List of top Mathematics Questions asked in AP EAMCET

Let $D=R-\{0,1\}$ and $f: D \rightarrow D, g: D \rightarrow D$ and $h: D \rightarrow D$ be three functions defined by $f(x)=\frac{1}{x} ; g(x)=1-x$ and $h(x)=\frac{1}{1-x} .$ If $j: D \rightarrow D$ is such that $(gojof)$ $(x)=f(x)$ for all $x \in D$, then which one of the following is $j(x) ?$

If $y = f(x)$ is twice differentiable function such that at a point $P , \frac{dy}{dx} = 4 , \frac{d^2 y}{dx^2} = - 3$ , then $\left( \frac{d^2 x}{dy^2} \right)_P =$

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

If $x = \frac{3}{10} + \frac{3.7}{10.15} + \frac{3.7.9}{10.15.20} +$ ...., then $5x + 8$ =

If each line of a pair of lines passing through origin is at a perpendicular distance of $4$ units from the point $(3, 4)$, then the equation of the pair of lines 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

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

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

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 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 $y = \sin^2 (\cot^{-1} \sqrt{\frac{1+x}{1-x}} )$, then $\frac{dy}{dx}$ =

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

The variance of the following continuous frequency distribution is

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

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

The polynomial equation of degree $4$ having real coefficients with three of its roots as $2 \pm \sqrt{3}$ and $1+2i$. 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 $pe^{-4} + qe^4 =$

If $\cos \theta \neq 0$ and $\sec \theta - 1 = ( \sqrt{2} - 1 ) \tan \theta$ then $\theta$ =

If $\alpha$ and $\beta$ are the roots of $x^{2}+7 x+3=0$ and $\frac{2 \alpha}{3-4 \alpha}, \frac{2 \beta}{3-4 \beta}$ are the roots of $a x^{2}+b x+c=0$ and $GCD$ of $a, b, c$ is $1$ , then $a+b+c=$

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 $\alpha , \beta , \gamma$ are the roots of $x^3 - 6x^2 + 11x - 6 = 0$ , then the equation having the roots $\alpha^2 + \beta^2 + \gamma^2$ and $\gamma^2 + \alpha^2$ is

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 $\alpha =\displaystyle\lim_{x\to0} \frac{x.2^{x}-x}{1-\cos x}$ and $\beta =\displaystyle\lim_{x\to0} \frac{x.2^{x}-x}{\sqrt{1+x^{2} } - \sqrt{1-x^{2}} } ,$ then