Two stones are thrown up simultaneously from the edge of a cliff $$240$$ $$m$$ high with initial speed of $$10$$ $$m/s$$ and $$40$$ $$m/s$$ respectively. Which of the following graph best represents the time variation of relative position of the second stone with respect to the first ? (Assume stones do not rebound after hitting the ground and neglect air resistance, take $$g=10m/s^2$$) (The figures are schematic and not drawn to scale)

Match List - $$\mathrm{I}$$ (Fundamental Experiment) with List - $$\mathrm{II}$$ (its conclusion) and select the correct option from the choices given below the list:

From a solid sphere of mass $$M$$ and radius $$R,$$ a spherical portion of radius $$R/2$$ is removed, as shown in the figure. Taking gravitational potential $$V=0$$ at $$r=\infty ,$$ the potential at the center of the cavity thus formed is: ($$G=gravitational$$ $$constant$$)

On a hot summer night, the refractive index of air is smallest near the ground and increases with height from the ground. When a light beam is directed horizontally, the Huygens' principle leads us to conclude that as it travels, the light beam :

Assuming human pupil to have a radius of $$0.25$$ $$cm$$ and a comfortable viewing distance of $$25$$ $$cm$$, the minimum separation between two objects that human eye can resolve at $$500$$ $$nm$$ wavelength is :

In the given circuit, charges $$Q_2$$ on the $$2\mu F$$ capacitor changes as $$C$$ is varied from $$1\mu F$$ to $$3\mu F.$$ $$Q_2$$ as a function of $${}^{\prime }{C}^{\prime }$$ is given properly by: $$\left(figuresaredrawnschematicallyandarenottoscale\right)$$

A train is moving on a straight track with speed $$20m{s}^{-1}.$$ It is blowing its whistle at the frequency of $$1000$$ $$Hz$$. The percentage change in the frequency heard by a person standing near the track as the train passes him is (speed of sound $$=320m{s}^{-1}$$) close to :

Two long current carrying thin wires, both with current $$I,$$ are held by insulating threads of length $$L$$ and are in equilibrium as shown in the figure, with threads making an angle $${}^{\prime }{\theta }^{\prime }$$ with the vertical. If wires have mass $$\lambda$$ per unit-length then the value of $$I$$ is : ($$g=$$ $$gravitational$$ $$acceleration$$ )

A rectangular loop of sides $$10$$ $$cm$$ and $$5$$ $$cm$$ carrying a current $$1$$ of $$12A$$ is placed in different orientations as shown in the figures below : If there is a uniform magnetic field of $$0.3$$ $$T$$ in the positive $$z$$ direction, in which orientations the loop would be in $$(i)$$ stable equilibrium and $$(ii)$$ unstable equilibrium ?

Given in the figure are two blocks $$A$$ and $$B$$ of weight 20 N and 100 N, respectively. These are being pressed against a wall by a force $$F$$ as shown. If the coefficient of friction between the blocks is 0.1 and between block $$B$$ and the wall is 0.15, the frictional force applied by the wall on block $$B$$ is :

Two coaxial solenoids of different radius carry current $$I$$ in the same direction. $$\overrightarrow{F_1}$$ be the magnetic force on the inner solenoid due to the outer one and $$\overrightarrow{F_2}$$ be the magnetic force on the outer solenoid due to the inner one. Then :

From a solid sphere of mass $$M$$ and radius $$R$$ a cube of maximum possible volume is cut. Moment of inertia of cube about an axis passing through its center and perpendicular to one of its face is:

The number of geometric isomers that can exist for square planar [Pt (Cl) (py) (NH3) (NH2OH)]+ is (py = pyridine) :

Which of the following compounds is not colored yellow?

Which of the following is the energy of a possible excited state of hydrogen?

The ionic radii (in Å) of N3–, O2– and F– are respectively:

From the following statements regarding H2O2, choose the incorrect statement :

Sodium metal crystallizes in a body centred cubic lattice with a unit cell edge of 4.29 Å . The radius of sodium atom is approximately :

The synthesis of alkyl fluorides is best accomplished by:

Higher order (>3) reactions are rare due to