(d) Simplify: `a^n times b^n times c^n times d^n`

The time of flight of a body becomes n times the original value if its speed is made n times. This due to the range of the projectile which becomes n times.

The resistance of a wire is 'R' ohm. If it is melted and stretched to n times its origianl length, its new resistance will be (a) nR (b) R/n (c) n^(2)R (d) R/(n^(2))

A coin is tossed 2n times. The chance that the number of times one gets head is not equal to the number of times one gets tails is ((2n !))/((n !)^2)(1/2)^(2n) b. 1-((2n !))/((n !)^2) c. 1-((2n !))/((n !)^2)1/(4^n)^ d. none of these

Simplify the following: (i)\ (3^n\ xx\ 9^(n+1))/(3^(n-1)\ xx\ 9^(n-1)) ,

If ""^(n)C _r denotes the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals

If A=d i ag\ (a\ \ b\ \ c) , show that A^n=d i ag\ (a^n\ \ b^n\ \ c^n) for all positive integer n .

If ""^(n)C _r denots the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals ""^(n+2) C_(r+1)

If ""^(n)C _r denots the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals ""^(n+2) C _(r+1)

If ""^(n)C _4 denots the numbers of combinations of n things taken r at a time, then the expression ""^(n) C_(r+1) +""^(n)C_(r-1) +2 xx ""^(n)C_r equals ""^(n+2)C_(r+1)

Simplify each of the following: (a)\ (7^n-3\ xx\ 7^(n+1))/(20\ xx\ 7^n-2\ xx\ 7^n) (b)\ (5^n-6\ xx\ 5^(n+1))/(9\ xx\ 5^n-2^2xx\ 5^n) (c)\ (16\ xx\ 2^(n+1)-4\ xx\ 2^n)/(16\ xx\ 2^(n+2)-2\ xx\ 2^(n+2))