ISC (Arts) इयत्ता १२ - CISCE Question Bank Solutions

If the function `f(x) = sqrt(2x - 3)` is invertible then find its inverse. Hence prove that `(fof^(-1))(x) = x`

Let \[f\left(x\right) = x^3\] be a function with domain {0, 1, 2, 3}. Then domain of \[f^{-1}\] is ______.

Let A = R – {2} and B = R – {1}. If f: A `→` B is a function defined by f(x) = `(x - 1)/(x - 2)` then show that f is a one-one and an onto function.

Which one of the following graphs is a function of x?

Graph A	Graph B

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(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 ______.

Discuss any four factors affecting price elasticity of demand.

Draw a diagram to show the elasticity of demand when it is greater than one.

The price of a good decreases from ₹100 to 80 per unit. If the price elasticity of demand for the good is 2 and the original quantity demanded is 30 units, calculate the new quantity demanded.

Normal profits for a firm imply that the firm is breaking even. Explain.

The aggregate utility obtained from the consumption of a specific unit of a commodity is called ______.

Give two differences between intended supply and actual supply.

Prices of air conditioners and refrigerators have shot up in the new year as consumer durables makers pass on the impact of rising raw material costs and higher freight charges to customers, while home appliances like washing machines may witness a 5–10 per cent price hike later this month or by March.

(Source: The Economic Times)

Explain the behaviour of supply of this consumer durable. Illustrate the same in a diagram.