Test: Continuity & Differentiability(3 Sep) - JEE MCQ
15 Questions MCQ Test - Test: Continuity & Differentiability(3 Sep)
Let f : [0, 
) 
[0, 3] be a function defined by:
f(x) = 
Then which of the following is true?
) [0, 3] be a function defined by:f(x) =
Then which of the following is true?
t 
x} in x 
[0, 
]
[
, 
)
).
, 
, then 
is
and cot
in sin
and cos
:
= 
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If 'R' is the least value of 'a' such that the function f(x) = x2 + ax + 1 is increasing on [1, 2] and 'S' is the greatest value of 'a' such that the function f(x) = x2 + ax + 1 is decreasing on [1, 2], then the value of |R - S| is _______. (in integer)
x 
x ∈ [1, 2]
x ∈ [1, 2]
x ∈ [1, 2]Let f : R 
R and g : R 
R be defined as
and
where a, b are non-negative real numbers. If (gof)(x) is continuous for all x 
R, then a + b is equal to ___________. (in integer)
a + b = 1Let f : R 
R be defined as f(x) = x3 + x - 5. If g (x) is a function such that f(g(x)) = x, 
x ∈ R, then g'(63) is equal to ________.
f'(x) = 3x2 + 1 
increasing function
g(x) is the inverse of f(x).
g(f(x)) = x
g'(f(x)) f'(x) = 1
x3 + x - 5 = 63
x = 4
Let f(x) = min {1, 1 + x sin x}, 0 ≤ x ≤ 2π. If m is the number of points, where f is not differentiable and n is the number of points, where f is not continuous, then the ordered pair (m, n) is equal to
f(x) = 1 = 
f(x)
If c is a point at which Rolle's theorem holds for the function f(x) = loge 
in the interval [3, 4], where 
∈ R, then f''(c) is equal to
36 + 4
= 48 + 3
= 12
f'(x) = 
2c2 = c2 + 12 
c2 = 12
Let the functions f : 
and g : 
be defined as:
and g(x) = 
Then the number of points in 
where (fog)(x) is NOT differentiable is equal to:
fog(x) is differentiable for x 
- {0}.If f(x) = sin
and its first derivative with respect to x is -
loge2 when x = 1, where a and b are integers, then the minimum value of |a2 - b2| is ________. (in integer)
= 
f'(x) = 
f'(1) = 
|a2 - b2| = 252 - 122Let f, g : R 
R be two real valued functions defined as f(x) = 
and g(x) = 
, where k1 and k2 are real constants. If (gof) is differentiable at x = 0, then (gof) (–4) + (gof) (4) is equal to:
The value of loge2
(logcosx cosecx) at x = 
is
Let 
R be such that the function f(x) = 
is continuous at x = 0, where {x} = x - [x], [x] is the greatest integer less than or equal to x.
Then,
RHL 
LHL
No value of 
exists.If the function 
is continuous at x = 0, then k is equal to:
If for p ≠ q ≠ 0, the function f(x) = 
is continuous at x = 0, then:
The number of points where the function
where [t] denotes the greatest integer ≤ t, is discontinuous is ______________. (in integer)
x = 
, 
and 
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