What will be the half life of a radioactive isotope whose \(\left(\frac{1}{16}\right)^{\text {th }}\) of initial amount remains unchanged after 2 hours ?

The same current is flowing in two AC circuits. The first circuit contains a pure inductor and the second, a capacitor. If the frequency of the AC is increased, then the current will :

Which of the following statements are not true for equipotential surfaces ?
A. Equipotential surface through a point is normal to electric field at that point.
B. There is a constant potential difference between any two points on the equipotential surface.
C. No work is required to move a test charge on the equipotential surface.
D. The vale of electric potential is constant at all points on the equipotential surface.
E. Equipotential surfaces can not be drawn for an electric dipole.
Choose the correct answer from the options given below :

A plane electromagnetic wave is travelling along +y-axis. The value of electric field at a point is \( \vec{E} = 12.3 \hat{i} \frac{N}{C} \). The magnitude and direction of magnetic field \( \vec{B} \) at this point is:

Kirchhoff's junction rule and loop rule are based on which of the following conservation laws respectively ?

If charge is moving perpendicular to uniform magnetic field then its time period of revolution is:

A short bar magnet of magnetic dipole moment \( 10^{-5} \text{ A m}^{2} \) is kept in a uniform magnetic field \( 3 \times 10^{-4} \text{ T} \) at an angle of \( 30^{\circ} \). The torque acting on it is :

Patients with diabetes have :

Read the passage carefully and give the answers to the question .
India was amongst the first countries in the world to initiate action plans plans and programmes at a national level to attain total reproductive health as a social goal.
These programmes called 'family planning' were initiated in 1951 and were periodically assessed over the past decades. Improved programmes covering wider reproduction-related areas are currently in operation. Creating awareness among the people about various reproduction-related aspects and providing facilities and support for building up a reproductively healthy society are the major tasks under these programmes.
Which of the following methods of contraception is not meant for females?

If the system of equations
\(x-3 y+5 z=3\)
\(x-2 y+4 z=4\)
\(2 x-7 y+\lambda z=5\)
has infinite number of solutions, then the value of \(\lambda\) is:

Which of the following is not a natural method of birth control?

Genetically modified rice i.e. Golden rice is enriched with:

Consider the differential equation, \(x \frac{d y}{d x}=y\left(\log _e y-\log _e x+1\right)\), then which of the following are true?
(A) It is a linear differential equation
(B) It is a homogenous differential equation
(C) Its general solution is \(\log _e\left(\frac{y}{x}\right)=C x\), where \(C\) is constant of integration
(D) Its general solution is \(\log _e\left(\frac{x}{y}\right)=C_y\), where \(C\) is constant of integration
(E) If \(y(1)=1\), then its particular solution is \(y=x\)
Choose the correct answer from the options given below: