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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 .

Vectors

Differential Equations

Application of Integrals

Find the area bounded by the curve:

and the line: