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Let $\underset{a}{\overset{b}{\int }}f\left(x\right)dx=\underset{a+c}{\overset{b+c}{\int }}f(x-c)dx$.



Then the value of $\underset{0}{\overset{\pi }{\int }}{\sin }^{2010}x{\cos }^{2009}xdx$is

Draw a ray diagram to show the formation of image by a concave mirror for the object beyond its centre of curvature. State three characteristics of the image.

Magnetic susceptibility ${\chi }_m$ for the super conductor is–

A substance of mass m kg requires a power input of P watts to remain in the molten state at its melting point. When the power is turned off, the sample completely solidifies in time t sec. What is the latent heat of fusion of the substance

A point traversed half of the distance with a velocity $v_0$. The remaining part of the distance was covered with velocity $v_1$ for half the time and with velocity $v_2$ for the other half of the time. The mean velocity of the point averaged over the whole time of motion

An ideal gas expands isothermally from a volume $V_1$ to $V_2$ and then compressed to original volume $V_1$ adiabatically. Initial pressure is $P_1$ and final pressure is $P_3$. The total work done is $W$. Then

A battery of emf 10 V
and internal resistance 3 Ω is
connected to a resistor. If the current in the circuit is 0.5 A, what
is the resistance of the resistor? What is the terminal voltage of
the battery when the circuit is closed?

A mosquito net over a 7 ft.$\times$ 4 ft. bed is 3 ft. high. The net has a hole at the corner on the top through which a mosquito enters the net. It flies and sits at the diagonally opposite bottom corner of the net. Taking the hole as the origin, the length of the bed as the X-axis, its width as the Y-axis, and vertically up as the Z-axis, write the components of the displacement vector.

A disk of radius$\frac{a}{4}$ having a uniformly distributed charge $6\text{C}$ is placed in the $x-y$ plane with its centre at $(\frac{-a}{2},0,0)$. A rod of length $a$ carrying a uniformly distributed charge $8\text{C}$ is placed on the $x$-axis from $x=\frac{a}{4}tox=\frac{5a}{4}.$Two point charges $–7\text{C}$ and $3\text{C}$ are placed at $(\frac{a}{4},\frac{-a}{4},0)and(\frac{-3a}{4},\frac{3a}{4},0),$respectively. Consider a cubical surface formed by six surfaces $x=\pm \frac{a}{2},y=\pm \frac{a}{2},z=\pm \frac{a}{2}$. The electric flux through this cubical surface is:

Find the ratio of the weights, as measured by a spring balance, of a 1 kg block of iron and a 1 kg block of wood. Density of iron = 7800 kg $m^{-3}$, density of wood = 800 kg $m^{-}3$ and density of air = 1.293 kg $m^{-3}$.

The electrostatic potential existing in space is given by V= xy +yz +zx. The angle made by electric field at (2,2,2) with positive x axis is alpha.Then value of $cos\alpha$

1. 75

Two blocks 'A' and 'B' each of mass 'm' are placed on a smooth horizontal surface. Two horizontal force F and 2F are applied on both the blocks 'A' and 'B' respectively as shown in figure. The block A does not slide on block B. Then the normal reaction acting between the two blocks is: (Assume no friction between blocks)

Magnifying power of a terrestrial telescope is $40$ in the case of normal adjustment. Find its maximum magnifying power, if focal length of eyepiece is $6.25\text{cm}$.

Figure shows a transparent hemisphere of radius $3.0\text{cm}$ made of a material of refractive index $2.0$. A narrow beam of parallel rays is incident on the hemisphere as shown in the figure. Find the location of the image formed after the refraction at the first surface among the points given in the options.

How we can find antilog( - 18.832 ) using log table

A stone tied to a string of length $L$ is whirled in a vertical circle with the other end of the string at the centre. At a certain instant of time, the stone is at its lowest position and has a speed $u$. The magnitude of the change in its velocity as it reaches a position where the string is horizontal is

A curved road of $50\text{m}$ radius is banked at correct angle for a given maximum speed $vm/s$. If the radius of curvature of the road is changed to $200\text{m}$ keeping the same banking angle, the maximum safe speed on the road is

Find the equivalent capacitance between $\text{A}$ and $\text{B}$ of the circuit shown in the figure.





Given:

$C_1=5\mu \text{F};C_2=20\mu \text{F};C_3=10\mu \text{F};C_4=40\mu \text{F};C_5=30\mu \text{F}$

In a Carnot heat engine, the temperature of source and sink are $500\text{K}$ and $375\text{K}$. If the engine consumes $25\times {10}^5\text{J}$ per cycle, then work done by engine per cycle is

Which of the following is not equal to $1$ in boolean algebra?

The drift current in a p-n junction is $20.0\mu A.$ Estimate the number of electrons crossing a cross section per second in the depletion region.

Two blocks ‘$A$’ and ‘$B$’ of same mass '$m$' connected by a light spring are suspended by a string as shown in figure. Find the acceleration of block ‘$A$’ and ‘$B$’ just after the string is cut.

A coil of resistance $40\Omega$ is connected across a $4.0\text{V}$ battery. If $0.10\text{s}$ after the battery is connected, the current in the coil is $63\text{mA}$. Find the inductance of the coil.



[Use $\ln \left(2.70\right)=1$]

Figure represents a part of the closed circuit. If a current of 2A flows in from A, the potential difference between points A and B, $V_A-V_B$ is: