List of top Questions asked in TS EAMCET

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 2 and 3 are the two roots of the equation \[ 2x^3 + mx^2 - 13x + n = 0, \] then the values of \(m, n\) are respectively

If \(P(X=k)=c\left(\frac{2}{7}\right)^k,\ k=0,1,2,\dots\), then \(P(X=2)=\)

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

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

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

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

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

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

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

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

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

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 \[ f'(3)-f'\!\left(\frac13\right). \]

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 \(m:n=\)

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

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

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

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

Common tangent to circle \(x^2+y^2=4\) and parabola \(y^2=8\sqrt2 x\) is \(y=mx+c\). Then \(\sqrt{m+c^2}=\)

\(f(x)\) 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.}