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Question Paper - Mathematics and Statistics 2014 - 2015-H.S.C-12th Board Exam Maharashtra State Board (MSBSHSE)

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SubjectMathematics and Statistics
Year2014 - 2015 (March)

 Topics
 Marks
 Topics
 Marks

Marks: 80
Q: 1 | Attempt any SIX of the following [12]
Q: 1.1[2]

Express the following statement in symbolic form and write its truth value.

"If 4 is an odd number, then 6 is divisible by 3 "

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Q: 1.2[2]
 

Find the values of x and y, if 

`2[[1,3],[0,x]]+[[y,0],[1,2]]=[[5,6],[1,8]]`

 

 
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Q: 1.3[2]

Find the value of 'k' if the function

`f(X)=(tan7x)/(2x) , `

`  =k,            for 

`=k,            for x=0`

is continuos at x=0

 

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Q: 1.4[2]

Find dy/dx if `y=cos^-1(sqrt(x))`

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Q: 1.5[2]

price P for demand D is given as P = 183 +120D - 3D2 Find D for which the price is increasing

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Q: 1.6[2]

Evaluate : `int1/(x(3+logx))dx`

 

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Q: 1.7[2]

If   `a=[[2,1],[1,1]] " then show taht " A^2-3A+I=0`

 

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Q: 1.8[2]

evaluate : `int xcosxdx`

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Q: 2[14]
Q: 2.1 | Attempt any TWO of the following[6]
Q: 2.1.1[3]

Prove that the following statement pattern is equivalent :

(p ∨ q)  r and (p → r) ∧ (q → r)

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Q: 2.1.2[3]

Examine the continuity of the following function : ``

 

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Q: 2.1.3[3]

find dy/dx if `y=tan^-1((6x)/(1-5x^2))`

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Q: 2.2 | Attempt any TWO of the following :[8]
Q: 2.2.1[4]

 Find the inverse of the following matrix by elementary row transformations if it exists. `A=[[1,2,-2],[0,-2,1],[-1,3,0]]`

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Q: 2.2.2[4]
Q: 2.2.3[4]
Q: 3[14]
Q: 3.1 | Attempt any TWO of the following :[6]
Q: 3.1.1[3]

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

(a) Some hardworking students are obedient.

(b) No circles are polygons.

(c) All teachers are scholars and scholars are teachers. 

 

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Q: 3.1.2[3]

 If 'f' is continuous at x = 0, then find f(0).

`f(x)=(15^x-3^x-5^x+1)/(xtanx) , x!=0`

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Q: 3.1.3[3]

find dy/dx if x=e2t , y=`e^sqrtt`

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Q: 3.2 | Attempt any TWO of the following :[8]
Q: 3.2.1[4]
Q: 3.2.2[4]
Q: 3.2.3[4]

A firm wants to maximize its profit. The total cost function is C = 370Q + 550 and revenue is R = 730Q-3Q2. Find the output for which profit is maximum and also find the profit amount at this output.

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Q: 4 | Attempt any SIX of the following :[12]
Q: 4.1[2]

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 students who are not scholarship holders.

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Q: 4.2[2]
Q: 4.3[2]

Coefficient of rank correlation between x and y is 0.5 and `sumd_i^2`= 42. Assuming that no ranks are repeated, find the number of pairs of observations.

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Q: 4.4[2]

An agent charges 12% commission on the sales. What does he earn if the total sale amounts to Rs. 36,000? What does the seller get?     

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Q: 4.5[2]
Q: 4.6[2]
Q: 4.7[2]

The present worth of the sum of Rs. 5,830, due 9 months hence, is Rs. 5,500. Find the rate of interest.

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Q: 4.8[2]

For a binomial distribution mean is 6 and variance is 2. Find n and p.

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Q: 5[14]
Q: 5.1 | Attempt any TWO of the following :[6]
Q: 5.1.1[3]
Q: 5.1.2[3]
Q: 5.1.3[3]

From a lot of 25 bulbs of which 5 are defective a sample of 5 bulbs was drawn at random with replacement. Find the probability that the sample will contain -

(a) exactly 1 defective bulb.

(b) at least 1 defective bulb.

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Q: 5.2 | Attempt any TWO of the following :[8]
Q: 5.2.1[4]

Given the following table which relates to the number of parrots at age x, complete the life table for parrots.

X

0

1

2

3

4

5

 lx

1000

940

780

590

25

0

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Q: 5.2.2[4]
Q: 5.2.3[4]
Q: 6[14]
Q: 6.1 | Attempt any TWO of the following :[6]
Q: 6.1.1[3]

The equations given of the two regression lines are :

2x + 3y-6 = 0 and 5x + 7y-12 = 0.

Find :

(a) Correlation coefficient

(b) `sigma_x/sigma_y`

 

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Q: 6.1.2[3]
Q: 6.1.3[3]

The number of complaints which a bank manager receives per day is a Poisson random variable with parameter m = 4. Find the probability that the manager will receive -

(a) only two complaints on any given day.

(b) at most two complaints on any given day

[Use e-4 =0.0183]

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Q: 6.2 | Attempt any TWO of the following :[8]
Q: 6.2.1[4]
Q: 6.2.2[4]

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

X

6

2

10

4

8

Y

9

11

?

8

7

 (a) Estimate the missing observation.

 (b) Calculate correlation coefficient.

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Q: 6.2.3[4]
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