TG EAPCET 2025 (Online) 2nd May Morning Shift

If three cards are drawn randomly from a pack of 52 playing cards then the probability of getting exactly, one spade card, exactly one king and exactly one card having a prime number is

Urn A contains 6 white and 2 black balls; run B contains 5 white and 3 black balls and urn C contains 4 white and 4 black balls. if an urn is chosen at random and a ball is drawn at random from it, then the probability that the ball drawn i...

If $p_1, p_2, p_3$ are the altitudes and $a=4, b=5, c=6$ are the sides of a $\triangle A B C$, then $\frac{1}{p_1^2}+\frac{1}{p_2^2}+\frac{1}{p_3^2}=$

Let the angles $A, B, C$ of a $\triangle A B C$ be in arithmetic progression. If the exradii $r_1, r_2, r_3$ of $\triangle A B C$ satisfy the condition $r_3^2=r_1 r_2+r_2 r_3+r_3 r_1$, then $b=$

The number of integral values of ' $a$ ' for which the quadratic equation $a x^2+a x+5=0$ cannot have real roots is

If the roots of the equation $32 x^3-48 x^2+22 x-3=0$ are in arithmetic progression, then the square of the common difference of the roots is

If the sum of two roots of the equation $x^4-2 x^3+x^2+4 x-6=0$ is zero, then the sum of the squares of the other two roots is

$1+(1+3)+(1+3+5)+(1+3+5+7)+\ldots$ to 10 terms $=$

The mean deviation from the median for the following data is
$$ \begin{array}{cllllll} x_i & 2 & 9 & 8 & 3 & 5 & 7 \\ \hline f_i & 5 & 3 & 1 & 6 & 6 & 1 \\ \hline \end{array} $$

If three dice are thrown, then the mean of the sum of the numbers appearing on them is

If the points $A(2,3), B(3,2)$ form a triangle with a variable point $p\left(t, t^2\right)$, where $t$ is a parameter, then the equation of the locus of the centroid of $\triangle A B C$ is

If $(h, k)$ is the new origin to be chosen to eliminate first degree terms from the equation $S \equiv 2 x^2-x y-y^2-3 x+3 y=0$ by translation and if $\theta$ is the angle with which the axes are to be rotated about the origin in anti-clock...

A line $L$ perpendicular to the line $5 x-12 y+6=0$ makes positive intercept on the $Y$-axis. If the distance from the origin to the line $L$ is 2 units and the angle made by the perpendicular drawn from the origin to the line $L$ with posi...

If a line $L$ passing through a point $A(2,3)$ intersects another line $4 x-3 y-19=0$ at the point $B$ such that $A B=4$, then the angle made by the line $L$ with positive $X$-axis in anti-clockwise direction is

A variable straight-line $L$ with negative slope passes through the point $(4,9)$ and cuts the positive coordinate axes in $A$ and $B$. If $O$ is the origin, then the minimum value of $O A+O B$ is

If $4 x^2+12 x y+9 y^2+2 g x+2 f y-1=0$ represent a pair of parallel lines, then

The shortest distance between the lines
$$ \begin{aligned} & \mathbf{r}=(3 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}+2 \hat{\mathbf{k}})+t(4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}) \text { and } \\ & \mathbf{r}=(\hat{\mathbf{i}}+2 \...

If $A(0,3,4), B(1,5,6), C(-2,0,-2)$ are the vertices of a $\triangle A B C$ and the bisector of angle $A$ meets the side $B C$ at $D$, then $A D=$

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

If the equation of the plane passing through the points $(2,1,2),(1,2,1)$ and perpendicular to the plane $2 x-y+2 z=1$ is $a x+b y+c z+d=0$, then $\frac{a+b}{c+d}=$

$\alpha, \beta$ are the roots of the equation $\sin ^2 x+b \sin x+c=0$. If $\alpha+\beta=\frac{\pi}{2}$, then $b^2-1=$

The general solution of the equation $\sqrt{6-5 \cos x+7 \sin ^2 x}-\cos x=0$ also satisfies the equation

If $\sin A=-\frac{60}{61}, \cot B=-\frac{40}{9}$ and neither $A$ and $B$ is in 4th quadrant, then $6 \cot A+4 \sec B=$

The period of the function $f(x)=\frac{2 \sin \left(\frac{\pi x}{3}\right) \cos \left(\frac{2 \pi x}{5}\right)}{3 \tan \left(\frac{7 \pi x}{2}\right)-5 \sec \left(\frac{5 \pi x}{3}\right)}$ is

If $A+B+C=4 S$, then $\sin (2 S-A)$
\(+\sin (2 S-B)+\sin (2 S-C)-\sin 2 S=\)

If $1^{\circ}=0.0175$ radians, then the approximate value of $\sec 58^{\circ}$ is

The position vectors of two points $A$ and $B$ are $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $7 \hat{\mathbf{i}}-\hat{\mathbf{k}}$ respectively. The point $P$ with position vector $-2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5...

The point of intersection of the line joining the points $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and the plane passing through the points $\hat{\mathbf{i}}, 2 \hat{\mathbf...

If $\mathbf{a}$ and $\mathbf{b}$ are two vectors such that $|\mathbf{a}|=5,|\mathbf{b}|=12$ and $|\mathbf{a}-\mathbf{b}|=13$, then $|2 \mathbf{a}+\mathbf{b}|=$

If $\mathbf{a}=\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-2 \hat{\mathbf{k}}$ and $\mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ are two vectors, then $(\mathbf{a}+2 \mathbf{b}) \times(3 \mathbf{a}-\mathbf{b})$