List of top Questions asked in AP EAPCET- 2026

5 letters are randomly selected from English alphabets and they are arranged in alphabetical order. The probability that the 5 letters selected and arranged has \(M\) in the middle place is

In a pack of 6 cards, two cards are marked with \(5\), two cards are marked with \(6\), one card is marked with \(7\) and another card is marked with \(8\). In another pack of 6 cards, one card is marked with \(5\), two cards are marked with \(6\), two cards are marked with \(7\) and one card is marked with \(8\). If one card from each pack is drawn at random, the probability that the sum of the numbers on the cards is \(12\) or \(13\) is

Let \(S\) be the set of all words formed by arranging all the letters of the word HOMOGENEOUS. If a word is randomly chosen from the set \(S\), then the probability that the word selected has all the consonants together is

A box \(P\) contains 3 white and 7 red balls. A bag \(Q\) contains 4 green and 5 blue balls. Two balls are randomly drawn from box \(P\). If both are of the same color, one ball is drawn from bag \(Q\), and if the two balls are of different colors, 2 balls are drawn from bag \(Q\). If it is known that there is exactly one green ball among the balls drawn from bag \(Q\), then the probability that the two balls drawn from box \(P\) are of different colors is

Two balls are drawn at random from a box containing 4 white and 6 black balls one after the other without replacement. If it is known that the second ball drawn is black, then the probability that the first ball drawn is also black is

If \(\vec c\) and \[ (\vec b\times \vec c)\times(\vec c\times \vec a) \] are parallel vectors, then \[ \left[\vec c\times\vec a\;\;\; \vec a\times\vec b\;\;\; \vec b\times\vec c\right] = \]

If the vector components of a vector \(\vec a\) along a vector \[ \vec b=4\hat i+5\hat j+3\hat k \] and perpendicular to \(\vec b\) are respectively \[ \frac{7}{25}(4\hat i+5\hat j+3\hat k) \] and \[ \frac{1}{25}(47\hat i-10\hat j-46\hat k), \] then \[ |\vec a|^2= \]

If standard deviation of the data \[ 1,15,35,53,72,64 \] is \(x\), then the variance of the data \[ 62,70,51,33,13,-1 \] is

The position vectors of the vertices \(A\) and \(B\) of a triangle \(ABC\) are \[ \hat{i}+3\hat{j}+4\hat{k} \] and \[ 2\hat{i}+\hat{j}+2\hat{k} \] respectively. If \[ |AC|=5 \] and \[ \angle A=\frac{\pi}{3}, \] then \[ |BC|= \]

If \[ \vec a=\hat i-\hat j+2\hat k,\qquad \vec b=-\hat i+2\hat j \] and \(\vec c\) are three vectors such that \(\vec a+\vec b\) is parallel to \(\vec c\) and \[ (\vec c+\vec a)\cdot(\vec c+\vec b)=7, \] then the vector \(\vec c\) having minimum length is

If the equation of the plane containing the line \[ \vec r=\hat i+2\hat j+\hat k+t(\hat i-\hat j+2\hat k) \] and parallel to the line \[ \vec r=-\hat i+2\hat j+s(-\hat i+2\hat j+\hat k) \] in Cartesian coordinates is \[ \frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1, \] then \(a+3b+c=\)

In \(\triangle ABC\), if \[ r_1=\frac{21}{2},\qquad r_2=12,\qquad r_3=14, \] then \(\Delta=\)

If \[ \sinh x=-\frac12,\qquad \cosh y=2, \] and \[ x+y=\log p, \] then \(p=\)

The sum of all the values of \(\theta\in(0,2\pi)\) satisfying the equation \[ \sin\theta+3\cos2\theta+\sin3\theta = \cos\theta+3\sin2\theta+\cos3\theta \] is

If the sides of a triangle \(ABC\) are in arithmetic progression, then \[ b\cos\left(\frac{A-C}{2}\right)= \]

In a \(\triangle ABC\), if \[ \cot\frac{A}{2}:\cot\frac{B}{2}:\cot\frac{C}{2} = 3:5:7, \] then \[ \cos A:\cos B:\cos C= \]

If \[ \tan^{-1}\left(\frac{1}{2\sqrt2}\right) - \cos^{-1}\left(\frac{1}{\sqrt3}\right) + \sin^{-1}(x) = 0, \] then \(x=\)

The coefficient of \(x^3\) in the power series expansion of \[ \frac{x}{x^2-x-2} \] is

Find the sum of the infinite series \[ -1+\frac{7}{10}\cdot 2^2-\frac{7\cdot 9}{10\cdot 15}\cdot 2^3+\frac{7\cdot 9\cdot 11}{10\cdot 15\cdot 20}\cdot 2^4-\cdots\infty \]

If \[ \tan\alpha=-\frac{7}{24}, \qquad \sec\beta=\frac{61}{60} \] and both \(\alpha,\beta\) lie in the same quadrant, then \[ \cos(\alpha+\beta)= \]

The period of the function \[ f(x)=\log(\cos x)+\cot^4\left(\frac{x}{2}\right)+\sin(3x+7) \] is

If \(A\) and \(B\) are the minimum and maximum values of \[ \sin^6 x+\cos^6 x, \] then \(A+B=\)

The coefficient of \(x^{12}\) in the expansion of \[ (x^2+x+2)^8 \] is

All possible 3 digit numbers are formed using all the digits \(2,3,5,7,9\) without using any digit more than once. Among these 3 digit numbers, the number of numbers which are divisible by \(3\) but not divisible by \(5\) is

A positive root of the equation \[ 18x^3-9x^2-5x+2=0 \] is twice another root of it. If among its three roots, the least value is \(a\) and the greatest value is \(b\), then \(2a+3b=\)