List of top Mathematics Questions asked in AP EAPCET

Bag $A$ contains $3$ white and $4$ black balls. Bag $B$ contains $4$ white and $3$ black balls. Bag $C$ contains $2$ white and $5$ black balls. A bag is randomly selected and then a ball is randomly drawn from that bag. If the ball drawn was found to be white, then the probability that the ball is drawn from bag $C$ is

The equation of the conjugate hyperbola of the hyperbola $x^{2}-4y^{2}-2x-8y-19=0$ is

If the local maximum 'M' and local minimum 'm' of the function $f(x)=x-\frac{x^{2}}{2}-xe^{2-x}$ exist at $x=\alpha$ and $x=\beta$ respectively, then $2\alpha m+\beta M=$

The area of the region bounded by the curve $y=x^{2}+x$, the lines $y=x$, $x=1$ and $y=2$ 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

The number of distinct real roots of \[ \begin{vmatrix} \sin x & \cos x & \cos x\\ \cos x & \sin x & \cos x\\ \cos x & \cos x & \sin x \end{vmatrix}=0 \] in the interval \[ \left(-\frac{\pi}{4},\frac{\pi}{4}\right) \] is

Let $f:\mathbb{R}\rightarrow\mathbb{R}$ be such that $f(2+x)=f(2-x)\,\,\forall x\in\mathbb{R}$. If $f(x)$ is twice differentiable such that $f^{\prime}(1)=0$, then which one of the following is true?

Out of the first $20$ consecutive natural numbers, $3$ numbers are chosen at random. If these $3$ numbers are in arithmetic progression with common difference $d\in\mathbb N$, then the probability of getting those $3$ numbers whose common difference is a prime number is

If $y=mx+c$, $m>0$ is a common tangent to the parabolas $y^{2}=8x$ and $y^{2}=1+4x$, then $m+c=$

If five unit squares are selected at random from a chess board, then the probability that they all lie on a diagonal is

The value of \[ \tan81^\circ-\tan63^\circ-\tan27^\circ+\tan9^\circ \] is

The mean deviation about the mean for the following data is \[ \begin{array}{c|cccc} x_i & 1 & 2 & 4 & 7\\ \hline f_i & 3 & 2 & 4 & 1 \end{array} \]

For $n\in\mathbb Z$, a set of values of $\theta$ satisfying \[ \sec\theta-1=(\sqrt2-1)\tan\theta \] is

Evaluate \[ \cos\frac{6\pi}{17}\cos\frac{10\pi}{17}\cos\frac{12\pi}{17}\cos\frac{14\pi}{17}. \]

The number of real solutions of the equation \[ \tan^{-1}\sqrt{x(x+1)} + \sin^{-1}\sqrt{x^2+x+1} = \frac{\pi}{2} \] is

If the length of the tangent at a point on the parabola $y^{2}=4ax$ is $4a\sqrt{5}$, then the length of the sub-normal at that point 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

Let $[y]$ represent the greatest integer less than or equal to $y$. Then the set of all $x$ at which $f(x)=\cos^{-1}[4x+3]$ is differentiable is

Let $A(1,2)$ and $C(3,4)$ be the end points of one of the diagonals of a square $ABCD$. If $B(\alpha,\beta)$ and $D(\gamma,\delta)$ are the end points of another diagonal of this square, then $\alpha+\beta-\gamma+\delta=$

Through the focus of the parabola $x^{2}-4x-8y+44=0$, if tangents are drawn to another parabola $y^{2}=20x$, then the sum of the Y - coordinates of the points of contact of these tangents is

If the major axis of an ellipse subtends an angle of $120^{\circ}$ at one end of its minor axis and the length of its semi latus rectum is $\frac{4}{\sqrt{3}}$, then the sum of the lengths of its axes is

The product of the lengths of the perpendiculars drawn from the point $(1, 2)$ to the pair of lines $2x^{2}-3xy-2y^{2}=0$ is

The equation of a line $L_{1}$ passing through the point $(2, 4)$ and making an angle $\tan^{-1}(2)$ with another line $x+2y=4$ is $ax+by+c=0$. If this line $L_{1}$ is neither horizontal nor vertical, then $\frac{b+c}{a}=$

Let $A$ and $B$ be two non-empty sets with $n(A)=4$ and $n(B)=5$. If a mapping is selected at random from the set of all mappings from $A$ to $B$, then the probability of getting a many-one mapping 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