AP EAPCET 2024 - 19th May Evening Shift

If 7 different balls are distributed among 4 different boxes, then the probability that the first box contains 3 balls is

If two cards are drawn randomly from a pack of 52 playing cards, then the mean of the probability distribution of number of kings is

In $\triangle A B C$, if $B=90^{\circ}$, then $2(r+R)=$

In a $\triangle A B C$, if $(a-b)(s-c)=(b-c)(s-a)$, then $r_1+r_3=$

In a $\triangle A B C$, if $r_1=2 r_2=3 r_3$, then $\sin A: \sin B: \sin C=$

\(4+\frac{1}{4+\frac{1}{4+\frac{1}{4+\ldots \infty}}}=\)

If $x^2+5 a x+6=0$ and $x^2+3 a x+2=0$ have a common root, then that common root is

If $\alpha, \beta, \gamma$ are roots of equations $x^3+a x^2+b x+x=0$, then $\alpha^{-1}+\beta^{-1}+\gamma^{-1}=$

If the roots of equation $x^3-13 x^2+K x-27=0$ are in geometric progression, then $K=$

\(1-\frac{2}{3}+\frac{2 \cdot 4}{3 \cdot 6}-\frac{2 \cdot 4 \cdot 6}{3 \cdot 6 \cdot 9}+\ldots \infty=\)

\(2 \cdot 5+5 \cdot 9+8 \cdot 13+11 \cdot 17+\ldots \text { to } 10 \text { terms }=\)

If $m$ and $M$ denote the mean deviations about mean and about median respectively of the data $20,5,15,2$, $7,3,11$, then the mean deviation about the mean of $m$ and $M$ is

If a variable straight line passing through the point of intersection of the lines $x-2 y+3=0$ and $2 x-y-1=0$ intersects the $X, Y$-axes at $A$ and $B$ respectively, then the equation of the locus of a point which divides the segment $A B$...

Point $(-1,2)$ is changed to $(a, b)$, when the origin is shifted to the point $(2,-1)$ by translation of axes, Point $(a, b)$ is changed to $(c, d)$, when the axes are rotated through an angle of $45^{\circ}$ about the new origin, $(c, d)$...

The area (in sq units) of the triangle formed by the lines $6 x^2+13 x y+6 y^2=0$ and $x+2 y+3=0$ is

The point $(a, b)$ is the foot of the perpendicular drawn from the point $(3,1)$ to the line $x+3 y+4=0$. If $(p, q)$ is the image of $(a, b)$ with respect to the line $3 x-4 y+11=0$, then $\frac{p}{a}+\frac{q}{b}=$

A ray of light passing through the point $(2,3)$ reflects on $Y$-axis at a point $P$. If the reflected ray passes through the point $(3,2)$ and $P=(a, b)$, then $5 b=$

A line $L$ passes through the points $(1,2,-3)$ and $(\beta, 3,1)$ and a plane $\pi$ passes through the points $(2,1,-2)$, $(-2,-3,6),(0,2,-1)$. If $\theta$ is the angle between the line $L$ and plane $\pi$, then $27 \cos ^2 \theta=$

The shortest distance between the skew lines $\mathbf{r}=(-\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}})+t(3 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}})$ and $\mathbf{r}=(7 \hat{\mathbf{i}}+4 \hat{\mathbf{k}})+s(\hat{\...

If $A(1,2,0), B(2,0,1), C(-3,0,2)$ are the vertices of $\triangle A B C$, then the length of the internal bisector of $\angle B A C$ is

The perpendicular distance from the point $(-1,1,0)$ to the line joining the points $(0,2,4)$ and $(3,0,1)$ is

The general solution of
$$ \begin{aligned} & 4 \cos 2 x-4 \sqrt{3} \sin 2 x+\cos 3 x-\sqrt{3} \sin 3 x \\ & \qquad+\cos x-\sqrt{3} \sin x=0 \end{aligned} $$

The smallest positive value (in degrees) of $\theta$ for which $\tan \left(\theta+100^{\circ}\right)=\tan \left(\theta+50^{\circ}\right) \tan (\theta) \tan \left(\theta-50^{\circ}\right)$ is valid, is

The general solution of $2 \cos ^2 x-2 \tan x+1=0$ is

Statement $(\mathrm{S} 1) \sin 55^{\circ}+\sin 53^{\circ}-\sin 19^{\circ}-\sin 17^{\circ}=\cos 2^{\circ}$
Statement (S2) Range of $\frac{1}{3-\cos 2 x}$ is $\left[\frac{1}{4}, \frac{1}{2}\right]$
Which one of the following is correct?

The value of $5 \cos \theta+3 \cos \left(\theta+\frac{\pi}{3}\right)+3$ lies between

Let $\mathbf{a} \times \mathbf{b}=7 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}-4 \hat{\mathbf{k}}$ and $\mathbf{a}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$. If the length of projection of $\mathbf{b}$ on $\mathbf{a}$ is

$$
\frac{8}...

Let $A B C$ be an equilateral triangle of side a. $M$ and $N$ are two points on the sides $A B$ and $A C$, respectively such that $\mathbf{A N}={ }^{\prime} K \mathbf{A C}$ and $\mathbf{A B}=3 \mathbf{A M}$. If the vectors $\mathbf{B N}$ an...

Let $\mathbf{a}$ and $\mathbf{b}$ be two non-collinear vector of unit modulus. If $\mathbf{u}=\mathbf{a}-(\mathbf{a} \cdot \mathbf{b}) \mathbf{b}$ and $\mathbf{v}=\mathbf{a} \times \mathbf{b}$, then $|\mathbf{v}|=$

If $L M N$ are the mid-points of the sides $P Q, Q R$ and $R P d$ $\triangle P Q R$ respectively, then

$$ \begin{aligned} & \mathbf{Q M}+\mathbf{L N}+\mathbf{M L}+\mathbf{R N}-\mathbf{M N}-\mathbf{Q L}= \end{aligned} $$