ISC (Science) ISC Class 12 - CISCE Question Bank Solutions

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

If the function f : R → R be defined by f(x) = 2x − 3 and g : R → R by g(x) = x³ + 5, then find the value of (fog)⁻¹ (x).

Let f : W → W be defined as

`f(n)={(n-1, " if n is odd"),(n+1, "if n is even") :}`

Show that f is invertible a nd find the inverse of f. Here, W is the set of all whole
numbers.

If f : R → R, f(x) = x³  and g: R → R , g(x) =  2x² + 1, and R is the set of real numbers, then find fog(x) and gof (x)

If f(x) = [4 – (x – 7)³]^1/5 is a real invertible function, then find f^–1(x).

Let `f : R {(-1)/3} → R - {0}` be defined as `f(x) = 5/(3x + 1)` is invertible. Find f^–1(x).

if A =`((5,a),(b,0))` is symmetric matrix show that a = b

If the matrix `((6,-"x"^2),(2"x"-15 , 10))` is symmetric, find the value of x.

For what value of k the matrix `[(0, k),(-6, 0)]` is a skew symmetric matrix?

If A and B are symmetric matrices of the same order, then AB – BA is ______.

A rectangular coil having 60 turns and area of 0.4m² is held at right angles to a uniform magnetic field of flux density 5 × 10^-5T. Calculate the magnetic flux passing through it.

Obtain an expression for electric potential ‘V’ at a point in an end-on position i.e. axial position of the electric dipole. 

Calculate magnetic flux density of the magnetic field at the centre of a circular coil of 50 turns, having a radius of 0.5m and carrying a current of 5 A.

Find magnetic flux density at a point on the axis of a long solenoid having 5000 tums/m when it carrying a current of 2 A.

Define Curie temperature.

If magnetic susceptibility of a certain magnetic material is 0 0001, find its relative permeability.

A circular coil has radius ‘r', number of turns ‘N’ and carries a current ‘I’. Magnetic flux density ‘B’ at its centre is ______.

Calculate electric potential at a point P which is at a distance of 9 cm from a point charge of 50 μC.

The Figure below shows an infinitely long metallic wire YY' which is carrying a current I'.

P is a point at a perpendicular distance r from it.

An emf of 2V is induced in a coil when the current in it is changed from 0A to 10A in 0·40 sec. Find the coefficient of self-inductance of the coil.