AP EAPCET 2024 - 20th May Morning Shift

For the probability distribution of a discrete random variable $X$ as given below, then mean of $X$ is

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S is the sample space and $A, B$ are two events of a random experiment. Match the items of List $A$ with the items of List B

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In a random experiment, two dice are thrown and the sum of the numbers appeared on them is recorded. This experiment is repeated 9 times. If the probability that a sum of 6 appears atleast once is $P_1$ and a sum of 8 appears atleast once i...

$P(A \mid A \cap B)+P(B \mid A \cap B)=$

In $\triangle A B C$, if $r_1=4, r_2=8$ and $r_3=24$, then $a=$

Match the items of List I with those of List II (here, $\Delta$ denotes the area of $\triangle A B C$ )

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If $2 x^2+3 x-2=0$ and $3 x^2+\alpha x-2=0$ have one common root, then the sum of all possible values of $\alpha$ is

If $\alpha$ and $\beta$ are two double roots of $x^2+3(a+3) x-9 a=0$ for different values of $a(\alpha>\beta)$, then the minimum value of $x^2+\alpha x-\beta=0$ is

If the sum of two roots of $x^3+p x^2+q x-5=0$ is equal to its third root, then $p\left(p^2-4 q\right)=$

$ \frac{1}{3 \cdot 7}+\frac{1}{7 \cdot 11}+\frac{1}{11 \cdot 15}+\ldots$ to 50 terms $=$

\(1+\frac{1}{3}+\frac{1 \cdot 3}{3 \cdot 6}+\frac{1 \cdot 3 \cdot 5}{3 \cdot 6 \cdot 9}+\ldots \text { to } \infty=\)

$x$ and $y$ are the arithmetic means of the runs of two batsmen $A$ and $B$ in 10 innings respectively and $\sigma_A, \sigma_B$ are the standard deviations of their runs in them. If batsman $A$ is more consistent than $B$, then he is also a...

If the origin is shifted to a point $P$ by the translationd axes to remove the $y$-term from the equation $x^2-y^2+2 y-1=0$, then the transformed equation of it is

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

If the equation of the pair of straight lines passing through the point $(1,1)$ and perpendicular to the pair of lines $3 x^2+11 x y-4 y^2=0$ is $a x^2+2 h x y+b y^2+2 g x+2 f y+12=0$, then $2(a-h+b-g+f-12)=$

A line $L$ intersects the lines $3 x-2 y-1=0$ and $x+2 y+1=0$ at the points $A$ and $B$. If the point $(1,2)$ bisects the line segment $A B$ and $\frac{x}{a}+\frac{y}{b}=1$ is the equation of the line $L$, then $a+2 b+1=$

A line $L$ passing through the point $(2,0)$ makes an angle $60^{\circ}$ with the line $2 x-y+3=0$. If $L$ makes an acute angle with the positive X-axis in the anti-clockwise direction, then the $Y$-intercept of the line $L$ is

The distance from a point $(1,1,1)$ to a variable plane $\pi$ is 12 units and the points of intersections of the plane $\pi$ and $X, Y, Z$ - axes are $A, B, C$ respectively, If the point of intersection of the planes through the points $A, ...

The direction cosines of two lines are connected by the relations $l+m-n=0$ and $l m-2 m n+n l=0$. If $\theta$ is the acute angle between those lines, then $\cos \theta=$

If $A(1,0,2), B(2,1,0), C(2,-5,3)$ and $D(0,3,2)$ are four points and the point of intersection of the lines $A B$ and $C D$ is $P(a, b, c)$, then $a+b+c=$

The distance of the point $O(\mathbf{O})$ from the plane $\mathbf{r}$. $(\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}})=5$ measured parallel to $2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-6 \hat{\mathbf{k}}$ is

Let $O(\mathbf{O}), A(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}), B(-2 \hat{\mathbf{i}}+3 \hat{\mathbf{k}}), C(2 \hat{\mathbf{i}}+\hat{\mathbf{j}})$ and $D(4 \hat{\mathbf{k}})$ are position vectors of the points $O, A, B, C$ and ...

If $5 \sin h x-\cos h x=5$, then one of the values of $\tan h x$ is

The number of ordered pairs $(x, y)$ satisfying the equations $\sin x+\sin y=\sin (x+y)$ and $|x|+|y|=1$ is

If $\cos \alpha+\cos \beta+\cos \gamma=\sin \alpha+\sin \beta+\sin \gamma=0$, then $\left(\cos ^3 \alpha+\cos ^3 \beta+\cos ^3 \gamma\right)^2+\left(\sin ^3 \alpha+\sin ^3 \beta+\sin ^3 \gamma\right)^2=$

$\frac{\sin 1^{\circ}+\sin 2^{\circ}+\ldots . . .+\sin 89^{\circ}}{2\left(\cos 1^{\circ}+\cos 2^{\circ}+\ldots+\cos 44^{\circ}\right)+1}=$

\(\text { } \frac{\cos 10^{\circ}+\cos 80^{\circ}}{\sin 80^{\circ}-\sin 10^{\circ}}=\)

If $\mathbf{a}$ and $\mathbf{b}$ are the two non collinear vectors, then $|\mathbf{b}|\mathbf{a}+|\mathbf{a}| \mathbf{b}$ represents

$\mathbf{u}, \mathbf{v}$ and $\mathbf{w}$ are three unit vectors. Let $\hat{\mathbf{p}}=\hat{\mathbf{u}}+\hat{\mathbf{v}}+\hat{\mathbf{w}} \cdot \hat{\mathbf{q}}=\hat{\mathbf{u}} \times(\hat{\mathbf{v}} \times \hat{\mathbf{w}})$. If $\hat{\...

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are non-coplanar vectors. If $\alpha \mathbf{d}=\mathbf{a}+\mathbf{b}+\mathbf{c}$ and $\beta \mathbf{a}=\mathbf{b}+\mathbf{c}+\mathbf{d}$, then $|\mathbf{a}+\mathbf{b}+\mathbf{c}+\mathbf{d}|=$