For what value of the system of equations x + y + z = 6, x + 2y + 3z = 10, x + 2y + z = 10 is consistent ?
1
2
- 1
3
Let f(x) be twice differentiable such that f''(x) = - f(x), f'(x) = g(x), where f'(x) and f''(x) represent the first and second derivatives of f(x) respectively. Also, if h(x) = [f(x)]2 + [g(x)]2 and h(S) = 5, then h(10) is equal to :
3
10
13
5
If a = 1 + 2 + 4 + ... to n terms, b = 1 + 3 + 9 + ... to n terms and c = 1 + 5 + 25 + ... to n terms, then
equals :
(30)n
(10)n
0
2n + 3n + 5n
For non-singular square matrices A, B and C of the same order, (AB-1C)-1 is equal to :
A-1BC-1
C-1B-1A-1
CBA-1
C-1BA-1
Let A = and B = , then AB = 0 if :
C.
where, n = 0, 1, 2, ...
If a particle is moving such that the velocity acquired is proportional to the square root of the distance covered, then its acceleration is :
a constant