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

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

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

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

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

State whether the following statement is True or False :

x² = 25 is true statement.

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

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

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

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

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.

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.

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Regression analysis is the theory of

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

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In the regression equation of X on Y

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`

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

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.

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

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.

A random variable X has the following probability distribution:

Determine P(X > 4)

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