ISC Class 12th Mathematics Chapter 2 - Algebra Important Questions with Answers

A furniture factory uses three types of wood namely, teakwood, rosewood and satinwood for manufacturing three types of furniture, that are, table, chair and cot.

The wood requirements (in tonnes) for each type of furniture are given below:

It is found that 29 tonnes of teakwood, 13 tonnes of rosewood and 16 tonnes of satinwood are available to make all three types of furniture.

Using the above information, answer the following questions:

1. Express the data given in the table above in the form of a set of simultaneous equations.
2. Solve the set of simultaneous equations formed in subpart (i) by matrix method.
3. Hence, find the number of table(s), chair(s) and cot(s) produced.

A matrix which is both symmetric and skew symmetric matrix is a ______.

if `|(a, b, c),(m, n, p),(x, y, z)| = k`, then what is the value of `|(6a, 2b, 2c),(3m, n, p),(3x, y, z)|`?

In a third order matrix a_ij denotes the element of the i^th row and the j^th column.

A = `a_(ij) = {(0",", for, i = j),(1",", f or, i > j),(-1",", f or, i < j):}`

Assertion: Matrix ‘A’ is not invertible.

Reason: Determinant A = 0

Which of the following is correct?

The value of the determinant of a matrix A of order 3 is 3. If C is the matrix of cofactors of the matrix A, then what is the value of determinant of C²?

Answer the following question:

1. Translate the problem into a system of equations.
2. Solve the system of equation by using matrix method.
3. Hence, find the cost of one paper bag, one scrap book and one pastel sheet.

The monthly incomes of Aryan and Babban are in the ratio 3 : 4 and their monthly expenditures are in the ratio 5 : 7. If each saves Rs 15,000 per month, find their monthly incomes using matrix method. This problem reflects which value?

If ` f(x)=|[a,-1,0],[ax,a,-1],[ax^2,ax,a]| ` , using properties of determinants find the value of f(2x) ? f(x).

Three schools A, B and C organized a mela for collecting funds for helping the rehabilitation of flood victims. They sold hand made fans, mats and plates from recycled material at a cost of Rs 25, Rs 100 and Rs 50 each. The number of articles sold are given below:

Find the funds collected by each school separately by selling the above articles. Also find the total funds collected for the purpose.

Write one value generated by the above situation.

Using properties of determinants, prove that

`|[b+c , a ,a  ] ,[ b , a+c, b ] ,[c , c, a+b ]|` = 4abc