HSC Science (General) 12th Standard Board Exam - Maharashtra State Board Important Questions for Mathematics and Statistics

A company manufactures bicycles and tricycles each of which must be processed through machines A and B. Machine A has maximum of 120 hours available and machine B has maximum of 180 hours available. Manufacturing a bicycle requires 6 hours on machine A and 3 hours on machine B. Manufacturing a tricycle requires 4 hours on machine A and 10 hours on machine B.
If profits are Rs. 180 for a bicycle and Rs. 220 for a tricycle, formulate and solve the L.P.P. to determine the number of bicycles and tricycles that should be manufactured in order to maximize the profit.

Solve the following L. P. P. graphically:Linear Programming

Minimize Z = 6x + 2y

Subject to

5x + 9y ≤ 90

x + y ≥ 4

y ≤ 8

x ≥ 0, y ≥ 0

Solve the following LPP by graphical method:

Minimize Z = 7x + y subject to 5x + y ≥ 5, x + y ≥ 3, x ≥ 0, y ≥ 0

 Maximize: z = 3x + 5y  Subject to

x +4y ≤ 24                3x + y  ≤ 21 

x + y ≤ 9                     x ≥ 0 , y ≥0

Feasible region is the set of points which satisfy ______.

Find the graphical solution for the system of linear inequation 2x + y ≤ 2, x − y ≤ 1

If `y=cos^-1(2xsqrt(1-x^2))`, find dy/dx

If  `log_10((x^3-y^3)/(x^3+y^3))=2 "then show that"  dy/dx = [-99x^2]/[101y^2]`

Find `dy/dx if y=cos^-1(sqrt(x))`

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

If `y=sec^-1((sqrtx-1)/(x+sqrtx))+sin_1((x+sqrtx)/(sqrtx-1)), `

(A) x

(B) 1/x

(C) 1

(D) 0

If x = f(t), y = g(t) are differentiable functions of parammeter ‘ t ’ then prove that y is a differentiable function of 'x' and  hence, find dy/dx if x=a cost, y=a sint

If x=at², y= 2at , then find dy/dx.

If `x=a(t-1/t),y=a(t+1/t)`, then show that `dy/dx=x/y`

If `ax^2+2hxy+by^2=0` , show that `(d^2y)/(dx^2)=0`

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`

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.

Derivatives of  tan³θ with respect to sec³θ at θ=π/3 is

(A)` 3/2`

(B) `sqrt3/2`

(C) `1/2`

(D) `-sqrt3/2`