HSC Commerce: Marketing and Salesmanship १२ वीं कक्षा - Maharashtra State Board Important Questions

If y =1 − cos θ, x = 1 − sin θ, then `dy/dx  "at"  θ =pi/4` is ______

If x=α sin 2t (1 + cos 2t) and y=β cos 2t (1−cos 2t), show that `dy/dx=β/αtan t`

If x cos(a+y)= cosy then prove that `dy/dx=(cos^2(a+y)/sina)`

Hence show that `sina(d^2y)/(dx^2)+sin2(a+y)(dy)/dx=0`

Find the value of `dy/dx " at " theta =pi/4 if x=ae^theta (sintheta-costheta) and y=ae^theta(sintheta+cos theta)`

If x = cos t (3 – 2 cos² t) and y = sin t (3 – 2 sin² t), find the value of dx/dy at t =4/π.

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

If X = f(t) and Y = g(t) Are Differentiable Functions of t ,  then prove that y is a differentiable function of x and

`"dy"/"dx" =("dy"/"dt")/("dx"/"dt" ) , "where" "dx"/"dt" ≠ 0`

Hence find `"dy"/"dx"` if x = a cos² t and y = a sin² t.

If x⁷ . y⁹ = (x + y)¹⁶ then show that `"dy"/"dx" = "y"/"x"`

If y = sin ^-1 `((8x)/(1 + 16x^2))`, find `(dy)/(dx)`

If `x^3y^5 = (x + y)^8` , then show that `(dy)/(dx) = y/x`

Evaluate : `int  (sec^2 x)/(tan^2 x + 4)` dx

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?  

Price P for demand D is given as P = 183 +120D - 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` 

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

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

Find the marginal revenue if the average revenue is 45 and elasticity of demand is 5.

A manufacturing company produces x items at the total cost of Rs (180 + 4x). The demand function of this product is P = (240 − x). Find x for which profit is increasing.

Find the elasticity of demand, if the marginal revenue is 50 and price is Rs 75.