List of top Mathematics Questions asked in AP EAPCET

If $ \sin x \cosh y = \cos \theta $ and $ \cos x \sinh y = \sin \theta $, then find $ \sin^2 x + \cosh^2 y $.

Match the items of List - A with those of the entries of List - B.

If $ \alpha, \beta, \gamma $ are the roots of the equation $ x^3 + 3x^2 + 4x + 5 = 0 $, then the cubic equation whose roots are $ 1 + 4\alpha, 1 + 4\beta, 1 + 4\gamma $ is:
The coefficient of $ x^2 $ in the expansion of \[ (1 - 3x)^{\frac{-1}{4}} \] is

If $ N(n) = n \prod_{r=1}^{2023} (n^2 - r^2) $ where $ n > 2023 $, then the value of $ {}^{n}C_{N-1} $ when $ n = 2024 $ is:

The number of natural numbers less than 500 in which no two digits are repeated is:
The number of elements in the set $ S = \{x \in \mathbb{Z} : x^2 - 7x + 6 \le 0 \text{ and } x^2 - 3x>0 \} $ is
Arg \[ \frac{4 + 2i}{1 - 2i} + \frac{3 + 4i}{2 + 3i} \] lies in the interval \[ \text{Arg} \left( \frac{4 + 2i}{1 - 2i} + \frac{3 + 4i}{2 + 3i} \right) \]
The multiplicative inverse of $ z $ is:
If \( \frac{d}{dx} \left( \frac{x^2+1}{(x^2+5)(x^2+9)} \right) = \frac{2x(x^2+1)}{(x^2+5)(x^2+9)} \left[ \frac{1}{f(x)} - \frac{1}{g(x)} - \frac{1}{h(x)} \right] \), then \( 2h(x)-f(x)-g(x) = \)
\( \int \frac{dx}{(1+\sqrt{x})^{2022}} = \)
If \( \int \frac{\sin(x-\pi/4)}{2+\sin 2x} dx = -\frac{1}{\sqrt{2}} \tan^{-1}(f(x)) + C \), then \(f(x) = \)
\( \int_{a-1}^{a} \frac{e^x(a-x)}{(x-a+1)^2} dx = \)
For \(n \in N\), If \( I_n = \int \frac{\sin nx}{\sin x} dx = \frac{2}{n-1}\sin((n-1)x) + I_{n-2} \) and \( \int_0^{\pi} \frac{\sin nx}{\sin x} dx = \frac{k\pi}{2} \) then k =
If a and b are respectively the order and degree of a differential equation \( y^2(y'')^2 + 3x(y')^{1/3} + x^2y^2 = \sin x \), then
An integrating factor of the differential equation \( (x^2+1)\frac{dy}{dx} + xy = x^3 \) is
If the general solution of \( \frac{dy}{dx} = \frac{-y^2}{xy-y^2-x^2} \) is \( \tan^{-1}\left(\frac{x}{y}\right) = f(y) + C \), then \( f(e^3) = \)
\( \int_{-\pi/4}^{\pi/4} \cos^8 x \ dx = \)
If \( f(x) = \sin(\tan^{-1} x) \), then \( \int_0^1 xf''(x)dx = \)
If an open cylinder of given surface area has maximum volume then its radius is
If \(x+y=k, x>0, y>0\) then \(x^2+y^2\) is minimum if
If \( \int \frac{x^8+4}{x^4-2x^2+2} dx = Ax^5+Bx^3+Cx+K \), then \(5A+3B+C = \)
\( \int \sqrt{x+\sqrt{x^2+2}} \ dx = \)
If \( f(x) = \begin{cases 4 & -\infty<x<-\sqrt{5}
x^2-1 & -\sqrt{5} \le x \le \sqrt{5}
4 & \sqrt{5}<x<\infty \end{cases} \). If k is the number of points where f(x) is not differentiable then k -- 2 =}
Assertion (A) : \( f(x)=|x| \) is differentiable at \( x=a \neq 0 \) and continuous but not differentiable at \( x=0 \) Reason (R) : If a function is differentiable at a point then it is continuous at that point. But converse is not true. .