List of top Questions asked in AP EAPCET- 2026

All the solutions \((n,r)\) of the equation \( \frac{{}^nC_r}{{}^{n+1}C_r} = \frac{1}{3} \) can be obtained from one of the following equations given in the options for \( k=1,2,3, \dots \):

Let $P$ and $Q$ are two sets such that \[ n(P)=27,\quad n(Q)=17,\quad n(P\cap Q)=5. \] If $x$ is the number of ways of selecting $7$ elements from $P$ such that all the elements of $P\cap Q$ are in each selection and $y$ is the number of ways of selecting $10$ elements from $Q$ such that no element of $P\cap Q$ is present in any selection, then $x+y+1=$

All the letters of the word REMAIN are permuted in all possible ways and the words (with or without meaning) thus formed are arranged in the dictionary order. The rank of the word REMAIN, when counted from the rank of the word MARINE beginning with $1$ itself, is

In each of its move, a pawn in a chess board can move one step either horizontally or vertically to its adjacent cell from its current position. If a pawn is initially located at the South-West corner cell of the chess board, then the number of ways it can reach the North-East corner cell with minimum number of moves, is

If $^{n}C_{12} = ^{n}C_{8}$, then $^{n}C_{17} =$

If all the letters of the word RANKS are permutated in all possible ways and the words (with or without meaning) thus formed are arranged in dictionary order, then the rank of the word RANKS is

A student has to answer 10 out of 13 questions in an examination choosing atleast 3 from the 5 particular questions. The number of choices available to the student is

If all the letters of the word MESSI are permuted in all possible ways and the words [with or without meaning] thus formed are arranged in dictionary order, then the rank of the word MESSI is

The number of skew symmetric matrices of order \( 3 \times 3 \) that can be formed by using all the elements 0, \( \pm a, \pm b, \pm c \) is:

If the number of permutations of $n$ different things taken all at a time is $5040$, then $n =$

If the number of permutations of $n$ different things taken all at a time is $5040$, then $n =$

The number of different nine-digit numbers that can be formed by rearranging all the digits of the number $223355888$ so that odd digits always occupy even positions is

A student is allowed to select at most $n$ books from a collection of $2n+1$ books. If the total number of ways in which he can select at least one book is $255$, then the value of $n$ is

The number of ways of arranging the letters of the word "EAPCET" is:

If \(\alpha,\beta\) are the roots of the quadratic equation \[ x^2-3x+1=0, \] then the value of \(\alpha^3+\beta^3\) is:

If the minimum value of \[ f(x)=x^2+2bx+2c^2 \] is greater than the maximum value of \[ g(x)=-x^2-2cx+b^2, \] \(x\) being real, then

If the equation \[ 2x^2-5x+k=0 \] has equal roots, then the value of \(k\) is

Let \(\alpha\) and \(\beta\) be the roots of \[ x^2+bx+c=0. \] If \[ \alpha^2+\beta^2=14 \] and \[ \alpha\beta=3, \] then the value of \(b^2\) is:

If \(x=\sinh^{-1}t+\log(t^{2}+1)\) and \(y=\tan^{-1}t+\log|t|\), then \(\frac{dy}{dx}=\)

If $y = \sqrt{\tan x + \sqrt{\tan x + \sqrt{\tan x + \dots \infty}}}$, then $(2y - 1)\frac{dy}{dx} =$

If \[ f(x)=\sqrt{2^{2x}\log(3x-2)} \] then \(f'(2)=\)

If \( y=\text{sech}^{-1}\left(\frac{9}{9x^{2}+10}\right) \), then \( \frac{dy}{dx} = \)

If \(f\) is a differentiable function such that \[ f(1)=8 \] and \[ f'(1)=\frac18. \] If \(f\) is invertible and \(g=f^{-1}\), then

If \(f(x)=\sqrt{-(1+x)}\sec^{-1}x\) is a real valued function, then \(f'(x)=\)

If \[ f(x)=\cot^{-1}\!\left(\sqrt{\cos 2x}\right), \] then \[ f'\!\left(\frac{\pi}{6}\right)= \]