HSC Commerce: Marketing and Salesmanship इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

A manufacturing company is allowed to charge a 10% depreciation on its stock. The initial value of the stock was Rs.60,000/-. After how many years the value of the stock will be 39366?

Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify : {(1,0), (3, 3), (2,−1), (4, 1), (2, 2)}

Which sets of ordered pairs represent functions from A = {1, 2, 3, 4} to B = {−1, 0, 1, 2, 3}? Justify : {(1, 2), (2,−1), (3, 1), (4, 3)}

Which set of ordered pair represent function from A = {1, 2, 3, 4}to B = {−1, 0, 1, 2, 3}? Justify : {(1, 3), (4,1), (2, 2)}

Which set of ordered pair represent function from A = {1, 2, 3, 4}to B = {−1, 0, 1, 2, 3}? Justify : {(1, 1), (2, 1), (3, 1), (4, 1)}

Find x, if `"g"(x)` = 0 where `"g"(x)` = `(5x−6)/7`

Find x, if `"g"(x)` = 0 where `"g"(x)`= `(18−2x^2)/ 7`

Find x, if `"g"(x)` = 0 where `"g"(x)` = 6x² + x − 2

Find x, if f(x) = g(x) where f(x) = x⁴ + 2x² , g(x) = 11x²

if f(x) = `{(4x - 2","   x ≤ - 3),(5","  -3 < x < 3),(x^2","  x ≥ 3):},`the find f(– 4)

If f(x) = 2x² + 3, g(x) = 5x – 2, then find gog.

Find variance and S.D. for the following set of numbers.
25, 21, 23, 29, 27, 22, 28, 23, 27, 25
(Given `sqrt(6.6)` = 2.57)

Following data gives no. of goals scored by a team in 100 matches:

Compute the variance and standard deviation for the above data.

The value of the machine depreciates at the rate of 15% p.a. It was purchased 2 years ago. Its present value is Rs. 7225. What was the purchase price of the machine?

A tree increases annually by 1/8 of its height. By how much will it increase after 2½ years. If its length today is 8 m.?

A building worth Rs. 121000 is constructed on land worth Rs. 81000. After how many years will the value of both be the same if land appreciates at 10% pa. and buildings depreciate at 10% p.a.

Following data gives the coded price (X) and demand (Y) of a commodity.

Classify the data by taking classes 0 – 4, 5 – 9, etc. for X and 5 – 8, 9 – 12, etc. for Y. Also find conditional frequency distribution of Y when X is less than 10

Following data gives the age in years and marks obtained by 30 students in an intelligence test.

Prepare a bivariate frequency distribution by taking class intervals 16 – 18, 18 – 20, … etc. for age and 10 – 20, 20 – 30, … etc. for marks. Find conditional frequency distribution of marks obtained when the age of students is between 20 – 22.

Following data gives Sales (in Lakh ₹) and Advertisement Expenditure (in Thousand ₹) of 20 firms. (115, 61) (120, 60) (128, 61) (121, 63) (137, 62) (139, 62) (143, 63) (117, 65) (126, 64) (141, 65) (140, 65) (153, 64) (129, 67) (130, 66) (150, 67) (148, 66) (130, 69) (138, 68) (155, 69) (172, 68) Conditional frequency distribution of Sales when the advertisement expenditure is between 64 – 66 (Thousand ₹)

Following data gives Sales (in Lakh Rs.) and Advertisement Expenditure (in Thousand Rs.) of 20 firms.
(115, 61) (120, 60) (128, 61) (121, 63) (137, 62) (139, 62) (143, 63) (117, 65) (126, 64) (141, 65) (140, 65) (153, 64) (129, 67) (130, 66) (150, 67) (148, 66) (130, 69) (138, 68) (155, 69) (172, 68)
Conditional frequency distribution of advertisement expenditure when the sales are between 125 – 135 (lakh Rs.)