List of top Questions asked in TS EAMCET

If the mean and variance of a binomial distribution are \(\frac{10}{3}\) and \(\frac{10}{9}\) respectively, then the probability of having at least one success is

A straight line passes through a point \(A(2,5)\) and makes an angle of \(45^\circ\) with the positive X-axis when measured in positive direction. If this line intersects the line passing through the points \((1,-2)\) and \((3,-4)\) at \(B\), then \(AB=\)

If \((h,k)\) is the point to which the origin has to be shifted by translation of axes to remove the terms containing \(x\) and \(y\) from the equation \[ 2x^2+3xy+y^2+4x-8y+5=0 \] then \(2h+k=\)

Bag A contains 3 red and 5 black balls, bag B contains 5 red and 3 black balls and bag C contains 4 red and 4 black balls. A bag is chosen randomly and a ball is drawn randomly from the chosen bag. If the ball drawn is found to be black, then the probability that it is drawn from bag B is

If \[ \vec a=2\hat i+3\mu\hat j-\hat k, \qquad \vec b=\mu\hat i-2\hat j+3\hat k, \qquad \vec c=\hat i+3\hat j-2\mu\hat k \] are three vectors such that \[ \alpha\vec a+\beta\vec b+\gamma\vec c=\vec 0 \] only when \[ \alpha=\beta=\gamma=0, \] then the set of all real values of \(\mu\) is

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

Mean deviation from the mean for the ungrouped data \[ 8,\,7,\,15,\,12,\,12,\,60,\,15,\,6,\,65,\,4,\,6,\,18 \] is

If \[ |\vec a|=3,\qquad |\vec b|=4 \] and the angle between \(\vec a\) and \(\vec b\) is \[ \frac{\pi}{6}, \] then \[ \left|(4\vec a+\vec b)\times(\vec a-3\vec b)\right| = \]

If \(A\) and \(B\) are any two events of a random experiment, then evaluate \[ P\Big[(A\cap B^c)\cup(A^c\cap B)\cup(A\cap B)\Big] \]

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

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 \[ \overrightarrow{AB}\cdot\overrightarrow{BC} + \overrightarrow{BC}\cdot\overrightarrow{CA} + \overrightarrow{CA}\cdot\overrightarrow{AB} = \]

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

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 \(2\alpha+6\beta=\)

If \[ \vec{OA}=\hat i-6\hat j+9\hat k,\qquad \vec{OB}=\hat i+3\hat j+5\hat k, \qquad \vec{OC}=2\hat i+\beta\hat j+7\hat k \] are the position vectors of three collinear points \(A,B,C\), then the ratio in which \(B\) divides \(AC\) is

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

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

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

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

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

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

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

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

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