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Twelve wires, each having equal resistance of 2 $\Omega$, are joined to form a cube. Equivalent resistance between the ends of a face diagonal is.

A particle is moving in a straight line with initial velocity u and uniform acceleration a . If the sum of distances travelled in Tth and (T + 1)th second is 100 cm then its velocity after t seconds in cm/s is ?

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A boat moves relative to water with a velocity $u$ and river is flowing with $2u$. At what angle with the stream should the boat move to have minimum drift ?

Two thin convex lenses of focal lengths 20cm and 5cm respectively are placed at a distance s. If a parallel beam incident in the first lens emerges as a parallel beam from the second lens then the value of d is

From below figure shows a small block of mass m which is started with a speed v on the horizontal part of the bigger block of mass M placed on a horizontal floor.The curved part of the surface shown is semicircular.All the surfaces are friction less. Find the speed of the bigger block when the smaller block reaches the point A of the surface.

A rabbit runs across a parking lot on which a set of coordinate axes has, strangely enough, been drawn.

The coordinates (meters) of the rabbit's position as function of time t(seconds) are given by



$x\left(t\right)=-\frac{t^2}{2}+5t+20$

And $y\left(t\right)=t^2-10t+30$

Find the velocity at time t = 15s.

A long straight rod $\text{AB}$ of length $2\text{m}$ moves in a uniform magnetic field of magnitude $B=0.5\text{T}$ with a velocity of $10{\text{ms}}^{-1}$ as shown in the figure. Find the emf induced in the rod.

The horizontal range of projectile fired at ${75}^{\circ }$ is $R$. If it is fired with same speed at ${45}^{\circ }$, what would be its range?

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The compressiblity factor for nitrogen at $330\text{K}$ and $800\text{atm}$ is $1.90$ and at $570\text{K}$ and $200\text{atm}$ is $1.10$. A certain mass of $N_2$ occupies a volume of $1{\text{dm}}^3$ at $330\text{K}$ and $800\text{atm}$. Calculate volume occupied by same quantity of $N_2$ gas at $570\text{K}$ and $200\text{atm}$:

A neutron mass $1.67\times {10}^{-27}kg$ moving with a velocity $1.2\times {10}^{7}m{s}^{-1}$ collides head-on with a deuteron of mass $3.34\times {10}^{-27}kg$ initially at rest. If the collision is perfectly inelastic, the speed of the composite particle will be

The bar ABC fixed at both ends consists of a solid circular portion AB and hollow circular portion BC as shown in figure. The ratio $\left(\frac{a}{L}\right)$ for which reactive torque at A and C are of equal magnitude is

The rear side of a truck is open and a box of mass $20\text{kg}$ is placed on the truck $4\text{m}$ away from the open end, $\mu =0.15$ and $g=10{\text{m/sec}}^2$. The truck starts from rest with an acceleration of $2{\text{m/sec}}^2$ on a straight road. The distance moved by the truck when box starts fall down.

Let $f:[0,\infty )\to R$ be a continuous and strictly increasing function such that $f^3\left(x\right)={\int }_0^{x}t.f^2\left(t\right)dt,\forall x>0$ The area enclosed by y=f(x) , the x-axis and the ordinate at x=3, is

The capacitors shown in the figure are in steady state. If at $t=0$ switch $S$ is closed, then find the heat generated in the circuit.

The fundamental frequency of a closed organ pipe is equal to the first overtone frequency of an open organ pipe. If the length of open organ pipe is $80\text{cm}$ then the length of the closed organ pipe will be

A mutual inductor consists of two coils X and Y as shown in fig. In which one-quarter of the magnetic flux produced by X links with Y, giving a mutual inductance M. What will be the mutual inductance when Y is used as the primary?

Find $\overrightarrow{A}\times \overrightarrow{B}$, if $\overrightarrow{A}=\hat{i}+4\hat{k}\text{and}\overrightarrow{B}=-\hat{j}$?

At time $t=0$, $N_1$ nuclei of decay constant ${\lambda }_1$ and $N_2$ nuclei of decay constant ${\lambda }_2$ are mixed. The decay rate of the mixture is :

The three concentric conducting spherical shells of radii $R,2R$ and $3R$ carry charges $Q,-2Q$ and $3Q$ respectively. The total electrostatic energy stored in the system

Unpolarized light of intensity $32\frac{W}{m^2}$ passes through three polarizers such that the transmission axis of the last polarizer is crossed with that of the first. The intensity of final emerging light is $3\frac{W}{m^2}$ . The angle between the first two transmission axes of the polarizers is:

A telescope $T$, has objective of diameter $100\text{inch}$ and the wavelength of light used for this telescope is $5000A^{\circ }$. Another telescope $T_2$ has objective of diameter $50\text{inch}$ and the wavelength of light used for this telescope is $6000A^{\circ }$. If $P_1,P_2$ represents the resolving powers of $T_1$ and $T_2$ respectively whereas $\Delta {\theta }_1,\Delta {\theta }_2$ represents the limit of resolutions of $T_1$ and $T_2$ respectively, then choose the correct option (s).

At $t=0$, a particle starts from $(-1,0)$ and moves towards positive $x-$axis with speed of $v=3t^2+2t\text{m/s}$. The final position of the particle and the distance travelled by the particle respectively, as a function of time are

A convex lens forms a real image three times larger than the object on a screen. Object and screen are moved until the image formed becomes twice the size of the object. If the shift of the object is $6\text{cm}$ then find the distance by which screen is shifted.

What could be the maximum value for gravitational potential energy?

Pranathi is excited because her grandfather is going to teach her how to make pralines. There is a proportional relationship between the amount of pecans used (y) and the cups of pralines made (x).



Which one of these following equations gives the correct relationship between x and y?

Water flows through a vertical tube of variable cross section. The area of cross - section at $A$ and $B$ are $6{\text{mm}}^2$ and $3{\text{mm}}^2$ respectively. If $12{\text{cm}}^3$ of water enters per second through $A$, find the pressure difference $|P_A-P_B|$. The separation between the cross-section at $A$ and $B$ is $100\text{cm}$. (Take density of water as $1000{\text{kg/m}}^3$ and $g=10{\text{m/s}}^2$)

A particle of mass ${10}^{-2}\text{kg}$ is moving along the positive $\text{x-axis}$ under the influence of a force $F\left(x\right)=-\frac{K}{2x^2}$ where $K={10}^{-2}{\text{Nm}}^2$. At time $t=0$, particle is at $x=1\text{m}$ and its velocity is $v=0$. The time at which it reaches $x=0.25\text{m}$ is

In the diagram shown, the separation between the slit is equal to $3\lambda$, where $\lambda$ is the wavelength of the light incident on the plane of the slits. A thin film of thickness $3\lambda$ & refractive index $2$ has been placed in the front of the upper slit. The distance of the central maxima on the screen from $O$ is-