12th Maths Guide Solution Application of Matrices and Determinants Exercise 1.4

Class 12th maths guide solutions of Chapter 1 Application of Matrices and Determinants Exercise 1.4, according to the Samacheer Kalvi syllabus for Tamil Nadu state board students.

Question no 1: Solve the following linear equations system using Cramer’s rule.

(i) 5x – 2y + 16 = 0, x + 3y – 7 = 0

Solution:

Solution:

(iii) 3x + 3y – z = 1 1, 2x – y + 2z = 9, 4x + 3y + 2z = 25

Solution:

Question no 2:

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

Solution:

No. of Questions answered = 100
Let the No. of questions answered correctly be x
and the No. of questions answered wrongly be y
Here, x + y = 100 and x – 14 y = 80
(i.e) x + y = 100 and 4x – y = 320

Question no 3:

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.

Solution:

Let two solutions, x and y
x + y = 10 ………………(1)
0.25 x + (0.50)y = (0.40) ……….….. (2)
(2) × 100 ⇒ 25x + 50y = 400
(2) ÷ 5 ⇒ 5x + 10y = 80 ……..………. (3)

Question no 4:

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 problems.

Solution:

By Using Cramer’s Rule:

Question no 5: