Forum

Motion

Joseph jogs from one end A to the other end B of a straight 300 m road in 2 minutes 30 seconds and then turns around and jogs 100 m back to point C in another 1 minute. What are Joseph’s average speeds and velocities in jogging (a) from A to B and (b) from A to C?

Motion

An athlete completes one round of a circular track of diameter 200 m in 40 s. What will be the distance covered and the displacement at the end of 2 minutes 20 s?

Complex Numbers

Find the modulus and argument of the complex number:

Binomial Theorem

Expand  using the binomial theorem and find the term independent of x.

Principle of Mathematical Induction

 Prove by mathematical induction that: 1+3+5+…+(2n−1)=n².

Trigonometric Identities

Sets and Functions

Probability

A box contains 5 red, 4 white, and 6 blue balls. Two balls are drawn at random. Find the probability that they are both of the same color.

Linear Programming

A manufacturer produces two types of products A and B, which require 2 hours and 3 hours respectively for production on machine I, and 4 hours and 2 hours respectively on machine II. The machine I has 20 hours and machine II has 18 hours available per week. The profit on each product of type A is ₹6 and on type B is ₹8. Formulate the problem as a linear programming problem to maximize the profit.

Three-Dimensional Geometry

Find the equation of the plane passing through the point (1,−2,3) and perpendicular to the vector .