List of top Mathematics Questions asked in AP EAMCET

For \(i=1,2,3\) and \(j=1,2,3\), if
\[ a_i^2+b_i^2+c_i^2=1 \] and
\[ a_ia_j+b_ib_j+c_ic_j=0 \quad \forall \; i\neq j \] and
\[ A= \begin{bmatrix} a_1 & a_2 & a_3 \\ b_1 & b_2 & b_3 \\ c_1 & c_2 & c_3 \end{bmatrix} \] then \(\det(AA^T)=\)

If
\[ A=\frac{1}{7} \begin{bmatrix} 3 & -2 & 6 \\ -6 & -3 & 2 \\ -2 & 6 & 3 \end{bmatrix}, \] then

If
\[ A= \begin{bmatrix} \alpha^2 & 5 \\ 5 & -\alpha \end{bmatrix} \] and
\[ \det(A^{10})=1024, \] then \(\alpha=\)

The range of the real valued function \(f(x)=\sqrt{\dfrac{x^2+2x+8}{x^2+2x+4}}\) 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} = $

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

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 $\sqrt{1-x^{6} }+ \sqrt{1-y^{6}} =a\left(x^{3} -y^{3}\right) , $ then $ y^{2} \frac{dy}{dx} = $

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 $a+b+c=$

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 $\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

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 $z = x - iy $ and $z^{\frac{1}{3}} = a + ib$, then $\frac{\left(\frac{x}{a}+\frac{y}{b}\right)}{a^{2}+b^{2}} = $

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

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

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

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

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

If $\displaystyle\sum^n_{k - 1} \tan^{-1} \left( \frac{1}{k^2 + k + 1} \right) = \tan^{-1} (\theta) $ , then $\theta$ =

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