A carnot engine, whose efficiency is \(40 \%\) takes heat from a source maintained at temperature 600 K . It is desired to have an efficiency \(60 \%\), then the intake temperature for the same exhaust (sink) temperature should be

Moving coil galvanometers \(\mathrm{M}_{1}\) and \(\mathrm{M}_{2}\) have resistance, number of turns, area of coil and magnetic field as follows.
\(\mathrm{R}_{1}=10 \Omega, \mathrm{R}_{2}=14 \Omega, \mathrm{N}_{1}=30, \mathrm{~N}_{2}=42\)
\(\mathrm{A}_{1}=3 \cdot 6 \times 10^{-3} \mathrm{~m}^{2}, \mathrm{~A}_{2}=1 \cdot 8 \times 10^{-2} \mathrm{~m}^{2},\) \(\mathrm{~B}_{1}=0 \cdot 25 \mathrm{~T}, \mathrm{~B}_{2}=0 \cdot 50 \mathrm{~T}\)
(Spring constants are same for both materials)
The ratio of (i) current sensitivity and (ii) voltage sensitivity for galvanometer
\(\left(\mathrm{M}_{2}\right.\) to \(\left.\mathrm{M}_{1}\right)\) is respectively

The resultant $\overrightarrow{R}$ of $\overrightarrow{P}$ and $\overrightarrow{Q}$ is perpendicular to $\overrightarrow{P}.$ Also $\left|\overrightarrow{P}\right|=\left|\overrightarrow{R}\right|.$ The angle between $\overrightarrow{P}$ and $\overrightarrow{Q}$ is $\left[\tan {45}^{\mathrm{o}}=1\right]$

Two circular coils 1 and 2 are made from the same wire but the radius of the first coil is twice that of the second coil. What is the ratio of potential difference applied across them, so that the magnetic field at their centres is same?

A molecule of mass ' \(m\) ' moving with velocity ' \(\mathrm{v}\) ' makes 5 elastic collisions with a wall of container per second. The change in momentum of the wall per second in 5 collisions will be

Let \(\gamma_1\) be the ratio of molar specific heat at constant pressure and molar specific heat at constant volume of a monoatomic gas and \(\gamma_2\) be the similar ratio of diatomic gas. Considering the diatomic gas molecule as a rigid rotator, the ratio \(\frac{\gamma_2}{\gamma_1}\) is

In which layer of the atmosphere, the water vapour is present?

\(\sec 2 \theta-\tan 2 \theta=\)

To induce early flowing in plants, pre-treatment of seeds or seedlings is done at ______________ \(^{\circ} \mathrm{C}\) temperature.

A Carnot engine with efficiency \(50 \%\) takes heat from a source at \(600 \mathrm{~K}\). To increase the efficiency to \(70 \%\), keeping the temperature of the sink same, the new temperature of the source will be

Given below are the list of different hormones.
(a) Prostaglandins\(\quad\)(b) Relaxin
(c) Oxytocin\(\quad\)(d) Aldosterone
(e) ADH\(\quad\)(f) GnRH
Select the hormones secreted by hypothalamus.

If \(\triangle \mathrm{ABC}\) is right angled at \(\mathrm{A}\), where \(\mathrm{A} \equiv(4,2, x), \mathrm{B} \equiv(3,1,8)\) and \(\mathrm{C} \equiv(2,-1,2)\), then the value of \(x\) is

A parallel plate air capacitor has a uniform electric field \(E\) in the space between the plates. Area of each plate is \(A\) and the distance between the plates is \(d\). The energy stored in the capacitor is \(\left[\varepsilon_0=\right.\) permittivity of free space \(]\)