List of top Mathematics Questions asked in AP EAPCET

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

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

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 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:

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

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

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

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

If \(x=\sinh^{-1}t+\log(t^{2}+1)\) and \(y=\tan^{-1}t+\log|t|\), 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 \[ f(x)=\sqrt{2^{2x}\log(3x-2)} \] then \(f'(2)=\)

If $\tan^{-1}x^{2}+\tan^{-1}y^{2}=\frac{\pi}{2}$, then $\left(\frac{dy}{dx}\right)_{(-1,2)}=$

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

Gas is being pumped into a spherical balloon at the rate of $ 30 \, \text{ft}^3/\text{min} $. Then the rate at which the radius increases when it reaches the value $ 15 \, \text{ft} $ is:

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

If \[ y=\sec^{-1}\left(\frac{1+x^2}{2x}\right) \quad \text{and} \quad x>1, \] then \[ \frac{dy}{dx}= \]

If $f(x)=\begin{cases}\frac{1-\sin^{3}x}{3\cos^{2}x}, & x\ne\frac{\pi}{2} \\ \frac{1}{2}, & x=\frac{\pi}{2}\end{cases}$, then $f^{\prime}\left(\frac{\pi}{2}\right)=$

If \(x \in [-1,1]\) and \(y=(\cot^{-1}x)^{\cot^{-1}x}\), then \(\left(\frac{dy}{dx}\right)_{x=0}=\)

If \( x^{2}y - xy^{2} + x^{3} - y^{3} = 0 \), then \( \frac{dy}{dx} \) at the point (1, 1) is