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

Find `dy/(dx)` if, y = `e^(5x^2 - 2x + 4)`

If y = `root{5}{(3x^2 + 8x + 5)^4)`, find `(dy)/(dx)`

Find `dy/dx` if, `y = e^(5x^2 - 2x +  4)`.

Solve the following:

If y = `root5((3x^2 + 8x + 5)^4)`, find `dy/(dx)`.

Evaluate `int1/(x(x - 1))  dx`

Price P for demand D is given as P = 183 +120D - 3D² Find D for which the price is increasing

Write down the following statements in symbolic form :

(A) A triangle is equilateral if and only if it is equiangular.
(B) Price increases and demand falls

Test whether the function is increasing or decreasing. 

f(x) = `"x" -1/"x"`, x ∈ R, x ≠ 0, 

The price P for demand D is given as P = 183 + 120 D – 3D².
Find D for which the price is increasing.

If x = cos2 θ and y = cot θ then find `dy/dx  at  θ=pi/4` 

The consumption expenditure E_c of a person with the income x. is given by E_c = 0.0006x² + 0.003x. Find MPC, MPS, APC and APS when the income x = 200.

Find `dy/dx,if e^x+e^y=e^(x-y)`

Using truth table show that ∼ (p → ∼ q) ≡ p ∧ q 

Evaluate: ∫ x . log x dx

For manufacturing x units, labour cost is 150 – 54x and processing cost is x². Price of each unit is p = 10800 – 4x². Find the value of x for which Total cost is decreasing.

The total cost of manufacturing x articles is C = 47x + 300x² − x⁴.  Find x, for which average cost is increasing.

Write converse, inverse contrapositive of the statement "If two triangles are not congruent then their areas are not equal.

Find MPC ( Marginal propensity to Consume ) and APC ( Average Propensity to Consume ) 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.

If the demand function is D = 50 - 3p - p², find the elasticity of demand at (a) p = 5 (b) p = 2 ,  Interpret your result. 

Find the area of the ellipse `x^2/4 + y^2/25 = 1`