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Free download in PDF Class 11 Maths Chapter 13 Introduction to Limits and Derivatives Multiple Choice Questions and Answers for Board, JEE, NEET, AIIMS, JIPMER, IIT-JEE, AIEE and other competitive exams. MCQ Questions for Class 11 Maths with Answers were prepared based on the latest exam pattern. These short solved questions or quizzes are provided by Gkseries. These will help the students for preparation of their examination./p>
(1)
The derivative of f(x) = |x| at x = 0 is ____.
[A]
-1
[B]
1
[C]
0
[D]
does not exist
(2)
If y = 2 sin 3x cos x, then d20y/dx20 is ____.
[A]
y20=−240cos4x−240cos2x
[B]
y20=240cos4x−240cos2x
[C]
y20=240cos4x+240cos2x
[D]
y20=240sin4x+240sin2x
Answer: y20=240sin4x+240sin2x
(3)
The displacement time relating to a speeding vehicle is given by D(t) = 5 t2- 3t + 30. Then, its speed at the end of 5 seconds is given by ____.
[A]
50 units/ sec
[B]
115 units/ sec
[C]
47 units/ sec
[D]
30 units/ sec
(4)
The point on the curve x2 + y2 - 2x + 1 = 0, at which the tangent is parallel to Y axis is given by ____.
[A]
(0, -1)
[B]
(0, 1)
[C]
(1, 0)
[D]
(-1, 0)
(5)
The degree of a polynomial function is 5. Then, the degree of it's third derivative is ____.
(6)
The number of points in (1, 2) where f(x) = a[x2],a > 1 is not differentiable is ____.
[A]
0
[B]
2
[C]
at least 5 points
[D]
3 points
(7)
The slope of the normal at the point θ=π/4 of the curve sin θ - cos θ is ____.
[A]
2
[B]
-1/2
[C]
1/2
[D]
-2
(8)
If f(x) = ex log x, then f'(x) is ____.
[A]
xf'(x) - xf(x) = e-x
[B]
ex f'(x) - ex f(x) = 1/x
[C]
f1(x) = f(x) + ex/x
[D]
f'(x) - f(x) = ex
Answer: f1(x) = f(x) + ex/x
(9)
The displacement of a particle describing a non - linear motion is given by s = (1/6) t3 - 8t. Then, the acceleration at the time when velocity vanishes is ____.
[A]
6 units/ s2
[B]
0
[C]
4 units/ s2
[D]
16 units/ s2
(10)
The mathematical expression x→a means_____
[A]
x = a
[B]
x ≠ a
[C]
x is approaching a
[D]
x is greater than a
Answer: x is approaching a
(11)
In the curve y2 = x3, the slope of the tangent at (4, 8) is ____.
[A]
4
[B]
8
[C]
1/2
[D]
3
(12)
If f(x) = emx + enx, then the second derivative f'(x) is ____.
[A]
m2emx + n2enx
[B]
memx + nenx
[C]
emx + enx
[D]
emx - enx
(13)
The deleted neighborhood of a is ____.
[A]
(a - δ, a] i.e. left neighborhood
[B]
[a, a + δ) i.e. right neighborhood
[C]
a sphere of radius 'a' with the point 'a' deleted
[D]
(a - δ, a + δ) - {a}
Answer: (a - δ, a + δ) - {a}
(14)
If y = tan x + sec x, then d2y/dx2 is ____.
[A]
0
[B]
1
[C]
y
[D]
(dy/dx)y
(15)
If y = x2 sin 2x, then the first derivative is ____.
[A]
2(x cos 2x + sin 2x)
[B]
(x cos 2x + sin 2x)
[C]
2x (x cos 2x + sin 2x)
[D]
x2 (x cos 2x + sin 2x)
Answer: 2x (x cos 2x + sin 2x)
(16)
The differential of (sin x + cos x)2is
[A]
0
[B]
cos x - sin x
[C]
2 cos 2x
[D]
cos2 x - sin2 x
(17)
In a real number line, the neighbourhood of positive real number 'a' with a very small radius δ>0 will be ____.
[A]
(a - δ, a]
[B]
[a, a + δ)
[C]
(a - δ, a + δ)
[D]
a sphere of radius a
(18)
If fx = 1 + x + x2/2+x3/3, then f' (x) is ____.
[A]
1/1 - x2
[B]
1+ x + x2
[C]
1 + x
[D]
1 - x
(19)
The ratio of the rate of change of area and the rate of change of radius with respect to given circle is ____.
[A]
radius of the circle
[B]
perimeter of the circle
[C]
diameter of the circle
[D]
area of the circle
Answer: perimeter of the circle
(20)
The limit of a function exists only if the left hand limit and the right hand limit coincide with each other.
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