HSC Commerce Class 12 - Tamil Nadu Board of Secondary Education Question Bank Solutions for Business Mathematics and Statistics

Consider the following transportation problem

Determine an initial basic feasible solution using Least cost method

Consider the following transportation problem

Determine an initial basic feasible solution using Vogel’s approximation method

Determine an initial basic feasible solution to the following transportation problem by using north west corner rule

Determine an initial basic feasible solution to the following transportation problem by using least cost method

Explain Vogel’s approximation method by obtaining initial basic feasible solution of the following transportation problem.

Using second fundamental theorem, evaluate the following:

`int_0^1 "e"^(2x)  "d"x`

Using second fundamental theorem, evaluate the following:

`int_0^(1/4) sqrt(1 - 4)  "d"x`

Using second fundamental theorem, evaluate the following:

`int_1^2 (x "d"x)/(x^2 + 1)`

Using second fundamental theorem, evaluate the following:

`int_0^3 ("e"^x "d"x)/(1 + "e"^x)`

Using second fundamental theorem, evaluate the following:

`int_0^1 x"e"^(x^2)  "d"x`

Using second fundamental theorem, evaluate the following:

`int_1^"e" ("d"x)/(x(1 + logx)^3`

Using second fundamental theorem, evaluate the following:

`int_(-1)^1 (2x + 3)/(x^2 + 3x + 7)  "d"x`

Using second fundamental theorem, evaluate the following:

`int_0^(pi/2) sqrt(1 + cos x)  "d"x`

Using second fundamental theorem, evaluate the following:

`int_1^2 (x - 1)/x^2  "d"x`

Evaluate the following:

`int_1^4` f(x) dx where f(x) = `{{:(4x + 3",", 1 ≤ x ≤ 2),(3x + 5",", 2 < x ≤ 4):}`

Evaluate the following:

`int_0^2 "f"(x)  "d"x` where f(x) = `{{:(3 - 2x - x^2",", x ≤ 1),(x^2 + 2x - 3",", 1 < x ≤ 2):}`

Evaluate the following:

`int_(-1)^1 "f"(x)  "d"x` where f(x) = `{{:(x",", x ≥ 0),(-x",", x  < 0):}`

Evaluate the following:

f(x) = `{{:("c"x",", 0 < x < 1),(0",",  "otherwise"):}` Find 'c" if `int_0^1 "f"(x)  "d"x` = 2

Evaluate the following using properties of definite integral:

`int_(- pi/4)^(pi/4) x^3 cos^3 x  "d"x`

Evaluate the following using properties of definite integral:

`int_(- pi/2)^(pi/2) sin^2theta  "d"theta`