List of top Mathematics Questions asked in AP EAPCET

For \(n\in\mathbb{N}\), \[ 1^2+2^2+3^2+\cdots+n^2 > \]

Let \(S\) be a symmetric matrix obtained from \[ A= \begin{bmatrix} 1 & 2 & -3\\ 2 & -2 & 1\\ 3 & 1 & -1 \end{bmatrix} \] and \(T\) be a skew-symmetric matrix obtained from \[ B= \begin{bmatrix} 4 & 2 & 0\\ 1 & -1 & 3\\ 0 & 2 & -3 \end{bmatrix} \] If trace of \(S=-4\) and the non-zero elements of \(T\) are \(-1,1\), then \(S+T=\)

If \[ A= \begin{bmatrix} b+c & a & a\\ b & c+a & b\\ c & c & a+b \end{bmatrix} \] is a matrix such that trace of $A=18$ and \[ \det(A)=96, \] if $a,b,c\in \mathbb{N}$ and $ab=6$, then $ab+bc+ca=$

If \(f:(-\infty,0)\to \mathbb{R}\) is defined by \[ f(x)=\frac{[x]}{|x|} \] then \(f(x):x\in(-\infty,0)\) is:

If a real valued function \(f : A \to B\) defined by \(f(x)=|x|-[x]\) is a bijection, then \(A\) and \(B\) are respectively:

Evaluate $\int_{-\pi}^{\pi} \frac{\cos^2 x}{1+a^x} dx$

Evaluate $\int_0^{\pi/2} \sin^6 x \cos^4 x dx$

Solve $\cos(x+y)dy=dx$

Eliminate constants from $y=A(x+B)^2$

Solve $(1+y^2)+(x-e^{-\tan^{-1}y})\frac{dy}{dx}=0$

If $\int x^5 e^{-4x^3} dx = \frac{1}{48}e^{-4x^3} f(x) + c$, then $f(x) =$

Area between $y^2=x$ and $y=|x|$ is:

Evaluate $\int \frac{x-1}{(x+1)^3}e^x dx$:

The evaluation of the indefinite integral $\int \frac{dx}{\sin x + \sin 2x}$ is:

Evaluate $\lim_{n\to\infty} \frac{1}{n^2}\sum_{r=1}^n r e^{r/n}$

If $\int \frac{\cos 8x + 1}{\cot 2x - \tan 2x} dx = A\cos 8x + c$, then $A =$

The maximum value of $y = x(\log x)^2$ is:

If $f(x) = \sqrt{3}\sin x - \cos x - 2ax + b$ decreases for all $x \in \mathbb{R}$, then:

The maximum area of a rectangle inscribed in a circle of radius $r$ is:

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

If the displacement of a particle at time $t$ ($0 < t < \pi$) is given by $s = 3 \sin 2t - 6 \cos t$, then the acceleration for the values of $t$ at which its velocity is zero is:

The value of \[ \sin20^\circ\sin40^\circ\sin80^\circ \] is:

Let \[ \vec a=\hat i+2\hat j+2\hat k, \qquad \vec b=2\hat i+\hat j+2\hat k. \] If \(\theta\) is the angle between \(\vec a\) and \(\vec b\), then the value of \[ \cos\theta \] is:

Let \[ A= \begin{bmatrix} 1 & 2\\ 2 & 1 \end{bmatrix}. \] Then the determinant of \(A^2\) is:

The value of \[ \lim_{x\to0}\frac{\sin5x-5\sin x}{x^3} \] is: