List of top Questions asked in AP EAPCET- 2022

In a trapezium \(ABCD\), \[ \overrightarrow{BC}=\lambda \overrightarrow{AD} \] and \[ \vec{x}=\overrightarrow{AC}+\overrightarrow{BD}. \] If \[ \vec{x}=p\overrightarrow{AD}, \] then \(p=\)

The vectors \[ \vec{a}=2\hat{i}+3\hat{j}+6\hat{k} \] and \(\vec{b}\) are collinear and \[ |\vec{b}|=21, \] then \(\vec{b}=\)

In a \(\triangle ABC\), \[ |\overrightarrow{CB}|=a,\quad |\overrightarrow{CA}|=b,\quad |\overrightarrow{AB}|=c \] and \(CD\) is the median through the vertex \(C\). Then \[ \overrightarrow{CA}\cdot \overrightarrow{CD}= \]

In a triangle \(ABC\), if \(\angle A=60^\circ\), then \[ \frac{b}{c+a}+\frac{c}{a+b}= \]

In a triangle \(ABC\), if \[ a\cos A=b\cos B \] where \(a\neq b\), then \(\triangle ABC\) is

Simplify: \[ \frac{1}{1+\sin\theta}+\frac{1}{1-\sin\theta}= \]

Simplify: \[ \frac{\cos x}{1+\sin x}+\tan x= \]

Evaluate: \[ \cos^2 45^\circ+\cos^2 135^\circ+\cos^2 225^\circ+\cos^2 315^\circ= \]

In a triangle \(ABC\), \[ \frac{a-b}{a+b}= \]

Let \(\theta\in \mathbb{R}\) such that \[ 3\sinh(2\theta)=13-3e^{2\theta}, \] then \(\theta=\)

If \(\theta\) is any angle, then \[ \sin^2\theta \cos^2\theta= \]

Evaluate: \[ (4\cos^2 9^\circ-3)(4\cos^2 27^\circ-3)= \]

The number of numbers between \(2000\) and \(5000\) that can be formed with the digits \(0,1,2,3,4\), repetition of digits not allowed, and are multiples of \(3\), is

How many numbers between \(10\) and \(10,000\) can be formed by using the digits \(1,2,3,4,5\), if no digit is repeated in any number?

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

Let \(T_n\) be the number of all possible triangles formed by joining vertices of an \(n\)-sided regular polygon. If \[ T_{n+1}-T_n=10, \] then the value of \(n\) is

If \(a\), \(b\), \(c\), \(d\) are real numbers such that \[ a\lt b\lt c\lt d, \] then the roots of the equation \[ (x-a)(x-c)+2(x-b)(x-d)=0 \] are

If one root of the quadratic equation \[ ax^2+bx+c=0 \] is equal to the \(n^{th}\) power of the other, then \[ (ac^n)^{\frac{1}{n+1}}+(a^nc)^{\frac{1}{n+1}}= \]

In how many ways can the letters of the word ``ASSASSINATION'' be arranged so that all \(S\)'s are together?

If \(a\), \(b\), \(c\) are distinct positive real numbers and \[ a^2+b^2+c^2=1, \] then the value of \(ab+bc+ca\) is

For any complex number \(z\), the minimum value of \[ |z|+|z-1| \] is

Evaluate: \[ (-1+\sqrt{3})^{60}= \]

If \(\alpha_1,\alpha_2,\ldots,\alpha_{23}\) are the \(23^{rd}\) roots of unity, then \[ \alpha_1^{47}+\alpha_2^{47}+\cdots+\alpha_{23}^{47}= \]

The sum of squares of roots of the equation \[ x^{\frac{2}{3}}+x^{\frac{1}{3}}-2=0 \] is

If the vertices \(A\), \(B\) and \(C\) of an isosceles triangle \(ABC\) are respectively \(z_1\), \(z_2\) and \(z_3\), and if \(\angle C=90^\circ\), then