# HSC Commerce (Marathi Medium) 12th Board Exam [इयत्ता १२ वि] - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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Mathematics and Statistics
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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

The total cost of manufacturing x articles is C = 47x + 300x2 − x4.  Find x, for which average cost is increasing.

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

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Choose the correct alternative :

If p : He is intelligent.
q : He is strong
Then, symbolic form of statement “It is wrong that, he is intelligent or strong” is

[0.011000000000000001] Mathematical Logic
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Truth Value of Statement

Choose the correct alternative :

If p and q are two statements then (p → q) ↔ (∼ q → ∼ p) is

[0.011000000000000001] Mathematical Logic
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Truth Value of Statement

State whether the following statement is True or False :

x2 = 25 is true statement.

[0.011000000000000001] Mathematical Logic
Chapter: [0.011000000000000001] Mathematical Logic
Concept: Truth Value of Statement

Form the differential equation from the relation x2 + 4y2 = 4b2

[0.018000000000000002] Differential Equation and Applications
Chapter: [0.018000000000000002] Differential Equation and Applications
Concept: Differential Equations

Find the rate of change of demand (x) of a commodity with respect to its price (y) if y = (5x + 7)/(2x - 13)

[0.013000000000000001] Differentiation
Chapter: [0.013000000000000001] Differentiation
Concept: Derivatives of Composite Functions - Chain Rule

Find the equation of tangent to the curve y = sqrt(x - 3) which is perpendicular to the line 6x + 3y – 4 = 0.

[0.013999999999999999] Applications of Derivatives
Chapter: [0.013999999999999999] Applications of Derivatives
Concept: Introduction of Derivatives

Evaluate the following definite integrals: int_1^3 logx.dx

[0.016] Definite Integration
Chapter: [0.016] Definite Integration
Concept: Fundamental Theorem of Integral Calculus

A retailer sold a suit for ₹ 8,832 after allowing 8% discount on marked price and further 4% cash discount. If he made 38% profit, find the cost price and the marked price of the suit.

[0.021] Commission, Brokerage and Discount
Chapter: [0.021] Commission, Brokerage and Discount
Concept: Commission and Brokerage Agent

The rate of premium is 2% and other expenses are 0.75%. A cargo worth ₹ 3,50,100 is to be insured so that all its value and the cost of insurance will be recovered in the event of total loss.

[0.022000000000000002] Insurance and Annuity
Chapter: [0.022000000000000002] Insurance and Annuity
Concept: Concept of Insurance

Choose the correct alternative:

Regression analysis is the theory of

[0.023] Linear Regression
Chapter: [0.023] Linear Regression
Concept: Regression

Choose the correct alternative:

We can estimate the value of one variable with the help of other known variable only if they are

[0.023] Linear Regression
Chapter: [0.023] Linear Regression
Concept: Regression

Choose the correct alternative:

In the regression equation of X on Y

[0.023] Linear Regression
Chapter: [0.023] Linear Regression
Concept: Regression

Find the equation of the line of regression of Y on X for the following data:

n = 8, sum(x_i - barx).(y_i - bary) = 120, barx = 20, bary = 36, sigma_x = 2, sigma_y = 3

[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

Choose the correct alternative :

The assignment problem is said to be balanced if it is a ______.

[0.027000000000000003] Assignment Problem and Sequencing
Chapter: [0.027000000000000003] Assignment Problem and Sequencing
Concept: Assignment Problem

Solve the following problem :

A dairy plant has five milk tankers, I, II, III, IV and V. These milk tankers are to be used on five delivery routes A, B, C, D and E. The distances (in kms) between the dairy plant and the delivery routes are given in the following distance matrix.

 I II III IV V A 150 120 175 180 200 B 125 110 120 150 165 C 130 100 145 160 175 D 40 40 70 70 100 E 45 25 60 70 95

How should the milk tankers be assigned to the chilling center so as to minimize the distance travelled?

[0.027000000000000003] Assignment Problem and Sequencing
Chapter: [0.027000000000000003] Assignment Problem and Sequencing
Concept: Assignment Problem

A sample of 4 bulbs is drawn at random with replacement from a lot of 30 bulbs which includes 6 defective bulbs. Find the probability distribution of the number of defective bulbs.

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

A random variable X has the following probability distribution:

 x 1 2 3 4 5 6 7 P(x) k 2k 2k 3k k2 2k2 7k2 + k

Determine P(X > 4)

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

A die is thrown 4 times. If ‘getting an odd number’ is a success, find the probability of 2 successes

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