Two light beams of intensities in the ratio of \(9: 4\) are allowed to interfere. The ratio of the intensity of maxima and minima will be

The area of cross section of the rope used to lift a load by a crane is \(2.5 \times 10^{-4} m ^{2}\). The maximum lifting capacity of the crane is \(10\) metric tons. To increase the lifting capacity of the crane to \(25\) metric tons, the required area of cross section of the rope should be.\(.........\times 10^{-4} \,m ^{2}\) (take \(g =10\, ms ^{-2}\) )

A zener diode with 5 V zener voltage is used to regulate an unregulated dc voltage input of 25 V. For a \(400 \Omega\) resistor connected in series, the zener current is found to be 4 times load current. The load current \(\left(I_L\right)\) and load resistance \(\left(R_{\mathrm{L}}\right)\) are :

In a Vernier calipers, when both jaws touch each other, zero of the Vernier scale is shifted to the right of zero of the main scale and \(7^{\text{th}}\) Vernier division coincides with a main scale reading. If the value of \(1\) main scale division is \(1\) mm and there are \(10\) Vernier scale divisions, then the Vernier caliper has

12 wires each having resistance \(2 \Omega\) are joined to form a cube. A battery of \(6 \mathrm{~V}\) emf is joined across point \(\mathrm{a}\) and \(\mathrm{c}\). The voltage difference between \(e\) and \(f\) is ______V.

A straight wire \(AB\) of mass \(40\,g\) and length \(50\,cm\) is suspended by a pair of flexible leads in uniform magnetic field of magnitude \(0.40\,T\) as shown in the figure. The magnitude of the current required in the wire to remove the tension in the supporting leads is ...........\(A\). (Take \(g=10\,ms ^{-2}\) ).

The total kinetic energy of \(1\) mole of oxygen at \(27^{\circ} \mathrm{C}\) is : [Use universal gas constant \((R)=8.31 \mathrm{~J} / \mathrm{mole} \mathrm{K}\) ]

The number of electrons flowing per second in the filament of a \(110 \mathrm{~W}\) bulb operating at \(220 \mathrm{~V}\) is _______. (Given \(\mathrm{e}=1.6 \times 10^{-19} \mathrm{C}\) )

The surface of water in a water tank of cross section area \(750\,cm ^2\) on the top of a house is \(h m\). above the tap level. The speed of water coming out through the tap of cross section area \(500\,mm ^2\) is \(30\,cm / s\). At that instant, \(\frac{d h}{d t}\) is \(x \times 10^{-3} m / s\). The value of \(x\) will be \(.............\).

If the sum of the series \(20+19 \frac{3}{5}+19 \frac{1}{5}+18 \frac{4}{5}+\ldots .\) upto \(n ^{ th }\) term is \(488\) and the \(n^{\text {th }}\) term is negative, then

A capillary tube of radius 0.1 mm is partly dipped in water (surface tension \(70 \mathrm{dyn} / \mathrm{cm}\) and glass water contact angle \(\simeq 0^{\circ}\)) with \(30^{\circ}\) inclined with vertical. The length of water risen in the capillary is ________ cm.
\(\left(\right.\) Take \(\left.\mathrm{g}=9.8 \mathrm{~m} / \mathrm{s}^2\right)\)

Consider two vectors \(\overrightarrow{\mathrm{u}}=3 \hat{\mathrm{i}}-\hat{\mathrm{j}}\) and \(\overrightarrow{\mathrm{v}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}-\lambda \hat{\mathrm{k}}, \lambda \gt 0\). The angle between them is given by \(\cos ^{-1}\left(\frac{\sqrt{5}}{2 \sqrt{7}}\right)\). Let \(\overrightarrow{\mathrm{v}}=\overrightarrow{\mathrm{v}}_1+\overrightarrow{\mathrm{v}}_2\), where \(\overrightarrow{\mathrm{v}}_1\) is parallel to \(\overrightarrow{\mathrm{u}}\) and \(\overrightarrow{\mathrm{v}}_2\) is perpendicular to \(\overrightarrow{\mathrm{u}}\). Then the value \(\left|\overrightarrow{\mathrm{v}}_1\right|^2+\left|\overrightarrow{\mathrm{v}}_2\right|^2\) is equal to

The temperature dependence of resistances of \(Cu\) and undoped \(Si\) in the temperature range \(300-400\;K\), is best described by