right) = f(x) \left[ \frac{2}{x+1} + \frac{1}{2(x-1)} - \frac{3}{x+4} - 1 \right] \] Then find \( f(5) \).

If the slope of the line through \( (0, 0) \) which is tangent to the curve \( y = x^2 + x + 16 \) is \( m \), then find the value of \( m - 4 \).

Evaluate: $$ \int \frac{dx}{(x - 3)^{4/5} (x + 1)^{6/5}} = ? $$

The discrete random variables $X$ and $Y$ are independent from one another and are defined as $X \sim B(16, 0.25)$ and $Y \sim P(2)$. Then the sum of the variances of $X$ and $Y$ is

For any two nonzero real numbers $a$ and $b$, if the line $\dfrac{x}{a} + \dfrac{y}{b} = 1$ is a tangent to the circle $x^2 + y^2 = 1$, then which of the following is true?

There are 10 points in a plane, out of which 6 are collinear. If $ N $ is the number of triangles that can be formed, then $ N = $ ?

During the winter months, in a certain village in Scotland, the probability of a day having severe fog is 0.6. The probability that in a given week there will be exactly two days with severe fog is

Let $\vec{a} = xi + yj + zk$ and $x = 2y$. If $|\vec{a}| = 5\sqrt{2}$ and $\vec{a}$ makes an angle of $135^\circ$ with the z-axis then $\vec{a} =$

The pairs of straight lines \( 2x^2 + axy + 3y^2 = 0 \) and \( 2x^2 + bxy - 3y^2 = 0 \) share a common line, and the other lines are perpendicular. Then values of \( a \) and \( b \) are?

Sides passing through vertex $ (\alpha, \beta) $ of a triangle are bisected at right angles by the lines: $$ y^2 - 8xy - ax^2 = 0 $$ Find the coordinates of the centroid of the triangle.

If $$ ^{10}C_2 = ^{3^{n+1}}C_3 $$ then the value of $ n $ is:

Find the distance between the directrices of the ellipse: \[ \frac{x^2}{36} + \frac{y^2}{20} = 1 \]

If variance of a Poisson distribution is 3, find: \[ P(1<X<4) \]