List of top Mathematics Questions asked in AP EAPCET

If \[ A= \begin{bmatrix} c & -a & b\\ a & b & -c\\ -b & c & a \end{bmatrix}, \qquad B= \begin{bmatrix} 1 & 0 & 2\\ 0 & 1 & 2\\ 1 & 2 & 0 \end{bmatrix} \] and \[ AB= \begin{bmatrix} 4 & 4 & -2\\ 1 & 1 & 10\\ -1 & 5 & -4 \end{bmatrix}, \] then \(a^2+b^2+c^2=\)

If \[ A= \begin{bmatrix} 3 & x & 2\\ 2x & 3 & -1\\ 1 & 2 & 3x \end{bmatrix} \] is a singular matrix and \(x\gt 0\), then \(\sqrt{3}\,x=\)

Assertion (A): If \[ 2+6+16+40+\cdots \text{ to } k \text{ terms}=4608, \] then \(k=9\). Reason (R): \[ 2+3\cdot2+4\cdot2^2+\cdots+n\cdot2^{\,n-1}=n\cdot2^n, \qquad \forall n\in\mathbb N \] Which one of the following options is correct?

If the co-domain of the function \[ f(x)= \begin{cases} 3\sin x-4\cos x, & x\in \left(\tan^{-1}\frac{4}{3}-\frac{\pi}{2},\,\tan^{-1}\frac{4}{3}+\frac{\pi}{2}\right)\\[2mm] \log(\sin x), & x\in \left(\frac{5\pi}{6},\pi\right) \end{cases} \] is \((-\infty,5)\), then \(f\) is

Let \[ f(x)=\frac{|x|-1}{|x-1|} \] be a real valued function from \( \mathbb{R}-\{1\} \) to \(B\). If \(f\) is a surjection, then \(B=\)

The general solution of the differential equation \[ \frac{dy}{dx}+\frac{y}{x}=x^2 \] is

Evaluate \[ \int_{1/e}^{e^2} \left| \frac{\log_e x}{x} \right| \,dx \]

If \[ \int \frac{dx}{2\sin^2x+\sin2x} = \frac12\log|f(x)|+C \] and \[ f\!\left(\frac{\pi}{4}\right)=\frac12, \] then \(f(x)\) is

If \[ \int \frac{2\cos x+3\sin x} {3\cos x+4\sin x}\,dx = Ax+B\log|3\cos x+4\sin x|+C, \] then \[ A\cdot B= \]

The closest point on the parabola \[ y=x^2+7x+2 \] to the straight line \[ y=3x-2 \] is

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

Evaluate \[ \lim_{n\to\infty} \frac{1+2^4+3^4+\cdots+n^4}{n^5} - \lim_{n\to\infty} \frac{1+2^3+3^3+\cdots+n^3}{n^5}. \]

If \[ f(x)=\frac1{x^2}\int_{3}^{x}\left(2t-3f'(t)\right)\,dt, \] then \[ f'(3)= \]

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

Evaluate \[ I=\int_{-2}^{0} \Big(x^3+3x^2+3x+3+(x+1)\cos(x+1)\Big)\,dx \]

The order and degree of the differential equation \[ \left\{1+\left(\frac{dy}{dx}\right)^2\right\}^{3/2} = \frac{d^2y}{dx^2} \] are respectively

Given that \[ \frac{dy}{dx}=ye^x \] and when \[ x=0,\quad y=e, \] then the value of \(y\) (\(y>0\)) when \(x=1\) is

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

The area of the region enclosed between the curve \[ y=\log_e(x+e) \] and the coordinate axes is

The function \[ f(x)=2x+\cot^{-1}x+\log\!\left(\sqrt{1+x^2}-x\right) \] is

A particle is moving on a straight line so that its distance \(s\) from a fixed point at any time \(t\) is proportional to \(t^n\). If \(v\) is the velocity and \(a\) is the acceleration of the particle at any time \(t\), then \[ \frac{nas}{n-1} = \]

If \[ y= \tan^{-1}\!\left(\frac{1}{1+x+x^2}\right) + \tan^{-1}\!\left(\frac{1}{x^2+3x+3}\right) + \tan^{-1}\!\left(\frac{1}{x^2+5x+7}\right), \] then \[ y'(0)= \]

If \[ y=a\log|x|+bx^2+x \] has its extremum values at \[ x=-1 \quad\text{and}\quad x=2, \] then \((a,b)=\)

A(3,1,2), B(-1,6,2) and C(1,1,-2) are three points. A plane passes through \(A\) and is perpendicular to the line joining \(B\) and \(C\). If \((\alpha,\beta,\gamma)\) is the image of \(C\) with respect to the plane, then \[ 3\alpha-\gamma+2\beta= \]

If \(f\) is a derivable function and \[ 2f(\sin x)+f(\cos x)=x \qquad \forall x\in \mathbb{R}, \] then \[ f'(x)= \]