List of top Questions asked in AP EAPCET- 2022

The vector \(\vec{x}\) is perpendicular to the vectors \(\vec{a}=3\hat{i}+2\hat{j}+2\hat{k}\), \(\vec{b}=18\hat{i}-22\hat{j}-5\hat{k}\) and makes an obtuse angle with \(\hat{j}\). If \(|\vec{x}|=14\), then \(\vec{x}=\)

The set of real values of \(\lambda\) for which the vectors \[ \lambda \hat{i}-3\hat{j}+5\hat{k} \] and \[ 2\lambda \hat{i}-\lambda \hat{j}+\hat{k} \] are perpendicular to each other is

If \(\vec{a}=\vec{i}+2\vec{j}+3\vec{k}\), \(\vec{b}=2\vec{i}+3\vec{j}+\vec{k}\), \(\vec{c}=8\vec{i}+13\vec{j}+9\vec{k}\) and \(x\vec{a}+y\vec{b}+z\vec{c}=0\), then \(\dfrac{xy}{z^2}=\)

Let \[ \vec{a}=\hat{i}+x\hat{j}+\hat{k}, \qquad \vec{b}=\hat{i}+\hat{j}+\hat{k} \] and \[ |\vec{a}+\vec{b}|=|\vec{a}|+|\vec{b}|. \] Then

Let \(ABC\) be an acute-angled triangle with circumradius \(R\). Then \[ \sqrt{a^2b^2-4R^2} + \sqrt{b^2c^2-4R^2} + \sqrt{c^2a^2-4R^2} = \] is equal to:

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

The value of \[ \tanh(\log x) \] is

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

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 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

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:

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:

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

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

If \(\alpha,\beta\) 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

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