AP EAPCET 2024 - 22th May Morning Shift

In a binomial distribution the difference between the mean and standard deviation is 3 and the difference between their squares is 21 , then $P(x=1): P(x=2)=$

When an unfair dice is thrown the probability of getting a number $k$ on it is $P(X=k)=k^2 P$, where $k=1,2,3,4,5,6$ and $X$ is the random variable denoting a number on the dice, then the mean of X is

In a $\triangle A B C$, if $A, B$ and $C$ are in arithmetic progression and $\cos A+\cos B+\cos C=\frac{1+\sqrt{2}+\sqrt{3}}{2 \sqrt{2}}$, then $\tan A$ :

In $\triangle A B C$, if $b+c: c+a: a+b=7: 8: 9$, then the smaller angle (in radians) of that triangle is

In $\triangle A B C$, if $(a+c)^2=b^2+3 c a$, then $\frac{a+c}{2 R}=$

In $\triangle A B C$, if $A, B$ and $C$ are in arithmetic progression $\Delta=\frac{\sqrt{3}}{2}$ and $r_1 r_2=r_2 r$, then $R=$

If both the roots of the equation $x^2-6 a x+2-2 a+9 a^2=0$ exceed 3 , then

If $\alpha$ and $\beta$ are two distinct negative roots of $x^5-5 x^3+5 x^2-1=0$, then the equation of least degree with integer coefficients having $\sqrt{-\alpha}$ and $\sqrt{-\beta}$ as its roots, is

\(2+3+5+6+8+9+\ldots .2 n \text { terms }=\)

If $\alpha, \beta$ are the roots of the equation $x^2-6 x-2=0$, $\alpha>\beta$ and $a_n=\alpha^n-\beta^n, n \geq 1$, then the value of $\frac{a_{10}-2 a_8}{2 a_9}$ is equal to

$|x|<1$, The coefficient of $x^2$ in the power series expansion of $\frac{x^4}{(x+1)(x-2)}$ is

If set $A$ has 5 elements, set $B$ has 7 elements, then the number of many one functions that can be defined from $A$ to $B$ is

If $x_1, x_2, x_3, \ldots . x_n$ are $n$ observations such, that $\Sigma\left(x_i+2\right)^2=28 n$ and $\Sigma\left(x_1-2\right)^2=12 n$, then the variance is

The equation of the locus of points which are equidistant from the point $(2,3)$ and $(4,5)$ is

If the slope of one of the pair of lines represented by $2 x^2+3 x y+K y^2=0$ is 2 , then the angle between the pair of lines is

The length of $x$-intercept made by pair of lines $2 x^2+x y-6 y^2-2 x+17 y-12=0$ is

The orthocentre of the triangle formed by lines $x+y+1=0, x-y-1=0$ and $3 x+4 y+5=0$ is

The equation of the side of an equilateral triangle is $x+y=2$ and one vertex is $(2,-1)$. The length of the side is

The distance of a point $(2,3,-5)$ from the plane $\hat{\mathbf{r}} \cdot(4 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})=4$ is

The orthocentre of triangle fromed by points $(2,1,5)$ $(3,2,3)$ and $(4,0,4)$ is

If $P=(0,1,2), Q=(4,-2,1)$, and $O=(0,0,0)$, then $\angle P O Q=$

If the perpendicular distance from $(1,2,4)$ to the plane $2 x+2 y-z+k=0$ is 3 , then $k=$

The general solution of the equation $\tan x+\tan 2 x-\tan 3 x=0$ is

If $M_1$ and $M_2$ are the maximum values of $\frac{1}{11 \cos 2 x+60 \sin 2 x+69}$ and $3 \cos ^2 5 x+4 \sin ^2 5 x$ respectively, then $\frac{M_1}{M_2}=$

\(4 \cos \frac{\pi}{7} \cos \frac{\pi}{5} \cos \frac{2 \pi}{7} \cos \frac{2 \pi}{5} \cos \frac{4 \pi}{7}=\)

If $\tanh x=\operatorname{sech} y=\frac{3}{5}$ and $e^{x+y}$ is an integer, then $e^{x+ y}$ =

Let $\hat{\mathbf{a}}=3 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}, \hat{\mathbf{b}}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$. The projection d the sum of the vectors $\hat{\mathbf{a}}$ and $\hat{\mathbf{b}}$ on t...

In $\triangle P Q R,(4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}),(2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})$ and $(3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \mathbf{k})$are$\mathbf{}$ the position vectors of the ve...

If $\hat{\mathbf{f}}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\hat{\mathbf{g}}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$, then the projection vector of $\hat{\mathrm{f}}$ on $\hat{\mathrm{g}}$ is

If $\theta$ is the angle between $\hat{\mathbf{f}}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}$ and $\hat{\mathbf{g}}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+a \hat{\mathbf{k}}$ and $\sin \theta=\sqrt{\frac{24}{28}}$, then $7 a^2+...