TS EAMCET 2020 (Online) 11th September Morning Shift

The centre of the circle passing through the points of intersection of the circles $(x+3)^2+(y+2)^2=25$ and $(x-2)^2+(y-3)^2=25$ and cutting the circle $(x+1)^2+(y-2)^2=16$ orthogonally is

For $n \in \mathbf{N}$, If $A_n=\cos \left(\frac{\pi}{2^n}\right)+i \sin \left(\frac{\pi}{2^n}\right)$, then $\left(A_1 A_2 A_3 A_4\right)^4=$

Let $A_r=\left(x+\frac{1}{x}\right)^3 \cdot\left(x^2+\frac{1}{x^2}\right)^3 \cdot\left(x^3+\frac{1}{x^3}\right)^3 \cdots\left(x^r+\frac{1}{x^r}\right)^3$. If $x^2+x+1=0$, then $\frac{1}{A_3}+\frac{1}{A_6}+\frac{1}{A_9}+\frac{1}{A_{12}}+\ldo...

$A\left(z_1=2+2 i\right), B\left(z_2\right), C\left(z_3\right)$ are three points on the Argand plane satisfying $\left|z_k-2 i\right|=2,(k=1,2,3)$. If $\triangle A B C$ encloses the maximum area, then the sum of the imaginary parts of $z_2$...

The positive integer $n \leq 5$ for which $\int_0^1 e^x(x-1)^n d x=16-6 e$ is

If $f(x)=\sin ^6 x+\cos ^6 x+2 \sin ^3 x \cos ^3 x$, then $\int_0^{\pi / 4} \frac{\sin ^2 2 x}{f(x)} d x=$

\(\int_3^5(x-3)^3(5-x)^5 d x=\)

The differential equation for which $l x^2+m y^2=x+y$ is the general solution is

The general solution of the differential equation $(x-2 y+1) d y-(3 x-6 y+2) d x=0$ is

The general solution of the differential equation $\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y$ is

If $x \sqrt{1+y}+y \sqrt{1+x}=0$, then $\frac{d y}{d x}=$

If $p(x)$ be a polynomial satisfying $p(2 x)=p^{\prime}(x) \cdot p^{\prime \prime}(x)$, then $\sum_{x=1}^5 p(x)=$

If $2^x+2^y=2^{x+y}$, then $\frac{d y}{d x}=$

If $A=(1,2), B=(2,1)$ and $P$ is any point satisfying the condition $P A+P B=3$, then the equation of the locus of $P$ is

If the sum of the distances from the foci to the centre $O(0,0)$ of an ellipse is $8 \sqrt{6}$ units and the area of the smallest rectangle in which that ellipse is inscribed is 80 sq. units, then the equation of such an ellipse is

The equation of the ellipse with directrix $3 x+4 y-5=0$, focus $(1,2)$ and eccentricity $1 / 2$, is

If $f:[-3,2] \rightarrow[0, \sqrt[3]{x}]$ is an onto function defined by $f(n)=\left\{\begin{array}{cc}2+\sqrt[3]{n}, & -3 \leq n \leq-1 \\ n^{2 / 3}, & -1 \leq n \leq 2\end{array}\right.$, then $x=$

Let $[x]$ denote the greatest integer not more than $x$. If $A$ and $B$ are the domains of the functions $f(x)=\frac{x-[x]}{\sqrt{|x|-x}}$ and $g(x)=\frac{x-[x]}{\sqrt{|x|+x}}$ respectively, then

If $\operatorname{sech}^{-1}(1 / 2)-\operatorname{cosech}^{-1}(3 / 4)=\log _e k$, then

A rectangular hyperbola passing through $(3,2)$ has its asymptotes parallel to the coordinate axes. If $(1,1)$ is the point of intersection of the two perpendicular tangents of that hyperbola, then its equation is

If $\int e^{\sin ^2 x}\left(\sin x \cos x+\cos ^3 x \sin x\right) d x=e^{\sin ^2 x}(1+f(x))+c$, then $f^{\prime}(x)=$

\(\int \frac{25 x^2+8}{\sqrt{25 x^2+9}} d x=\)

\(I_{m, n}=\int x^m(\log x)^n d x=\)

If $\frac{1}{x^4+x^2+1}=\frac{A x+B}{x^2+x+1}+\frac{C x+D}{x^2-x+1}$, then $\cos ^{-1}(A+B+C+D)=$

The number of real roots of the equation $\sin \left[2 \cos ^{-1}\left\{\cot \left(2 \tan ^{-1} x\right)\right\}\right]=0$ that are greater than or equal to one are

\(\mathop {\lim }\limits_{x \to 0} \frac{x \tan 4 x-2 x \tan 2 x}{(1-\cos 4 x)^2}=\)

Assertion (A) $f(x)=|x-a|+|x-b|$, is continuous on $\mathbf{R}$
Reason (R) $\frac{|x-\alpha|}{x-\alpha}$ is continuous at $x \in \mathbf{R}-\{\alpha\}$.
The correct option among the following is

A function $y=f(x)$ with $f(-1)=-249$ has no maximum and has only one minimum at $x=5$ with $f(5)=75$. Which one of the following is true?

