TS EAMCET 2020 (Online) 14th September Morning Shift

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 $\frac{D P}{P E}+\frac{A P}{P C}=$

A $L-C-R$ series circuit is connected to a source of alternating current. At resonance, the applied voltage and the current flowing through the circuit will have a phase difference of

The shortest wavelength in Lyman series is $912 \mathop {\rm{A}}\limits^{\rm{o}}$. Then, the longest wavelength in the series must be

Half-life of radioactive sample is 24 h . If a newly prepared radioactive sample shows 4 times the allowed and safe value of radio activity, the minimum time after which one can work safely with the source is

Two blocks of equal masses are connected with a massless spring of spring constant $2500 \mathrm{~N} / \mathrm{m}^2$ and length 10 cm at rest on the frictionless horizontal plane. If a constant horizontal force 10 N is applied as shown in t...

Consider a particle is moving with a minimum speed $v$ at highest point of vertical circle of radius $R$. If the radius of the circle doubled the corresponding minimum speed will be

Assume proton is rotating along a circular path of radius 1 m under a centrifugal force of $4 \times 10^{-12} \mathrm{~N}$. If the mass of proton is $1.6 \times 10^{-27} \mathrm{~kg}$, then its angular velocity of rotation is

The function of a detector is to demodulate the modulated carrier wave and the steps for this process are

The resistance of a wire is $20 \Omega$. It is stretched, so that the length becomes three times, then the new resistance of the wire will be

In a meter bridge the resistances $R$ and $S$ are such that the null point is found at a distance of 40 cm from one end. If a resistance of $10 \Omega$ is connected in parallel with shunt $S$, then the null point occurs at 90 cm from the sa...

A radiation of energy $E$ falls on a perfectly reflecting surface. The momentum transferred to the surface is (let $c \equiv$ speed of light)

According to the photoelectric effect, the plot of kinetic energy of the emitted photo-electrons from a metal versus the frequency of the incident radiation gives a straight line whose slope

If the bulk modulus of water is $2 \times 10^9 \mathrm{Nm}^{-2}$, then the required pressure to reduce the given volume of water by $2 \%$ is

Two concentric circular coils, one of small radius $r$ and the other of large radius $R$ are placed co-axially with centres coinciding. If the radius $r$ is changed by $2 \%$, then the change in mutual inductance of the arrangement is (assu...

Choose the correct statement.

Choose the incorrect statement.

In a regular polygon of 10 sides, each corner is at a distance $R$ from the centre. Identical charges are placed at 9 corners. At the centre, the magnitude of electric field is $E$ and the potential is $V$. The ratio $\frac{V}{E}$ is

If the escape velocity on earth is $11.2 \mathrm{~km} / \mathrm{s}$, its value for a planet having double the radius and 8 time the mass of earth is

Assertion A thermos bottle consists of a double walled glass vessel with the space between the two walls evacuated, so that the heat transfer between the contents of the bottle and outside is minimised.
Reason The vacuum between the two wal...

How much heat energy is supplied when 5 kg of water at $20^{\circ} \mathrm{C}$ is brought to its boiling point? (Assume, specific heat of water $=4.2 \mathrm{~J} / \mathrm{g}^{\circ} \mathrm{C}$ )

What is the name of ideal-gas process in which no heat is transferred?

Mean free path of molecules in a polyatomic gas is independent of

A block rests on a fixed wedge inclined at an angle $\theta$. The coefficient of friction between the block and plane is $\mu$. The maximum value of $\theta$ for the block to remain motionless on the
wedge is

A block of mass 4 kg at rest on a rough inclined plane making an angle of $\theta$ with the horizontal. The coefficient of static friction between the block and plane is 0.5 and the frictional force on the block is 14.14 N , find the value ...

A short bar magnet placed with its axis at $30^{\circ}$ with an external field of 800 G experiences a torque of 0.016 Nm . The magnetic moment of the bar magnet is

A point moves in the $x y$-plane according to the following equation, $x=a \sin \omega t, y=a(1-\cos \omega t)$, where $a$ and $\omega$ are positive constants. Find the angle between the point's velocity and acceleration vectors.

A ball is projected with a velocity $5 \mathrm{~m} / \mathrm{s}$, so that its horizontal range is twice the greatest height attained. The value of range is

A body moves in a straight line with speed $v_1$ and $v_2$ for distance which are in ratio $1: 2$. Find the average speed.

A particle of mass $m$ and charge $Q$ moving with a speed $v$ in a circular path of radius $R$ has magnetic moment $\mu$. If the mass of the particle is doubled and maintains the same speed while revolving in the same circular path, then th...

Two similar coils which are separated by 2 m having radius of 1 m and number of turns 80 have a common axis. Calculate the strength of magnetic field at a point midway between them on their common axis when a current is 0.2 A .

A thin prism of angle $6^{\circ}$ made of glass of refractive index 1.5 is combined with another prism made of refractive index 1.75 to produce dispersion without deviation. Then, the angle of the second prism is