HSC Arts Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions

Choose the correct alternative:

If a compound statement involves 3 simple statements, then the number of rows in the truth table is

Choose the correct alternative:

Which one is the inverse of the statement (p v q) → (p ∧ q)?

Choose the correct alternative:

Which one is the contrapositive of the statement (p v q) → r?

Choose the correct alternative:

The truth table for (p ∧ q) v ¬q is given below

Which one of the following is true?

Choose the correct alternative:

In the last column of the truth table for ¬(p v ¬q) the number of final outcomes of the truth value ‘F’ is

Choose the correct alternative:

Which one of the following is incorrect? For any two propositions p and q, we have

Choose the correct alternative:

Which one of the following is correct for the truth value of (p ∧ q) → ¬p

Choose the correct alternative:

The dual of ¬(p v q) v [p v(p ∧ ¬r)] is

Choose the correct alternative:

The proposition p∧(¬p∨q)] is

Choose the correct alternative:

Determine the truth value of each of the following statements:
(a) 4 + 2 = 5 and 6 + 3 = 9
(b) 3 + 2 = 5 and 6 + 1 = 7
(c) 4 + 5 = 9 and 1 + 2 = 4
(d) 3 + 2 = 5 and 4 + 7 = 11

Choose the correct alternative:

Which one of the following is not true?

Solve the following system of linear equations by matrix inversion method:

2x + 5y = – 2, x + 2y = – 3

Solve the following system of linear equations by matrix inversion method:

2x – y = 8, 3x + 2y = – 2

Solve the following system of linear equations by matrix inversion method:

2x + 3y – z = 9, x + y + z = 9, 3x – y – z = – 1

Solve the following system of linear equations by matrix inversion method:

x + y + z – 2 = 0, 6x – 4y + 5z – 31 = 0, 5x + 2y + 2z = 13

If A = `[(-5, 1, 3),(7, 1, -5),(1, -1, 1)]` and B = `[(1, 1, 2),(3, 2, 1),(2, 1, 3)]`, Find the products AB and BA and hence solve the system of equations x + y + 2z = 1, 3x + 2y + z = 7, 2x + y + 3z = 2

A man is appointed in a job with a monthly salary of certain amount and a fixed amount of annual increment. If his salary was ₹ 19,800 per month at the end of the first month after 3 years of service and ₹ 23,400 per month at the end of the first month after 9 years of service, find his starting salary and his annual increment. (Use matrix inversion method to solve the problem.)

Four men and 4 women can finish a piece of work jointly in 3 days while 2 men and 5 women can finish the same work jointly in 4 days. Find the time taken by one man alone and that of one woman alone to finish the same work by using matrix inversion method

The prices of three commodities A, B and C are ₹ x, y and z per units respectively. A person P purchases 4 units of B and sells two units of A and 5 units of C. Person Q purchases 2 units of C and sells 3 units of A and one unit of B . Person R purchases one unit of A and sells 3 unit of B and one unit of C. In the process, P, Q and R earn ₹ 15,000, ₹ 1,000 and ₹ 4,000 respectively. Find the prices per unit of A, B and C. (Use matrix inversion method to solve the problem.)

Solve the following systems of linear equations by Cramer’s rule:

5x – 2y + 16 = 0, x + 3y – 7 = 0