Sequences and S...

If P (n, n) denotes the number of permutations of n different things taken all at a time then P (n, n ) is also identical to:

Observe the given pattern
$4\times 0+1=01$
$4\times1+2=06$ 
$4\times 2+3=11$
$4\times 3+4=16$
Then the value of $4\times8+9$ is -----

When we realize a specific implementation of a pancake algorithm, every move when we find the greatest of the sized array and flipping can be modeled through ____________.

The value of $\displaystyle E = \frac { (1+17)(1+\frac { 17 }{ 2 } )(1+\frac { 17 }{ 3 } )......(1+\frac { 17 }{ 19 } ) }{ (1+19)(1+\frac { 19 }{ 2 } )(1+\frac { 19 }{ 3 } ).....(1+\frac { 19 }{ 17 } ) }$ is,

A point $(a, b)$ is called a good point if both $a$ and $b$ are integers. Number of good points on the curve $xy$ $=$ $225$ are

The area of a triangle with vertices $(a, b + c), (b, c + a)$ and $(c, a + b)$ is

 In a class there are $10$ boys and $8$ girls. The teacher wants to select either a boy or a girl to represent the class in a function. The number of ways the teacher can make this selection.

Plot $(3, 0), (5, 0)$ and $(0, 4)$ on cartesian plane. Name the figure formed by joining these points and find its area.

The area of a triangle with vertices $A (3, 0), B (7, 0)$ and $C (8, 4)$ is

Three Men have $4$ coats $5$ waist Coats, and $6$ caps. The number of ways they can wear them is