List of top Mathematics Questions asked in AP EAPCET

If \[ \int \frac{dx}{\sin^3x+\cos^3x} = A\log\left| \frac{\sqrt2+t}{\sqrt2-t} \right| + B\tan^{-1}(t)+C, \] then \[ \left(\frac{B}{A},\,t\right) = \]

If \(x > 0\), then \(\int \frac{1}{\sqrt{x^4 + 2x^3 + 2x^2}} dx =\)

If \( \int \frac{2x+5}{(x-1)(x+1)(x+4)(x+6)} \, dx = \frac{1}{10}\log\left(\frac{f(x)}{g(x)}\right)+c \) and \( \frac{f(-2)}{g(-2)}=6 \), then \( \frac{f(10)}{g(10)} = \)

The integral \( \int \frac{\cos x - \sin x}{10 + \sin 2x} dx \) is equal to:

If \[ \int 4^x \cdot 4^{4^x}\cdot 4^{\,4^{4^x}}\,dx = A\,4^{\,4^{4^x}}+C, \] then \(A=\)

The integral $\int \frac{e^x (1 + x)}{\cos^2(x e^x)} \, dx =$

Evaluate the integral: \[ \int \frac{x}{x^2-5x+4}\,dx \]

The value of the integral \(\int \frac{dx}{\cos 2x + \sin 2x + 2\sin^2 x}\) is:

The integral $\int \frac{1}{\cos^2 x (1 - \tan x)^2} \, dx =$

If $\int\frac{2\sin x+a\cos x}{b\sin x+4\cos x}dx=\frac{2}{5}x-\frac{1}{5}\log(b\sin x+4\cos x)+c$, then $a+b=$

The integral $\int \frac{dx}{x(x^4 + 1)} =$

Evaluate: \[ \int \frac{\sin^2 x \cos^2 x}{\cos^6 x+\sin^6 x}\,dx \]

If \( \int e^{x}\left(\frac{1}{n}+\tan nx\right)\sec nx \, dx = \frac{1}{n}(g(x)+k) = F(x) \) and \( F(0)=1 \), then \( k = \)

Evaluate \[ \int \frac{1}{(x^4+1)^{5/4}}\,dx. \]

If \[ \int (x+5)\sqrt{x-5}\,dx = \frac{2(x-5)^{5/2}}{15}f(x)+c, \] then \(f(6)=\)

For \( x>0 \), if \( \int \frac{1}{x^{2}+5x+7} \, dx = \frac{2}{\sqrt{3}}F(x)+k \) and \( F\left(-\frac{5}{2}\right)=0 \), then \( \sin(F(x)) = \)

The integral \( \int \frac{\cos^3 x}{(1+\sin x)^4} dx \) is equal to:

Evaluate: \[ \int \frac{dx}{(x^5+1)^{6/5}} \]

If $\int(4\sin\theta+\cos\theta)\cot\theta\cos\theta d\theta=2\theta+\sin2\theta+\log(\sin\theta)+f(2\theta)+c$ and $f(0)=\frac{1}{2}$, then $f(x)=$

If \( \int e^{5x}x^{n} \, dx = F(n, x) + c \), then \( 5F(n, x) + nF(n-1, x) = \)

If \[ \int e^x\frac{x^3+3x^2+4}{(x+1)^3}\,dx = e^x f(x)+C, \] then \(f(x)\) is

Evaluate: \[ \int \frac{e^{2x}-1}{e^{2x}+e^x+1}\,dx \]

Evaluate $\int \frac{1+x^2}{\sqrt{1-x^2}} dx$:

If $A$ and $B$ are two events such that $P(A) = 0.4$, $P(B) = 0.8$ and $P(B|A) = 0.6$, then $P(\bar{A} \cap B) =$

From the set of numbers \[ \{1,2,3,4,5,6,7,8,9,10,11,12\}, \] two numbers are selected at random. The probability that the two numbers selected differ by a prime number is