TS EAMCET 2020 (Online) 10th September Morning Shift

If the mean of the discrete distribution $8,9,6,5, x, 4$, 6, 5 is 6 , then its standard deviation (nearest to two decimal places) is

When the origin is shifted to the point $\left(\frac{3}{2}, \frac{3}{2}\right)$ by the translation of coordinate axes, then the transformed equation of $32 x^2+8 x y+32 y^2-108 x-108 y+99=0$ is

Angles made with the $X$-axis by the two lines passing through the point $P(1,2)$ and cutting the line $x+y=4$ at a distance $\frac{\sqrt{6}}{3}$ units from the point $P$ are

The straight lines $x+3 y-9=0,4 x+5 y-1=0$, $p x+q y+10=0$ are concurrent, if the line $5 x+6 y+10=0$ passes through the point

The centroid of the triangle formed by the lines $x+y=1$ and $2 y^2-x y-6 x^2=0$ is

A line $L_1$ passing through $A(3,4)$ and having slope 1 cuts another line $L_2$ passing through $C$ at $B$, such that $A B=A C$. If the equation of line $B C$ is $2 x-y+4=0$, then the equation of $A C$ is

The straight lines $x+3 y-9=0,4 x+5 y-1=0$, $p x+q y+10=0$ are concurrent, if the line $5 x+6 y+10=0$ passes through the point

If $M$ is the foot of the perpendicular drawn from the origin $O$ on to the variable line $L$, passing through a fixed point $(a, b)$, then the locus of the mid-point of $O M$ is

The position vector of a point $P$ is $2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}$ and $\mathbf{a}=-\hat{\mathbf{i}}-2 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ are two vectors which dete...

The shortest distance between the line $\mathbf{r}=2 \hat{\mathbf{i}}-2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}}+\lambda(\hat{\mathbf{i}}-\hat{\mathbf{j}}+4 \hat{\mathbf{k}})$ and the plane $\mathbf{r} \cdot(\hat{\mathbf{i}}+5 \hat{\mathbf{j}}+\...

The direction cosines $l, m, n$ of two lines are satisfying $3 l+m+5 n=0$ and $6 m n-2 n l+5 l m=0$. If $\theta$ is the angle between those lines then $|\cos \theta|=$

A tetrahedron has vertices $O(0,0,0), A(1,2,1)$, $B(2,1,3), C(-1,1,2)$. If $\theta$ is the angle between the faces $O A B$ and $A B C$, then $\cos \theta=$

If the points $A(-1,0,7), B(3,2, t), C(5, k,-2)$ are collinear, then the ratio in which the point $P(t, k-2 t, t+k)$ divides the line segment $B C$ is

The solution set of the trigonometric equation $\tan \theta+5 \cot \theta=\sec \theta$ is

$$ \begin{aligned} \sin ^4 \frac{\pi}{8}+\cos ^4 \frac{3 \pi}{8}-\sin ^4 \frac{3 \pi}{8} & +\sin ^4 \frac{5 \pi}{8} +\cos ^4 \frac{7 \pi}{8}-\sin ^4 \frac{7 \pi}{8}= \end{aligned} $$

Assertion (A) If $A=15^{\circ}, B=17^{\circ}$ and $C=13^{\circ}$, then $\cot 2 A+\cot 2 B+\cot 2 C=\cot 2 A \cot 2 B \cot 2 C$
Reason (R) In a $\triangle P Q R$,
$$ \tan \frac{P}{2} \tan \frac{Q}{2}+\tan \frac{Q}{2} \tan \frac{R}{2}+\tan \f...

$\mathbf{p}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{q}=\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$. If the vectors $\mathbf{a}$ and $\mathbf{b}$ are the orthogonal projections of $\mathbf{p}$ on $\mathbf{q}$ ...

Let $\mathbf{a}=2 \hat{\mathbf{i}}-3 \hat{\mathbf{j}}+4 \hat{\mathbf{k}}, \mathbf{b}=7 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-3 \hat{\mathbf{k}}, \mathbf{c}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$. The vector $\mathbf{x}$ such that...

In a quadrilateral $A B C D$, the point $P$ divides $D C$ in the ratio $1: 3$ internally and $Q$ is the mid-point of $A C$. If $\mathbf{A B}+\mathbf{A D}+\mathbf{B C}-2 \mathbf{D C}=\lambda \mathbf{P Q}$, then the value of $\lambda$ is

Let $\mathbf{O A}=\mathbf{a}, \mathbf{O B}=\mathbf{b}$ be two non collinear vectors,
$\mathbf{O P}=x_1 \mathbf{a}+y_1 \mathbf{b}, \mathbf{O Q}=x_2 \mathbf{a}+y_2 \mathbf{b}$ and $\mathbf{A}^{\prime} \mathbf{O}=\mathbf{O A}$,
$\mathbf{B}^{\p...

