# HSC Commerce (English Medium) 12th Board Exam - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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An urn contains 5 red and 2 black balls. Two balls are drawn at random. X denotes number of black balls drawn. What are the possible values of X?

[0.027999999999999997] Probability Distributions
Chapter: [0.027999999999999997] Probability Distributions
Concept: Mean of a Random Variable

Find the mean of number of heads in three tosses of a fair coin

[0.027999999999999997] Probability Distributions
Chapter: [0.027999999999999997] Probability Distributions
Concept: Mean of a Random Variable

Two dice are thrown simultaneously. If X denotes the number of sixes, find the expectation of X

[0.027999999999999997] Probability Distributions
Chapter: [0.027999999999999997] Probability Distributions
Concept: Mean of a Random Variable

Let X denote the sum of the numbers obtained when two fair dice are rolled. Find the variance of X.

[0.027999999999999997] Probability Distributions
Chapter: [0.027999999999999997] Probability Distributions
Concept: Mean of a Random Variable

State whether the following is True or False :

X is the number obtained on upper most face when a die is thrown then E(X) = 3.5.

[0.027999999999999997] Probability Distributions
Chapter: [0.027999999999999997] Probability Distributions
Concept: Mean of a Random Variable

Prove that: int_0^(2a)f(x)dx=int_0^af(x)dx+int_0^af(2a-x)dx

[0.07] Definite Integrals
Chapter: [0.07] Definite Integrals
Concept: Properties of Definite Integrals

A random variable X has the following probability distribution:

then E(X)=....................

[0.14] Random Variable and Probability Distribution
Chapter: [0.14] Random Variable and Probability Distribution
Concept: Random Variables and Its Probability Distributions

If int_0^alpha3x^2dx=8 then the value of α is :

(a) 0

(b) -2

(c) 2

(d) ±2

[0.07] Definite Integrals
Chapter: [0.07] Definite Integrals
Concept: Properties of Definite Integrals

Evaluate : int e^x[(sqrt(1-x^2)sin^-1x+1)/(sqrt(1-x^2))]dx

[0.07] Definite Integrals
Chapter: [0.07] Definite Integrals
Concept: Properties of Definite Integrals

Evaluate :int_0^pi(xsinx)/(1+sinx)dx

[0.07] Definite Integrals
Chapter: [0.07] Definite Integrals
Concept: Properties of Definite Integrals

Find the value of 'k' if the function

f(X)=(tan7x)/(2x) ,  "for " x != 0

=k,            for x=0

is continuos at x=0

[0.03] Continuity
Chapter: [0.03] Continuity
Concept: Continuous Function of Point

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

[0.05] Applications of Derivative
Chapter: [0.05] Applications of Derivative
Concept: Increasing and Decreasing Functions

Examine the continuity of the following function :

{:(,,f(x)= x^2 -x+9,"for",x≤3),(,,=4x+3,"for",x>3):}}"at "x=3

[0.03] Continuity
Chapter: [0.03] Continuity
Concept: Continuous Function of Point

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

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

[0.03] Continuity
Chapter: [0.03] Continuity
Concept: Continuous Function of Point

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.

[0.08] Ratio, Proportion and Partnership
Chapter: [0.08] Ratio, Proportion and Partnership
Concept: Ratio, Proportion and Partnership

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?

[0.09] Commission, Brokerage and Discount
Chapter: [0.09] Commission, Brokerage and Discount
Concept: Commission, Brokerage and Discount

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

[0.09] Commission, Brokerage and Discount
Chapter: [0.09] Commission, Brokerage and Discount
Concept: Commission, Brokerage and Discount

Natarajan and Mr. Gopalan are partners in the company having capitals in the ratio 4 : 5 and the profits received by them are in the ratio 5 :4. If Mr. Gopalan invested capital in the company for 16 months, how long was Mr. Natarajan’s investment in the company?

[0.09] Commission, Brokerage and Discount
Chapter: [0.09] Commission, Brokerage and Discount
Concept: Commission, Brokerage and Discount

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.

[0.14] Random Variable and Probability Distribution
Chapter: [0.14] Random Variable and Probability Distribution
Concept: Random Variables and Its Probability Distributions

 Advertisement Expenditure (Rs. in lakh)             (X) Sales (Rs. in lakh)            (Y) Arithmetic mean 10 90 Standard deviation 3 12

Correlation coefficient between X and Y = 0.8.

(a) Obtain the two regression equations.

(b) What is the likely sales when the advertising budget is ? 15 lakh?

(c) What should be the advertising budget if the company wants to attain sales target of ₹ 120 lakh?

[0.13] Regression Analysis Introduction
Chapter: [0.13] Regression Analysis Introduction
Concept: Lines of Regression of X on Y and Y on X Or Equation of Line of Regression
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