List of top Questions asked in TS EAMCET- 2026

If the system \[ x+y-z=\lambda, \] \[ 2x-y+\mu z=2, \] \[ x-y+3z=1 \] is inconsistent, then

If \((h,k)\) is the centre of a circle cutting three circles orthogonally, then \(\frac{3}{h}+\frac{1}{k}=\)

If both foci of a hyperbola having eccentricity \(\sqrt3\) lie on x-axis and x coordinates of foci are roots of equation \[ x^2-4x+1=0 \] then length of chord passing through focus and perpendicular to transverse axis is

Evaluate \[ \frac{1}{1\cdot6}+\frac{1}{6\cdot11}+\frac{1}{11\cdot16}+\cdots \] for \(n\) terms.

If two cards are drawn at a time from a well shuffled pack of 52 cards, then the probability of getting a result containing only one king and only one spade is

In triangle ABC, \[ (r_1-r)\cos\frac{B-C}{2} = ? \]

Area enclosed by \(x^2-2x+y+1=0\) and \(3x+y-3=0\)

The term independent of \(x\) in expansion of \[ \left(\frac{\sqrt{x}}{2}-\frac{3}{x}\right)^{12} \] is

If \[ \vec r=2\hat i-\hat j+2\hat k,\qquad \vec s=3\hat i-3\hat j+3\hat k,\qquad \vec t=\hat i+2\hat j+\hat k \] are three vectors and \(\vec a\) is a vector such that \[ \vec s\times\vec a=\vec r\times\vec a \] and \[ \left|\vec t\times\vec a\right|=\sqrt{128}, \] then \(|\vec t-\vec a|=\)

The standard deviation of the data \[ 2,3,4,5,6,7,10,11,13,19 \] is

Evaluate \[ \int_{\frac{\pi}{4}}^{\frac{3\pi}{4}} \frac{x\sin x}{1+\cos2x}\,dx \]

If \((1,-2,2)\) and \((2,6,-3)\) are the direction ratios of two straight lines, then the direction cosines of the line bisecting an angle between these two lines are

The value of the greatest integer \(k\) satisfying the inequation \(2^{n+4} + 12 \ge k(n + 4)\) for all \(n \in N\) is

If \(f:\mathbb{R}-\{0\}\rightarrow\mathbb{R}\) is a differentiable function such that \[ \frac{1}{3}f(x)+3f\!\left(\frac1x\right) = x-\frac{10}{3}, \] then find \[ f'(3)-f'\!\left(\frac13\right). \]

Evaluate \[ 4\sin\frac{\pi}{6}\sin\frac{2\pi}{6}\sin\frac{3\pi}{6}\sin\frac{4\pi}{6}\sin\frac{5\pi}{6} \]

For ellipse \(9x^2+25y^2=225\), focal chord \(L_1\) makes equal intercepts on axes. Intersection with tangent at end of latus rectum lies in

Let \[ A=\{1,2,3,4,\ldots,20\}. \] If three distinct elements are drawn from the set \(A\) at random, then the probability that the three numbers drawn are in increasing G.P. with common ratio as a non integral rational value is

If number of circular permutations of 10 distinct things taken 5 at a time is \(m\) and number of linear permutations of 9 distinct things taken 4 at a time is \(n\), then \(m:n=\)

If number of circular permutations of 10 distinct things taken 5 at a time is \(m\) and number of linear permutations of 9 distinct things taken 4 at a time is \(n\), then \(m:n=\)

If \[ (2\sin^{-1}x)^3=\pi^3-(2\cos^{-1}x)^3 \] then one value of \[ \cos(2\sin^{-1}x-3\cos^{-1}x) \] is

Let \[ \vec a=3\vec i-2\vec j+5\vec k,\qquad \vec b=\vec i+3\vec j-2\vec k \] If \(\vec c\) is a vector such that \[ \vec b\times\vec c=\vec a \] and \[ \vec b\cdot\vec c=5 \] then \[ 14\vec c\times\vec a= \]

The rank of the word ‘NEEDED’, when all letters of this word are permuted in all possible ways to form different 6-letter words and arranged in dictionary order, is

In the binomial expansion of \((1+x)^n\), the coefficients of \(x^{k-1}\), \(x^k\), \(x^{k+1}\) and also the coefficients of \(x^{l-1}\), \(x^l\), \(x^{l+1}\) are in A.P.

Then, the numerically greatest term in the expansion of \((1+x)^{14}\) when \(x=\dfrac{2}{3}\) is

If line \(2y-3=0\) bisects angle between \(x+2y-k=0\) and \(x-2y+k=0\), then a point on the bisector of other angle is

\(f(x)\) is an \(n^{th}\) degree polynomial and \(\alpha_1,\alpha_2,\ldots,\alpha_n\) are distinct zeros of \(f(x)\). \(g(x)\) is a polynomial having three zeros common with the zeros of \(f(x)\). Assertion (A): \(|f(x)|g(x)\) is continuous and differentiable at all \(\alpha_i\).
Reason (R): \[ \lim_{x\to a}\frac{|x-a|}{x-a} \] does not exist and \[ \lim_{x\to a}|x-a|=0. \] Choose the correct option.}