The number of real roots of equation loge(x) + ex = 0 is
0
1
2
3
B.
1
We have,
Since, both the graphs intersect at only one point.
Hence, the number of real roots of equation is one.
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
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