List of top Mathematics Questions asked in AP EAMCET

$P$ is a variable point on the ellipse $\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1 $ with foci $F_1$ and $F_2$ . If $A$ is the area of the triangle $PF_1F_2$. then the maximum value of $A$ is

If $k$ is one of the roots of the equation $x^2 - 25x + 24 = 0 $ such that $A = \begin{bmatrix}1&2&1\\ 3&2&3\\ 1&1&k\end{bmatrix} $ is a non-singular matrix, then $A^{-1}$ =

If a random variable $X$ has the probability distribution given by $P(X = 0) = 3C^3, P(X = 2 ) = 5C - 10C^2 $ and $P(X = 4) = 4C - 1$, then the variance of that distribution is

If $p$ and $q$ are respectively the global maximum and global minimum of the function $f(x) = x^2 e^{2x}$ on the interval $[-2, 2]$ , then $pe^{-4} + qe^4 = $

If $f(x)=(2k + 1)x - 3 - ke^{-x } + 2e^x$ is monotonically increasing for all $x \in R$, then the least value of $k$ is

If the perpendicular bisector of the line segment joining $A(\alpha, 3)$ and $B (2, -1)$ has $y$-intercept $1$, then $\alpha$ =

Variable straight lines $y = mx + c$ make intercepts on the curve $y^2 - 4ax = 0$ which subtend a right angle at the origin. Then the point of concurrence of these lines $y = mx + c$ is

$\cos ^{2} 5^{\circ}-\cos ^{2} 15^{\circ}-\sin ^{2} 15^{\circ}+\sin ^{2} 35^{\circ}$ $+\cos 15^{\circ} \sin 15^{\circ}-\cos 5^{\circ} \sin 35^{\circ}=$

If $\begin{vmatrix}a+b+2c&a&b\\ c&2a+b+c&b\\ c&a&a+2b+c\end{vmatrix} = 2 $, then $a^3 + b^3 + c^3 - 3abc$ =

If two unbiased six-faced dice are thrown simultaneously until a sum of either $7$ or $11$ occurs, then the probability that $7$ comes before $11$ is

There are $3$ bags $A, B$ and $C$. Bag $A$ contains $2$ white and $3$ black balls, bag $B$ contains $4$ white and $2$ black balls and Bag $C$ contains $3$ white and $2$ black balls. If a ball is drawn at random from a randomly chosen bag. then the probability that the ball drawn is black, is

If two sections of strengths $30$ and $45$ are formed from $75$ students who are admitted in a school, then the probability that two particular students are always together in the same section is

In a $\Delta ABC, 2x + 3y + 1 = 0 , x + 2y - 2 = 0 $ are the perpendicular bisectors of its sides $AB$ and $AC$ respectively and if $A = (3,2)$, then the equation of the side $BC$ is

When the coordinate axes are rotated about the origin in the positive direction through an angle $\frac{\pi}{4}$, if the equation $25 x^2 + 9y^2 = 225$ is transformed to $\alpha x^2 + \beta xy + \gamma y^2 = \delta$, then $(\alpha + \beta + \gamma - \sqrt{\delta})^2$ =

If $a$ makes an acute angle with $b , r \cdot a =0$ and $r \times b = c \times b$, then $r =$

Bag $A$ contains $6$ Green and $8$ Red balls and bag $B$ contains $9$ Green and $5$ Red balls. A card is drawn at random from a well shuffled pack of $52$ playing cards. If it is a spade, two balls are drawn at random from bag $A$, otherwise two balls are drawn at random from bag $B$. If the two balls drawn are found to be of the same colour, then the probability that they are drawn from bag $A$ is

All the letters of the word $ANIMAL$ are permuted in all possible ways and the permutations thus formed are arranged in dictionary order. If the rank of the word $ANIMAL$ is $x$ . then the permutation with rank $x$ , among the permutations obtained by permuting the word $PERSON$ and arranging the permutations thus formed in dictionary order is

If $\alpha, \beta, \gamma$ are any three angles, then $\cos \, \alpha + \cos \beta - \cos \, \gamma - \cos (\alpha + \beta + \gamma) =$

In triangle ABC. if a = 3 ,b = 4,c = 6, then $\frac{\cot \frac{A}{2} + \cot \frac{B}{2} + \cot \frac{C}{2}}{\cot A +\cot B + cot C} = $

If $\tan \, \theta = \frac{\cos 25^{\circ} + \sin 25^{\circ} }{\cos 25^{\circ} - \sin 25^{\circ} }$ and $\theta$ is in the third quadrant, then $\theta = $

If $\frac{x^{3}}{\left(2x-1\right)\left(x-1\right)^{2}} = A + \frac{B}{2x-1}+ \frac{C}{x-1}+ \frac{D}{\left(x-1\right)^{2}} $, then $2A - 3B + 4C + 5D = $

If $\frac{x^{4} + 24 x^{2} + 28}{\left(x^{2} + 1\right)^{3}} = \frac{A }{\left(x^{2} + 1\right)} + \frac{B}{\left(x^{2} + 1\right)^{2}} + \frac{C}{\left(x^{2} + 1\right)^{3}} $ then $A + C = $

If $\alpha$ and $\beta$ are the roots of the equation $x^2 - 4x + 5 = 0$. then the quadratic equation whose roots are $\alpha^2 + \beta$ and $\alpha + \beta^2 $ is

Let $z = x + iy$ and a point $P$ represent $z$ in the Argand plane. If the real part of $\frac{z - 1}{z + i}$ is 1. then a point that lies on the locus of $P$ is

If $z_{1} = 1 -2i ; z_{2} = 1 + i$ and $z_{3 } = 3 + 4i,$ then $ \left( \frac{1}{z_{1}} + \frac{3}{z_{2}}\right) \frac{z_{3}}{z_{2}} = $