In a photoelectric effect, the number of photo electrons emitted per second is directly proportional to

In the expression of Gauss's Law.
\( \oint \vec{E} \cdot d\vec{s} = \frac{q}{\epsilon_0} \)
(A) The electric field on LHS is only due to the charges inside the Gaussian surface.
(B) The electric field on LHS is due to charges inside and outside the Gaussian surface.
(C) The electric charge on RHS represents all the charges inside and outside the Gaussian surface.
(D) The electric charges on RHS represent only the charges outside the Gaussian surface.

A carrier wave of peak voltage 24 V is used to transmit a message signal. What should be the peak voltage of the modulating signal in order to have a modulation index of 70% ?

The drift speed of electrons in a conductor is estimated to be only a few \( \text{mm s}^{-1} \). But on closing a circuit, how current is established almost instantly in an electric circuit?

When copper and germanium are cooled from room temperature to 100 K, then :

A magnetic substance has a susceptibility \( - 0.05 \) at 300 K. The magnetic susceptibility at 600 K is :

A concave mirror of focal length 6 cm is placed at a distance 'd' from the convex lens of focal length 8 cm. A beam of light coming from infinity and falling on this convex lens-concave mirror combination returns to infinity. The distance 'd' must be equal to:

Let \(\vec{a}=\hat{i}+4 \hat{j}, \vec{b}=4 \hat{j}+\hat{k}\) and \(\vec{c}=\hat{i}-2 \hat{k}\). If \(\vec{d}\) is a vector perpendicular to both \(\vec{a}\) and \(\vec{b}\) such that \(\vec{c} \cdot \vec{d}=16\), then \(|\vec{d}|\) is equal to:

Let \(y(x)=a(x+1) \log (x+1)+b x+5\) be the solution of the differential equation \(e^{\frac{d y}{d x}}=x+1, y(0)=5\), then the value of \((a+b)\) is :

The corner points of the feasible region determined by the system of linear constraints are \((0,0),(0,40),(20,40),(60,20),(60,0)\).
The objective function is \(z=4 x+3 y\).
Compare the quantity in Column - A and Column - B.

Column - A	Column - B
Maximum value of z	350

The points on the curve \(\frac{x^2}{9} + \frac{y^2}{16} = 1\) at which the tangents are parallel to x-axis :

Read the following passage carefully and answer the given questions. During anaerobic sludge digestion, bacteria produce a mixture of gases such as methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as source of energy as it is inflammable. The bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. You must have noticed that bottled fruit juices bought from the market are clearer as compared to those made at home. This is because the bottled juices are clarified by the use of pectinases and proteases. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. The BOD test measures the rate of uptake of oxygen by microorganisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water.
The bottled juices are clarified by the combination of -

Choose the correct statements regarding infra red waves from the following.
(A) Infra red waves produced by hot bodies and molecules.
(B) This radiation is trapped by greenhouse gases such as \( CO_2 \) and water vapour.
(C) These waves are used in earth satellites.
(D) Exposure to these radiation induces the production of more melanin.
(E) These radiations are used in eye surgery.
Choose the correct answer from the options given below :