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1. 9.42

1. 284.24

If $f:R\to R$ be an odd function and $f\left(e^x\right)=e^{f\left(x\right)}$ for all $x\in R,$ then

A particle is projected at an angle of ${60}^{\circ }$ above the horizontal with a speed of $10m/s$. After some time, the direction of its velocity makes an angle of ${30}^{\circ }$ above the horizontal. The speed of the particle at this instant is

A particle is moving in a circular path of radius $a$ with constant speed under the action of an attractive conservative force. Potential energy of the particle is given by the relation $U=\frac{K}{2r^2}$, where $r$ is the radial distance of the particle from the centre of the circular path. Its total energy will be:

Four large identical metal plates are placed as shown in the figure. Plate $2$ is given a charge $Q$. All other plates are neutral. Now Plate $1$ and $4$ are earthed. Area of each plates is $A$. The charge appearing on the right side of plate $3$ is

A body falls freely from rest. It covers as much distance in the last second of its motion as covered in the first three seconds. The body has fallen for a time;

For a satellite escape velocity is $11km/s$. If the satellite is launched at an angle of ${60}^o$ with the vertical then the new escape velocity will be

why does light defy the laws of thermodynamics?

it moves on for ever, it dose infinite work without a constant energy supply. why?

A rectangular film of liquid is extended from $(2\text{cm}\times 8\text{cm})$ to $(4\text{cm}\times 16\text{cm})$. If work done is $5\times {10}^{-4}\text{J}$, value of the surface tension of the liquid is

The given four terminal network is part of a larger circuit. The points $A,B,C$ are at the same potential. The potential difference between any one of $A,B$ or $C$ and $D$ is $40\text{V}$. The potential difference between $A$ and $O$ is

If $\overrightarrow{A}$ = 2 $\hat{i}$ + 3$\hat{j}$ - $\hat{k}$ and $\overrightarrow{B}$ = -$\hat{i}$ + 3$\hat{j}$ + 4$\hat{k}$ then find the projection of

$\overrightarrow{A}$ on $\overrightarrow{B}$

1. 159.15

If the shortest distance between the lines $\overrightarrow{r}=(\hat{i}+2\hat{j}+3\hat{k})+\lambda (\hat{i}-3\hat{j}+2\hat{k})$ and $\overrightarrow{r}=(4\hat{i}+5\hat{j}+6\hat{k})+\mu (2\hat{i}+3\hat{j}+\hat{k})$ is $d,$ then which of the following is/are correct ?

(where $[.]$ denotes $G.I.F.$)

A beaker of circular cross section of radius 4 cm is filled with mercury up to a height of 10 cm. find the force exerted by the mercury on the bottom of the beaker. The atmospheric pressure = ${10}^{5}N{m}^{-2}$. Density of mercury = $13600kg{m}^{-3}$. Take $g=10m{s}^{-2}$.

A planet of mass $m$ moves along an ellipse around the sun of mass $M$ so that its maximum and minimum distances from sun are $a$ and $b$ respectively. The angular momentum $L$ of this planet about the centre of sun will be:

(Assume, sun is stationary and $a=2b)$

All plates are of same area (A). Find effective capacitance between A & B

Find the inductance $\ell$ of a solenoid of length whose winding are made of material of density D and resistivity $\rho$.The winding resistance is R:

Two particles A & B are projected with same speed so that the ratio of their maximum height reached is 3:1. If the speed of A is doubled without altering other parameters, the ratio of their horizontal ranges is

Two white dots are $1\text{mm}$ apart on a black paper. They are viewed by eye of pupil diameter $3\text{mm}$. What is the maximum distance from the black paper at which these dots can be resolved by the eye? $(\lambda =500\text{nm}$)

x- coordinate is negative and y-coordinate is positive in ______.

A source emitting sound of frequency 180 Hz is placed in front of a wall at a distance of 2 m from it. A detector is also placed in front of the wall at the same distance from it. Find the minimum distance between the source and the detector for which the detector detects a maximum of sound. Speed of sound in air = 360 $m{s}^{-1}$

Centre of mass of three particles of masses $1\text{kg},2\text{kg}$ and $3\text{kg}$ lies at the point $(1,2,3)$ and centre of mass of another system of particles $3\text{kg}$ and $2\text{kg}$ lies at the point $(-1,3,-2)$. Where should we put a particle of mass $5\text{kg}$ so that the centre of mass of entire system lies at the centre of mass of $1^{st}$ system?

When a force is applied on a wire of uniform cross-sectional area $3\times {10}^{-6}{m}^2$and length $4m$, the increase in length is $1mm$. Energy stored in it will be

$(Y=2\times {10}^{11}N{m}^{-2})$

(a)Three resistors 1 Ω,2 Ω, and 3 Ω are combined in series. What is the total resistance of the combination?

(b) If the combination is connected to a battery of emf 12V and negligible internal resistance, obtain the potential drop across each resistor.

The resultant of two vectors $\overrightarrow{P}$ and $\overrightarrow{Q}$ is $\overrightarrow{R}$. If magnitude of $\overrightarrow{Q}$ is doubled, the new resultant is perpendicular to $\overrightarrow{P}.$ Then $|\overrightarrow{R}|$ equals

Mr. Sharma goes for jogging every morning in a circular park whose circumference is $1\text{km}$. He makes $3$ complete circles in $50\text{minutes}$. Find his average velocity.

Shown below is a semi-infinite wire carrying current I. What will be magnetic field at point P, which is d units away from one of its end?