Let f : R → R be a function defined by f(x) = min(x + 1, |x| + 1) then which of the following is true?
a) f(x) ≥ 1 for all x R
b) f(x) is not differentiable at x = 1
c) f(x) is differentiable everywhere
d) f(x) is not differentiable at x = 0
Your Answer
Evaluate
a)
b)
c)
d) 4f(2)
Let be a differentiable function having . Then, is equal to
a) 18
b) 12
c) 36
d) 24
, then equals
b) 1
d) 0
Suppose the cubic x3 – px + q has three distinct real roots when p > 0 and q > 0 then which one of the following is true?
a) The cubic has maximum at both and
b) The cubic has minimum at and maximum at
c) The cubic has minimum at and maximum at
d) The cubic has minimum at both and at
How many real solutions does the equation have a) 5
b) 7
c) 1
d) 3
The value of c for which the conclusion of mean value theorem holds for the function f(x) = lnex on the interval [1, 3] is
d)
The function f(x) = tan− 1 (sinx + cosx) is an increasing function in
The function f : R – {0} → R given by can be made continuous by defining f(0) as
a) 2
b) -1
c) 0
d) 1
The function has a local minimum at
a) x = − 2
b) x = 0
c) x = 1
d) x = 2
Angle between the tangents to the curve y = x2 – 5x + 6 at the points (2, 0) and (3, 0) is
If x is real the maximum value of is
a) 41
If xm yn = (x + y)m + n then is
b) xy
A function is matched below against an interval where it is supposed to be increasing. Which of the following pairs is incorrectly matched?
Interval
Function
A.
(−∞, −4)
x3 + 6x2 + 6
B.
3x2 – 2x + 1
C.
[2, ∞)
2x3 – 3x2 + 12x +6
D.
(−∞, ∞)
x3 − 3x2 + 3x + 3
Suppose f(x) is differentiable at x = 1 and
a) 6
b) 5
c) 4
If f is a real differentiable function satisfying |f(x) – f(y)| ≤ (x – y)2, x, y R and f(0) = 0, then f(1) equals
a) 1
b) 2
d) – 1
The normal to the curve x = a(cosθ + θsinθ), y = a(sinθ – θcosθ) at any point θ is such that
a) It is a constant distance from the origin
b) It passes through
c) It makes angle with x – axis
d) It passes through the origin
Let α, β be the distinct roots of ax2 + bx + c = 0 then is equal to
A spherical iron ball 10cm in radius is coated with a layer of ice of uniform thickness that melts at the rate of 50 cm3/min. When the thickness of ice is 15 cm than the rate at which the thickness of the ice decreases, is
If the difference between the maximum and minimum value of u2 is given by
If then the values of a, b are
a) a R, b R
b) a = 1, b R
c) a R, b = 2
d) a = 1, b = 2
Let . If f(x) is continuous in then is
If then is
The normal to the curve x = a (1 + cosθ), y = asinθ at θ always passes through the fixed point
a) (a, 0)
b) (0, a)
c) (0, 0)
d) (a, a)
