TS EAMCET 2020 (Online) 11th September Evening Shift

If $E_1, E_2 \ldots, E_n$ are an independent events such that $P\left(E_r\right)=\frac{1}{1+r},(r=1,2, \ldots, n)$, then the probability that atleast one of $E_1, E_2, \ldots, E_n$ happens is

An urn contains five balls. Two balls are drawn at random and they are found to be white. The probability that all the balls in the urn are white, is

If the probability function of a random variable $X$ is given by $P(X=n)=\frac{k(n+1)}{3 n}$ for $n \in \mathbf{N} \cup\{0\}$ where $k$ is a constant, then $P(X<2)=$

An observer counts 240 vehicles per hour at a specific location on a highway. Assuming that the arrival of vehicles at the location follows Poisson distribution, the probability that more than two vehicles arrive over a 30 sec time interval...

In a triangle $A B C$, if $a

In a triangle $A B C$, if $c=9, s=10$ and $\Delta=10 \sqrt{2}$ then $b\left[1+\sqrt{2} \tan \left(\frac{A-B}{2}\right)\right]=$

In a $\triangle A B C, \cot A+\cot B+\cot C=$

For $n>2$ and $n \in \mathbf{N}$, the product of the roots of $(x-n)\left(\left(x^2-2 n x\right)^2+\left(2 n^2-5\right)\left(x^2-2 n x\right)\right. \left.+\left(n^4-5 n^2+4\right)\right)=0$ is divisible by

If $\alpha, \beta$ are the roots of $a x^2+b x+c=0$ then $\left(\frac{\alpha}{a \beta+b}\right)^3-\left(\frac{\beta}{a \alpha+b}\right)^3=$

The maximum value of $\left\{x \in \mathbf{R} / \sqrt{x+2}>\sqrt{8-x^2}\right\}=$

If $S_1$ and $S_2$ are the variances of the first $2 k$ and $k(k>1)$ natural numbers respectively, then ( $S_1 / S_2$ ) lies in the interval

The standard deviations of two sets of observations $X=\left\{x_i\right\}$ and $Y=\left\{y_i\right\}(i=1,2, \ldots, 100)$ are respectively 5 and 6 . If $\bar{x}, \bar{y}$ are their means and $\sum_{i=1}^{100}\left(x_i-\bar{x}\right)\left(y_...

When the coordinate axes are rotated through an angle $\theta$ in anti clockwise direction, if the transformed equation of $x^2+y^2+2 x y+2 x+6 y+1=0$ is $(2+\sqrt{3}) X^2+2 X Y+(2-\sqrt{3}) Y^2+a X+b Y+2=0$, then $3 a-b=$

If $\left|\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right|=0$, then the lines $a_i x+b_i y+c_i=0$
( $i=1,2,3$ ) represent

If the sides of a triangle $A B C$ are $2 x^2-y^2=0$, $x+y-1=0$ and the sides of another triangle $P Q R$ are $2 x^2-5 x y+2 y^2=0,7 x-2 y-12=0$, then the distance between the centroid of $\triangle A B C$ and the orthocentre of $\triangle ...

If the lines $3 x+y-4=0, x-a y-10=0, b x+2 y+9=0$ form three successive sides of a rectangle in that order and the fourth side passes through $(1,2)$, then the area of that rectangle (in sq. units) is

For integer $k$, if the area of the triangle formed by the pair of lines $S=3 x^2-2 k x y+y^2=0$ with the line $L=2 x-y-6=0$ is 36 sq. units, then for the angle $\theta$ between the lines $S=0, \sin \theta=$

The points $A(2,1), B(3,-2)$ and $C(a, b)$ are vertices of the rectangle $A B C D$. If the point $P(3,4)$ lies on $C D$ produced, then $5 a+10 b=$

If $A(4,7,8), B(2,3,4)$ and $C(2,5,7)$ are the vertices of $\triangle A B C$, then the length of the internal bisector of the angle $A$ is

For scalars $\lambda, \mu$ if the vector equation of a plane is $\mathbf{r}=(2+3 \lambda-\mu) \hat{\mathbf{i}}+(1-2 \lambda+3 \mu) \hat{\mathbf{j}}+(-2+2 \lambda+\mu) \hat{\mathbf{k}}$, then its Cartesian equation is

If $A(4,3,2), B(5,4,6), C(-1,-1,5)$ are the vertices of a triangle, then the coordinates of the point in which the bisector of the angle $A$ meet the side $B C$ is

Assertion (A) The direction ratios of line $L_1$ are 2, 5, 7 and those of line $L_2$ are $\frac{4}{\sqrt{19}}, \frac{10}{\sqrt{19}}, \frac{14}{\sqrt{19}}$. The lines $L_1, L_2$ are parallel.
$\boldsymbol{\operatorname { R e a s o n }}(R)$ T...

If $\frac{x-4}{1}=\frac{y-2}{1}=\frac{z-7}{2}$ lies in the plane $a x+b y+z=7$, then $a+b=$

The position vectors of the points $A$ and $B$ are respectively $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}$ and $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$. If the points $P$ and $Q$ are respectively the orthogonal projections of $A$ a...

\(\text { Match the items of List-I with those of List-II }\)


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overflow:hid...

The period of $\cos (3 x+5)+7$ is

If $\cos \left(\frac{\alpha-\beta}{2}\right)=2 \cos \left(\frac{\alpha+\beta}{2}\right)$, then $\tan \frac{\alpha}{2} \tan \frac{\beta}{2}=$

$\mathbf{x}, \mathbf{y}, \mathbf{z}$ are three vectors each of magnitude $\sqrt{2}$ and each making an angle $60^{\circ}$ with one another. If $\mathbf{a}=\mathbf{x} \times(\mathbf{y} \times \mathbf{z}), \mathbf{b}=\mathbf{y} \times(\mathbf...

Let $\mathbf{a}=2 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=-\hat{\mathbf{j}}+\hat{\mathbf{k}}$. If $\mathbf{c}$ is a vector such that $\mathbf{a} \cdot \mathbf{c}=|\mathbf{c}|,|\mathbf{c}-\mathbf{a}|=2 \sqrt{2}$ and ...

The equation of the plane in normal form passing through the point $A(\bar{a})$, parallel to a vector $\bar{b}$ and containing a vector $\bar{c}$ is