A mixture of carbon dioxide and oxygen has volume \(8310\) cm\(^3\), temperature \(300\) K, pressure \(100\) kPa and mass \(13.2\) g. The number of moles of carbon dioxide and oxygen gases in the mixture respectively are _______.
(Assume both carbon dioxide and oxygen gases behave like ideal gases) \([R = 8.31\) J/mol.K\(]\)

A particle is projected with velocity \(u\) so that its horizontal range is three times the maximum height attained by it. The horizontal range of the projectile is given as \(\frac{n u^2}{25 g}\), where value of \(n\) is : (Given ' \(g\) ' is the acceleration due to gravity).

A spaceship in space sweeps stationary interplanetary dust. As a result, its mass increases at a rate \(\frac{ dM ( t )}{ dt }= bv ^{2}( t ),\) where \(v ( t )\) is its instantaneous velocity. The instantaneous acceleration of the satellite is

List\(-I\)	List\(-II\)
\(UV\) rays	\((i)\) Diagnostic tool in medicine
\(X-\) rays	\((ii)\) Water purification
Microwave	\((iii)\) Communication, Radar
Infrared wave	\((iv)\) Improving visibility in foggy days

Choose the correct answer from the options given below.

An object of mass \(0.2 \mathrm{~kg}\) executes simple harmonic motion along \(\mathrm{x}\) axis with frequency of \(\left(\frac{25}{\pi}\right) \mathrm{Hz}\). At the position \(\mathrm{x}=0.04 \mathrm{~m}\) the object has kinetic energy \(0.5 \mathrm{~J}\) and potential energy \(0.4 \mathrm{~J}\) The amplitude of oscillation is _______ cm.

A perfectly dimagnetic sphere has a small spherical cavity at its centre, which is filled with a paramagnetic substance. The whole system is placed in a uniform magnetic field \(\overrightarrow{ B }\). Then the field inside the paramagnetic substance is:

The box of a pin hole camera, of length \(L\), has a hole of radius \(a\). It is assumed that when the hole is illuminated by a parallel beam of light of wavelength \(\lambda\), the spread of the spot (obtained on the opposite wall of the camera) is the sum of its geometrical spread and the spread due to diffraction. The spot would then have its minimum size ( say \(b_{min}\)) when

The mass of a hydrogen molecule is \(3.32 \times 10^{-27 } \) \(kg\). If \(10^{23}\) hydrogen molecules strike, per second, a fixed wall of area \(2\) \(cm^2\) at an angle of \(45^o \) to the normal, and rebound elastically with a speed of \(10^3\ m/s\), then the pressure on the wall is nearly:

The sum \(\dfrac{1^3}{1} + \dfrac{1^3 + 2^3}{1 + 3} + \dfrac{1^3 + 2^3 + 3^3}{1 + 3 + 5} + \cdots\) up to 8 terms, is:

A block of mass \(m =1\, kg\) slides with velocity \(v=6\, m / s\) on a frictionless horizontal surface and collides with a uniform vertical rod and sticks to it as shown. The rod is pivoted about \(O\) and swings as a result of the collision making angle \(\theta\) before momentarily coming to rest. If the rod has mass \(M =2 \,kg \) and length \(l=1\, m\) the value of \(\theta\) is approximately (Take \(\left.g=10 \,m / s ^{2}\right)\)

A player kicks a football with an initial speed of \(25\, {ms}^{-1}\) at an angle of \(45^{\circ}\) from the ground. What are the maximum height and the time taken by the football to reach at the highest point during motion ? (Take g \(=10 \,{ms}^{-2}\) )

In photoelectric effect, the stopping potential \(\left(\mathrm{V}_0\right) \mathrm{v} / \mathrm{s}\) frequency \((\nu)\) curve is plotted.
( h is the Planck's constant and \(\phi_0\) is work function of metal )
(A) \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) is linear.
(B) The slope of \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) curve \(=\frac{\phi_0}{\mathrm{~h}}\)
(C) h constant is related to the slope of \(\mathrm{V}_0 \mathrm{v} / \mathrm{s} \nu\) line.
(D) The value of electric charge of electron is not required to determine \(h\) using the \(V_0 \mathrm{v} / \mathrm{s} \nu\) curve.
(E) The work function can be estimated without knowing the value of \(h\).
Choose the correct answer from the options given below :

If the system of linear equations \(x + ky + 3z = 0;3x + ky - 2z = 0\) ; \(2x + 4y - 3z = 0\)  has a non-zero solution \(\left( {x,y,z} \right)\) then \(\frac{{xz}}{{{y^2}}} = \). . . . .