TS EAMCET 2023 (Online) 12th May Morning Shift

The number of ways of arranging all the letters of the word "SUNITHA" so that the vowels always occupy the first, middle and last places is

The number of all four digit numbers that can be formed with the digits $0,1,2,3,4,5$ when the repetition of the digits is not allowed, is

The number of four digit numbers that can be formed using the digits $1,2,3,4,5,6$ and 7 which are divisible by 4 , when the repetition of any digit is not allowed,

A student is given 6 questions in an examination with true or false type of answers. If he writes 4 or more correct answers, he passes in the examination. The probability that he passes in the examination is

In a non-leap year, the probability of getting 53 Sundays or 53 Tuesdays or 53 Thursdays is

If $A$ and $B$ are two events in a random experiment such that $P(A)+P(B)=2 P(A \cap B)$, then

The equation of the parabola with $x+2 y=1$ as directrix and $(1,0)$ as focus is

If $P(X=x)=c\left(\frac{2}{3}\right)^x ; x=1,2,3,4, \ldots$ is a probability distribution function of a random variable $X$, then the value of $c$ is

In a $\triangle A B C$, if $r_1=2 r_2=3 r_3$, then $\frac{a}{b}+\frac{b}{c}+\frac{c}{a}=$

In an isosceles right angled triangle, a straight line is drawn from the mid-point of one of the equal sides to the opposite vertex. Then, a pair of possible values of the cotangents of the two angles so formed at that vertex are

If $(x-2)$ is a common factor of the expressions $x^2+a x+b$ and $x^2+c x+d$, then $\frac{b-d}{c-a}=$

If one root of the equation $4 x^2-2 x+k-4=0$ is the reciprocal of the other, then the value of $k$ is

Two numbers $b$ and $c$ are chosen at random in succession without replacement from the set $\{1,2,3, \ldots \ldots, 9\}$. Then, the probability that $x^2+b x+c>0, \forall x \in R$ i

The sum of the roots of the equation $e^{4 t}-10 e^{3 t}+29 e^{2 t}-20 e^t+4=0$ is

The roots of the equation $x^3-14 x^2+56 x-64=0$ are in

The angle, by which the coordinate axes are to be rotated about the origin so that the transformed equation of $\sqrt{3} x^2+(\sqrt{3}-1) x y-y^2=0$ would be free from $x y$-term is

If each of the points $(a, 4),(-2, b)$ lies on the line joining the points $(2,-1)$ and $(5,-3)$, then the point $(a, b)$ lies on the line

If the slope of a straight line passing through $A(3,2)$ is $3 / 4$, then the coordinates of the two points on the same line that are 5 units away from $A$ are

The sum of the squares of the perpendicular distances of a point $(x, y, z)$ from the coordinate axes is $k$ times the square of the distance of the point from the origin Then, $k=$

If the direction cosines $(l, m, n)$ of two lines are connected by the relations $l+m+n=0$ and $l m=0$, then the angle between those lines is

Equation of the plane through the mid-point of the line segment joining the points $A(4,5,-10)$ and $B(-1,2,1)$ and perpendicular to $A B$ is

\(\sin \alpha+\cos \alpha=m \Rightarrow \sin ^6 \alpha+\cos ^6 \alpha=\)

For $0 \leq x \leq \pi$, if $81^{\sin ^2 x}+81^{\cos ^2 x}=30$, then $x=$

\(\frac{\left(1+\tan 32^{\circ}\right)}{\left(1-\tan 48^{\circ}\right)}=\)

If $\mathbf{a}$ is a vector such that $\mathbf{a} \times \hat{\mathbf{i}}=\hat{\mathbf{j}}+\hat{\mathbf{k}}$ and $\mathbf{a} \cdot \hat{\mathbf{i}}=1$, then equation of the line passing through the point $\hat{\mathbf{i}}+\hat{\mathbf{j}}+\...

If the position vectors of $\mathbf{P}$ and $\mathbf{Q}$ are $\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-7 \hat{\mathbf{k}}$ and $5 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}$ respectively, then the cosine of the angle between $P Q$ an...

The position vectors of the point $A, B$ are $\mathbf{a}, \mathbf{b}$ respectively. If the position vector of the point $C$ is $\frac{a}{2}+\frac{b}{3}$, then

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are three-unit yectors such that $|\mathbf{a}+\mathbf{b}+\mathbf{c}|=1$ and $\mathbf{a}$ is perpendicular to $\mathbf{b}$. If $\mathbf{c}$ makes angles $\alpha, \beta$ with $\mathbf{a}, \mathbf{b}$ respe...

If $|\mathbf{a}|=1,|\mathbf{b}|=2,|\mathbf{a}-\mathbf{b}|^2+|\mathbf{a}+2 \mathbf{b}|^2=20$, then $(a, b)=$