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

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

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

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

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

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

If $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

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

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 = $

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

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

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 $\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

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