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Find the differential equation of family of all ellipse whose major axis is twice the minor axis
Concept: Formation of Differential Equations
Verify y = log x + c is the solution of differential equation `x ("d"^2y)/("d"x^2) + ("d"y)/("d"x)` = 0
Concept: Formation of Differential Equations
For the differential equation, find the particular solution (x – y2x) dx – (y + x2y) dy = 0 when x = 2, y = 0
Concept: Differential Equations
Find the expected value, variance and standard deviation of random variable X whose probability mass function (p.m.f.) is given below:
| X = x | 1 | 2 | 3 |
| P(X) | `1/5` | `2/5` | `2/5` |
Concept: Probability Distribution of Discrete Random Variables >> Expected Value and Variance of a Random Variable
The probability mass function for X = number of major defects in a randomly selected
appliance of a certain type is
| X = x | 0 | 1 | 2 | 3 | 4 |
| P(X = x) | 0.08 | 0.15 | 0.45 | 0.27 | 0.05 |
Find the expected value and variance of X.
Concept: Mean and Variance of Binomial Distribution
If the mean and variance of a binomial distribution are 18 and 12 respectively, then n = ______.
Concept: Binomial Distribution
If X ~ B (n, p) and E(X) = 6 and Var (X) = 4.2, then find n and p.
Concept: Mean and Variance of Binomial Distribution
Prove the theorem of parallel axes about moment of inertia
Concept: Theorems of Perpendicular and Parallel Axes
Write the necessary equation for maximum safety, speed and state the significance of each term involved in it.
Concept: Banking of Roads
Define moment of inertia. State its SI unit and dimensions.
Concept: Angular Momentum or Moment of Linear Momentum
The moment of inertia of a circular loop of radius R, at a distance of R/2 around a rotating axis parallel to horizontal diameter of the loop is ______
Concept: Moment of Inertia as an Analogous Quantity for Mass
A flywheel is revolving with a constant angular velocity. A chip of its rim breaks and flies away. What will be the effect on its angular velocity?
Concept: Angular Momentum or Moment of Linear Momentum
Derive an expression for maximum safety speed with which a vehicle should move along a curved horizontal road. State the significance of it.
Concept: Rotational Dynamics
The moment of inertia of a body about a given axis is 1.2 kgm2. initially, the body is at rest. For what duration on the angular acceleration of 25 radian/sec2 must be applied about that axis in order to produce rotational kinetic energy of 1500 joule?
Concept: Moment of Inertia as an Analogous Quantity for Mass
Derive an expression for the difference in tensions at the highest and lowest point for a particle performing the vertical circular motion.
Concept: Vertical Circular Motion
Derive an expression for critical velocity of a satellite revolving around the earth in a circular orbit.
Concept: Variation in the Acceleration>Variation in Gravity with Altitude
Explain why an astronaut in an orbiting satellite has a feeling of weightlessness.
Concept: Weightlessness
State Kepler's law of orbit and law of equal areas.
Concept: Kepler’s Laws
Why two or more mercury drops form a single drop when brought in contact with each other?
Concept: Fluid and Its Properties
Two capillary tubes of radii 0.6 cm and 0.3 cm are dipped in the same liquid. The ratio of heights through which the liquid will rise in the tubes is ______.
Concept: Fluid and Its Properties
