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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)
Let f(x) = cos x, when x ≥ 0 and f(x) = x + k, when x < 0 Find the value of k given that Limx→0 f(x) exists
[A]
0
[B]
1
[C]
-1
[D]
None of these
(2)
The expansion of log(1 – x) is
[A]
x – x²/2 + x³/3 – ……..
[B]
x + x²/2 + x³/3 + ……..
[C]
-x + x²/2 – x³/3 + ……..
[D]
-x – x²/2 – x³/3 – ……..
Answer: -x – x²/2 – x³/3 – ……..
(3)
The value of limit Limx→0 {sin (a + x) – sin (a – x)}/x is
[A]
0
[B]
1
[C]
2 cos a
[D]
2 sin a
(4)
The derivative of [1+(1/x)] /[1-(1/x)] is
[A]
1/(x-1)²
[B]
-1/(x-1)²
[C]
2/(x-1)²
[D]
-2/(x-1)²
(5)
The value of the limit Limx→0 {log(1 + ax)}/x is
[A]
0
[B]
1
[C]
a
[D]
1/a
(6)
If f(x) = x × sin(1/x), x ≠ 0, then Limx→0 f(x) is
[A]
1
[B]
0
[C]
-1
[D]
does not exist
(7)
If f(x) = (x + 1)/x then df(x)/dx is
[A]
1/x
[B]
-1/x
[C]
-1/x²
[D]
1/x²
(8)
The value of Limn→∞ (sin x/x) is
[A]
0
[B]
1
[C]
-1
[D]
None of these
(9)
The value of limy→0 {(x + y) × sec (x + y) – x × sec x}/y is
[A]
x × tan x × sec x
[B]
x × tan x × sec x + x × sec x
[C]
tan x × sec x + sec x
[D]
x × tan x × sec x + sec x
Answer: x × tan x × sec x + sec x
(10)
The value of Limx→01 (1/x) × sin-1 {2x/(1 + x²) is
(11)
The value of Limx→0 ax is
[A]
0
[B]
1
[C]
1/2
[D]
3/2
(12)
Limx→0 (ex² – cos x)/x² is equals to
[A]
0
[B]
1
[C]
2/3
[D]
3/2
(13)
The value of the limit Limx→0 (cos x)cot2 x is
[A]
1
[B]
e
[C]
e1/2
[D]
e-1/2
(14)
Limx→0 {(ax – bx)/ x} is equal to
[A]
log a
[B]
log b
[C]
log (a/b)
[D]
log (a×b)
(15)
Limx→-1 [1 + x + x² + ……….+ x10] is
(16)
Limy→∞ {(x + 6)/(x + 1)}(x+4) equals
[A]
e
[B]
e³
[C]
e5
[D]
e6
(17)
The value of Limn→∞ {1² + 2² + 3² + …… + n²}/n³ is
(18)
The value of Limx→0 (1/x) × sin-1 {2x/(1 + x²) is
(19)
Limx→0 sin (ax)/bx is
[A]
0
[B]
v
[C]
a/b
[D]
b/a
(20)
Limx→0 log(1 – x) is equals to
[A]
0
[B]
1
[C]
1/2
[D]
None of these
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