List of top Mathematics Questions asked in AP EAMCET

If $'a'$ is the middle term in the expansion of $(2x - 3y)^8$ and $b, c$ are the middle terms in the expansion of $(3x + 4y)^7$ , then the value of $\frac{b +c}{a}$ ,when $x = 2$ and $y = 3$, is

If $ABCD$ is a cyclic quadrilateral with $AB = 6, BC = 4, CD = 5, DA = 3$ and $\angle ABC$ = $\theta$ then $cos\, \theta$ =

If the line joining the points $A(\alpha)$ and $B(\beta)$ on the ellipse $\frac{x^2}{25} + \frac{y^2}{9} = 1$ is a focal chord, then one possible values of $\cot \frac{\alpha}{2} . \cot \frac{\beta}{2}$ is

$P$ 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 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

Let $A$ and $B$ be finite sets and $P_{A}$ and $P_{B}$ respectively denote their power sets. If $P_{B}$ has $112$ elements more than those in $P_{A^{\prime}}$ then the number of functions from $A$ to $B$ which are injective is

In triangle $\Delta A B C$ , if $\frac{b + c}{9} = \frac{c + a}{10} = \frac{a+b}{11},$ then $\frac{\cos A + \cos B}{\cos C} = $

The variance of the following continuous frequency distribution 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

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

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 = $

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 $\int \cos x . \cos 2x . \cos 5x dx = A \; \sin 2x + B \sin 4x + C \sin 6x + D \sin 8x + k $ (where $k$ is the arbitrary constant of integration), then $\frac{1}{B} + \frac{1}{C} = $

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 $\alpha$ 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

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

If $1 , \omega , \omega^2$ are the cube roots of unity, then $\frac{1}{1+2\omega} + \frac{1}{2+\omega } - \frac{1}{1+\omega } = $

In $\Delta ABC. a^3 . \cos (B - C) + b^3 . \cos(C - A) + c^3 . \cos (A - B) = $

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}} = $

The length of the transverse common tangent of the circles $x^2 + y^2 - 2x + 4y + 4 = 0$ and $x^2 + y^2 + 4x - 2y + 1 = 0 $ is

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 = $