Binomial Theorem Questions for CAT

In the expansion of $(1+4x)^{10}$, which term is the greatest when $x=1$?

Find the coefficient of $x^6$ in $(1+x)^{12}$.

Using Binomial Theorem, approximate $(1.01)^{2}$ up to two decimals:

If $T_{r+1}$ and $T_r$ are consecutive terms of $(1+x)^9$, find $\frac{T_{r+1}}{T_r}$.

Expand up to 3 terms: $(1 - x)^{-2}$. Which is correct?

Evaluate $\sum_{r=0}^{4} \binom{4}{r} 2^r$.

Approximate $(1.005)^6$ to three decimal places:

If the ratio of the 5th term to the 4th term in the expansion of (1+x)^12 is 3:2, then the value of x is:

Let $nC_3 : nC_2 = 10 : 5$. Then the value of n is:

The sum of coefficients of odd powers of x in $(1+x)^{12}$ is:

What is the remainder when $\$(13^{100} + 17^{100})\$$ is divided by 25?

If the coefficients of $x^2$ and $x^3$ in $(1+x)^n$ are in ratio 5:6, then n equals:

If $(1+x)^8$ expansion has middle term coefficient equal to 70, find that term’s index:

If the ratio of successive terms $T_5$ and $T_4$ in $(1+x)^n$ is 2:1 when x=1, then n is:

If $nC_3:nC_2=9:4$, then n is:

In the expansion of $((1 + x)^{12})$, the ratio of the coefficients of $x^6$ to $x^5$ is:

Approximate $(0.98)^4$ using binomial theorem, up to two decimals:

The remainder when ($17^50 + 8^50$) is divided by 25 is:

In a certain examination paper, there are $n$ questions. For $j=1,2 \ldots . n$, there are $2^{n-j}$ students who answered $j$ or more questions wrongly. If the total number of wrong answers is 4095 , then the value of $n$ is (2003C)

Find the sum of the last 3 digits of number $23^{500}$.