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The instantaneous values of current and voltage in an ac circuit are $I=100sin\left(314\right)t$ A and $E=200sin(314t+\frac{\pi }{3})V$ respectively. If the resistance is 1W then the reactance of the circuit will be

There is a circle $x^2+y^2=9.$ Two chords are drawn with centres at $(0,1)$ and $(1,1).$ What is the angle between these chords

Find the area of the region bounded by $y^2=9x,x=2,x=4$ and the $x$ axis in the first quadrant.

The capillary action for various liquid-solid pairs is given below.

Match the correct meniscus, angle of contact and what happens to the level of liquid.



$\begin{array}{ccc}& & \\ \text{Meniscus}& \text{Angle of contact}& \text{Level}\\ \text{(A) Concave}& \left(i\right)\theta >{90}^{\circ }& \left(a\right)\text{Fall}\\ \text{(B) Plane}& \left(ii\right)\theta <{90}^{\circ }& \left(b\right)\text{No rise or fall}\\ \text{(C)Convex}& \left(iii\right)\theta ={90}^{\circ }& \left(c\right)\text{Rise}\end{array}$

The electrostatic potential inside a charged spherical ball is given by $V=a{r}^2+b$, where $r$ is the distance from the centre; $a$ and $b$ are constants. Then the charge density inside ball is

Calculate the energy in kilo joule per mole of electronic charge accelerated by a potential of 1 volt

A point charge causes an electric flux of $–1.0\times {10}^{3}N{m}^2/C$ to pass through a spherical Gaussian surface of 10.0 cm radius centred on the charge.
If the radius of the Gaussian surface were doubled, how much flux would pass through the surface?

What is the value of the point charge?

A square column section of size $400mm$ is subjected to a concentrated load of magnitude $400kN$ causing compression in member at an eccentricity of $50mm$ from centroid measured along one of its diagonal. The maximum compressive and tensile stress respectively are:

If the strings are inextensible and pulleys are frictionless, the speed of point $G$ on block $M$ is

Gold has a cubic close packed structure where $Au$ spheres occupying $0.74$ of the total volume. If the density of gold is $20g/cc$, calculate the apparent radius of a gold atom in the solid. $(\text{Mass of Au}=197amu)$

Given: $1amu=1.66\times {10}^{-24}g$

When a boy is pulling a trolley by a handle (the direction of force applied makes an acute angle with the direction of displacement) is there any work? Why or why not?

A Tennis ball is released from a height $h$ and after freely falling on a wooden floor it rebounds and reaches height $\frac{h}{2}.$ The velocity versus height of the ball during its motion may be represented graphically by

(graph are drawn schematically and on not to scale)

A photon and an electron have equal energy E. Then the ratio of wavelength of photon to that of electron is proportional to

If $\left(x\right)=\frac{1}{3}\left(f\right(x+1)+\frac{5}{f(x+2)})andf\left(x\right)>0forallxϵR,then\underset{x\to \infty }{lim}f\left(x\right)is$

1. 1

A ball is thrown vertically up from a tower of height $60\text{m}$ with a speed of $20\text{m/s}$. The $v-t$ curve of the ball is
[Take $g=10{\text{m/s}}^2$]

Two wires of same mass having ratio of lengths $1:2$, density $1:3$ and resistivity $2:1$. These are connected one by one to the same voltage supply. The rate of heat dissipation in the first wire is found to be $10\text{W}$. Find the rate of heat dissipation in the second wire.

A capacitor carrying charge and an inductor (both ideal) are connected across each other such that at initial moment , current in the circuit is zero. If the resulting $\text{LC}$ oscillation has a time period of $T.$ Then after what minimum time from the initial moment will the charge on capacitor be maximum.

Evaluate $\int \sqrt{1+y^2}.2ydy$

A rectangular coil is placed in a uniform magnetic field directed in its plane and parallel to one of its sides. The graph of $\tau vs\theta$ will be:

$(\theta$ is angular displacement of coil$)$

Find the magnetic field at point $P$ due to a straight wire segment $AB$ of length $6\text{cm}$ carrying a current of $5\text{A}$.

