HSC Commerce: Marketing and Salesmanship इयत्ता १२ वी - Maharashtra State Board Question Bank Solutions

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

Fill in the blank :

Addictive models of time series _______ independence of its components.

Fill in the blank :

Multiplicative models of time series _______ independence of its components.

State whether the following is True or False :

Additive model of time series does not require the assumption of independence of its components.

State whether the following is True or False :

Multiplicative model of time series does not require the assumption of independence of its components.

The time interval between starting the first job and completing the last job including the idle time (if any) in a particular order by the given set of machines is called _______.

Fill in the blank :

In a sequencing problem, all machines are of _______ types.

If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x)` is ______

State whether the following statement is True or False:

If `sqrt(x) + sqrt(y) = sqrt("a")`, then `("d"y)/("d"x) = 1/(2sqrt(x)) + 1/(2sqrt(y)) = 1/(2sqrt("a"))`

If the marginal revenue is 28 and elasticity of demand is 3, then the price is ______.