HSC Commerce (English Medium) १२ वीं कक्षा - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

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

Solve

`y log y  dx/ dy = log y  – x`

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.

The false statement in the following is ______.

Write the dual of the following

(p ˄ ∼q) ˅ (∼p ˄ q) ≡ (p ˅ q) ˄ ∼(p ˄ q)

Choose the correct alternative:

If p is any statement, then (p ˅ ~p) is a

Choose the correct alternative:

If p → q is an implication, then the implication ~q → ~p is called its

The contrapositive of p → ~ q is ______

Write the dual of the following.

13 is prime number and India is a democratic country