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### The maximum and minimum distances of a comet ....

The maximum and minimum distances of a comet from the Sun are $1.6 \times 10^{12}$ m and $8.0 \times 10^{10}$ m respectively. If the speed of the comet at the nearest point is $6 \times 10^4$ m/s, the speed at the farthest point is:

(A) $3.0 \times 10^3$ m/s
(B) $1.5 \times 10^3$ m/s
(C) $4.5 \times 10^3$ m/s
(D) $6.0 \times 10^3$ m/s

Solution

We have, $v_1 r_1 = v_2 r_2$

$\therefore v_1 \times 1.6 \times 10^{12} = 6 \times 10^4 \times 8.0 \times 10^ {10}$

$\Rightarrow v_1 = 3.0 \times 10^3$ m/s

### Sum of the coefficients in the expansion of $(x+y)^n$ ....
If the sum of the coefficients in the expansion of $(x+y)^n$ is 4096, then the greatest coefficient in the expansion is _ _ _ _ . Solution $C_0 + C_1 + C_2 + C_3 + ......................... + C_n =4096$ $\therefore 2^n = 4096 =2^{12}$ $\Rightarrow n = 12$ Greatest coefficient = ${}^{12}{C_6} = 924$