List of top Questions asked in TS EAMCET- 2026

If \[ \vec a=\hat i+p\hat j-3\hat k,\qquad \vec b=2\hat i-3\hat j+q\hat k,\qquad \vec c=\hat i+2\hat j+2\hat k\;(p0) \] are three vectors such that the magnitude of projection of \(\vec a\) on \(\vec c\) is \(3\) and the magnitude of projection of \(\vec b\) on \(\vec c\) is \(2\), then the magnitude of projection of \(\vec a\) on \(\vec b\) is

The straight line given by the equation \[ \vec r=(4\hat{i}+5\hat{j}+\hat{k})+s(4\hat{i}+6\hat{j}+2\hat{k}) \] is coplanar with the straight line given below. Choose the correct option.

In a triangle \(ABC\), if \(s=\dfrac{15}{2},\; a=3,\; b=5\), then \[ \frac{\sin \dfrac{B}{2}}{\sin \dfrac{A}{2}}= \]

\(\coth^{-1}2=\)

If \( \theta \) is an acute angle, \( x = \sum_{n=0}^{\infty} \cos^{2n} \theta \), \( y = \sum_{n=0}^{\infty} \sin^{2n} \theta \), then \( \frac{1}{x^2} + \frac{1}{y^2} = \)

For \( A = \frac{\pi}{24} \), if \( \frac{\sin 2A + \sin 3A + \sin 4A}{\cos 2A + \cos 3A + \cos 4A} = k \), then \( (k+1)^2 = \)

If \[ \sin^{-1}(2x)-2\cos^{-1}\sqrt{1-x^2}=\frac{\pi}{2}, \] then \(\tan^{-1}(2x+1)=\)

The sum of all the values of \( \theta \in \left[\frac{\pi}{2}, 2\pi\right] \) satisfying the equation \( \sin^2\theta \tan\theta + \cos^2\theta \cot\theta = \sin 2\theta \) is:

If \( a \) is the coefficient of \( x^7 \) and \( b \) is the term independent of \( x \) in the expansion of \( \left( \frac{3x^4}{4} - \frac{4}{3x^3} \right)^7 \), then \( \frac{b}{a} = \)

If all the letters of the word 'ASSOCIATION' are permuted in all possible ways to form all 11-letter words (with or without meaning), then among these words, the number of words in which the identical letters are always together but no two such groups of identical letters are together is:

The number of ways of distributing 5 identical things to 4 persons so that any person may get at most 5 things is:

By using all the letters of the word 'LETTER', all possible 6-letter words (with or without meaning) are formed. If all these words are arranged in dictionary order, then the rank of the word 'TRELET' is:

If \( \alpha, \beta \in \mathbb{R} \) and \( \alpha \leq \frac{x^2 - 3x + 4}{x^2 - 4x + 5} \leq \beta \) for all \( x \in \mathbb{R} \), then \( (2\alpha - 3)^2 + (2\beta - 3)^2 = \)

If two roots of the equation \( x^5 - 9x^4 + 27x^3 - 23x^2 - 24x + 36 = 0 \) are repeated roots of multiplicity 2 and all the roots are integers then the sum of the squares of all different roots of the equation is:

If \( \alpha, \beta, \gamma, \delta \) are the roots of the equation \( x^4 - 10x^3 + 35x^2 - 50x + 24 = 0 \) and \( \alpha^2, \beta^2, \gamma^2, \delta^2 \) are the roots of the equation \( x^4 + ax^3 + bx^2 + cx + d = 0 \), then \( a = \)

If \( \alpha \) and \( \beta \) are the roots of the quadratic equation \( x^2 - 2x + 2 = 0 \), then \( \alpha^{2026} + \beta^{2026} = \)

If the sum of the squares of two consecutive positive odd integers is 1354, then one of them is:

If \( z = x+iy \) and the point \( P \) denotes \( z \) in the Argand plane, then the locus of \( P \) satisfying the condition \( \text{Im}\left(\frac{z-3i}{z+2}\right) = 1, z \neq -2 \) is:

If \( a, b, c \in \mathbb{R} \), \( a < b < c \), \( A = \begin{bmatrix} -c & 0 & c 0 & -b & b a & a & 0 \end{bmatrix} \), \( 12A^{-1} = \begin{bmatrix} -b & c & bc b & -c & bc b & c & bc \end{bmatrix} \) and Trace of \( A = -5 \), then \( a^2 + b^2 + c^2 = \)

Number of values of \( \theta \) lying in the interval \( (-\pi, \pi) \) such that \( \begin{vmatrix} \cos\theta & -\sin\theta & 1 \sin\theta & 1 & -\cos\theta 1 & \cos\theta & \sin\theta \end{vmatrix} = 2 \) is:

If \( A = \begin{bmatrix} \alpha & 3 & 1 2 & \beta & 6 -2 & -1 & \gamma \end{bmatrix} \) and \( AA^T = \begin{bmatrix} 35 & 28 & -13 28 & 56 & -8 -13 & -8 & 5 \end{bmatrix} \), then Trace of \( A = \)

If the system of linear equations \( x + y + z = 1 \), \( 2x + 2y + 3z = 6 \), \( x + 4y + 9z = 3 \) has a unique solution \( x = \alpha, y = \beta, z = \gamma \), then the value of \( \beta \) is:

Number of values of a complex number \( z \) satisfying the condition \( z = z^2 + i\text{Im}(\overline{z}) \) is:

The function \( f : \mathbb{R} \to \mathbb{R} \) defined by \( f(x) = x|x+2| \) is:

\[ \sin9^\circ\sin18^\circ\sin36^\circ\sin54^\circ\sin72^\circ\sin81^\circ \]