Advertisements
Advertisements
प्रश्न
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).
उत्तर
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 - 1/4 y` = 80
(i.e) x + y = 100 and 4x – y = 320
Δ = `|(1, 1),(1, -1/4)| = - 1/4 - 1 = (-5)/4 ≠ 0`
Δx = `|(100, 1),(80, -1/4)|` = – 25 – 80 = – 105
Δy = `|(1, 100),(1, 80)|` = 80 – 100 = – 20
x = `Delta_x/Delta = (- 105)/((- 5)/4)` = 21 × 4 = 84
y = `Delta_y/Delta = (- 20)/((- 5)/4)` = 4 × 4 = 16
Correct questions = 84
Wrong questions = 16.
APPEARS IN
संबंधित प्रश्न
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
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
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).
Solve the following systems of linear equations by Gaussian elimination method:
2x + 4y + 6z = 22, 3x + 8y + 5z = 27, – x + y + 2z = 2
A boy is walking along the path y = ax2 + bx + c through the points (– 6, 8), (– 2, – 12), and (3, 8). He wants to meet his friend at P(7, 60). Will he meet his friend? (Use Gaussian elimination method.)
Choose the correct alternative:
If `("AB")^-1 = [(12, -17),(-19, 27)]` and `"A"^-1 = [(1, -1),(-2, 3)]` then `"B"^-1` =
Choose the correct alternative:
If A = `[(3/5, 4/5),(x, 3/5)]` and AT = A–1, then the value of x is
Choose the correct alternative:
If adj A = `[(2, 3),(4, 1)]` and adj B = `[(1, -2),(-3, 1)]` then adj (AB) is
Choose the correct alternative:
If ρ(A) ρ([A|B]), then the system AX = B of linear equations is