The nuclear forces are

The ratio of maximum to minimum wavelength in Balmer series of an hydrogenic atom is

Alpha rays emitted from a radioactive substance are

Assume each oil drop consists of a capacitance of $C$. If combine $n$ drops to form a bigger drop, then the capacitance of bigger drop $C^{\prime}$ would be

In $C R$-circuit the growth of charge on the capacitor is

A circular hole of radius 3 cm is cut out from a uniform circular disc of radius 6 cm . The centre of the hole is at 3 cm , from the centre of the original disc. The distance of centre of gravity of the resulting flat body from the centre o...

A bullet of mass 25 g moves horizontally at a speed of $250 \mathrm{~m} / \mathrm{s}$ is fired into a wooden block of mass 1 kg suspended by a long string. The bullet crosses the block and emerges on the other side. If the centre of the mas...

If a body moving in a circular path maintains constant speed of $10 \mathrm{~ms}^{-1}$, then which of the following correctly describes the relation between acceleration (a) and radius $(r)$ ?

A message signal of frequency 10 kHz and peak voltage of 15 V is used to modulate a carrier frequency of 1 MHz and peak voltage of 30 V . Determine the modulation index.

A conductor of length 100 cm and area of cross-section $1 \mathrm{~mm}^2$ carries a current of 5 A . If the resistivity of the material of the conductor is $3.0 \times 10^{-8} \Omega-\mathrm{m}$, then the electric field across the conductor...

If the Wheatstone's bridge with four resistors $R_1, R_2$ and $R_3, R_4$ is balanced, then the correct expression is

A moving coil galvanometer of resistance $100 \Omega$ is used as an ammeter using a resistance $0.1 \Omega$. The maximum deflection current in the galvanometer is $100 \mu \mathrm{~A}$. Find the minimum current in the circuit, so that ammet...

Photons of energy 2.4 eV and wavelength $\lambda$ fall on a metal plate and release photoelectrons with a maximum velocity $v$. By decreasing $\lambda$ by $50 \%$, the maximum velocity of photoelectrons becomes $3 v$. The work function of t...

A slab of side 50 cm and thickness 10 cm is subjected to a shearing force of $10^5 \mathrm{~N}$ on its narrow edge. If the lower edge is riveted to the floor and upper edge is displaced by 0.2 mm , then shear modulus of the material of the ...

What is the amplitude of the electric field in a parallel beam of light intensity $\left(\frac{15}{\pi}\right) \frac{\mathrm{W}}{\mathrm{m}^2}$ ?
$$ \left[\text { Assume }, \frac{1}{4 \pi \varepsilon_0}=9 \times 10^9 \frac{\mathrm{Nm}^2}{\m...

If a proton is moved against the coulomb force of an electric field, then

A meniscus drop of radius 1 cm is sprayed into $10^6$ droplets of equal size. Calculate the energy expended if surface tension of mercury is $435 \times 10^{-3} \mathrm{~N} / \mathrm{m}$.

Choose the correct statement.

The specific heat of helium at constant volume is 12.6 J $\mathrm{mol}^{-1} \mathrm{~K}^{-1}$. The specific heat of helium at constant pressure in $\mathrm{J} \mathrm{mol}^{-1} \mathrm{~K}^{-1}$ is approximately (assume, the universal gas c...

Work done on heating one mole of monoatomic gas adiabatically through $20^{\circ} \mathrm{C}$ is $W$. Then, the work done on heating 6 moles of rigid diatomic gas through the same change in temperature

If a gas has $n$ degrees of freedom, then the ratio of $\frac{C_p}{C_V}$ is

A composite slab is prepared with two different materials $A$ and $B$. The relation between their coefficient of thermal conductivity and thickness is given as $K_A=\frac{K_B}{2}$ and $X_A=2 X_B$, respectively. If the temperature of faces o...

When a bullet is fired from a rifle its momentum becomes $20 \mathrm{~kg}-\mathrm{ms}^{-1}$. If the velocity of the bullet is $1000 \mathrm{~ms}^{-1}$, then what is its mass?

A block is between two surfaces as shown in the figure. Find the normal reaction at both surfaces. [Assume, $g=10 \mathrm{~m} / \mathrm{s}^2$ ]

If relative permeability of iron is 5500 , then its susceptibility is

A projectile is launched from point $A$ of the given landscape with a water body as shown in the diagram. The launching angle is $15^{\circ}$. From the following, identify the right initial velocity of the projectile with which it will fall...

A car travelling at $15 \mathrm{~m} / \mathrm{s}$ overtake another car travelling at $10 \mathrm{~m} / \mathrm{s}$. Assuming, each car is 4 m long. What is the time taken during the overtake?

A circular coil of 10 turns and radius 10 cm is placed in a uniform magnetic field of 0.1 T normal to the plane of the coil. If the current in the coil is 5 A , then the magnitude of the torque on the coil is

A 50 cm long solenoid has winding of 400 turns. What current must pass through it to produce a magnetic field of induction $4 \pi \times 10^{-3} \mathrm{~T}$ at the centre?

If the image of an object is at the focal point $f$ to the right side of a convex lens, the position of the object on the left of the lens is at