List of top Questions asked in TS EAMCET- 2026

If the vector \[ \alpha\hat i+\beta\hat j+\hat k \] is along the bisector of the angle between the vectors \[ 2\hat i-\hat j+2\hat k \] and \[ \hat i+2\hat j+2\hat k, \] then \(2\alpha+6\beta=\)

In a triangle \(ABC\), if \[ \tan\frac{A}{2}:\tan\frac{B}{2}:\tan\frac{C}{2}=1:2:3, \] then \[ \frac{a+3c}{b}= \]

In a triangle \(ABC\), if \[ r_2+r_3=2R, \] then \[ r+2r_2+2r_3-r_1= \]

If \(A,B,C\) are the vertices of a triangle \(ABC\), \[ AB=2,\qquad BC=3,\qquad CA=4, \] then \[ \overrightarrow{AB}\cdot\overrightarrow{BC} + \overrightarrow{BC}\cdot\overrightarrow{CA} + \overrightarrow{CA}\cdot\overrightarrow{AB} = \]

If \[ \tanh^{-1}(x)=\log\sqrt3 \] and \[ \cosh^{-1}(y)=\log(1+\sqrt2), \] then \[ \operatorname{sech}^{-1}(xy)= \]

If \(2\cos\theta+3\sin\theta=3\) and \(\tan\theta\) is defined, then \(\tan\theta=\)

Evaluate: \[ \tan^{-1}\left(\frac12\right) +\tan^{-1}\left(\frac13\right) +\tan^{-1}\left(\frac23\right) +\tan^{-1}\left(\frac15\right) \]

If \[ \frac{2x^{6}+3x^{4}+1}{(x^{2}+2)^{4}}=\frac{Ax+P}{x^{2}+2}+\frac{Bx+Q}{(x^{2}+2)^{2}}+\frac{Cx+R}{(x^{2}+2)^{3}}+\frac{Dx+T}{(x^{2}+2)^{4}}, \] then $3P+2Q+R+4T=$

If \[ S=\left\{\theta\in\left[\frac{\pi}{2},\frac{3\pi}{2}\right]:\cos^2\theta+\sin\theta\tan\theta=\cos2\theta\right\, \] then \[ \sum_{\theta\in S}(\sin\theta+\cos\theta)= \]

If \(\sin\theta \sin(60^\circ-\theta)\sin(60^\circ+\theta)=\dfrac18\), then \(\cos6\theta=\)

If \(A\) and \(B\) are the roots of the equation \(2x^2-9x-16=0\), then \(9\sin^2(A+B)-\cos^2(A+B)=\)

Approximate $(0.98)^{0.2}$ using binomial expansion.}

Evaluate binomial sum involving $\sum C_r \frac{2^r}{r+1}$ for $n=10$.}

Number of 5-digit numbers using digits 3–9 with repetition, divisible by 7.

Committee of 5 from 5 Indians, 4 Americans, 3 Australians with at least one from each and max 2 per country.

Compute $p$ and $q$ ratio for circular + linear arrangements with constraints.

If the minimum value of $ax^2-7x+3a$ is $-\frac{1}{8}$, find sum of roots of $ax^2-7x+3a=0$.}

If $\alpha,\beta,\gamma$ are roots of $x^3-ax^2-4x+4a=0$ with $\alpha+\beta=0$, $\beta+\gamma=5$, find sum of all possible $a$.

If $2x^5+ax^4-12x^3+bx^2+x+c=0$ is reciprocal equation of class one, find sum of rational roots.

\[ \frac{\left(1+\sin\frac{4\pi}{9}-i\cos\frac{4\pi}{9}\right)^6} {\left(1+\sin\frac{4\pi}{9}+i\cos\frac{4\pi}{9}\right)^6} = \ ? \]

If $\omega$ is a complex cube root of unity, evaluate $\left(\frac{\sqrt{3}-i}{-\sqrt{2}+\sqrt{2}i}\right)^{20}$.}

If $\alpha,\beta$ are roots of $2x^2-x-3\lambda=0$ and $\alpha,\gamma$ are roots of $2x^2+9x+2\lambda=0$, find equation of roots $2\alpha+\beta$ and $\beta+\gamma$.

The rank of the matrix \[ \begin{bmatrix} -4 & -1 & 1 & 4 \\ -3 & 0 & 2 & 3 \\ -2 & -1 & 0 & -4 \end{bmatrix} \] is:

If \[ \sum_{n=1}^{10}(i^n+i^{n+1}+i^{n+2}) = x+iy, \] then $2x+3y=$

If \[ A= \begin{bmatrix} 3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1 \end{bmatrix}, \] then $A^{4}=$}