HSC Commerce: Marketing and Salesmanship १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which profit is increasing.

A manufacturing company produces x items at a total cost of ₹ 40 + 2x. Their price is given as p = 120 – x. Find the value of x for which also find an elasticity of demand for price 80.

Find MPC, MPS, APC and APS, if the expenditure E_c of a person with income I is given as E_c = (0.0003) I² + (0.075) I ; When I = 1000.

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A road of 108 m length is bent to form a rectangle. If the area of the rectangle is maximum, then its dimensions are _______.

Evaluate: `int (2"x" + 1)/(("x + 1")("x - 2"))` dx

Evaluate:

`int (2x + 1)/(x(x - 1)(x - 4)) dx`.

Evaluate: `int ("x"^2 + "x" - 1)/("x"^2 + "x" - 6)` dx

Evaluate:

`int x/((x - 1)^2(x + 2)) dx`

Evaluate: `int "3x - 2"/(("x + 1")^2("x + 3"))` dx

Evaluate: `int 1/("x"("x"^5 + 1))` dx

Evaluate: `int 1/("x"("x"^"n" + 1))` dx

Evaluate: `int (5"x"^2 + 20"x" + 6)/("x"^3 + 2"x"^2 + "x")` dx

`int "dx"/(("x" - 8)("x" + 7))`=

State whether the following statement is True or False.

If `int (("x - 1") "dx")/(("x + 1")("x - 2"))` = A log |x + 1| + B log |x - 2| + c, then A + B = 1.

For `int ("x - 1")/("x + 1")^3  "e"^"x" "dx" = "e"^"x"` f(x) + c, f(x) = (x + 1)².

Evaluate: `int ("3x" - 1)/("2x"^2 - "x" - 1)` dx

Evaluate: `int (2"x"^3 - 3"x"^2 - 9"x" + 1)/("2x"^2 - "x" - 10)` dx

Evaluate: `int (1 + log "x")/("x"(3 + log "x")(2 + 3 log "x"))` dx

For the certain bivariate data on 5 pairs of observations given

∑x = 20, ∑y = 20, ∑x² = 90, ∑y² = 90, ∑xy = 76

Calculate: 

1. cov(x, y)
2. b_yx and b_xy
3. r

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Addictive models of time series _______ independence of its components.