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

find dy/dx if `y=tan^-1((6x)/(1-5x^2))`

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, 

Find `dy/dx` if `y = tan^(-1) ((5x+ 1)/(3-x-6x^2))`

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. 

If `x^y = e^(x - y)` , show that `(dy)/(dx) = logx/(1 + logx)^2`

If `x^y = e^(x - y)` , show that `(dy)/(dx) = logx/(1 + logx)^2`

The total cost function of a firm is C = x² + 75x + 1600 for output x. Find the  output for which the average cost ls minimum. Is C_A= C_m at this output?  

A doctor has prescribed two different units of foods A and B to form a weekly diet for a sick person. The minimum requirements of fats, carbohydrates and proteins are 18, 28, 14 units respectively. One unit of food A has 4 units of fat, 14 units of carbohydrates and 8 units of protein. One unit of food B has 6 units of fat, 12 units of carbohydrates and 8 units of protein. The price of food A is ₹ 4.5 per unit and that of food B is ₹ 3.5 per unit. Form the LPP, so that the sick person’s diet meets the requirements at a minimum cost.

If John drives a car at a speed of 60 km/hour, he has to spend ₹ 5 per km on petrol. If he drives at a faster speed of 90 km/hour, the cost of petrol increases ₹ 8 per km. He has ₹ 600 to spend on petrol and wishes to travel the maximum distance within an hour. Formulate the above problem as L.P.P.