Mathematics & Statistics (Commerce) – Important Question Bank for Maharashtra Board HSC 2016 Examination

1. Write converse, inverse and contrapositive of the statement “if two triangles are not congruent then there areas are not equal”

2. Use the quantifiers to convert each of the following sentences defined on N into true statement:

a) 5x – 3 < 10  b) x² ≤ 1

4. Find the elasticity of demand if the marginal revenue is Rs. 50 and price is Rs 75.

5. If the demand function is D = 50 – 3p – p²,  find the elasticity of demand at (a) p = 5, (b) p = 2. Interpret your result

6. By construction the truth table, determine whether the following statement pattern is a tautology, contradiction of contingency.
(p→q)˄(p˅~q)

7. Ales spend 20% of his income on food items and 12% on conveyance. If for the month of June 2010, he spent Rs. 900 on conveyance, find his expenditure on food items during the same month.

8. A building is insured for 80% of its value. The annual premium at 70 paisa percent amounts of Rs. 2,800. Fire damaged the building to the extent of 60% of its value. How much amount for damage can be claimed under the policy
9. Mrs. Menon plans to save for her daughter’s marriage? She wants to accumulate a sum of rs. 4,00,000 at the end of 4 years. How much should she invest at the end of the year from now, if she can get interest compounded at 10%p.a? [Give: (1.1)⁴ = 1.4641]

10. A fair coin tossed 12 times. Find the probability of getting

(a) Exactly 7 heads   (b) at least 2 heads

11. A bill of Rs. 2,000 draw on 15^th February 2003  for 10 months was discounted on 13^th May 2003 at 3 ^¾ % p.a Calculate the banker’s discount

12. A person make two types of gift items A and B requiring the services of a cutter and a finisher. Gift item A requires 4 hours of the cutter’s time and 2 hours of finisher’s time. Gift item B requires 2 hours of the cutters’ time and 4 hours of finisher’s time. The cutter and finisher have 208 hours and 152 hours available time respectively every month. The profit on one gift item of type A is Rs. 75 and on one gift item of type B is Rs. 125. Assuming that the person can sell all the gift items produced, determine how many gift items of each type should he make every month to obtain the best returns?

13. In a partially destroyed laboratory record of an analysis of regression date, the following data are legible:

Variance X = 9

Regression  equation : 8x – 10 y +66 = 0 and 40x – 18 y = 214

Find on the basis of the above the information –

a) Mean values of X and Y.

b) correlation coefficient between X and Y

14.  Mr. Rajesh has Rs 1,800 to spend on fruits for a meeting. Grapes cost Rs. 150/Kg and peaches Rs. 200/Kg. Let x and y represent the number of kilograms of grapes and peaches he can buy. Write and graph an inequation to model the amounts of grapes and peaches he can buy within his budget

15. If a random variable X follows Poisson distribution such that P(X = 1) = P(X = 2), find

a) mean of the distribution     b) P(X = 0). [Given: e^-2 = 0.1353].

16. Find the ate specific Death Rates for the following data:

17. Express the following statement in symbolic from and write its truth value. “If 4 is an odd number, then 6 is divisible by 3”

18. The price P for demand D is given as P = 183 + 3D²  . Find D for which the price is increasing

19. Express the truth of each of the following statements by Venn diagram:

i) Some hardworking students are obedient.

ii) No circles are polygons

iii) All teachers are scholars and scholars are teachers

20. The ratio of number of boys and girls in a school is 3 : 2. If 20% of the boys and 30% of the girls are scholarship holders, find the percentage of the students who are not scholarship holders

21. In the following data, one of the values of Y is missing. Arithmetic means of X and Y series are 6 and 8 respectively.

a) Estimate the missing observation

b) Calculate correlation coefficient.

22. Electro Crop.Co. manufactures two electrical produces: Air conditioners and Fans. The assembly process for each is similar in which both require a certain amount of wiring and drilling. Each air conditioner takes 4 hours for wiring and 2 hours for drilling. Each fan also take 2 hours for wiring and 1 hour for drilling. During the next production period, 240 hours of wiring time are available and upto 100 hours of drilling time may be used. Each air conditioner assembled may be sol for Rs. 2,000 profit and each fan assembled may be sold for Rs. 1,000 profit. Formulate this problem as an L.P.P. in order to maximize the profit.

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