Class 11

Math

JEE Main Questions

Binomial Theorem

Evaluate the following: $(3 +1)_{5}−(3 −1)_{5}$

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Find the term in $(b a 3+a3b )_{21}$ which has the same power of $aandb˙$

Find the last three digits of the number $27_{27}˙$

If the number of terms in the expansion of $(x+y+z)_{n}$ are 36, then find the value of $n˙$

Find $a$ if the 7th and 18th terms of the expansion $(2+a)_{50}$ are equal.

Using binomial theorem (without using the formula for $_{n}C_{r}$ ) , prove that $_{n}C_{4}+_{m}C_{2}−_{m}C_{1}C_{2}=_{m}C_{4}−_{m+n}C_{1}C_{3}+_{m+n}C_{2}C_{2}−_{m+n}C_{3}C_{1}+_{m+n}C_{4}˙$

If $pandq$ are ositive, then prove that the coefficients of $x_{p}andx_{q}$ in the expansion of $(1+x)_{p+q}$ will be equal.

Find an approximation of $(0.99)_{5}$using the first three terms of its expansion.

Show that $9_{n+1}−8n−9$ is divisible by 64, where $n$ is a positive integer.