List of top Questions asked in AP EAPCET

A variable line passing through \((l,m)\) intersects the coordinate axes at the points \(A\) and \(B\). If the lines drawn parallel to \(y\)-axis through \(A\) and parallel to \(x\)-axis through \(B\) meet at \(P\), then the locus of \(P\) is

An unbiased coin is tossed \(3\) times. If the third toss gets head, then the probability of getting at least one more head is

If the variance of four numbers \(w,x,y,z\) is \(9\), then the variance of \[ 5w,5x,5y,5z \] is

Two dice are rolled. Then, the probability that the total score is a prime number is

An unbiased dice with faces marked \(1,2,3,4,5,6\) is rolled four times. Out of four face values obtained, the probability that the minimum face value is not less than \(2\) and the maximum face value is not greater than \(5\) is

A bag contains \(19\) red balls and \(19\) black balls. Two balls are chosen at a time repeatedly and discarded if they are of the same color, but if they are different, black ball is discarded and red ball is returned to the bag. The probability that this process will terminate with one red ball is

Let \(P\) be a real number and \(|P|\geq 2\). If \(A\), \(B\), \(C\) are variable angles such that \[ \sqrt{P^2-4}\tan A+P\tan B+\sqrt{P^2+4}\tan C=6P, \] then the minimum value of \[ \tan^2 A+\tan^2 B+\tan^2 C \] is

If \[ \vec{a}=\hat{i}+\hat{j}+\hat{k},\quad \vec{c}=\hat{j}-\hat{k}, \] \[ \vec{a}\times \vec{b}=\vec{c} \] and \[ \vec{a}\cdot \vec{b}=3, \] then \(\vec{b}=\)

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

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

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

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

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

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

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

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

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?

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 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

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

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