List of top Questions asked in AP EAMCET- 2022

In a lottery containing \(35\) tickets, exactly \(10\) tickets bear a prize. If a ticket is drawn at random, then the probability of not getting a prize is

The mean deviation about the mean for the following data:
\[ 5,6,7,8,6,9,13,12,15 \] is

The point of intersection of the lines
\[ \vec r=2\vec b+t(6\vec c-\vec a) \] and
\[ \vec r=\vec a+s(\vec b-3\vec c) \] is

In quadrilateral \(ABCD\),
\[ \overrightarrow{AB}=\vec a, \qquad \overrightarrow{BC}=\vec b, \qquad \overrightarrow{DA}=\vec a-\vec b \] \(M\) is the midpoint of \(BC\) and \(X\) is a point on \(DM\) such that
\[ \overrightarrow{DX}=\frac45\overrightarrow{DM}. \] Then the points \(A,X,C\)

Let \(\vec a=x\hat i+y\hat j+z\hat k\) and \(x=2y\). If \(|\vec a|=5\sqrt2\) and \(\vec a\) makes an angle of \(135^\circ\) with the \(z\)-axis, then \(\vec a=\)

Let \(\vec a,\vec b,\vec c\) be the position vectors of the vertices of a triangle \(ABC\). Through the vertices, lines are drawn parallel to the sides to form the triangle \(A'B'C'\). Then the centroid of \(\triangle A'B'C'\) is

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

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

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

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

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

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.

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 \(f(x)=ax^2+bx+c\) 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
\[ \sum_{n=1}^{10} f(n)= \]