List of top Questions asked in AP EAPCET- 2022

Person A can solve \(90\%\) of the problems given in the book and Person B can solve \(70\%\). Then the probability that at least one of them will solve the problem selected at random from the book is:

A bag contains \(3\) white, \(2\) blue and \(5\) red balls. One ball is drawn at random from this bag. Then, the probability that the ball drawn is not red is

From a well shuffled pack of \(52\) cards, two cards are drawn at random. Then, the probability of both the cards being kings is:

A person \(P\) speaks truth in \(75\%\) cases and another person \(R\) in \(80\%\) cases. Then the probability that they are likely to contradict each other in narrating the same event is

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

\(\vec{a},\vec{b}\) are two vectors such that \(|\vec{a}|=\sqrt{3}\), \(|\vec{b}|=\sqrt{2}\). If \(\vec{x}\) is a unit vector satisfying \(\vec{x}\times \vec{a}=\vec{b}\), then \(\vec{x}=\)

The standard deviation of the first \(10\) multiples of \(4\) is

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

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 \(\dfrac{xy}{z^2}=\)

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

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

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

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

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

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

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

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

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

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 \(x=\)

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

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?

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?