List of top Questions asked in TS EAMCET- 2026

Probability for a person A to have success in one trial is \(\frac{2}{5}\). In 7 Bernoulli trials, if the probability that A has \(k\) successes is maximum, then \(k = \):

The mean deviation from the median of the given frequency distribution is:

Bag A contains 5 white and 2 black balls. Bag B contains 2 white and 5 black balls. Two balls are randomly chosen from bag A and placed in bag B. Now a ball is drawn randomly from bag B and found that it is white. The probability that the two balls drawn from bag A are of different colour is:

Let \(\overline{OA} = \overline{i} + 2\overline{j} + 2\overline{k}\), \(\overline{OB} = 3\overline{i} + 4\overline{k}\). If \(x\overline{i} + y\overline{j} + z\overline{k}\) is the vector along the bisector of \(\angle AOB\) and of length 2 units, then a possible value of \(x + y + z\) is:

If the line \(\overline{r}=\overline{a}+t\overline{b}\) lies on the plane \(\overline{r}\cdot\overline{n}=p\), then \(p=\):

If \(\overline{AB}=\overline{i}+\overline{j}-2\overline{k}\), \(\overline{CB}=2\overline{i}-\overline{j}+\alpha\overline{k}\) \((\alpha\in Z)\) are two sides of a triangle ABC and the angle between these two sides is \(\frac{\pi}{3}\), then the length of its third side is:

\(\overline{a}, \overline{b}, \overline{c}\) are non-coplanar vectors. If \(\overline{x}=2\overline{a}+3\overline{b}+4\overline{c}\), \(\overline{y}=3\overline{a}+4\overline{b}+5\overline{c}\), \(\overline{z}=4\overline{a}+5\overline{b}+6\overline{c}\), then \([\overline{x}\ \overline{y}\ \overline{z}]=\):

If the shortest distance between the two skew lines \(\overline{r}=\overline{i}+\overline{j}+\overline{k}+t(3\overline{i}+2\overline{j}+\overline{k})\) and \(\overline{r}=\overline{i}-\overline{j}+x\overline{k}+s(\overline{i}+2\overline{j}+3\overline{k})\) is at most \(2\sqrt{6}\), then all values of \(x\) lie in the interval:

In a triangle ABC, if \( a = 2 \), \( \sin A = \frac{2}{3} \), \( B = \frac{\pi}{3} \), then \( \sqrt{5}b - 3c = \):

If \( a \) is a real number and \( 2\sinh^2 x - 3\cosh x + a = 0 \) has a solution, then the range of \( a \) is:

If \(\cos 6\theta + \cos 4\theta + \cos 2\theta + 1 = 0\) for \(0 \le \theta \le \pi\), then \(\theta = \):

There are 7 men and 5 women in a park. The number of ways of arranging them around a circular path such that 4 particular persons which include 2 particular men and 2 particular women never stand together is:

If \[ \frac{x^{2}+1}{(x^{4}+5x^{2}+6)(x^{6}+x^{4})} = \frac{A}{x^{4}}+\frac{B}{x^{2}}+\frac{C}{x^{2}+2}+\frac{D}{x^{2}+3}, \] then \(A-B=\):

If \(\alpha\) and \(\beta\) are acute angles and \[ \cos\alpha(1+\tan\alpha\tan\beta)=1, \] then \[ \sin\left(\frac{\alpha-2\beta}{3}\right)= \]

If \(\theta=\frac{11\pi}{7}\), then \[ \frac{1+\cos 8\theta}{\cot^{2}4\theta} + \frac{1-\cos 8\theta}{\tan^{2}4\theta} = \]

If \(a\in \mathbb{Z}\) and the equation \[ (x-a)(x-10)+1=0 \] has integral roots, then the values of \(a\) are:

The number of integral solutions of \[ x+y+z=13 \] such that \[ 1\le x\le9,\qquad 0\le y\le9,\qquad 0\le z\le9 \] is

If \(\dfrac{{}^{\,n-1}C_{r-1}}{{}^{\,n}C_r}=\dfrac{3}{5}\) and \(\dfrac{{}^{\,n+1}C_{r+1}}{{}^{\,n}C_r}=\dfrac{11}{7}\), then \({}^{\,n}C_{r+3}\div{}^{\,r}C_{n/2}\) is equal to:

The number of real roots of the equation \[ x^7+3x^5-13x^3-15x=0 \] is:

If \(\alpha,\beta\) are the rational roots and \(l,m\) are the irrational roots of \[ (x^2-9x+11)^2-(x-4)(x-5)=3, \] then \(\alpha+\beta+lm=\)

Let \(\alpha,\beta,\gamma,\delta\) be the roots of \[ 4x^4+8x^3-17x^2-12x+9=0. \] If \[ 4(\alpha+4)(\beta+4)(\gamma+4)(\delta+4)=k, \] then \(k=\)

If \(\omega\) is a complex cube root of unity, then \[ (1+\omega)(1+\omega^2)(1+\omega^4)(1+\omega^5)(1+\omega^7)(1+\omega^8)\cdots \] (2n factors) is equal to

$m,n$ and $k$ are integers and $9.5\le n\le12$. If \[ \frac{(\cos\theta+i\sin\theta)^m} {(\sin\theta+i\cos\theta)^n} = k(\sin17\theta-i\cos17\theta), \] then $n-m-k=$

If \[ A= \begin{bmatrix} \cos\alpha& 0 &\sin\alpha\\ 0& 1& 0 -\sin\alpha& 0 &\cos\alpha\\ \end{bmatrix} \] and \(A^2=A^T\) for one value of \(\alpha\in(0,\pi)\), then \(A^3=\):

If \[ A=\{z=x+iy:|z-4||z-3|\}, \] \[ B=\{z=x+iy:-3\le y\le3,\;x\in N,\;y\in N\}, \] and \(C=A\cap B\), then \(n(C)=\)