List of top Mathematics Questions asked in AP EAMCET

The vectors \(3\vec a-5\vec b\) and \(2\vec a+\vec b\) are mutually perpendicular and the vectors \(\vec a+4\vec b\) and \(-\vec a+\vec b\) are also mutually perpendicular. Then the acute angle between \(\vec a\) and \(\vec b\) is

In a triangle \(ABC\), if \(a\neq b\), then
\[ \frac{a\cos A-b\cos B}{a\cos B-b\cos A}+\cos C= \]

If in a triangle \(ABC\), \(a=2\), \(b=3\) and \(c=4\), then
\[ \tan\left(\frac{A}{2}\right)= \]

If the angles of a triangle \(ABC\) are in the ratio \(1:2:3\), then the corresponding sides are in the ratio

In a triangle \(ABC\),
\[ r_1\cot\frac{A}{2}+r_2\cot\frac{B}{2}+r_3\cot\frac{C}{2}= \] where \(r_1,r_2,r_3\) are the exradii and \(s\) is the semi-perimeter.

If
\[ \cosech x=\frac45, \] then \(\sinh x=\)

The value of
\[ \frac{1+\tanh x}{1-\tanh x} \] is

A person writes letters to \(6\) friends and addresses the corresponding envelopes. In how many ways can the letters be placed in the envelopes so that at least two of them are in the wrong envelopes?
\[ \text{Notation: } D_n=n!\left(\sum_{i=0}^{n}\frac{(-1)^i}{i!}\right) \]

The value of
\[ \frac{\sin\theta+\sin3\theta}{\cos\theta+\cos3\theta} \] is

If
\[ (1+\tan1^\circ)(1+\tan2^\circ)\cdots(1+\tan45^\circ)=2^n, \] then \(n=\)

The value of
\[ \frac{\cos\theta}{1-\tan\theta}+\frac{\sin\theta}{1-\cot\theta} \] is

If
\[ \frac{x^4+24x^2+28}{(x^2+1)^3} = \frac{Ax+B}{x^2+1} + \frac{Cx+D}{(x^2+1)^2} + \frac{Ex+F}{(x^2+1)^3}, \] then the value of \(A+B+C+D+E+F\) is

How many chords can be drawn through \(21\) points on a circle?

If a polygon of \(n\) sides has \(560\) diagonals, then \(n=\)

The number of positive real roots of the equation
\[ 3^{x+1}+3^{-x+1}=10 \] is

The number of real roots of the equation
\[ \sqrt{\frac{x}{1-x}}+\sqrt{\frac{1-x}{x}}=\frac{13}{6} \] is

If
\[ 4^x-3^{x-\frac12}=3^{x+\frac12}-2^{2x-1}, \] then the value of \(x\) is

The total number of permutations of \(n\) different things taken not more than \(r\) at a time, when each thing may be repeated any number of times is

If
\[ iz^3+z^2-z+i=0, \] then \(|z|=\)

If
\[ \frac{x-1}{3+i}+\frac{y-1}{3-i}=i, \] then the true statement among the following is

The number of integer solutions of the equation
\[ |1-i|^x=2^x \] is

If the identity
\[ \cos^4\theta=a\cos4\theta+b\cos2\theta+c \] holds for some \(a,b,c\in \mathbb{Q}\), then \((a,b,c)=\)

If \(f(x)=ax^2+bx+c\) for some \(a,b,c\in \mathbb{R}\) with \(a+b+c=3\) and
\[ f(x+y)=f(x)+f(y)+xy \quad \forall x,y\in \mathbb{R}, \] then
\[ \sum_{n=1}^{10} f(n)= \]

Let
\[ A= \begin{bmatrix} 5 & \sin^2\theta & \cos^2\theta \\ -\sin^2\theta & -5 & 1 \\ \cos^2\theta & 1 & 5 \end{bmatrix} \] Then, the maximum value of \(\det(A)\) is

If \(f(x)=\sqrt{2-x^2}\) and \(g(x)=\log(1-x)\) are two real valued functions, then the domain of the function \((f+g)(x)\) is