HSC Science कक्षा १२ - Tamil Nadu Board of Secondary Education Question Bank Solutions for Mathematics

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

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The proposition p∧(¬p∨q)] is

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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

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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

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

`3/2 + 2y = 12, 2/x + 3y` = 13

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

3x + 3y – z = 11, 2x – y + 2z = 9, 4x + 3y + 2z = 25

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

`3/x - 4/y - 2/z - 1` = 0, `1/x + 2/y + 1/z - 2` = 0, `2/x - 5/y - 4/z + 1` = 0

In a competitive examination, one mark is awarded for every correct answer while `1/4` mark is deducted for every wrong answer. A student answered 100 questions and got 80 marks. How many questions did he answer correctly? (Use Cramer’s rule to solve the problem).

A chemist has one solution which is 50% acid and another solution which is 25% acid. How much each should be mixed to make 10 litres of a 40% acid solution? (Use Cramer’s rule to solve the problem).

A fish tank can be filled in 10 minutes using both pumps A and B simultaneously. However, pump B can pump water in or out at the same rate. If pump B is inadvertently run in reverse, then the tank will be filled in 30 minutes. How long would it take each pump to fill the tank by itself? (Use Cramer’s rule to solve the problem)

A family of 3 people went out for dinner in a restaurant. The cost of two dosai, three idlies and two vadais is ₹ 150. The cost of the two dosai, two idlies and four vadais is ₹ 200. The cost of five dosai, four idlies and two vadais is ₹ 250. The family has ₹ 350 in hand and they ate 3 dosai and six idlies and six vadais. Will they be able to manage to pay the bill within the amount they had?