If a + b + c = 0, then the quadratic equation 3 ax2 + 2 bx + c = 0 has
Imaginary roots
At least one real root in (0, 1)
One root in [2, 3] and other in [3, 6]
None of these
If x be real the minimum value of x2 - 8x + 17 is
-1
0
1
2
For the curve y = xex, the point
x = -1 is a minimum
x = -1 is a maximum
x = 0 is a minimum
x = 0 is a maximum
The function f (x) = 2x3 - 3x2 - 12x + 4 has
Two maxima
Two minima
One maxima and One minima
No maxima and minima
Two towns A and B are 60 Km apart.A school is to be built to serve 150 students in town A and 50 students in town B.If the total distance to be travelled by all 200 students is to be as small as possible, then the school should be built at
Town B
45 km. from town A
Town A
45 km. from town B
Let f (x) satisfy the requirements of Lagrange's Mean Value Theorem in [0, 2].If f (0) = 0 and | f' (x) | ≤ 1/2 for all x in [0, 2], then
f (x) ≤ 2
| f (x) | ≤ 1
f (x) = 2x
f (x) = 3 for at least one x in [0, 2]
If a differentiable function f (x) has a relative minimum at x = 0, then the function y = f i.e. y = f (x) + ax + b has a relative minimum at x = 0 for
All a and all b
All b if a = 0
All b > 0
All a > 0
The maximum value of sin x cos x is
1/4
1/2
4
If y = a log x + bx2 + x has its extremum value at x = -1 and x = 2, then
a = 2, b = -1
a = 2, b = -1/2
a = -2, b = 1/2
f (x) = 1 + [cos x] x, in 0 < x ≤ π/2
Has a maximum value 2
Is continuous in [0, π/2]
Has a minimum value 0
Is not differentiable at x = π/2
