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Mathematical Induction and Binomial Theorem

54 Questions
All Exams JEE Mains JEE Advanced
1994 JEE Advanced Numerical
IIT-JEE 1994
Let $n$ be positive integer. If the coefficients of 2nd, 3rd, and 4th terms in the expansion of ${\left( {1 + x} \right)^n}$ are in A.P., then the value of $n$ is ................
1983 JEE Advanced Numerical
IIT-JEE 1983
If ${\left( {1 + ax} \right)^n} = 1 + 8x + 24{x^2} + .....$ then $a=..........$ and $n =............$
1982 JEE Advanced Numerical
IIT-JEE 1982
The sum of the coefficients of the plynomial ${\left( {1 + x - 3{x^2}} \right)^{2163}}$ is ...............
1982 JEE Advanced Numerical
IIT-JEE 1982
The larger of ${99^{50}} + {100^{50}}$ and ${101^{50}}$ is ..............