1A. Find the lowest positive angle that satisfies the equation expressed in degrees.
Now this gives
Thus the possible values of are or .
Since we require the smallest positive angle hence the answer is .
1B Let n be two times the tens digit of TNYWR. Find the coefficient of the term in the expansion of
TNYWR is 3. Hence n = 6 Thus we are required to find coefficient of term in the expansion of
This can be easily found from trinomial expansion. The required term is
1C Let k be TNYWR, and let n = k/2. Find the smallest integer m greater than n such that 15
divides m and 12 divides the number of positive integer factors of m.
k = 198, hence n = 99.
So we have to look at multiples of 15 greater than 99. We want 12 to divide the number of positive divisors of m.
Suppose . The number positive divisors of k is
The first multiple of 15 greater than 99 is . By inspection we see that m = 150.