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NCERT Solutions for class 13 Maths | Chapter 13 - Introduction to Limits and Derivatives

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>

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(1) Limx->∞ {(x + 6)/(x + 1)}(x + 4) equals
[A] e
[B] e3
[C] e5
[D] e6
Answer: e5
(2) Limx->0 (1 - cos x)/x is
[A] 0
[B] 1
[C] 1/2
[D] Limit does not exist
Answer: 0
(3) Limx->0 sin (ax)/bx is
[A] 0
[B] 1
[C] a/b
[D] b/a
Answer: a/b
(4) Then value of Limx->0 {ex - (1 + x)}/x2 is
[A] 0
[B] 2
[C] 1/2
[D] e
Answer: 1/2
(5) The value of the limit Limn->∞ (1 + 1/n)n+5 is
[A] 0
[B] 1
[C] e
[D] 1/e
Answer: e
(6) The value of the limit Limx->0 {log(1 + ax)}/x is
[A] 0
[B] 1
[C] a
[D] 1/a
Answer: a
(7) 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
Answer: -2/(x-1)2
(8) The value of limx->0 {(x3 * cotx)/(1-cosx)} is
[A] 0
[B] 1
[C] -1
[D] 2
Answer: 2
(9) The expansion of ex is
[A] ex = 1 - x/1! + x2 /2! - x3 /3! + x4 /4! - ..............
[B] ex = 1 + x/1! + x2 /2! + x3 /3! + x4 /4! + ..............
[C] ex = -1 - x/1! - x2 /2! - x3 /3! - x4 /4! - ..............
[D] None of these
Answer: ex = 1 + x/1! + x2 /2! + x3 /3! + x4 /4! + .............
(10) The derivative of x + 1/x is
[A] 1 + 1/x
[B] 1 - 1/x
[C] 1 - 1/x2
[D] 1 + 1/x2
Answer: 1 - 1/x2
(11) 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
Answer: 2 cos a
(12) 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 - ........
(13) Limx->0 {(ax - bx )/ x} is equal to
[A] log a
[B] log b
[C] log (a/b)
[D] log (a*b)
Answer: log (a/b)
(14) The value of Limx->∞ (sin x/x) is
[A] 0
[B] 1
[C] -1
[D] None of these
Answer: 0
(15) Limx->-1 [1 + x + x2 + ..........+ x10 ] is
[A] 0
[B] 1
[C] -1
[D] 2
Answer: 1
(16) The value of Limx->a (a*sin x - x*sin a)/(ax2 - xa2 ) is
[A] (a*cos a + sin a)/a2
[B] (a*cos a - sin a)/a2
[C] (a*cos a + sin a)/a
[D] (a*cos a - sin a)/a
Answer: (a*cos a - sin a)/a2
(17) The value of Limx->0 (sin ax/sin bx) is
[A] a+b
[B] a-b
[C] a*b
[D] a/b
Answer: a/b
(18) The value of Limx->0 (1 + x)n is equal to
[A] 0
[B] 1
[C] 1/2
[D] None of these
Answer: 1
(19) The value of the limit Limn->0 (1 + an)b/n is
[A] ea
[B] eb
[C] eab
[D] ea/b
Answer: eab
(20) The expansion of ax is
[A] ax = 1 + x/1! * (log a) + x2 /2! * (log a)2 + x3 /3! * (log a)3 + ...........
[B] ax = 1 - x/1! * (log a) + x2 /2! * (log a)2 - x3 /3! * (log a)3 + ...........
[C] ax = 1 + x/1 * (log a) + x2 /2 * (log a)2 + x3 /3 * (log a)3 + ...........
[D] ax = 1 - x/1 * (log a) + x2 /2 * (log a)2 - x3 /3 * (log a)3 + ...........
Answer: ax = 1 + x/1! * (log a) + x2 /2! * (log a)2 + x3 /3! * (log a)3 + ...........

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