List of top Mathematics Questions asked in AP EAPCET

If \(1,\omega,\omega^2\) denote the cube roots of unity, then the value of \[ (1-\omega+\omega^2)^5+(1+\omega-\omega^2)^5 \] is

If \[ a^2+b^2+c^2=1,\quad a,b,c\in \mathbb{R}, \] then the set of extreme values of \(ab+bc+ca\) is

If \(\alpha,\beta\) are the roots of \[ ax^2+bx+c=0, \] then the quadratic equation whose roots are \(\sqrt{5}\alpha,\sqrt{5}\beta\) is

The values of \(\theta\), for which \[ \frac{3+2i\sin\theta}{1-2i\sin\theta} \] is real are

If \[ \frac{(1+i)x-2i}{3+i}+\frac{(2-3i)y}{3-i}=i, \] then \(x+y=\)

Let \[ A= \begin{bmatrix} b^2+c^2 & a^2 & a^2 \\ b^2 & c^2+a^2 & b^2 \\ c^2 & c^2 & a^2+b^2 \end{bmatrix} \] If \[ a=\sin\frac{\pi}{6},\quad b=\cos\frac{\pi}{4},\quad c=\cot\frac{\pi}{2}, \] then \(A\) is

The rank of the matrix \[ A= \begin{bmatrix} 2 & 1 & 2 \\ 1 & 0 & 1 \\ 4 & 1 & 4 \end{bmatrix} \] is

If a matrix \(A\) satisfies the equation \[ A^3-6A^2+11A-6I=0, \] then \(A^{-1}\) can be

If \[ A= \begin{bmatrix} 1 & -2 & 2 \\ 2 & -6 & 5 \\ 5 & 0 & 4 \end{bmatrix}, \] then \(\operatorname{Adj}(A)=\)

If \(f\) is a relation from the set of positive real numbers to the set of positive real numbers defined by \[ f(x)=3x^2-2, \] then \(f\) is

Let \(f:\mathbb{R}\to \mathbb{R}\) be defined by \(f(x)=2x+3\). If \(\alpha,\beta\) are the roots of the equation \[ f(x^2)-2f\left(\frac{x}{2}\right)-1=0 \] then \(\alpha^2+\beta^2=\)

The differential equation of the family of circles passing through \((0,0)\) and having centre on \(x\)-axis is

Find the value of \[ \lim_{n\to\infty}\left(\frac{1^2}{n^3+1^3}+\frac{2^2}{n^3+2^3}+\cdots+\frac{1}{2n}\right) \] =

If \[ \int f(x)\,dx=F(x)+C, \] then \[ \frac{d}{dt}\int_{g(t)}^{h(t)}f(x)\,dx= \]

If \[ \int_{0}^{\pi/2}\sin^m x\cos^4 x\,dx=\frac{7\pi}{2048}, \] then \(m=\)

Evaluate \[ \int_{-\pi}^{\pi}\frac{\cos^{2022}x}{1+(2022)^x}\,dx \] =

For the differential equation \[ \frac{d^3y}{dx^3}=0, \] \(y=ax^2+bx+c\) is

If \[ \frac{a}{a_1}=\frac{b}{b_1}, \] then the substitution to be used to solve the differential equation \[ \frac{dy}{dx}=\frac{ax+by+c}{a_1x+b_1y+c_1} \] by using separation of variables is

If \[ \int \frac{\cosec^2x-2022}{\cos^{2022}x}\,dx=f(x)+C \Rightarrow f\left(\frac{\pi}{4}\right)= \]

If \[ \int \cos^{-1}\left(\sqrt{\frac{x}{a+x}}\right)\,dx=f(x)+C \Rightarrow f'(a)= \]

If \(f(x)\) is anti-derivative of \(g(x)\) and \[ \int f(x)g(x)(1+f^2(x))\,dx=F(x), \] then \(F(x)=\)

If \(k\in \mathbb{N}\), then \[ \int \frac{1-k\cos^2 x}{\sin^k x\cos^2 x}\,dx= \]

The function \(f(x)=2x^3-9ax^2+12a^2x+1\), where \(a\gt 0\), attains its maximum and minimum at \(p\) and \(q\) respectively and \(p^2=q\). Then \(a=\)

The set of all \(x\) for which \[ \sin x\leq x \] is

The curve \[ y=ax^3+bx^2+cx+5 \] touches the \(x\)-axis at \(P(-2,0)\), then \(c=\)