Find the number of trailing zeroes in $105!$

Important Questions on Permutations and Combinations

MEDIUM

Mathematics>Algebra>Permutations and Combinations>Permutations

The largest non-negative integer $k$ such that ${24}^k$ divides $13!$ is

EASY

Mathematics>Algebra>Permutations and Combinations>Permutations

If $*=+, /=-,+=*,-=/$ then $43\times 561+500-100/10=?$$43^{*} 561+500-100 / 10=?$

EASY

Mathematics>Algebra>Permutations and Combinations>Permutations

The exponent of $6$ in $72!$ is

EASY

Mathematics>Algebra>Permutations and Combinations>Permutations

The largest natural number $n$ such that $3^n$ divides $66!$ is $\_\_\_\_\_\_\_$

HARD

Mathematics>Algebra>Permutations and Combinations>Permutations

If $\sum _{r=1}^{10}r!\left(r^3+6r^2+2r+5\right)=\alpha \left(11!\right)$, then the value of $\alpha$ is equal to ___ .

MEDIUM

Mathematics>Algebra>Permutations and Combinations>Permutations

The number of distinct primes dividing $12!+13!+14!$ Is

MEDIUM

Mathematics>Algebra>Permutations and Combinations>Permutations

A natural number $n$ such that $n!$ ends in exactly $1000$  zeros is

HARD

Mathematics>Algebra>Permutations and Combinations>Permutations

The number of $3$ digit numbers, that are divisible by either $3$ or $4$ but not divisible by $48$ , is

MEDIUM

Mathematics>Algebra>Permutations and Combinations>Permutations

The largest power of $2$ that divides $\frac{200!}{100!}$ is

HARD

Mathematics>Algebra>Permutations and Combinations>Permutations

Among the inequalities below, which ones are true for all natural numbers $n$ greater than $1000$ ?
I. $n!\le n^n$
II. ${\left(n!\right)}^2\le n^n$
III. ${10}^n\le n!$
IV. $n^n\le \left(2n\right)!$

MEDIUM

Mathematics>Algebra>Permutations and Combinations>Permutations

How many natural numbers $n$ are there such that $\mathrm{n}!+10$ is a perfect square ?

MEDIUM

Mathematics>Algebra>Permutations and Combinations>Permutations

If $500!=2^{n}x$ is an integer, then

MEDIUM

Mathematics>Algebra>Permutations and Combinations>Permutations

The remainder when $x=1!+2!+3!+\mathrm{.....}+100!$ is divided by $240$, is

EASY

Mathematics>Algebra>Permutations and Combinations>Permutations

The missing value in the following figure is

MEDIUM

Mathematics>Algebra>Permutations and Combinations>Permutations

For which value of $n\in N, n!$ has $13$ trailing zeros?

MEDIUM

Mathematics>Algebra>Permutations and Combinations>Permutations

If $\frac{{\mathrm{ }}^{\mathrm{n}}{\mathrm{P}}_{\mathrm{r}-1}}{\mathrm{a}}=\frac{{\mathrm{ }}^{\mathrm{n}}{\mathrm{P}}_{\mathrm{r}}}{\mathrm{b}}=\frac{{\mathrm{ }}^{\mathrm{n}}{\mathrm{P}}_{\mathrm{r}+1}}{\mathrm{c}}$ then

EASY

Mathematics>Algebra>Permutations and Combinations>Permutations

The greatest positive integer which divides $\left(n+16\right) \left(n+17\right) \left(n+18\right) \left(n+19\right)$, for all positive integers $n$, is

EASY

Mathematics>Algebra>Permutations and Combinations>Permutations

For integer $n > 1$, the digit at unit place in the number $\sum _{r=0}^{100}r!+2^{2^n}$ is equal to .....

MEDIUM

Mathematics>Algebra>Permutations and Combinations>Permutations

In how many ways $3$ letters can be posted in $4$ letter-boxes, if all the letters are not posted in the same letter-box

EASY

Mathematics>Algebra>Permutations and Combinations>Permutations

Two numbers are: a= 3607 and b= 2601