List of top Mathematics Questions asked in AP EAPCET

If \[ {}^nC_{r-1}=36,\qquad {}^nC_r=84,\qquad {}^nC_{r+1}=126, \] then the value of \(nr^2\) is

The total number of positive integral solutions \((x,y,z)\) of \[ xyz=24 \] is

Which of the following quadratic equations whose real roots \(x_1,x_2\) satisfy the conditions \[ x_1^2+x_2^2=5, \quad 3(x_1^5+x_2^5)=11(x_1^3+x_2^3)? \]

The range of the function \[ f(x)=\frac{x^2+x+1}{x^2-x+1} \] is

Let \[ f(x)=x^2+\frac{1}{x^2} \] and \[ g(x)=x-\frac{1}{x} \] for \(x\in \mathbb{R}-\{-1,0,+1\}\), then the local minimum of \[ \frac{f(x)}{g(x)} \] is

If \(1,\omega,\omega^2\) are the cube roots of unity, then \[ (2-\omega)^2(2-\omega^2)^2(2-\omega^{10})^2(2-\omega^{11})^2= \]

If the complex numbers \(z_1\), \(z_2\), \(0\) are vertices of an equilateral triangle, then \[ z_1^2+z_2^2= \] is equal to:

Let \(z=x+iy\) be a complex number with \(x,y\in \mathbb{Z}\). Then the area (in square units) of the rectangle whose vertices are the roots of the equation \[ z\overline{z}^{\,3}+\overline{z}z^{3}=350 \] is:

Let \(z\) and \(w\) be two complex numbers such that \[ \overline{z}+i\overline{w}=0 \] and \[ \operatorname{Arg}(zw)=\pi. \] Then \(\operatorname{Arg}(z)=\)

If the system of simultaneous linear equations \(x+y-z=6\), \(3x-y+z=2\) and \(x+ky+z=-8\) has a unique solution \(x=2\), \(y=\beta\), \(z=\gamma\), then the value of \(k\) satisfies the following quadratic equation:

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

Let \[ A=\begin{bmatrix} n & 0 & 0\\ 0 & n & 0\\ 0 & 0 & n \end{bmatrix} \] and \[ B=\begin{bmatrix} 0 & 0 & n\\ 0 & n & 0\\ n & 0 & 0 \end{bmatrix}. \] Then \(A^2+B^2+AB=\)

If \[ A=\begin{bmatrix} x & 2 & 1\\ 2 & x & 1\\ 2 & 1 & 0 \end{bmatrix} \] and \(\det(A^3)=125\), then \(x=\)

The domain of the real valued function \[ f(x)=\frac{\sqrt{\log_{0.5}(x-3)}}{\sqrt{x-1}} \] is

If a function \(f\) satisfies \(f(x+1)+f(x-1)=\sqrt{2}f(x)\), then \(f(x+2)+f(x-2)=\)

If \[ \cos\frac{y}{x}=A\log x+C \] is the general solution of \[ \left(x\sin\frac{y}{x}\right)dy=\left(y\sin\frac{y}{x}-x\right)dx, \] then \(A=\)

Every curve represented by the general solution of \[ \frac{dy}{dx}-\frac{x\log x}{y^3e^{y^2-5}}=0 \] cuts every curve represented by the general solution of \[ \frac{dy}{dx}+\frac{y^3e^{y^2-5}}{x\log x}=0 \] at angle \(\theta\). Then \[ 4\theta-\frac{\pi}{2}= \]

If \(f\) is a continuous function and \(f(x+T)=f(x), \forall x\in R\), it is given that \[ \int_0^{NT} f(t)\,dt=N\int_0^T f(t)\,dt \] \((N\) is a natural number). Then \[ \int_0^{50\pi}\sqrt{1-\cos 2x}\,dx= \]

\(a,b,c,d\) are real numbers. The general solution of \[ \frac{dy}{dx}=\frac{ax+b}{cy+d} \] represents a family of straight lines, when

Assertion (A): \[ \int_{2}^{e}\left(\frac{1}{\log_e x}-\frac{1}{(\log_e x)^2}\right)\,dx = e-2\log_2 e \] Reason (R): \[ \int_{a}^{b} e^x\left(f(x)+f'(x)\right)\,dx = e^bf(b)-e^af(a) \]

If \[ \int_0^\pi \frac{dx}{1+2\sin^2x}=k, \] then greatest integer less than or equal to \(k\) is

Evaluate \[ \int_0^{\pi^2/4}\left(2\sin\sqrt{x}+\sqrt{x}\cos\sqrt{x}\right)\,dx \]

Evaluate \[ \int \frac{2\cos x+1}{(2+\cos x)^2}\,dx-\frac{\sin x}{2+\cos x} \]

If \[ \int \frac{1}{\cos 4x \cos 2x}\,dx = \frac{1}{4\sqrt{2}}\log\left|\frac{1+f(x)}{1-f(x)}\right| -\frac{1}{2}\log g(x)+C, \] then \[ g\left(\frac{\pi}{6}\right)-\sqrt{2}f\left(\frac{\pi}{6}\right)= \]

Evaluate \[ \int \sqrt{1+2\cot x(\cot x+\cosec x)}\,dx \]