The number of all possible matrices of order \(2 \times 2\) with each entry \(0,1,2\), and 3 is:

Let \(\vec{a}\) and \(\vec{b}\) be two unit vectors. If the vectors \(\vec{c}=5 \vec{a}-4 \vec{b}\) and \(\vec{d}=\vec{a}+2 \vec{b}\) are perpendicular to each other, then the angle between \(\vec{a}\) and \(\vec{b}\) is :

The number of all onto functions from the set \(\{1,2, \ldots, n\}\) to itself is

Area of the region bounded by the curve \(x^2=4 y, x\)-axis and \(x=3\) is:

If A is a square matrix of order \(3 \times 3\) and \(\left|A^T\right|=-3\), then \(\left|A A^T\right|\) is equal to

Differential equation of a parabola with vertex at origin and symmetric about \(x\)-axis is :

The function \(f(x)=\left\{\begin{array}{ll}\frac{x^2+2 x-3}{x-1}, & \text { if } x \neq 1 \\ 0, & \text { if } x=1\end{array}\right.\) is

Identify the incorrect statement(s) among the following:
(A) Two electric field lines of force never intersect.
(B) Two opposite charges, each of \( 10 \times 10^{-9} \, \text{C} \), separated by 5 mm. The magnitude of the dipole moment is \( 5 \times 10^{-11} \, \text{C-m} \).
(C) Electric field intensity due to a single charge varies as the square of the distance from the charge, whereas electric field intensity due to an electric dipole varies inversely as the cube of the distance of the point.
(D) Electric field intensity due to an electric dipole has spherical symmetry around it in space.
Choose the correct answer from the options given below:

The differential equation \(\frac{d y}{d x}+\frac{x}{y}=0\), represents the family of curves:

To avoid the unfavourable conditions, the zooplanktons enter into :

Self-inductance of a solenoid is

Which of the following show Pleiotropism?

In the (i) absence of electric field, and in the (ii) presence of electric field, the paths of electrons between successive collisions with the positive ions of the metal, are