TS EAMCET 2020 (Online) 14th September Morning Shift

If the sides of a triangle are in the ratio $\sqrt{3}: \sqrt{5}: \sqrt{8+\sqrt{15}}$, then the largest angle in that triangle is

In a $\triangle A B C$, if $\tan A: \tan B: \tan C=1: 2: 3$ and $\sin A: \sin B: \sin C=\sqrt{5}: 2 \sqrt{2}: k$, then $k=$

In $\triangle A B C$, if $R=\frac{65}{8}, r r_1=42$ and $r_1-r=6.5$, then $s(s-a)=$

In $\triangle A B C$ if $\angle C=\frac{\pi}{2}$ then
$\tan ^{-1}\left(\frac{a}{b+c}\right)+\tan ^{-1}\left(\frac{b}{c+a}\right)+\tan ^{-1}\left(\frac{c}{a+b}\right)=$

The number of integral values of $x$ satisfying $9 x-2<(x+2)^2<12 x-3$ is

If $2+\sqrt{3}$ is a root of the equation $f(x)=x^4+2 x^3-16 x^2-22 x+7=0$, then which one of the following is not a root of $f(x)=0$ ?

If $f(1)=3$, and $f(n+1)-f(n)=3\left(4^n-1\right)$, then $\forall n \in \mathbf{N}$, $f(n)=$

The mean and standard deviation of 100 observations $x_1, x_2, \ldots, x_{100}$ were calculated as 40 and 5.1 respectively by a student who took by mistake 50 instead of 40 for one observation. Then the correct value of $\sum_{i=1}^{100} x_...

The coefficient of variation of the first 5 prime numbers is

If a variable line is moving such that the intercepts made by it on the coordinate axes are reciprocal to each other, then the points $P(x, y)$ on such lines satisfy

If a variable line is moving such that the intercepts made by it on the coordinate axes are reciprocal to each other, then the points $P(x, y)$ on such lines satisfy

If $\pi / 3$ is the angle between the straight lines $p x+q y+r=0$ and $x \sin \alpha+y \cos \alpha=r(r \neq 0)$ which meet at a point $A$ and the straight line $x \cos \alpha-y \sin \alpha=0$ also passes through the point $A$, then

The distance between the point $(2,1)$ and the image of the point $(3,-1)$ with respect to the line $2 x+y-1=0$ is

The acute angle between the pair of straight lines joining the origin to the points of intersection of the line $x+y-1=0$ with the pair of straight lines $k x^2+8 x y-3 y^2+2 x-4 y-1=0$ is

If the lines drawn along the diagonals of the two squares formed by two pairs of lines $x^2-3|x|+2=0$ and $y^2-3 y+2=0$ form a square $A B C D$, then the equations of two adjacent sides of the square $A B C D$ are

Let $O A B C$ be a parallelogram. The equation of one diagonal $A C$ is $x+y-1=0$ and the combined equation of the sides $O A, O C$ is $2 x^2-y^2=0$. If $G$ is centroid of the triangle $O A C$, then $B G=$

$L_1$ is a line passing through the points with position vectors $\hat{\mathbf{i}}-2 \hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $4 \hat{\mathbf{i}}-3 \hat{\mathbf{k}} . L_2$ is a line passing through the points with position vectors $\hat{\math...

The quadrilateral formed by the points $A(1,2,5), B(-1,6,1), C(3,4,-3)$ and $D(5,0,1)$ is a

A line with direction cosines proportional to $2,1,2$ meets the line $L_1$ passing through $(0,-1,0)$ with direction ratios $1,1,1$ at $A(x, y, z)$ and another line $L_2$ at $B(1,1,1)$ then $x+y+z=$

If a plane $\pi$ passes through the point $(-1,6,2)$ is perpendicular to the planes $x+2 y+2 z-5=0$ and $3 x+3 y+2 z-8=0$, then, the perpendicular distance from the point $(1,-1,1)$ to the plane $\pi$ is

The smallest positive value of $x$ (in degrees) for which $\tan \left(x+100^{\circ}\right)=\tan \left(x+50^{\circ}\right) \tan (x) \tan \left(x-50^{\circ}\right)$ is

If the possible solution of the equation $2 \cos ^2 x+3 \sin x-3=0$ constitute two unequal angles of a triangle, then the third angle of that triangle is

For $n \in \mathbf{N}$, if $f(n)=(\cos n x)(\sec x)^n$ and $g(n)=(\sin n x)(\sec x)^n$, then $f(2020)-f(2019)+(\tan x) g(2019)=$

$\theta$ and $\alpha$ lie in $Q_3$. If $\cos (\theta-\alpha), \cos \theta, \cos (\theta+\alpha)$ are in harmonic progression, then $\cos \theta \sec \frac{\alpha}{2}=$

The ratio of the maximum and minimum values attained by the function $f(x)=1+2 \sin x+3 \cos ^2 x, 0 \leq x \leq \frac{2 \pi}{3}$ is

A vector $\mathbf{a}$ has components $2 p$ and 1 with respect to a two dimensional rectangular cartesian system. This system is rotated through a certain angle about the origin in the counter-clockwise direction. If $\mathbf{a}$ has compone...

If $\mathbf{a}=2 \mathbf{u}+3 \mathbf{v}+7 \mathbf{w}, b=\mathbf{u}+\mathbf{v}-2 \mathbf{w}$ and $\mathbf{c}=-\mathbf{u}-2 \mathbf{v}-3 \mathbf{w}$ then $\left|\frac{[\mathbf{u} \mathbf{v} \mathbf{w}]}{[\mathbf{a} \mathbf{b} \mathbf{c}]}\ri...

Let $\mathbf{V}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\mathbf{W}=\hat{\mathbf{i}}+3 \hat{\mathbf{k}}$. If $\mathbf{U}$ is a unit vector, then the maximum value of $[\mathbf{U} \mathbf{V} \mathbf{W}]$ is

Let $A(3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})$ and $B(13 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}+9 \hat{\mathbf{k}})$ be two points on a line $L . C$ and $D$ be the points on $L$ on either side of $A$ at distance of 9 and 6 units...

Let $A B C D$ be a parallelogram and $E$ be the mid-point of $A B$. If $P$ is the point of intersection of $D E$ and $A C$, then $\frac{D P}{P E}+\frac{A P}{P C}=$