Let x1, x2, ..., x15 be 15 distinct numbers chosen from 1, 2, 3, ..., 15. Then, the value of (x1 - 1)(x2 - 1)(x3 - 1)...(x15 - 1) is
always 0
0
always even
always odd
B.
0
Since x1, x2, ..., x15 be 15 distinct numbers chosen from 1, 2, 3, ..., 15. So, x1 can take any value from 1, 2, 3, ... , 15. Among these values, one of the number must be 1, hence product will be 0.
A particle starts moving from rest from a fixed point in a fixed direction. The distance s from the fixed point at a time t is given by s = t2 + at - b + 17, where a and b are real numbers. If the particle comes to rest after 5 s at a distance of s = 25 units from the fixed point, then values of a and b are, respectively
10, - 33
- 10, - 33
- 8, 33
- 10, 33
If the vertex of the conic y - 4y = 4x - 4a always lies between the straight lines x + y = 3 and 2x + 2y - 1 = 0, then
2 < a < 4
0 < a < 2