ISC (Science) ISC Class 12 - CISCE Important Questions

If f : R `rightarrow` R is defined by `f(x) = (2x - 7)/4`, show that f(x) is one-one and onto.

Statement 1: The intersection of two equivalence relations is always an equivalence relation.

Statement 2: The Union of two equivalence relations is always an equivalence relation.

Which one of the following is correct?

If `tan^-1 ((x - 1)/(x + 1)) + tan^-1 ((2x - 1)/(2x + 1)) = tan^-1 (23/36)` = then prove that 24x² – 23x – 12 = 0

The value of cosec `[sin^-1((-1)/2)] - sec[cos^-1((-1)/2)]` is equal to ______.

Solve for x: `sin^-1(x/2) + cos^-1x = π/6`

If sin^–1x + sin^–1y + sin^–1z = π, show that `x^2 - y^2 - z^2 + 2yzsqrt(1 - x^2) = 0`

A short electric dipole (which consists of two point charges, +q and -q) is placed at the centre 0 and inside a large cube (ABCDEFGH) of length L, as shown in Figure 1. The electric flux, emanating through the cube is:

a) `q"/"4piin_9L`

b) zero

c) `q"/"2piin_0L`

d) `q"/"3piin_0L`

Derive an expression for the intensity of electric field at a point in broadside position or on [4)
an equatorial line of an electric dipole.

The intensity of the electric field at a perpendicular distance of 0·5 m from an infinitely long line charge having linear charge density (λ) is 3-6 × 10³ Vm^-1. Find the value of λ.

The intensity of the electric field at a point at a perpendicular distance ‘r’ from an infinite line charge, having linear charge density ‘λ’ is given by:

A charged oil drop weighing 1.6 x 10^-15 N is found to remain suspended in a uniform electric field of intensity 2 x 10³ Nc^-1. Find the charge on the drop. 

Two-point charges Q₁ = 400 μC and Q₂ = 100 μC are kept fixed, 60 cm apart in a vacuum. Find the intensity of the electric field at the midpoint of the line joining Q₁ and Q₂.  

In an electric dipole, at which point is the electric potential zero ? 

In an electric dipole, what is the locus of a point having zero potential?

In case of an infinite line charge, how does intensity of electric field at a point change, if at all, when.

1. charge on it is doubled?
2. distance of the point is halved?

What is meant by the statement: "Relative permittivity of water is 81"?

 A closed surface in vacuum encloses charges –q and +3q. The total electric flux emerging out of the surface is :

A hollow sphere of radius R has a point charge Q at its centre. Electric flux emanating from it is `phi`. If both the charge and the radius of the sphere are doubled, electric flux emanating from the sphere will ______.

A hollow sphere of radius R has a point charge q at its centre. Electric flux emanating from the sphere is X. How will the electric flux change, if at all, when radius of the sphere is doubled?

A hollow sphere of radius R has a point charge q at its centre. Electric flux emanating from the sphere is X. How will the electric flux change, if at all, when charge q is replaced by an electric dipole?