Electron beam when accelerated by a voltage of 10 kV , has a de-Broglie wavelength ' \(\lambda\) '. If the voltage is increased to 20 kV then the de-Broglie wavelength associated with the electron beam would be

The following figures show the variation of displacement with time of a particular object.
(a)

(b)

(c)

(d)

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

A photoelectric cell is illuminated by a point source of light \(1 \mathrm{~m}\) away. When the source is shifted to \(2 \mathrm{~m}\) then

In an ideal step-down transformer, out of the following quantities, which quantity increases in the secondary coil?

A series LCR circuit with resistance \(R=500 \mathrm{ohm}\) is connected to an a.c. source of \(250 \mathrm{~V}\). When only the capacitance is removed, the current lags behind the voltage by \(60^{\circ}\). When only the inductance is removed, the current leads the voltage by \(60^{\circ}\). The impedance of the circuit is

A car is driven on the banked road of radius of curvature \(20 \mathrm{~m}\) with maximum safe speed. In order to increase its safety speed by \(10 \%\), the increase in the radius of curvature will be
[Angle of banking and friction is unchanged in both the cases.]

The logical statement
\((\sim(\sim \mathrm{p} \vee \mathrm{q}) \vee(\mathrm{p} \wedge \mathrm{r})) \wedge(\sim \mathrm{q} \wedge \mathrm{r})\) is equivalent to

Carbonated water is an example of a solution of

Identify ' \(A\) ' in the following reaction.
\(\text { A + Acetic anhydride } \xrightarrow{\mathrm{H}^{+}} \text {Aspirin + Acetic acid }\)

In an isobaric process of an ideal gas, the ratio of work done by the system (W) during the expansion and the heat exchanged \((\mathrm{Q})\) is \(\left(\gamma=\frac{C_p}{C_v}\right)\)

The pH of a sample of vinegar is 3.76. Calculate the concentration of hydrogen ion in it in \(\mathrm{mol~} \mathrm{dm}^{-3}\) ?

In the electrolysis of aqueous sodium chloride with inert electrodes the products obtained at anode and cathode respectively are