List of top Mathematics Questions asked in AP EAPCET

\(M\) and \(N\) are the mid points of the sides \(BC\) and \(CD\) of a parallelogram \(ABCD\) respectively, then \[ \overrightarrow{AM}+\overrightarrow{AN}= \]

A farmer owns a triangular plot in Guntur. He measures the lengths of the sides of his property as \(4\) cm, \(5\) cm and \(7\) cm. Then the area of land of the farmer in sq. cm is

If the position vectors of the points \(A,B,C,D\) are \[ 7\hat{i}-4\hat{j}+7\hat{k},\quad \hat{i}-6\hat{j}+10\hat{k},\quad -\hat{i}-3\hat{j}+4\hat{k},\quad 5\hat{i}-\hat{j}+5\hat{k} \] respectively, then \(ABCD\) is

Let \(x\in \mathbb{R}\) and \(|x|\lt 1\). Then \[ \tanh^{-1}x= \]

In a triangle, if \[ b=5,\quad c=6,\quad \tan\frac{A}{2}=\frac{1}{\sqrt{2}}, \] then \[ a= \] is:

In a triangle \(ABC\), \[ s\left[\frac{r_1-r}{a}+\frac{r_2-r}{b}+\frac{r_3-r}{c}\right] = \] is:

In a triangle \(ABC\), \[ \tan \frac{A}{2}\tan \frac{B}{2} +\tan \frac{B}{2}\tan \frac{C}{2} +\tan \frac{C}{2}\tan \frac{A}{2} = \]

Simplify \[ \sec^2 x+5\tan x+5= \]

Let \(\alpha,\beta\) be two real numbers such that \[ \pi\lt (\alpha-\beta)\lt 3\pi. \] If \[ \sin\alpha+\sin\beta=-\frac{21}{65} \] and \[ \cos\alpha+\cos\beta=-\frac{2}{65}, \] then \[ \cos\left(\frac{\beta-\alpha}{2}\right)= \]

If \[ \cos\theta-\sin\theta=\sqrt{5}\sin\theta, \] then \[ \cos\theta+4\sin\theta \] is equal to:

If \[ \operatorname{cosech}x=\frac{4}{5}, \] then \[ \cosh x= \] is:

The number of solutions of the equations \[ x+y+z=1;\quad x^2+y^2+z^2=1;\quad x^3+y^3+z^3=1 \] is:

Given \(5\) different green toys, \(4\) different blue toys, and \(3\) different red toys, how many combinations of toys can be chosen taking at least one green and one blue toy?

If \[ {}^{2n}C_3 : {}^{n}C_3 = 12:1, \] then \(n=\)

There are \(4\) oranges, \(5\) apples, \(7\) mangoes in a fruit basket. The number of ways of selecting at least one fruit from among the fruits in the basket is

If \[ {}^{9}C_3+{}^{9}C_5={}^{10}C_r \] for some \(r\in \mathbb{N}\), then \(r=\)

If the equivalent partial fraction of \[ \frac{x^3}{(2x-1)(x+2)(x-3)} \] is of the form \[ A+\frac{B}{2x-1}+\frac{C}{x+2}+\frac{D}{x-3}, \] then the value of \(A+B+C\) is:

A true statement among the following identities is:

All the pairs \((x,y)\) that satisfy the inequality \[ 2^{\sqrt{\sin^2 x-2\sin x+5}}-\frac{1}{4^{\sin y}}\leq 1 \] also satisfy the equation:

\(\alpha,\beta\) are the roots of \[ x^2-10x-8=0 \] with \(\alpha\gt \beta\). If \[ a_n=\alpha^n-\beta^n \] for \(n\in \mathbb{N}\), then the value of \[ \frac{a_{10}-8a_8}{5a_9} \] is:

If \[ x=-5+2\sqrt{-4}, \] then the value of \[ x^4+9x^3+35x^2-x+4 \] is:

The number of real values of \(m\) so that the equation \[ x^2+(2m+1)x+m=0 \] has equal roots is:

If \[ (x-iy)^{1/3}=a-ib, \] then the value of \[ \frac{x}{2a}+\frac{y}{2b} \] is:

Evaluate \[ \sum_{k=1}^{6}\sin\left(\frac{2\pi k}{7}\right) -i\cos\left(\frac{2\pi k}{7}\right) \]

If the solution of the system of simultaneous equations \[ \frac{1}{x}+\frac{2}{y}-\frac{3}{z}-1=0, \] \[ \frac{2}{x}-\frac{4}{y}+\frac{3}{z}-1=0 \] and \[ \frac{3}{x}+\frac{6}{y}-\frac{6}{z}-4=0 \] is \(x=\alpha,\ y=\beta,\ z=\gamma\), then \(\alpha^2+\gamma^2=\)