There are two force vectors, one of 5 N and other of 12 N at what angle the two vectors be added to get resultant vector of 17 N, 7 N and 13 N respectively

Light is incident normally on face AB of a prism as shown in figure. A liquid of refractive index μ is placed on face AC of the prism. The prism is made of glass of refractive index 3/2 . The limits of 'μ'for which total internal reflection takes place on face AC is

A double convex lens has focal length 25 cm. The radius of curvature of one of the surfaces is double of the other. Find the radii, if the refractive index of the material of the lens is 1.5.

In a closed organ pipe of length $105\text{cm}$, standing waves are set up corresponding to the third overtone. At what minimum distance from the closed end a pressure node is formed?

Obtain
the resonant frequency and Q-factor
of a series LCR circuit
with L =
3.0 H, C =
27 μF, and R =
7.4 Ω. It is desired to improve the sharpness of the resonance
of the circuit by reducing its ‘full width at half maximum’
by a factor of 2. Suggest a suitable way.

What is the acceleration (in ${\text{m/s}}^2)$ of the block of mass $m$ relative to the wedge of mass $M$ for the figure shown? Assume all surfaces to be smooth. Take $g=10{\text{m/s}}^2$.

When two tuning forks $A$ and $B$ are sounded together, the number of beats heard is $\nu$. The frequency of fork $A$ is $f$. If the prong of fork $B$ is loaded with a little wax, the number of beats decreases. The initial frequency of fork $B$ is

Consider the signal shown below:

This signal is passed through an AWGN channel with two sided noise power spectral density of $\frac{N_0}{2}$ and received by a filter matched to $s\left(t\right)$. The maximum signal-to-noise ratio possible at the output of the filter is .

Five capacitors $C_1,C_2,C_3,C_4$ and $C_5$ of capacitance $6\mu \text{F}$, $3\mu \text{F}$, $4\mu \text{F}$, $3\mu \text{F}$ and $6\mu \text{F}$ are charged upto potential difference $5\text{V},4\text{V},4\text{V},4\text{V}$ and $6\text{V}$ respectively. If terminal $\text{a}$ is connected with $\text{f}$, terminal $\text{e}$ is connected with $\text{h}$, terminal $\text{g}$ is connected with $\text{d}$, $\text{b}$ is connected with $\text{c}$ and terminal $\text{bc}$ is connected with $\text{eh}$, then find the charge flows through the branch $\text{bc}$ and $\text{eh}$?

If the absorptive power is $0.3$ then for zero transmissivity, the reflective power is -

Two rings of the same radius amd mass are olaced such that their centers are at a common point and their planes are perpendicular to each other. The moment of inertia of the system about an acis passing theough the center amd perpendicular to the olane of one the rings is ( mass of the ring = m, radius =r)

a) 1/2mr²

b) mr^{​​​​​2}

c) 3/2 mr^{​​​​​2}

d) 2mr²

Starting from rest, an observer moves with a constant acceleration a towards a stationary source emitting a sound of frequency $v_0$. Which of the graphs shown in Fig. correctly represents the variation of the apparent frequency v of sound as heard by the observer with time t?

A rain drop of mass $1\text{g}$ falling from a height of $1\text{km}$ hits the ground with a speed of $50\text{m/s}$. If a resistive force acts on the drop, then the work done by the resistive force is (Take $g:10{\text{m/s}}^2)$

If the voltage across a bulb rated $220V-100W$ drops by $2.5\%$ of its rated value, the percentage of the rated value by which the power would decrease is

A particle is placed at the origin. It starts from rest at $t=0$ and undergoes an acceleration $a$ as shown in the figure. Which of the following options correctly represent velocity $v$ vs. time $t$ and displacement $x$ vs. time $t$ plots?