HSC Science (Electronics) 12th Standard Board Exam - Maharashtra State Board Question Bank Solutions

Encryption consist of two processes ______ and ______.

Describe process of encryption.

Write Programs for the following.

Write a PHP code which calculates square of any number using form.

Write Programs for the following.

Create a website with two PHP webpage in which each webpage is connected.

The first page of the website contains two form fields for taking 'name' and 'password' from users. On onclick event, details of forms should be displayed on second webpage.

Prove that:

`int_0^(2a)f(x)dx = int_0^af(x)dx + int_0^af(2a - x)dx`

If x^myⁿ = (x + y)^m+n, prove that \[\frac{dy}{dx} = \frac{y}{x} .\]

Apply the given elementary transformation of the following matrix.

A = `[(1,0),(-1,3)]`, R₁↔ R₂

Apply the given elementary transformation of the following matrix.

B = `[(1, -1, 3),(2, 5, 4)]`, R₁→ R₁ – R₂

Apply the given elementary transformation of the following matrix.

A = `[(5,4),(1,3)]`, C₁↔ C₂; B = `[(3,1),(4,5)]` R₁↔ R₂.
What do you observe?

Apply the given elementary transformation of the following matrix.

A = `[(1,2,-1),(0,1,3)]`, 2C₂

B = `[(1,0,2),(2,4,5)]`, −3R₁

Find the addition of the two new matrices.

Apply the given elementary transformation of the following matrix.

A = `[(1,-1,3),(2,1,0),(3,3,1)]`, 3R₃ and then C₃ + 2C₂

Apply the given elementary transformation of the following matrix.

A = `[(1,-1,3),(2,1,0),(3,3,1)]`, 3R₃ and then C₃ + 2C₂

and A = `[(1,-1,3),(2,1,0),(3,3,1)]`, C₃ + 2C₂ and then 3R₃
What do you conclude?

Apply the given elementary transformation of the following matrix.

Use suitable transformation on `[(1,2),(3,4)]` to convert it into an upper triangular matrix.

Apply the given elementary transformation of the following matrix.

Convert `[(1,-1),(2,3)]` into an identity matrix by suitable row transformations.

Apply the given elementary transformation of the following matrix.

Transform `[(1,-1,2),(2,1,3),(3,2,4)]` into an upper triangular matrix by suitable column transformations.

The total cost of 3 T.V. sets and 2 V.C.R.’s is ₹ 35,000. The shopkeeper wants a profit of ₹ 1000 per T.V. set and ₹ 500 per V.C.R. He sells 2 T.V. sets and 1 V.C.R. and gets the total revenue as ₹ 21,500. Find the cost price and the selling price of a T.V. set and a V.C.R.

If A = `((1,0,0),(2,1,0),(3,3,1))`, then reduce it to I₃ by using column transformations.

If A = `[(2,1,3),(1,0,1),(1,1,1)]`, then reduce it to I₃ by using row transformations.