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

Evaluate the following.

`int x sqrt(1+x^2) dx`

If X ∼ P(m) with P(X = 1) = P(X = 2), then find the mean and P(X = 2).

Given e^–2 = 0.1353

Solution: Since P(X = 1) = P(X = 2)

∴ `("e"^square"m"^1)/(1!) = ("e"^"-m""m"^2)/square`

∴ m = `square`

∴ P(X = 2) = `("e"^-2. "m"^2)/(2!)` = `square`

Evaluate `int 1 / (x (x - 1)) dx`

If f'(x) = 4x³ - 3x² + 2x + k, f(0) = 1 and f(1) = 4, find f(x).

Evaluate `int1/(x(x - 1))  dx`

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

Write the following statement in symbolic form.

Milk is white if and only if the sky is not blue.

Fill in the blanks :

Conjunction of two statement p and q is symbolically written as ______.

State whether the following statement is True or False:

The negation of 10 + 20 = 30 is, it is false that 10 + 20 ≠ 30.

State whether the following statement is True or False.

The proper substitution for `int x(x^x)^x (2log x + 1)  "d"x` is `(x^x)^x` = t

In a cattle breeding firm, it is prescribed that the food ration for one animal must contain 14, 22, and 1 unit of nutrients A, B, and C respectively. Two different kinds of fodder are available. Each unit weight of these two contains the following amounts of these three nutrients:

The cost of fodder 1 is ₹ 3 per unit and that of fodder ₹ 2 per unit. Formulate the L.P.P. to minimize the cost.

Choose the correct alternative:

Negation of p → (p ˅ ~q) is

Choose the correct alternative:

A biconditional statement is the conjunction of two ______ statements

State whether the following statement is True or False:

The converse of inverse of ~ p → q is q → ~ p

Negation of “Some men are animal” is ______.

Write the negation of the statement “An angle is a right angle if and only if it is of measure 90°”

Write the following statements in symbolic form.

If Qutub – Minar is in Delhi then Taj-Mahal is in Agra

Choose the correct alternative:

What is the rate of change of demand (x) of a commodity with respect to its price (y) if y = 10 + x + 25x³.

Choose the correct alternative:

What is the rate of change of demand (x) of a commodity with respect to its price (y) if y = `(3x + 7)/(2x^2 + 5)`

Choose the correct alternative:

If x^m. yⁿ = `("x" + "y")^(("m" + "n"))`, then `("dy")/("dx")` = ?