## Monday, December 31, 2012

### Question 12/31/2012 10:06

What is the probability that the arrangement has both consecutive W's and consecutive Y's in WYSIWYG?

Ans. 0.0952

## Tuesday, December 25, 2012

### Question 12/25/2012 2012 7:23

In how many ways may fifty-two cards be divided amongst tour players, so that each may have thirteen ?

Ans. $\frac{52!}{(13!)^4}$

### Question 12/25/2012 6:57

In how many ways can three boys divide twelve oranges, each taking four, the oranges being all of different sizes ?

Ans. 34650

### Question 12/25/2012 5:45

Four flags are to be hoisted on one mast, and there are twenty different flags to choose from : what choice have we ?

Ans. 116280

### Question 12/25/2012 4:22

Probability of n Heads in 2n Tosses of a Coin?

Ans. $\frac{(2n)!}{{(n!)^2}{2^{(2n)}}}$

## Monday, December 24, 2012

### Question 12/24/2012 9:47

In how many ways can the following letters be divided between two persons :

a, a, a, a, b, b, b, c, c, d?

Ans. 118

### Question 12/24/2012 9:37

In how many ways can six different things be divided into two parcels ?

Ans. 31

### Question 12/24/2012 9:23

There are twenty candidates for an office, and seven electors. In how many ways can the votes be given ?

Ans. 1280000000

### Question 24/12/2012 7:14

In how many ways can you arrange on a shelf 6 books out of 10 (distinct) books?

Ans. 151200

### Question 12/24/2012 1:59

How many integers between 100 and 999 inclusive consist of distinct odd digits?

Ans. 60

## Sunday, December 23, 2012

### Question 11/23/2012 11:211

Suppose it is estimated that the chance that A can solve a certain problem is $\frac{2}{3}$ , and the chance that B can solve it is $\frac{5}{12}$ ;let us consider what is the chance of the problem being solved when they both try.

Ans.  $\frac{29}{36}$

## Wednesday, March 28, 2012

### Question Calculus 28/03/2012 10:58

$\int \! \frac{x^{2}}{\sqrt[4]{x^{3}+2}} \, \mathrm{d} x$

Ans $\frac{4}{9}({x^{3}+2})^{\frac{3}{4}}+C$

### Question Calculus 28/03/2012 10:45

$\int \! \frac{1}{e^{x}+1} \, \mathrm{d} x$

Ans: $x-\ln­|e^{x}+1|)+C$

### Question Calculus 28/03/2012 10:10

$\int \! \frac{(1+x)^{2}}{\sqrt{x}} \, \mathrm{d} x$

Ans $2x^{\frac{1}{2}}+\frac{4}{3}x^{\frac{3}{2}}+\frac{2}{5}x^{\frac{5}{2}}+C$

### Question Calculus 28/03/2012 2:05

$\int \! \frac{x^{3}}{x+1} \, \mathrm{d} x$

Answer $\frac{x^{3}}{3}-\frac{x^{2}}{2}+x-\ln(x+1)+C$

### Question Calculus 28/03/2012 2:02

$\int \! \frac{2x-1}{2x+3} \, \mathrm{d} x$

Answer $x-2\ln(2x+3)+C$

### Question Calculus 28/03/2012 1:52

$\int \! \frac{1}{x^{3}} \, \mathrm{d} x$

Answer $-\frac{1}{2x^{2}}+C$

## Monday, March 5, 2012

### Question Calculus 5/03/2012 11:15

$\lim_{x \to \infty} \frac{x^2x^{\frac{1}{2}} -1}{x^{3}+x^{2}-6}$

### Question Calculus 5/03/2012 11:11

$\lim_{x \to 3} \frac{6-\frac{18}{x}}{x-3}$

### Question Calculus 5/03/2012 10:56

$\lim_{x \to 3} \frac{x^2 -9}{2x-6}$

Answer : $0.9215$