miscellaneous-sequences and series (ncert class 11th maths)

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eduhilfe

Asked: August 21, 2020In: NCERT 11th Maths

32. 150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.

eduhilfe

Asked: August 21, 2020In: NCERT 11th Maths

31. A manufacturer reckons that the value of a machine, which costs him Rs. 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.

eduhilfe

Asked: August 21, 2020In: NCERT 11th Maths

30. A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.

eduhilfe

Asked: August 21, 2020In: NCERT 11th Maths

29. A person writes a letter to four of his friends. He asks each one of them to copy the letter and mail to four different persons with instruction that they move the chain similarly. Assuming that the chain is not broken and that it costs 50 paise to mail one letter. Find the amount spent on the postage when 8th set of letter is mailed.

eduhilfe

Asked: August 21, 2020In: NCERT 11th Maths

28. Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

eduhilfe

Asked: August 21, 2020In: NCERT 11th Maths

27. A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?

eduhilfe

Asked: August 21, 2020In: NCERT 11th Maths

26. Show that $\frac{1\times 2^2 + 2\times 3^2 + ........+ n\times(n+1)^2}{1^2\times 2 + 2^2 \times 3 + ...... + n^2 \times (n+1)} = \frac{3n + 5}{3n +1}$ .

eduhilfe

Asked: August 21, 2020In: NCERT 11th Maths

26. Find the sum of the series up to n terms: $\frac{1^3}{1} + \frac{1^3 + 2^3}{1 +3} + \frac{1^3 + 2^3 + 3^3}{1 +3 +5} + ......$

eduhilfe

Asked: August 21, 2020In: NCERT 11th Maths

24. If $S_1, S_2, S_3$ are the sum of first n natural numbers, their squares and their cubes, respectively, show that $9S_2^2 = S_3 (1 + 8S_1 )$ .

eduhilfe

Asked: August 21, 2020In: NCERT 11th Maths

23. Find the sum of the first n terms of the series: 3 + 7 + 13 + 21 + 31 + …

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32. 150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second day, 4 more workers dropped out on third day and so on. It took 8 more days to finish the work. Find the number of days in which the work was completed.

31. A manufacturer reckons that the value of a machine, which costs him Rs. 15625, will depreciate each year by 20%. Find the estimated value at the end of 5 years.

30. A man deposited Rs 10000 in a bank at the rate of 5% simple interest annually. Find the amount in 15th year since he deposited the amount and also calculate the total amount after 20 years.

28. Shamshad Ali buys a scooter for Rs 22000. He pays Rs 4000 cash and agrees to pay the balance in annual instalment of Rs 1000 plus 10% interest on the unpaid amount. How much will the scooter cost him?

27. A farmer buys a used tractor for Rs 12000. He pays Rs 6000 cash and agrees to pay the balance in annual instalments of Rs 500 plus 12% interest on the unpaid amount. How much will the tractor cost him?

26. Show that $\frac{1\times 2^2 + 2\times 3^2 + ........+ n\times(n+1)^2}{1^2\times 2 + 2^2 \times 3 + ...... + n^2 \times (n+1)} = \frac{3n + 5}{3n +1}$ .

26. Find the sum of the series up to n terms: $\frac{1^3}{1} + \frac{1^3 + 2^3}{1 +3} + \frac{1^3 + 2^3 + 3^3}{1 +3 +5} + ......$

24. If $S_1, S_2, S_3$ are the sum of first n natural numbers, their squares and their cubes, respectively, show that $9S_2^2 = S_3 (1 + 8S_1 )$ .

23. Find the sum of the first n terms of the series: 3 + 7 + 13 + 21 + 31 + …

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