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A manufacturer produces two products A and B. Both the products are processed on two different machines. The available capacity of first machine is 12 hours and that of second machine is 9 hours per day. Each unit of product A requires 3 hours on both machines and each unit of product B requires 2 hours on first machine and 1 hour on second machine. Each unit of product A is sold at Rs 7 profit and B at a profit of Rs 4. Find the production level per day for maximum profit graphically.
Concept: Graphical Method of Solving Linear Programming Problems
Find the derivative of the inverse of function y = 2x3 – 6x and calculate its value at x = −2
Concept: Derivatives of Inverse Functions
If y = cos(m cos–1x), then show that `(1 - x^2) ("d"^2y)/("d"x^2) - x("d"y)/("d"x) + "m"^2y` = 0
Concept: Higher Order Derivatives
The displacement of a particle at time t is given by s = 2t3 – 5t2 + 4t – 3. Find the velocity when ЁЭСб = 2 sec
Concept: Derivatives as a Rate Measure
Find `intsqrtx/sqrt(a^3-x^3)dx`
Concept: Methods of Integration: Integration by Substitution
Choose the correct alternative:
`int (x + 2)/(2x^2 + 6x + 5) "d"x = "p"int (4x + 6)/(2x^2 + 6x + 5) "d"x + 1/2 int 1/(2x^2 + 6x + 5)"d"x`, then p = ?
Concept: Methods of Integration: Integration Using Partial Fractions
If the population of a town increases at a rate proportional to the population at that time. If the population increases from 40 thousand to 60 thousand in 40 years, what will be the population in another 20 years? `("Given" sqrt(3/2) = 1.2247)`
Concept: Application of Differential Equations
From a lot of 15 bulbs which include 5 defectives, a sample of 4 bulbs is drawn one by one with replacement. Find the probability distribution of number of defective bulbs. Hence find the mean of the distribution.
Concept: Random Variables and Its Probability Distributions
Draw a diagram showing all components of forces acting on a vehicle moving on a curved banked road.
Concept: Banking of Roads
Derive an expression for the kinetic energy of a rotating body with uniform angular velocity.
Concept: Rotational Dynamics
State the theorem of parallel axes about moment of inertia.
Concept: Physical Significance of M.I (Moment of Inertia)
Derive an expression for maximum work in isothermal reversible expansion of two moles of an ideal gas.
Concept: Chemical Thermodynamics and Energetic >> First Law of Thermodynamics
Obtain the differential equation of linear simple harmonic motion.
Concept: Differential Equation of Linear S.H.M.
Obtain the differential equation of linear simple harmonic motion.
Concept: Differential Equation of Linear S.H.M.
What is Brewster’s law? Derive the formula for Brewster’s angle.
Concept: Polarization
Derive an expression for maximum work in isothermal reversible expansion of two moles of an ideal gas.
Concept: Chemical Thermodynamics and Energetic >> First Law of Thermodynamics
What is the value of resistance for an ideal voltmeter?
Concept: Potentiometer
A solenoid of length π m and 5 cm in diameter has a winding of 1000 turns and carries a current of 5 A. Calculate the magnetic field at its centre along the radius.
Concept: Applications of AmpereтАЩs Circuital Law > Magnetic Field of a Toroidal Solenoid
What is Magnetic intensity?
Concept: Magnetisation and Magnetic Intensity
