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

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

The differential equation of `y = k_1e^x+ k_2 e^-x` is ______.

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

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.

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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

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The price Index Number by Weighted Aggregate Method is given by ______.

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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?

If X has Poisson distribution with m = 1, then find P(X ≤ 1) given e⁻¹ = 0.3678

If X has Poisson distribution with parameter m and P(X = 2) = P(X = 3), then find P(X ≥ 2). Use e⁻³ = 0.0497

The number of complaints which a bank manager receives per day follows a Poisson distribution with parameter m = 4. Find the probability that the manager receives only two complaints on a given day

Solve the differential equation `("d"y)/("d"x) + y` = e^−x 

Solve `("d"y)/("d"x) = (x + y + 1)/(x + y - 1)` when x = `2/3`, y = `1/3`

Solve the differential equation (x² – yx²)dy + (y² + xy²)dx = 0

Solve: `("d"y)/("d"x) + 2/xy` = x² 

For the differential equation, find the particular solution (x – y²x) dx – (y + x²y) dy = 0 when x = 2, y = 0

Solve the following differential equation

`yx ("d"y)/("d"x)` = x² + 2y² 

For the differential equation, find the particular solution

`("d"y)/("d"x)` = (4x +y + 1), when y = 1, x = 0