List of top Questions asked in AP EAPCET

Evaluate \[ \frac{\sin x}{1+\cos x}+\frac{1+\cos x}{\sin x} \]

The expression \[ \frac{x^4}{(x^2+1)(x^2+3)} \] is equal to

If \[ {}^{\,n-1}P_r = {}^{\,n-1}P_{\,r} + x\cdot {}^{\,n-1}P_{(r+1)} \] for \(n,r\in \mathbb{N}\) and \(r\leq n\), then \(x=\)

Factorize \[ 2\cot^2\theta-\cot\theta-3 \]

The English alphabets have 5 vowels and 21 consonants. How many words with two different vowels and two different consonants can be formed from the alphabet?

The sum of all possible numbers that can be formed by using the digits \(2,3,5,7\) without repetition of digits is:

If \(y^2+z^2=3yz,\ z^2+x^2=8zx,\ x^2+y^2=4xy\), then the value of \(\dfrac{y^2}{xz}+\dfrac{xz}{y^2}\) is:

In a plane there are \(37\) straight lines of which \(13\) pass through point \(A\) and \(11\) pass through point \(B\). Moreover, no three lines apart from the lines passing through \(A\) and \(B\) pass through the same point and no two are parallel. What is the number of points of intersection of the straight lines?

If \(2,3,6\) are the roots of the polynomial \[ f(x)=x^3+ax^2+bx+c, \] where \(a,b,c\in \mathbb{C}\), then the value of \(a-c\) is

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

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

Let \(z\) and \(w\) be two distinct non-zero complex numbers. If \[ |z|^2w-|w|^2z=z-w, \] then

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

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

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

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

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 \(\alpha^2+\beta^2=\)

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

Identify \(P\) and \(Q\) respectively of the following reaction

Identify the major product from the following reaction sequence:

Which of the following can undergo disproportion reaction on heating with conc. alkali?

Identify the correct trend of acidic strength for the given alcohols