List of top Questions asked in AP EAMCET- 2024

The general solution of \( 4 \cos 2x - 4 \sqrt{3} \sin 2x + \cos 3x - \sqrt{3} \sin 3x + \cos x - \sqrt{3} \sin x = 0 \) is:
Statement (S1): \( \sin 55^\circ + \sin 53^\circ - \sin 19^\circ - \sin 17^\circ = \cos 2^\circ \)
Statement (S2): The range of \( \frac{1}{3 - \cos 2x} \) is \( \left[ \frac{1}{4}, \frac{1}{2} \right] \) Which one of the following is correct?
Evaluate: \[ \tan^{-1} 2 + \tan^{-1} 3 \]
Evaluate the expression: \[ \sin^2 76^\circ + \sin^2 16^\circ - \sin 76^\circ \sin 16^\circ \]
Evaluate: \[ \cosh^{-1} 2 \]
The value of \( 5 \cos \theta + 3 \cos \left( \theta + \frac{\pi}{3} \right) + 3 \) lies between:
The smallest positive value (in degrees) of \( \theta \) for which \( \tan(\theta + 100^\circ) = \tan(\theta + 50^\circ) \tan(\theta - 50^\circ) \) is valid, is:
The general solution of \( 2 \cos^2 x - 2 \tan x + 1 = 0 \) is:
Evaluate the expression: \[ \tan 6^\circ \tan 42^\circ \tan 66^\circ \tan 78^\circ \]

Let f(x) = \(\int \frac{x}{(x^2+1)(x^2+3)} dx\). If f(3) = \(\frac{1}{4} \log(\frac{5}{6})\), then f(0) =

Evaluate the limit: $$ \lim_{n \to \infty} n^4 \left[ \sum_{k=0}^{\infty} \frac{1}{(n^2 + k)^{5/2}} \right]. $$
Evaluate the integral: \[ \int \sin^4 x \cos^4 x \, dx. \]

 For all x ∈ [0, 2024] assume that f (x) is differentiable. f (0) = −2 and f ′(x) ≥ 5. Then the least possible value of f (2024) is:

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

Evaluate the integral: \[ I = \int_0^{\frac{\pi}{4}} \log(1 + \tan x) \,dx. \]
Evaluate the integral \( \int_0^{\pi} \frac{x \sin x}{4 \cos^2 x + 3 \sin^2 x} dx \):
Evaluate the integral: \[ \int \sin^{-1} \left( \sqrt{\frac{x - a}{x}} \right) dx \]
Evaluate the integral: \[ \int \frac{1}{x^5 \sqrt{x^5+1}} dx. \]
If \(\int \frac{\log(1+x^4)}{x^3} dx = f(x) \log(\frac{1}{g(x)}) + \tan^{-1}(h(x)) + c\), then \(h(x) [f(x) + f(\frac{1}{x})] =\)
Evaluate the integral: \[ I = \int \frac{\csc x}{3\cos x + 4\sin x} dx. \]
\(\int_{0}^{\pi}x \sin^4 x \cos^6 x dx = \)
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 \( \frac{2}{3} (A + B + C + D) = \)}

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=

Evaluate the integral: \[ \int e^{4x^2 + 8x -4} (x+1) \cos(3x^2 + 6x -4) \, dx.= \]
Evaluate the integral: \[ I = \int \frac{\sin 7x}{\sin 2x \sin 5x} \,dx. \]