List of top Mathematics Questions asked in AP EAMCET

$\int\frac{2x^{2}\cos(x^{2})-\sin(x^{2})}{x^{2}}dx=$

In a triangle ABC, if $ (r_1 + r_2) \csc^2 \frac{C}{2} = $

The number of all the values of $ x $ for which the function \[ f(x) = \sin x + \frac{1 - \tan^2 x}{1 + \tan^2 x} \] attains its maximum value on $ [0, 2\pi] $.

If 5 letters are to be placed in 5-addressed envelopes, then the probability that at least one letter is placed in the wrongly addressed envelope is:

If the function \[ f(x) = \frac{\sqrt{1+x} - 1}{x} \] is continuous at $ x = 0 $, then $ f(0) $ is:

If five-digit numbers are formed from the digits 0, 1, 2, 3, 4 using every digit exactly only once, then the probability that a randomly chosen number from those numbers is divisible by 4 is

The differential equation formed by eliminating arbitrary constants $ A $ and $ B $ from the equation \[ y = A \cos 3x + B \sin 3x \] is:

The equation of a circle which touches the straight lines \[ x + y = 2, \quad x - y = 2 \] and also touches the circle \[ x^2 + y^2 = 1 \] is:

If the $2^{\text{nd}}$, $3^{\text{rd}}$, and $4^{\text{th}}$ terms in the expansion of $ (x + a)^n $ are 96, 216, and 216 respectively, and $ n $ is a positive integer, then $ a + x $ is:

If $ A = \int_0^{\infty} \frac{1 + x^2}{1 + x^4} dx $ and $ B = \int_0^1 \frac{1 + x^2}{1 + x^4} dx $, then:

Evaluate the integral: $ I = \int e^{2x+3} \sin 6x \, dx $.

If the roots of the equation $x^3 + ax^2 + bx + c = 0$ are in arithmetic progression, then:

If $ f(x) $ is given as: $ f(x) = \begin{cases} 3ax - 2b, & x<1 ax + b + 1, & x<1 \end{cases} $ and $ \lim_{x \to 1} f(x) $ exists, then the relation between $ a $ and $ b $ is:

The equation of one of the tangents drawn from the point $ (0,1) $ to the hyperbola $ 45x^2 - 4y^2 = 5 $ is:

The general solution of the equation $ \sin^2 \theta + 3 \cos^2 \theta = 5 \sin \theta $ is:

A Circle S passes through the points of intersection of the circles $ x^2 + y^2 - 2x + 2y - 2 = 0 $ and $ x^2 + y^2 + 2x - 2y + 1 = 0 $. If the centre of this circle S lies on the line $ x - y + 6 = 0 $, then the radius of the circle S is:

The real part of $ \frac{\left( \cos a + i \sin a \right)^6}{\left( \sin b + i \cos b \right)^8} $ is:

If Rolle’s theorem is applicable for the function $ f(x) $ defined by $ f(x) = x^3 + Px - 12 $ on $ [0,1] $, then the value of $ C $ of the Rolle's theorem is:

If $y = \tan^{-1} \frac{x}{1+2x^2} + \tan^{-1} \frac{x}{1+6x^2} + \tan^{-1} \frac{x}{1+12x^2}$, then $\left(\frac{dy}{dx}\right)_{x=\frac{1}{2}} =$

$\int_{0}^{\pi}x \sin^4 x \cos^6 x dx = $

Given that: $M = \int_{0}^{\infty} \frac{\log t}{1 + t^3} \, dt$, and $N = \int_{-\infty}^{\infty} \frac{e^{2t} t}{1 + e^{3t}} \, dt$. Then, the relation between $M$ and $N$ is:

If a random variable $ X $ has the following probability distribution, then its variance is nearly:

Let $ f(x) $ be defined as: \[ f(x) = \begin{cases} 0, & x = 0 \\ 2 - x, & 0 < x < 1 \\ 2, & x = 1 \\ 1 - x, & 1 < x < 2 \\ -\frac{3}{2}, & x \geq 2 \end{cases} \] Then which of the following is true?

The number of ways of distributing 15 apples to three persons A, B, C such that A and C each get at least 2 apples and B gets at most 5 apples is:

Evaluate the integral: $$ I = \int \frac{2}{1 + x + x^2} \,dx. $$