TG EAPCET 2024 (Online) 9th May Evening Shift

The number of ways in which 4 different things can be distributed to 6 persons so that no person gets all the things is

If a random variable X has the following probability distribution, then the mean of $X$ is

$$ \begin{array}{c|c|c|c|c} X=x_1 & 1 & 2 & 3 & 5 \\ \hline p\left(X=x_i\right) & 2 k^2 & k & k & k^2 \end{array} $$

If 3 dice are thrown, the probability of getting 10 as the sum of the three numbers that appeared on the top faces of the dice is

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probability that no man is matched with name of his wife is

A A fair coin is tossed a fixed number of times. If the probability of getting 5 heads is equal to the probability of getting 4 heads, then the probability of getting 6 heads is

Three similar urns $A, B, C$ contain 2 red and 3 white balls; 3 red and 2 white balls; 1 red and 4 white balls respectively. If a ball selected at random from one of the urns is found to be red, then the probability that it is drawn from ur...

In a $\triangle A B C$, if $\tan \frac{A}{2}: \tan \frac{B}{2}: \tan \frac{C}{2}=15: 10: 6$, then $\frac{a}{b-c}=$

In a $\triangle A B C, \frac{a\left(r_1+r_2 r_3\right)}{r_1-r+r_2+r_3}=$

If $A+B+C=2 S$, then $\sin (S-A) \cos (S-B)-\sin (S-C) \cos S=$

$\alpha$ is a root of the equation $\frac{x-1}{\sqrt{2 x^2-5 x+2}}=\frac{41}{60}$. If $-\frac{1}{2}<\alpha<0$, then $\alpha$ is equal to

$\alpha, \beta, \gamma, 2$ and $\varepsilon$ are the roots of the equation
$$ \begin{aligned} & \alpha, \beta, \gamma+4 x^4-13 x^3-52 x^2+36 x+144=0 . \text { If } \\ & \alpha<\beta<\gamma<2<\varepsilon \text {, then } \alpha+2 \beta+3 \gam...

$\frac{1}{3 \cdot 6}+\frac{1}{6 \cdot 9}+\frac{1}{9 \cdot 12}+\ldots \ldots .$. to 9 terms $=$

The variance of the following continuous frequency distribution is


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If the origin is shifted to the point $\left(\frac{3}{2},-2\right)$ by the translation of axes, then the transformed equation of $2 x^2+4 x y+y^2+2 x-2 y+1=0$ is

$L \equiv x \cos \alpha+y \sin \alpha-p=0$ represents a line perpendicular to the line $x+y+1=0$. If $p$ is positive, $\alpha$ lies in the fourth quadrant and perpendicular distance from $(\sqrt{2}, \sqrt{2})$ to the line, $L=0$ is 5 units,...

If the ratio of the distances of a variable point $P$ from the point $(1,1)$ and the line $x-y+2=0$ is $1: \sqrt{2}$, then the equation of the locus of $P$ is

The slope of one of the pair of lines $2 x^2+h x y+6 y^2=0$ is thrice the slope of the other line, then $h=$

$(-2,-1),(2,5)$ are two vertices of a triangle and $\left(2, \frac{5}{3}\right)$ is its orthocenter. If $(m, n)$ is the third vertex of that triangle, then $m+n$ is equal to.

$L_1 \equiv 2 x+y-3=0$ and $L_2 \equiv a x+b y+c=0$ are two equal sides of an isosceles triangle. If $L_3 \equiv x+2 y+1=0$ is the third side of this triangle and $(5,1)$ is a point on $L_2=$ 0 , then $\frac{b^2}{|a c|}=$

If $\hat{\mathbf{i}}+\hat{\mathbf{j}}, \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{k}}+\hat{\mathbf{i}}, \hat{\mathbf{i}}-\hat{\mathbf{j}}, \hat{\mathbf{j}}-\hat{\mathbf{k}}$ are the position vectors of the points $A, B, C, D, E$ respec...

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

The solution set of the equation $\cos ^2 2 x+\sin ^2 3 x=1$ i

If $\cos x+\cos y=\frac{2}{3}$ and $\sin x-\sin y=\frac{3}{4}$, then $\sin (x-y)+\cos (x-y)=$

The maximum value of the function $f(x)=3 \sin ^{12} x+4 \cos ^{16} x$ is

$(3,0,2)$ and $(0,2, k)$ are the direction ratios of two lines and $\theta$ is the angle between them. If $|\cos \theta|=\frac{6}{13}$, then $k=$

If $\mathrm{a}, \mathrm{b}$ are two vectors such that $|\mathrm{a}|=3,|\mathrm{~b}|=4$, $|\mathbf{a}+\mathbf{b}|=\sqrt{37},|\mathbf{a}-\mathbf{b}|=k$ and $(\mathbf{a}, \mathbf{b})=\theta$, then $\frac{4}{13}(k \sin \theta)^2=$

$\mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \mathbf{k}, \quad \mathbf{c}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ are two vectors and $\mathbf{a}$ is a vector such that
$\cos (\mathbf{a}, \mathbf{b} \times \mathbf{c})=\sqrt...

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are non-coplanar vectors. If the three points $\lambda a-2 b+c, 2 a+\lambda b-2 \mathbf{c}$ and $4 \mathbf{a}+7 \mathbf{b}-8 \mathbf{c}$ are collinear, then $\lambda=$

$r$ is a vector perpendicular to the planet, determined by the vectors $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}$ and $\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$, If the magnitude of the projection of $\mathbf{r}$ on the vector $2 \hat{\mathbf{i}}+\ha...

$A(3,2,-1), B(4,1,0), C(2,1,4)$ are the vertices of a $\triangle A B C$. If the bisector of $B A C$ ! intersects the side $B C$ at $D(p, q, r)$, then $\sqrt{2 p+q+r}=$