List of top Questions asked in TS EAMCET

If $f:\mathbb{R}-\left\{\frac{2a}{3}\right\}\rightarrow \mathbb{R}$ is a function defined by \[ f(x)=\frac{2x+a}{3x-2a} \] and $(f\circ f)(x)=x$ for all $x\in \mathbb{R}-\left\{\frac{2a}{3}\right\}$, then $f(3)=$}

\(f(x)\) 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.}

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

If the shortest distance between the two skew lines \(\overline{r}=\overline{i}+\overline{j}+\overline{k}+t(3\overline{i}+2\overline{j}+\overline{k})\) and \(\overline{r}=\overline{i}-\overline{j}+x\overline{k}+s(\overline{i}+2\overline{j}+3\overline{k})\) is at most \(2\sqrt{6}\), then all values of \(x\) lie in the interval:

Evaluate \[ \int_{0}^{2}x^{3}(4-x^{2})^{\frac52}\,dx \]

If the system of equations \[ x + y + z = 1,\quad x + 2y + 4z = K,\quad x + 4y + 10z = K^2 \] is consistent, then \(K =\)

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

The term independent of \(x\) in the expansion of \[ \left(5x+\frac{6}{x}\right)^4\left(\frac{1}{1-2x}\right) \] is

Mean and variance of an ungrouped data of 15 numbers are \(12\) and \(14\) respectively. For another ungrouped data of 15 numbers the mean and variance are \(14\) and \(10\) respectively. If the two data are combined, then the variance of the combined data of 30 numbers is

If a straight line \[ y=mx+c \] touches the circle \[ x^2+y^2=4 \] and parabola \[ y^2=4x \] then \(2m^2=\)

If three dice are thrown, then the mean of the sum of the numbers appearing on them is

If the foci of the ellipse \[ \frac{x^2}{25}+\frac{y^2}{k^2}=1 \qquad (k^2<25) \] and the hyperbola \[ \frac{x^2}{k}-\frac{y^2}{5}=1 \] are the same, then the product of the lengths of the latus rectum of the ellipse and that of the hyperbola is:

Numerically greatest term in the expansion of \((2x-3y)^n\) for \(x=\frac{3}{2}, y=\frac{1}{3}, n=6\) is

In a shelf there are three mathematics and two physics books. A student takes a book randomly. If he randomly takes, successively for three time by replacing the book already taken every time, then the mean of the number of mathematics books which is treated as random variable is

Let \(L_{1}\equiv3x+4y-1=0,\; L_{2}\equiv8x-6y+1=0,\; L_{3}\equiv12x+9y-1=0\) be three tangents drawn to the circle \[ x^2+y^2+2gx+2fy+c=0 \] and \(L_1>0,\;L_2>0,\;L_3>0\) at the centre \((-g,-f)\). Then \(g+2f=\)

If \[ \int\frac{e^x+3}{\sqrt{e^x+4}}\,dx = 2\sqrt{e^x+4} +\frac32 \log\left| \frac{f(x)-2}{f(x)+2} \right| +c \] and \[ f(0)=\sqrt5, \] then \[ f(\log_e5)= \]

The area of a triangle is obtained with lengths of two sides and included angle between them. If the angle is measured as $60^{\circ}20^{\prime}$ instead of $60^{\circ}$, then the percentage error in its area is}

If \[ y=\frac{x^4+x^2+1}{x^2+x+1}, \] \[ \frac{dy}{dx}=y_1 \] and \[ \frac{d^2y}{dx^2}=y_2, \] then the value of \[ \left| \frac{(1+y_1^2)^{3/2}}{y_2} \right| \] at \[ x=\left(\frac12+\sqrt2\right) \] is

If the curve represented by the locus of a point in the Argand plane corresponding to the complex number \(z\) satisfying the relation \[ \operatorname{Re}\!\left(\frac{z+4}{2z-5}\right) + \operatorname{Re}\!\left(\frac{\bar z+4}{2\bar z-5}\right) =4 \] cuts the \(X\)-axis at two points \(A\) and \(B\), then the sum of the abscissae of those two points is

Bag A contains 5 white and 2 black balls. Bag B contains 2 white and 5 black balls. Two balls are randomly chosen from bag A and placed in bag B. Now a ball is drawn randomly from bag B and found that it is white. The probability that the two balls drawn from bag A are of different colour is:

Let \(O\) be the origin and \(\vec r\) be the position vector of a point \(P\). If \(\overline{OP}\) makes angles \(\frac{\pi}{3}\) and \(\frac{\pi}{6}\) with \(\overline{i}\) and \(\overline{j}\) respectively, then a vector along \(\overline{OP}\) with magnitude 2 is

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

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