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For the four bar mechanism shown in figure, the transmission angle for the given position is

A sound wave of frequency $10\text{kHz}$ is travelling in air with speed of $340\text{m/s}$. Find the minimum separation between two points in the medium where the phase difference is $2\pi$.

Given that $0.2\hat{i}+0.6\hat{j}+a\hat{k}$ is a unit vector. What is the value of a?

Fluid can rise upto height H in a capillary tube above level. Now if we dip capillary tube such that its height above fluid level is H/2, then which of the following figures shows correct behaviour of fluid?

A rotameter with a heavy float of density ${\rho }_f$ is used for mesuring gas flow is calibrated with a gas of density $\left(\rho \right)1.5kg/m^3$. If it measures the flow rate of a different gas having density of $2kg/m^3$ and indicates a flow rate of $10m^3/min$. The actual flow rate is ________ $m^3/min.$ $\text{(Assume}{\rho }_f>>\rho )$

The correct value of dip angle at a place is ${45}^{\circ }$. If the dip circle is rotated by ${45}^{\circ }$ out of the meridian, then the tangent of the angle of apparent dip at the place is

Find $\frac{dy}{dx}$ if $y=e^{x}sinx$

If height of mercury in a barometer is $760\text{mm}$ at any location. If mercury is replaced by water then height of water will be

What is the lenght of side C.

Calculate the number of photons emitted by a 100W yellow lamp in 1 s. Take the wavelength of yellow light as 560nm and assume 100 percent efficiency.

Work of $3.0\times {10}^{-4}$ joule is required to be done in increasing the size of a soap film from $10cm\times 6cm$ to $10cm\times 11cm$. The surface tension of the film is

Match the following.

$$\begin{array}{cccc}& \text{Column 1}& & \text{Column 2}\\ A& \text{Compressible fluid}& i& \text{Internal friction between adjacent layers is absent}\\ B& \text{Incompressible fluid}& ii& \text{Has variable density}\\ C& \text{Viscous fluid}& iii& \text{Internal friction between adjacent layers is present}\\ D& \text{Non-viscous fluid}& iv& \text{Has constant density}\end{array}$$

(a) Six lead-acid type of secondary cells each of emf 2.0 V
and internal resistance 0.015 Ω are
joined in series to provide a supply to a resistance of 8.5 Ω.
What are the current drawn from the supply and its terminal voltage?

(b) A secondary cell after long use has an emf of 1.9 V and a
large internal resistance of 380 Ω.
What maximum current can be drawn from the cell? Could the cell drive
the starting motor of a car?

For a function, $f\left(x\right)$ satisfying the following conditions

$1\left)f\right(0)=6,f(2)=16$

$2)f$ has a minimum value at $x=-4$

$3)$ For all $x,$

$f^{\prime }\left(x\right)=\left|\begin{array}{ccc}2ax& 4ax-1& 3ax-b+3\\ b& 2b+1& 2ax+1\\ 2b-2ax& 4b-4ax+3& b+ax\end{array}\right|,$



the values of $a$ and $b$ are

An angular magnification of $30\text{X}$ is desired using an eye piece of focal length $5\text{cm}$ and an objective lens. Find the magnifying power of objective lens. [Given angular magnification is achieved in case of normal adjustment]

The spring block system as shown in figure is in equilibrium. The string connecting blocks $A$ and $B$ is cut. The mass of all the three blocks is $m$ and spring constant of both the spring is $k$. The amplitude of resulting oscillation of block $A$ is

Electric potential at axial point P due to uniformly charged ring of radius R and charge Q is



त्रिज्या R तथा आवेश Q की एकसमान रूप से आवेशित वलय के कारण अक्षीय बिन्दु R पर विद्युत विभव है

A truck of mass $2\times {10}^3\text{kg}$ is coming towards a wall with a speed of $5\text{m/s}$. It collides with the wall and remain in its contact for $0.02\text{s}$. After collision, it travels in opposite direction, with a speed of $3\text{m/s}$. What force (assuming it to be constant), the wall must have exerted on the truck?

A point object is placed at a distance of $25\text{cm}$ from a convex lens of focal length $20\text{cm}$. If a glass slab of thickness $t$ and refractive index $1.5$ is inserted between the lens and the object, the image is formed at infinity. The thickness $t$ is

A laser beam has intensity $2.5\times {10}^{14}$${\text{Wm}}^{-2}$. The amplitudes of electric and magnetic fields in the beam are :

The deflection in a moving coil galvanometer falls from $50$ divisions to $10$ division , when a shunt of $12\Omega$ is applied, The resistance of the galvanometer is

An aeroplane moves $400\text{m}$ towards north, $300\text{m}$ towards west and then $1200\text{m}$ vertically upward, then its displacement from the initial position is

The voltage across a parallel plate capacitor of capacitance $127\mu \text{F}$ is increased from $3.887\text{V}$ to $4.887\text{V}$. The extra charge that flows through the battery is

A narrow
sound pulse (for example, a short pip by a whistle) is sent across a
medium. (a) Does the pulse have a definite (i) frequency, (ii)
wavelength, (iii) speed of propagation? (b) If the pulse rate is 1
after every 20 s, (that is the whistle is blown for a split of second
after every 20 s), is the frequency of the note produced by the
whistle equal to
or
0.05 Hz?

A particle is in a linear SHM. If the acceleration and the velocity of this particle are $a$ and $v$ respectively, then the graph relating to these values is

The vibrations of a string of length $20\text{cm}$ fixed at both ends are represented by the equation $y=2\sin \left(\frac{\pi x}{5}\right)\cos \left(12\pi t\right)$, where $x$ and $y$ are in $\text{cm}$ and $t$ in $\text{sec}$. How many nodes are located along the string?