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

Evaluate `int (2"e"^x + 5)/(2"e"^x + 1)  "d"x`

Evaluate `int x log x  "d"x`

Evaluate `int x^2"e"^(4x)  "d"x`

`int x/((x - 1)^2 (x + 2)) "d"x`

`int 1/(4x^2 - 20x + 17)  "d"x`

`int (3"e"^(2"t") + 5)/(4"e"^(2"t") - 5)  "dt"`

State whether the following statement is True or False:

A differential equation in which the dependent variable, say y, depends only on one independent variable, say x, is called as ordinary differential equation

Choose the correct alternative:

The regression line is obtained by

Choose the correct alternative:

The objective of sequencing problem is ______

In sequencing problems one has to ______ the total processing time or cost

In sequencing problem the time which required to complete all the jobs i.e. entire task is called ______

In sequencing problem one has to determine the ______ in which jobs has to processed through the machines

State whether the following statement is True or False:

In sequencing problem the processing times are dependent of order of processing the jobs on machine

Solve the following problem of sequencing for minimizing the total elapsed time and idle time for both the machines.

The optimal sequence of the jobs as follows:

Total elasped time is obtained as follows:

Total elapsed time T = `square` minutes

Idle time for Machine A = T – `square` = `square` minutes

Idle time for Machine B = `square`

Determine whether the following statement pattern is a tautology, contradiction, or contingency:

[(∼ p ∧ q) ∧ (q ∧ r)] ∧ (∼ q)

Solve the following differential equation

x²y dx – (x³ + y³)dy = 0

Complete the following activity to 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)I²

when I = 1000

Find `(d^2y)/(dy^2)`, if y = e^4x

If elasticity of demand η = 0 then demand is ______.

If f(x) = x³ – 3x² + 3x – 100, x ∈ R then f"(x) is ______.