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Find the co-ordinates of the foot of the perpendicular drawn from the point (0, 2, 3) to the line `(x + 3)/(5) = (y - 1)/(2) = (z + 4)/(3)`.
Concept: Equation of a Plane
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: Methods to Find the Solution of L.P.P> Graphical Method
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 Fraction
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)
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
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
Obtain an expression for the orbital magnetic moment of an electron rotating about the nucleus in an atom.
Concept: Origin of Magnetism in Materials
State the principle on which transformer works.
Concept: Transformers
State Lenz’s Law.
Concept: Faraday's Laws of Electromagnetic Induction
What is electromagnetic induction?
Concept: Electromagnetic Induction
