AP EAPCET 2024 - 20th May Evening Shift

A person is known to speak false once out of 4 times, If that person picks a card at random from a pack of 52 cards and reports that it is a king, then the probability that it is actually a king is

The probability that a man failing to hit a target is $\frac{1}{3}$. If he fires 4 times, then the probability that he hits the target at least thrice is

If five-digit numbers are formed from the digits $0,1,2,3,4$ using every digit exactly only once. Then, the probability that a randomly chosen number from those numbers is divisible by 4 is

Two natural numbers are chosen at random from 1 to 100 and are multiplied. If $A$ is the event that the product is an even number and $B$ is the event that the product is divisible by 4 , then $P(A \cap \bar{B})=$

In $\triangle A B C, b c-r_2 r_3=$

In $\triangle A B C$, if $4 r_1=5 r_2=6 r_3$, then $\sin ^2 \frac{A}{2}+\sin ^2 \frac{B}{2}+\sin ^2 \frac{C}{2}=$

In $\triangle A B C, r_1 \cot \frac{A}{2}+r_2 \cot \frac{B}{2}+m_3 \cot \frac{C}{2}=$

If $O(0,0,0), A(3,0,0)$ and $B(0,4,0)$ form a triangle, then the incentre of $\triangle O A B$ is

Let $[r]$ denote the largest integer not exceeditio $r$ and the roots of the equation $3 x^2+6 x+5+\alpha\left(x^2+2 x+2\right)=0$ are complex number when ever $\alpha>L$ and $\alpha

For any real value of $x$. If $\frac{11 x^2+12 x+6}{x^2+4 x+2} \notin(a, b)$, then the value $x$ for which $\frac{11 x^2+12 x+6}{x^2+4 x+2}=b-a+3$ is

If the roots of $\sqrt{\frac{1-y}{y}}+\sqrt{\frac{y}{1-y}}=\frac{5}{2}$ are $\alpha$ and $\beta(\beta>\alpha)$ and the equation $(\alpha+\beta) x^4-25 \alpha \beta x^2+(\gamma+\beta-\alpha)=0$ has real roots, then a possible value of $\gamm...

If $2 \cdot 4^{2 n+1}+3^{3 n+1}$ is divisible by $k$ for all $n \in N$, then $k=$

If the roots of the equation $x^3+a x^2+b x+c=0$ are in arithmetic progression. Then,

If the mean deviation about the mean is $m$ and variance is $\sigma^2$ for the following data, then $m+\sigma^2=$ .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;border-width:1px;font-family:A...

The equation for straight line passing through the point of intersection of the lines represented by $x^2+4 x y+3 y^2-4 x-10 y+3=0$ and the point $(2,2)$ is

If the line $2 x-3 y+5=0$ is the perpendicular bisector of the line segment joining $(1,-2)$ and $(\alpha, \beta)$, then $\alpha+\beta=$

If the area of the triangle formed by the straight lines $-15 x^2+4 x y+4 y^2=0$ and $x=\alpha$ is 200 sq unit, then $|\alpha|=$

If the origin is shifted to remove the first degree terms from the equation $2 x^2-3 y^2+4 x y+4 x+4 y-14=0$, then with respect to this new coordinate system the transformed equation of $x^2+y^2-3 x y+4 y+3=0$ is

The circumcentre of the triangle formed by the lines $x+y+2=0,2 x+y+8=0$ and $x-y-2=0$ is

If $L_1$ and $L_2$ are two lines which pass through origin and having direction ratios $(3,1,-5)$ and $(2,3,-1)$ respectively, then equation of the plane containing $L_1$ and $L_2$ is

The direction cosines of the line of intersection of the planes $x+2 y+z-4=0$ and $2 x-y+z-3=0$ are

The angle between the line with the direction ratios $(2,5,1)$ and the plane $8 x+2 y-z=14$ is

The general solution of the equation $\sin ^2 \theta+3 \cos ^2 \theta=$ $5 \sin \theta$ is

If $(\alpha+\beta)$ is not a multiple of $\frac{\pi}{2}$ and $3 \sin (\alpha-\beta)=5 \cos (\alpha+\beta)$, then $\tan \left(\frac{\pi}{4}+\alpha\right)+4 \tan \left(\frac{\pi}{4}+\beta\right)=$

If $\sec \theta+\tan \theta=\frac{1}{3}$, then the quadrant in which $2 \theta$ lies is

If $540^{\circ} < A < 630^{\circ}$ and $|\cos A|=\frac{5}{13}$, then $\tan \frac{A}{2} \tan A=$

If $|f|=10,|g|=14$ and $|f-g|=15$, then $|f+g|=$

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three vectors such that $|\mathbf{a}|=|\mathbf{b}|=|\mathbf{c}|=\sqrt{3}$ and $(a+b-c)^2+(b+c-a)^2+(c+a-b)^2=36$, then $|2 a-3 b+2 c|=$

The angle between the diagonals of the parallelogram whose adjacent sides are $2 \hat{\mathbf{i}}+4 \hat{\mathbf{j}}-5 \hat{\mathbf{k}}, \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ is

If the points having the position vectors $-i+4 j-4 k_{\text {, }}$, $3 i+2 j-5 k,-3 i+8 j-5 k$ and $-3 i+2 j+\lambda k$ are coplanar, then $\lambda=$