Class 11 Mathematics Limits And Derivatives MCQs Set 02

Question: lim_x→a Sinx - Sina /√x -√a is equal to
a) √a cos a
b) √a cos a
c) 2√a cos a
d) 2√a cos a
Answer: d

Question: lim_x→0 2Sinx - Sin2x / X³ is equal to
a) –1
b) 1
c) 2
d) –2
Answer: b

Question: lim_x→0 x² cosx / 1 -cosx is equal to
a) 2
b) 3/2
c) 3/2
d) 1
Answer: a

Question: The value of lim_x→0 sin²2x / sin²4x
a) 1/2
b) 1/4
c) 1/4
d) 1/2
Answer: c

Question: lim_Θ→0 1 - cos4Θ / 1 - cos6Θ is equal to
a) 4/9
b) 1/2
c) 1/2
d) –1
Answer: a

Question: If f(x) = 1 + x + x²/2 +..... x¹⁰⁰ / 100 then f '(1) is equal to
a) 1 /100
b) 100
c) does not exist
d) 0
Answer: b

Question: lim_x→0 1- Cos2x / x² is equal to
a) 2
b) –2
c) 3
d) –3
Answer: a

Question: lim_x→0 sin(πcos²x ) /x² equals
a) −π
b) π
c) π/2
d) 1
Answer: b

Question: If f(x) + f (y) = f (x+y/1−xy) for all x, y ∈ R (xy ≠ 1) and lim_x→0f(x)/x = 2. Then, f '(1/√3) is
a) 3/4
b) 4/3
c) 3/6
d) 3/2
Answer: d

Question: lim_x→π/6 Sinx / x-π is equal to
a) 1
b) 2
c) –1
d) –2
Answer: c

Question: The value of lim_x→1 (1+X)⁶ - 1 / (1+X²) - 1
a) 20
b) 21
c) 15
d) 17
Answer: b

Question: If y = sinx + cosx / sinx - cosx , then dy/dx at x=0 is
a) –2
b) 0
c) 1/2
d) does not exist
Answer: a

Question: If value of lim_x→π/44√2 −(cosx + sin x)⁵/1−sin 2x is a√2, then the value of ‘a’ is
a) 2
b) 3
c) 4
d) 5
Answer: d

Question: lim_x→π/6 Cot2x -3 / Cosecx -2 is equal to
a) 3
b) 4
c) 2
d) 1
Answer: b

Question: As x → a, f (x) → l, then l is called ............ of the function f (x),
a) limit
b) value
c) absolute value
d) None of the options
Answer: a  

Question: The derivative of 1+1/x / 1−1/x is
a) 2/(1+ x)²
b) −2/(1−x)²
c) −1/(1−x)²
d) 3/(1−x)²
Answer: b

Question: Derivative of e^{3 log x} is
a) e^x
b) 3x²
c) 3x
d) log x
Answer: b

Question: If f x = x- 4 / 2√x then f' (1) is
a) 5/4
b) 4/5
c) 1
d) 0
Answer: a

Question: Find n, if lim_x→2 Xn - 2n / x-2 = 80, n ∈ N.
a) 5
b) 6
c) 4
d) 7
Answer: a

Question: If value of lim_x→0 √2+x −√2/x is equal to 1/a√2 then ‘a’ equals
a) 1
b) 2
c) 3
d) 4
Answer: b

Question: The value of lim_x→1 X⁷ - 2X⁵ + 1 / X³ -3X² + 2
a) 0
b) 1
c) –1
d) 3
Answer: b

Question: lim_x→0 (1+x)n - 1 is equal to
a) n
b) 1
c) n
d) 0
Answer: a

Question: The value of lim_x→0 cosx/π − x is 
a) π
b) –π
c) 1/π 
d) − 1/π
Answer: c

Question: lim_x→1 X^m-1 / Xⁿ-1 is equal to
a) 1
b) m/n
c) m/n
d) m²/n²
Answer: b

Question: lim_x→0 cosecx -cotx /x is equal to
a) 1 /2
b) 1
c) 1/2
d) 1
Answer: c

Question:The value of

a) 7/3
b) 7/2
c) 7/3
d) 7/2
Answer: d

Question: The value of

a) 8/5
b) 7/5
c) 8/5
d) None of the options
Answer: c

Question: The value of

a) 2
b) –2
c) 0
d) –1
Answer: b

Question: Derivative of f at x = a is denoted by

Answer: d

Question: Match the terms given in column-I with the terms given in column-II and choose the correct option from the codes given below. 

Codes
    A B C D
a) 4 1 3 2
b) 1 4 3 2
c) 4 1 2 3
d) 4 3 1 2
Answer: a

STATEMENT TYPE QUESTIONS

Question: Consider the following limits which holds for function f and g:

Which of the above are true ?
a) Only I
b) Only II
c) Only III
d) All of the options
Answer: d

Question: Which of the following is/are true?

a) Both I and II are true
b) Only I is true
c) Only II is true
d) Both I and II are false
Answer: a

Question: Which of the following is/are true?
I. The derivative of f (x) = x³ is x²
II. The derivative of f (x) = 1/x³ is −1/x²
a) Both I and II are true
b) Only I is true
c) Only II is true
d) Both I and II are false
Answer: d

Question: lim_h→0 (a+h)²sin(a+h)−a²sin a/h is equal to
I. a² sin a + 2a cos a
II. a² cos a + 2a sin a
a) Both I and II are true
b) Only I is true
c) Only II is true
d) Both I and II are false
Answer: c

Question: Which of the following is/are true?
I. The derivative of x² – 2at x = 10 is 18.
II. The derivative of 99x at x = 100 is 99.
III. The derivative of x at x = 1 is 1.
a) I, II and III are true
b) I and II are true
c) II and III are true
d) I and III are true
Answer: c

Question: Consider the function g (x) = | x |, x ≠ 0. Then
I. g (0) is not defined.
II. lim_x→0 g(x) is not defined.
Which of the following is/are true?
a) Both I and II are true
b) Only I is true
c) Only II is true
d) Both I and II are false
Answer: b

Question: Which of the following is/are true?
I. The derivative of sin (x + a) is cos (x + a), where a is a fixed non-zero constant.
II. The derivative of cosec x cot x is cosec³ x – cot² x cosec x
a) Both I and II are true
b) Only I is true
c) Only II is true
d) Borh I and II are false
Answer: b

Question: Consider the following derivatives which holds for function u and v.
I. (u ± v)' = u' ± v'
II. (uv)' = uv' + vu'
III. (u/v)' = u'v−uv'/v²
Which of the above holds are true ?
a) Only I
b) Only II
c) Only III
d) All of the options
Answer: d