TS EAMCET 2023 (Online) 13th May Evening Shift

If the line $2 x+3 y+n=0$ is a tangent to the parabola $y^2=8 x$, then the equation of the normal drawn at the point $(2 n, 4 \sqrt{n})$ to the parabola $y^2=8 x$ is

All possible 5-digit numbers each having 5 distinct digits are formed using the digits $1,2,3,5,6,8$. Among them, the number of numbers which are divisible by 3 but not by 6 is

All the letters of the word 'INDEED' are taken and permuted in all possible ways to form distinct 6 letter strings (words with or without meaning). If they are listed in dictionary order, then the rank position of the string 'NIDDEE' is

The total number of ways of forming a committee of 5 members out of 7 Indians, 6 Americans, 5 Russians and 4 Australians, so that every committee contains atleast one member from each country is

Two players $A$ and $B$ alternatively toss 3 coins simultaneously. The player who gets 2 heads and 1 tail first, wins the game. If game continues until someone wins and if $A$ begins the game, the probability that B wins the game is

A bag contains 3 red, 5 black and 7 blue balls. If three balls are drawn at random simultaneously from the bag, then the probability of getting at least two blue balls is

In a game, two dice are thrown simultaneously by a person $A$ and two cards are drawn at random simultaneously from a pack of 52 playing cards by a person $B$. They win the game, if $A$ gets a prime score as the sum of the numbers appear on...

In $\triangle A B C$, if $a=7, b=8$ and $c=9$, then $\frac{1}{r_1^2}+\frac{1}{r_2^2}+\frac{1}{r_3^2}=$

In $\triangle A B C$, if $b=6, c=7$ and $\tan \frac{A}{2}=\frac{1}{\sqrt{6}}$, then the inradius of $\triangle A B C$ is

Let the equations $a x^2-7 x+c=0$ and $a x^2+5 x-c=0$ have a common root and $a c \neq 0$. If 3 is a root of $a x^2-7 x+c=0$ other than the common root, then the common root of the given equations is

The set of all values of $x$ for which the inequalities $x^2-7 x+10 \geq 0$ and $2 x+3-x^2>0$ hold simultaneously is

If $3 x=1+\frac{5}{8}+\frac{5}{8} \cdot \frac{9}{13}+\frac{5}{16}+\ldots$, then $x^4+4 x^3+6 x^2+4 x=$

If $M$ and $\sigma^2$ represent respectively the mean deviation from the mean and the variance for the data $1,3,5,7$, $11,13,17,19,23$, then $3\left(\sigma^2-M\right)=$

If $X$ is a Poisson variate satisfying the condition $3 P(X=2)=P(X=4)$, then $P(X=6)=$

If the lines $4 x+3 y-k=0,2 x+y+3=0$ and $3 x+2 y+k=0$ are concurrent, then the perpendicular distance from the point of concurrency of these lines to the line $3 x+4 y+2=0$ is

Let the angle between the lines $x-2 y+3=0$ and $k x-y+2=0$ be $45^{\circ}$. If $k_1, k_2\left(k_1>k_2\right)$ are two distinct real values of $k$, then $k_1-2=$

Two points $P(a, 2)$ and $Q(1, b)$ lie on either side of the line $2 x-3 y+1=0$. If $P$ is the point of intersection of the lines $4 x+3 y+k=0$ and $3 x+4 y+k=0$, then the range of $b$ is

Let $A(1,3)$ and $B(2,5)$ be two points and $C(h, k)$ be a point such that $B C$ is perpendicular to $A C$. If $\angle C A B=\angle C B A$, then $h=$

Let the line $2 x-3 y-1=0$ intersect the curve $x^2+2 x y+5 y^2+2 x+3 y-1=0$ in distinct points $A$ and $B$. If ' $O$ ' is the origin, then $\cos \angle A O B=$

A plane $\pi$ passing through the point $(1,1,1)$ is perpendicular to the line joining the points $(6,3,2)$ and $(1,-4,-9)$. If $a x+b y+c z-23=0$ is the equation of the plane $\pi$, then $a+b-c=$

If the image of the point $(1,-2,1)$ with respect to the line passing through the points $B(1,1,2)$ and $C(2,2,1)$ is $(l, m, n)$, then $l^2+m^2+n^2=$

$A(1,2,3), B(2,3,1)$ and $C(3,1,2)$ are three points. If the point $P$ divides $A B$ in the ratio $1: 2$ and the point $Q$ divides $B C$ in the ratio $-2: 3$, then the distance between $P$ and $Q$ is

$\cos \frac{\pi}{7} \cos \frac{2 \pi}{7} \cos \frac{3 \pi}{7} \cos \frac{\pi}{14} \cos \frac{3 \pi}{14} \cos \frac{5 \pi}{14}=$

\(\sin 6^{\circ}+\sin 54^{\circ}+\sin 126^{\circ}+\cos 156^{\circ}=\)

If $\tan \alpha=\frac{-12}{5}, \cot \beta=\frac{7}{24}, \alpha$ does not belong to second quadrant and $\beta$ does not belong to first quadrant, then $\sqrt{13} \sin \frac{\alpha}{2}+\cos \frac{\beta}{2}+\tan \frac{\alpha}{2} \cot \frac{\b...

Let $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+2 \hat{\mathbf{k}}, \mathbf{b}=6 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\mathbf{c}=3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}-12 \hat{\mathbf{k}}$ be three vectors. If $\m...

The volume of the tetrahedron with $\hat{\mathbf{i}}-\lambda \hat{\mathbf{j}}+\hat{\mathbf{k}}$, $\lambda \hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\lambda \hat{\mathbf{k}}$ as coterminous ed...

Let $\mathbf{a}, \mathbf{b}, \mathbf{c}$ be three non-coplanar vectors and $L$ be the line passing through the points $\mathbf{a}-\mathbf{b}+\mathbf{c}$ and $\mathbf{b}-\mathbf{c}$. If $\pi$ is a plane passing through the points $2 \mathbf{...

Let $\mathbf{a}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ and $\mathbf{c}=\hat{\mathbf{i}}-4 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ be three vectors. Let $\mathb...

II. If the points with position vectors $\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{k}}$, $\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\lambda \hat{\mathbf{k}}$ are co...