AP EAPCET 2025 - 23rd May Evening Shift

There are 8 boys and 7 girls in a class room. If the names of all those children are written on paper slips and 3 slips are drawn at random from them, then the probability of getting the names of one boy and two girls or one girl and two bo...

If $X \sim B(9, p)$ is a binomial variate satisfying the equation $P(X=3)=P(X=6)$, then $P(X<3)=$

A four member committee is to be formed from a group containing 9 men and 5 women. If a committee is formed randomly, then the probability that it contains atleast one woman is

A bag contains 5 balls of unknown colours. There are equal chances that out of these five balls, there may be 0 or 12 or or 3 or 4 or 5 red balls, A ball is taken out from the bag at random and is found to be red. The probability that it is...

In a $\triangle A B C$, if $\left(r_1-r_3\right)\left(r_1-r_2\right)-2 r_2 r_3=0$, then $a^2-b^2=$

If the median $A D$ of the $\triangle A B C$ is bisected at $E$ and $B E$ meets $A C$ in $E$, then $A F: A C=$

In $\triangle A B C$, if $a=8, b=10, c=12$, then $\frac{r}{R}=$

In $\triangle A B C$, if $a=13, b=8, c=7$, then $\cos (B+C)=$

If $\alpha, \beta, \gamma$ are the roots of the equation $x^3+p x^2+q x+r=0$, then $\alpha^3+\beta^3+\gamma^3=$

If the roots of the equation $x^2+2 a x+b=0$ are real, distinct and differ atmost by 2 m , then $b$ lies in the interval

The cubic equation whose roots are the squares of the roots of the equation $x^3-2 x^2+3 x-4=0$ is

Let $(a-3) x^2+12 x+(a+6)>0, \forall x \in R$ and $a \in(\ell, \infty)$. If $a$ is the least positive integral value of $a$, then the roots of $(\alpha-3) x^2+12 x+(\ell+2)=0$ are

\(1+\frac{4}{15}+\frac{4 \cdot 10}{15 \cdot 30}+\frac{4 \cdot 10 \cdot 16}{15 \cdot 30 \cdot 45}+\ldots . .+\infty=\)

Let $x_1, x_2, \ldots, x_{11}$ be the observations satisfying $\sum\limits_{i=1}^{11}\left(x_i-4\right)=22$ and $\sum\limits_{i=1}^{11}\left(x_i-4\right)^2=154$. If the mean and variance of the observations are $\alpha$ and $\beta$, then th...

$A(-2,3)$ is a point on the line $4 x+3 y-1=0$. If the points on the line that are 10 units away from the point $A$ are ( $x_1, y_1$ ) and ( $x_2, y_2$ ), then $\left(x_1+y_1\right)^2+\left(x_2+y_2\right)^2=$

If the equation of the pair of lines passing through $(1,1)$ and perpendicular to the pair of line $2 x^2+x y-y^2-x+2 y-1=0$ is $a x^2+2 h x y+b y^2+2 g x+3 y=0$, then $\frac{b}{a}=$

If $\alpha$ is the angle made by the perpendicular drawn from origin to the line $12 x-5 y+13=0$ with the positive $X$-axis in anti-clockwise direction, then $\alpha=$

If the combined equation of the lines joining the origin to the point of intersection of the curve $x^2+y^2-2 x-4 y+2=0$ and the line $x+y-2=0$ is $\left(l_1 x+m_1 y\right)\left(l_2 x+m_2 y\right)=0$, then $l_1+l_2+m_1+m_2=$

If the locus of a point which is equidistant from the coordinate axes forms a triangle with the line $y=3$, then the area of the triangle is

If $(2,-1,3)$ is the foot of the perpendicular drawn from the origin $(0,0,0)$ to a plane, then the equation of that plane is

If $A(0,1,2), B(2,-1,3)$ and $C(1,-3,1)$ are the vertices of a triangle, then the distance between its circumcentre and orthocentre is

If the direction cosines of two lines satisfy the equations $l-2 m+n=0, l m+10 m n-2 n l=0$ and $\theta$ is the angle between the lines, then $\cos \theta=$

The general solution satisfying both the equations $\sin x=-\frac{3}{5}$ and $\cos x=-\frac{4}{5}$ is

If $\sqrt{3} \cos \theta+\sin \theta>0$, then

If $\cos \theta=\frac{-3}{5}$ and $\theta$ does not lie in second quadrant, then $\tan \frac{\theta}{2}=$

$\operatorname{cosec} 48^{\circ}+\operatorname{cosec} 96^{\circ}+\operatorname{cosec} 192^{\circ}+\operatorname{cosec} 384^{\circ}=$

If $\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$ and $\mathbf{b}=-\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ are two vectors, then the vector of magnitude 28 units in the direction of the vector $\mathbf...

$3 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}+5 \hat{\mathbf{j}}$ are the position vectors of three non-collinear points $A, B, C$ respectively. If the perpendicular drawn from ...

If $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, \mathbf{b}=-2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, \mathbf{c}=5 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $\mathbf{d}=3 \hat{\mathbf...

If $\bar{a}$ is a unit vector, then
\(|\mathbf{a} \times \hat{\mathbf{i}}|^2+|\mathbf{a} \times \hat{\mathbf{j}}|^2+|\mathbf{a} \times \hat{\mathbf{k}}|^2=\)