New chat PYQ Library Doubts Rank report

Sign in to see Recents

Sign in to save progress →

Binomial Theorem question

2025 · 7 Apr · Shift 1 · Q34

Guest · try one question or challengeGuest · try one question or challenge

PYQ Library
JEE Main
Mathematics
Binomial Theorem
2025 · 7 Apr · Shift 1 · Q34

Binomial Theorem question

2025 · 7 Apr · Shift 1 · Q34

JEE MainMathematicsBinomial TheoremMCQ+4 / −1

The remainder when

\left((64)^{(64)}\right)^{(64)}

is divided by 7 is equal to

A
4
B
6
C
3
D
1

More from Binomial Theorem

The sum of the series $2 \times 1 \times^{20} C_{4} - 3 \times 2 \times^{20} C_{5} + 4 \times 3 \times^{20} C_{6} - 5 \times 4 \times^{20} C_{7} + \dots\dots + 18 \times 17 \times^{20} C_{20}$ ,…2025 · Numerical
The number of integral terms in the expansion of $(5^{\frac{1}{2}} + 7^{\frac{1}{8}})^{1016}$ is:2025 · MCQ
The product of the last two digits of $(1919)^{1919}$ is2025 · Numerical
If $\sum_{r = 0}^{5} \frac{^{11} C _{2 r + 1}}{2 r + 2} = \frac{m}{n}, gcd (m, n) = 1$ , then $m - n$ is equal to .2025 · Numerical
Let $α, β, γ$ and $δ$ be the coefficients of $x^{7}, x^{5}, x^{3}$ and $x$ respectively in the expansion of $(x + x^{3} - 1)^{5} + (x - x^{3} - 1)^{5}, x > 1 . If u and v satisfy the equations α u + β v = 18, γ u + δ v = 20,$ …2025 · MCQ
If $\sum_{r = 1}^{30} \frac{r ^{2} ( ^{30} C _{r} ) ^{2}}{^{30} C _{r - 1}} = α \times 2^{29}$ , then $α$ is equal to .2025 · Numerical
The sum of all rational terms in the expansion of $(1 + 2^{1/3} + 3^{1/2})^{6}$ is equal to .2025 · Numerical
If in the expansion of $(1 + x)^{p} (1 - x)^{q}$ , the coefficients of $x$ and $x^{2}$ are 1 and -2 , respectively, then $p^{2} + q^{2}$ is equal to :2025 · MCQ