A value of $\theta$ in $\left(0, \frac{\pi}{2}\right)$ and satisfying $\left|\begin{array}{ccc}1+\sin ^2 \theta & \cos ^2 \theta & 4 \sin 4 \theta \\ \sin ^2 \theta & 1+\cos ^2 \theta & 4 \sin 4 \theta \\ \sin ^2 \theta & \cos ^2 \theta & 1...

If $\left[\begin{array}{ccc}2 & 1 & 1 \\ 0 & 3 & -1 \\ 1 & -1 & 1\end{array}\right]\left[\begin{array}{l}x \\ y \\ z\end{array}\right]=\left[\begin{array}{l}1 \\ 1 \\ 0\end{array}\right]$, then $\left[\begin{array}{l}x \\ y \\ z\end{array}\...

Let $[A]_{3 \times 3}$ be a non-singular matrix such that
\(A^{-1}=\frac{1}{3}\left(A^2-5 A+7 I\right) .\)
Then $17 A^8-85 A^7+119 A^6-51 A^5-19 A^4+95 A^3-133 A^2+58 A+I=$

If a circle with its centre at the focus of the parabola $y^2=2 p x$ is such that it touches the directrix of the parabola, then a point of intersection of the circle and the parabola is

If the tangent drawn at the point $P(4,8)$ to the parabola $y^2=16 x$ meets the parabola $y^2=16 x+80$ at $A$ and $B$, then the mid-point of $A B$ is

$n^5-5 n^3+4 n$ is divisible by 120 is true for

The number of integers $x, y, z, w$ satisfying $x+y+z+w=25$ and $x, y, z \geq-1, w \geq 1$, is

If 3 sisters and 8 other girls are together playing a game, then the number of ways in which all the girls are seated around a circle such that the three sisters are not seated together, is

If the roots of each of the equations $2 x^2+x-1=0$, $3 x^2-10 x+3=0$ and $6 x^2+11 x-2=0$ corresponds to probabilities of three events of a random experiment, then those events are

Cards are drawn one after the other without replacement from a well shuffled pack of cards until and ace card appears. If the probability that exactly 5 cards are drawn before the first ace card appears is $\frac{4}{49}\left(\frac{p_1 \cdot...

A number is selected at random from the set $\{1,2, \ldots \ldots ., 100\}$. Given that the number selected is divisible 2 , the probability that it is also divisible by 3 or 5 , is

A target is to be destroyed in a bombing exercise and there is a $75 \%$ chance that a bomb will hit the target. Assuming that two direct hits are required to destroy the target completely, the minimum number of bombs to be dropped in order...

Let $X \sim B(n, p)$ with mean $\mu$ and variance $\sigma^2$. If $\mu=2 \sigma^2$ and $\mu+\sigma^2=3$, then $P(X \leq 3)=$

The perimeter of a $\triangle A B C$ is 6 times the arithmetic mean of the sine of its angles. If its side $B C$ is of unit length, then $\angle A=$

In a $\triangle A B C$, with usual notation, if $r=r_1-r_2-r_3$, then $2 R=$

In a $\triangle A B C$, let $a, b, c, s, r, R, I, S, r_1, r_2, r_3$ stand for their usual meaning. Then Match the items of List-I with those of the items of List-II.






List-I

List-II





A.

tan

⁡

A

2


...

$p$ and $q$ are two roots of the equation $x^2+7 x+3=0$. If $\frac{3 p}{1-2 p}, \frac{3 q}{1-2 q}$ are the roots of $l x^2+m x+n=0$ and the greatest common divisor of $l, m, n$ is 1 , then $l-m+n=$

If the quadratic equations $3 x^2-7 x+2=0$ and $k x^2+7 x-3=0$ have a common root then the positive value of $k$ is

If the roots of $x^3+a x^2+b x+c=0$ are in arithmetic progression with common difference 1 , then

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+3 x^2-x-3=0$, then $\left(1+\alpha^2\right)\left(1+\beta^2\right)\left(1+\gamma^2\right)=$

\(\text { The variance of the following frequency distribution is }\)
$$ \begin{array}{ccccccc} \hline \text { Classes } & 0-10 & 10-20 & 20-30 & 30-40 & 40-50 & 50-60 \\ \hline \text { Frequency } & 11 & 29 & 18 & 4 & 5 & 3 \\ \hline \en...

The mean deviation about the mean of the following data is nearly
$$ \begin{array}{ccccccccc} \hline \text { Size }(x) & 1 & 3 & 5 & 7 & 9 & 11 & 13 & 15 \\ \hline \text { Frequency }(f) & 3 & 3 & 4 & 14 & 7 & 4 & 3 & 4 \\ \hline \end{array...