TS EAMCET 2020 (Online) 11th September Morning Shift

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...

Let $C$ be a curvea $x^2+2 h x y+b y^2+2 g x+2 f y+c=0$ in a cartesian plane. By rotating the coordinate axes through an angle $\frac{\pi}{4}$ in the positive direction, if the transformed equation of $C$ is $Y^2+X Y-X=0$, then $\left(h^2-a...

If the straight line passing through the point $P(3,4)$ makes an angle $\frac{\pi}{6}$ with the positive direction of $X$-axis and meets the line $12 x+5 y+10=0$ at $Q$, then the length of $P Q$ is

If the equation of the straight line passing through the point of intersection of $x+2 y-19=0, x-2 y-3=0$ and which is at a perpendicular distance of 5 units from the point $(-2,4)$ is $5 x+b y+c=0$, then a possible value of $5+b+c$ is

If two equal sides of an isosceles triangle are given by the equations $7 x-y+3=0$ and $x+y-3=0$, then the equation of its third side passing through the point $(2,-5)$ is

Suppose $O(0,0)$ is the origin and the line $L=x+y-\lambda=0$ meets the curve $x^2+y^2-2 x-4 y+2=0$ at $A$ and $B$. If $\angle A O B=90^{\circ}$, then the distance between such lines $L=0$ is

Let $P$ be the point of intersection of the lines $L_1 \equiv x-y-7=0$ and $L_2 \equiv x+y-5=0 . A\left(x_1, y_1\right)$ and $B\left(x_2, y_2\right)$ are points on the lines $L_1=0$ and $L_2=0$ respectively such that $P A=3 \sqrt{2}$, $P B=...

If the point of intersection of the lines $\mathbf{r}=\hat{\mathbf{i}}-6 \hat{\mathbf{j}}+(p \sec \alpha) \hat{\mathbf{k}}+t(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}})$ and $\mathbf{r}=4 \hat{\mathbf{j}}+\hat{\mathbf{k}}+\lambda(...

$\mathbf{1}, \mathbf{m}, \mathbf{n}$ are three unit vectors in a right handed system and $L$ is a line through the points $A, B, C$ whose position vectors are $p \mathbf{1}+7 \mathbf{m}-6 \mathbf{n}, 2 \mathbf{1}+5 \mathbf{m}-4 \mathbf{n}$ ...

$E(1,0,0), F(0,2,0), G(0,0,3)$ are respectively the mid-points of the sides $A B, B C, C A$ of $\triangle A B C$. If $a_1, b_1, c_1$ and $a_2, b_2, c_2$ are respectively the direction ratios of $A F$ and $B G$, then $\frac{a_1^2+b_1^2+c_1^2...

If the direction ratios $a, b, c$ of a line $L$ satisfy the relations $a b+b c+c a=0$ and $6 a b+9 b c+8 c a=0$, then the direction cosines of the line $L$ are

The equation of the plane passing through the line of intersection of planes $\pi_1=2 x+6 y+4 z-7=0$, $\pi_2=x-y-2 z-2=03$ and perpendicular to the plane $x+y+2 z-5=0$ is

If $\left|\sin x-\cos ^2 x\right| \geq\left|3-3 \sin x+\sin ^2 x\right|+4|\sin x-1|$, then $x=$

For some $a, b, c \in \mathbf{R}$, if $\sin 5 \theta=a \cos ^4 \theta \sin \theta+b \cos ^2 \theta \sin ^3 \theta+c \sin ^5 \theta$, then $a b c=$

The period of $\frac{\sin x}{\cos 3 x}+\frac{\sin 3 x}{\cos 9 x}+\frac{\sin 9 x}{\cos 27 x}+\frac{\sin 27 x}{\cos 81 x}$ is

If $\alpha=\frac{\sin ^3 x}{\cos ^2 x}, \beta=\frac{\cos ^3 x}{\sin ^2 x}$ and $\sin x+\cos x=k$, then $\alpha \sin x+\beta \cos x+3=$

If $A+B+C=60^{\circ}$, then $\cos \left(30^{\circ}-A\right)+\cos \left(30^{\circ}-B\right)+\cos \left(30^{\circ}-C\right)+\sin (A+B+C)=$

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are the position vectors of the points $A, B, C$ respectively, then match the items of list-I with those of list-II.


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Let $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$. If the orthogonal projection vector of $\mathbf{a}$ on $\mathbf{b}$ be $\mathbf{x}$ and the ort...

Let $\mathbf{p}, \mathbf{q}, \mathbf{r}$ be three non-coplanar vectors and $\left[\begin{array}{lll}\mathbf{p} & \mathbf{q} & \mathbf{r}] \mathbf{a}=\mathbf{q} \times \mathbf{r},\left[\begin{array}{lll}\mathbf{p} & \mathbf{q} & \mathbf{r}] ...

If $\mathbf{b}, \mathbf{c}$ are non collinear vectors, $|\mathbf{c}| \neq 0$, $\mathbf{a} \times(\mathbf{b} \times \mathbf{c})+(\mathbf{a} \cdot \mathbf{b}) \mathbf{b}=(4-2 \beta-\sin \alpha) \mathbf{b}+\left(\beta^2-1\right) \mathbf{c}$ an...