Numerical Appli...

Number of five-digit numbers divisible by 5 that can be formed from the digits $$0,1, 2, 3, 4, 5$$ without repetition of digits are

$$S, T$$ and $$U$$ can complete a work in $$40, 48$$ and $$60$$ days respectively. They received$$Rs. 10800$$ to complete the work. They begin the work together but $$T$$ left $$2$$ days before the completion of the work and $$U$$ left $$5$$ days before the completion of work. $$S$$ has completed the remaining work alone. What is the share of $$S$$ (in Rs) from total money.

Let $$5 < n_1 < n_2 < n_3 < n_4$$ be integers such that $$n_1+n_2+n_3+n_4=35$$. The number of such distinct arrangements $$(n_1, n_2, n_3, n_4)$$.

Let $$p=\dfrac{1}{1\times2}+\dfrac{1}{3\times4}+\dfrac{5}{1\times6}+.......+\dfrac{1}{2013\times2014}$$ and $$Q=\dfrac{1}{1008\times2014}+\dfrac{1}{1009\times2013}+.........+\dfrac{1}{2014\times1008}$$
then $$\dfrac{P}{Q}=$$

Let the eleven letters, $$A, B, ....K$$ denote an artbitrary permutation of the integers $$(1,2,....11)$$, then $$(A-1)(B-2)(C-3)...(K-11)$$ is

Ten persons, amongst whom are $$A$$,$$B$$ and $$C$$ to speak at a function. The number of ways in which it can be done if $$A$$ wants to speak before $$B$$ AND $$B$$ wants to speak before $$C$$ is 

$$24$$ men working at $$8$$ hours per day can do a piece of work in $$15$$ days. In how many days can $$20$$ men working at $$9$$ hours per day do the same work?

$$10$$ Men begin to work together on a job, but after some days, $$4$$ if them left the job. As a result the job which could have  been completed in $$40$$ days is completed in $$50$$ days. How many days after the commencement of the work did the $$4$$ men level?

The number of permutation of the letters of the word $$HINDUSTAN$$ such that neither the pattern $$'HIN'$$ nor $$'DUS'$$ nor $$'TAN'$$ appears, are :