Arts (English Medium) Class 11 - CBSE Question Bank Solutions

if `a(1/b + 1/c), b(1/c+1/a), c(1/a+1/b)` are in A.P., prove that a, b, c are in A.P.

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

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

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 8^th set of letter is mailed.

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

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.

Find the distance between the pairs of points:

(2, 3, 5) and (4, 3, 1)

Find the distance between the following pairs of points:

(–3, 7, 2) and (2, 4, –1)

Find the distance between the following pairs of points:

(–1, 3, –4) and (1, –3, 4)

Find the distance between the following pairs of points:

(2, –1, 3) and (–2, 1, 3)

Verify the following:

(0, 7, –10), (1, 6, –6) and (4, 9, –6) are the vertices of an isosceles triangle.

Verify the following:

(0, 7, 10), (–1, 6, 6) and (–4, 9, 6) are the vertices of a right angled triangle.

Verify the following:

(–1, 2, 1), (1, –2, 5), (4, –7, 8) and (2, –3, 4) are the vertices of a parallelogram.

Find the equation of the set of points P, the sum of whose distances from A (4, 0, 0) and B (–4, 0, 0) is equal to 10.

For each of the following compound statements first identify the connecting words and then break it into component statements.

All rational numbers are real and all real numbers are not complex.

For each of the following compound statements first identify the connecting words and then break it into component statements.

Square of an integer is positive or negative.

For each of the following compound statements first identify the connecting words and then break it into component statements.

The sand heats up quickly in the Sun and does not cool down fast at night.

For each of the following compound statements first identify the connecting words and then break it into component statements.

x = 2 and x = 3 are the roots of the equation 3x² – x – 10 = 0.