List of top Mathematics Questions asked in AP EAPCET

In a triangle \(ABC\), if \[ a=4,\quad b=5,\quad c=7, \] then \[ \sin\left(\frac{A}{2}\right) \] is

In any triangle \(ABC\), \[ \frac{\cos 2A}{a^2}-\frac{\cos 2B}{b^2} = \] is equal to:

In a triangle \(ABC\), let \(\angle C=\dfrac{\pi}{2}\). If \(r\) and \(R\) are respectively the inradius and circumradius of \(ABC\), then \(R+r=\)

Evaluate \[ \cos\theta(\cosec\theta-\sec\theta)-\cot\theta \]

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 \(x=\)

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

The value of \[ \sin\left(\frac{5\pi}{24}\right)\cos\left(\frac{\pi}{24}\right) \] is

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

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?

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:

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

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

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

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

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

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

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

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