TS EAMCET 2023 (Online) 14th May Evening Shift

If the roots of the equation $k x^3-18 x^2-36 x+8=0$ are in harmonic progression, then $k=$

The mean and standard deviation of 100 observations were calculated as 40 and 5.1 respectively. Later on it was found that one of the observations was taken as 50 in the place of 40 . If the wrong entry is replaced by the correct one, then ...

If $k=\frac{a+b}{a b}$ is a non-zero constant, then the point which lies on the straight line $\frac{x}{a}+\frac{y}{b}=1$ is

If $\alpha, \beta(\alpha>\beta)$ are two values of $k$ such that the equations $2 x+(3-2 k) y+(2 k+1)=0$ and $k x+(k-1) y-4=0$ represents two perpendicular lines, then $\alpha^2+2 \beta=$

If the lines $x+y-1=0, k x+2 y+1=0$ and $4 x+2 k y+7=0$ are concurrent, then $k=$

When the origin is shifted to the point $P$ by translation of axes, the equation $2 x^2+y^2-4 x+4 y=0$ is transformed to $2 x^2+y^2-8 x+8 y+18=0$. Then, the transformed equation of the straight line $x+2 y+2=0$, if the origin is shifted to ...

The point of concurrence of all the chords of the curve $3 x^2-y^2-2 x+4 y=0$ which subtend a right angle at the origin is

A straight line passing through a fixed point $(-3,4)$ intersects the coordinate axes at $A$ and $B$. If $O$ is the origin and $O A B C$ forms a rectangle, then the locus of $C$ is

If the circumcenter of the triangle formed by the points $(1,2,3),(3,-1,5)$ and $(4,0,-3)$ is $(\alpha, \beta, \gamma)$, then $|\alpha|+|\beta|=$

If the foot of the perpendicular drawn from the point $(1,0,-2)$ to the plane $\pi$ is $(2,0,-1)$ and the equation of the plane $\pi$ is $a x+b y+c z=2$, then $a^2+b^2+c^2=$

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

If $\frac{\sin ^4 x}{2}+\frac{\cos ^4 x}{3}=\frac{1}{5}$, then $27 \sec ^6 \alpha+8 \operatorname{cosec}^6 \alpha=$

If $\tan \beta=\frac{n \sin \alpha \cos \alpha}{1-n \cos ^2 \alpha}$, then $\tan (\alpha+\beta) \cdot \cot \alpha=$

If $\cos A+\cos B+\cos C=0=\sin A+\sin B+\sin C$, then $\cos (A-B)+\cos (B-C)+\cos (C-A)=$

If $\sin x \cdot \cosh y=\cos \theta$ and $\cos x \cdot \sinh y=\sin \theta$, then $\sin ^2 x+\cosh ^2 y=$