List of top Mathematics Questions asked in AP EAMCET

If $\lim_{n\rightarrow\infty}[(1+\frac{1}{n^{2}})(1+\frac{4}{n^{2}})(1+\frac{9}{n^{2}})\cdots(1+\frac{n^{2}}{n^{2}})]^{\frac{1}{n}}=ae^{b}$, then a+b=

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

Evaluate the integral: \[ \int e^{4x^2 + 8x -4} (x+1) \cos(3x^2 + 6x -4) \, dx.= \]

If \[ \int \frac{\sqrt[4]{x}}{\sqrt{x} + \sqrt[4]{x}} \, dx = \frac{2}{3} \left[ A \sqrt[4]{x^3} + B \sqrt[4]{x^2} + C \sqrt[4]{x} + D \log \left( 1 + \sqrt[4]{x} \right) \right] + K \] then $ \frac{2}{3} (A + B + C + D) = $}

Evaluate the integral: \[ I = \int \frac{\sin 7x}{\sin 2x \sin 5x} \,dx. \]

Evaluate the integral: \[ \int \frac{1}{x^5 \sqrt{x^5+1}} dx. \]

Evaluate $ \int_{1}^{2} \frac{x^4 - 1}{x^6 - 1} dx $:

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

Find the area enclosed by the curve $ y = x^3 - 19x + 30 $ and the X-axis.

Evaluate the integral: \[ I = \int (\tan^7 x + \tan x) dx. \]

If $I_{n}=\int_{0}^{\pi/4}\tan^{n}x~dx,$ then $I_{13}+I_{11}=$

Evaluate the integral: \[ I = \int \frac{x+1}{\sqrt{x^2 + x + 1}} dx. \]

The area (in square units) of the smaller region lying above the X-axis and bounded between the circle \[ x^2 + y^2 = 2ax \] and the parabola \[ y^2 = ax \]

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

Evaluate the integral: \[ \int \frac{x^2 - 1}{x^3\sqrt{2x^4 - 2x^2 + 1}} \,dx. \]

Evaluate the integral: $$ \int \frac{x^3 \tan^{-1}(x^4)}{1 + x^8} \,dx. $$

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

Evaluate the integral: \[ \int \frac{1}{(1 + x^2) \sqrt{x^2 + 2}} \, dx. \]

Evaluate the integral: \[ \int_{-2}^{2} (4 - x^2)^{\frac{5}{2}} \, dx. \]

$\int\frac{2\cos 2x}{(1+\sin 2x)(1+\cos 2x)}dx=$

Evaluate the limit: \[ \lim_{n \to \infty} \left( \frac{1}{\sqrt{n^2}} + \frac{1}{\sqrt{n^2 - 1}} + \dots + \frac{1}{\sqrt{n^2 - (n-1)^2}} \right). \]

Evaluate $ \int_{ \log 4}^{ \log 5} \frac{e^{2x} + e^x}{e^{2x} - 5e^x +6} dx $:

Evaluate $ \int (\log x)^m x^n dx $.

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

Out of the first 5 consecutive natural numbers, if two different numbers x and y are chosen at random, then the probability that x⁴- y⁴is divisible by 5 is: