Limits and Derivatives Online Objective Test | Limits and Derivatives Online Objective Test

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q1.

A. Not continuous at x=0

B. not continuous at -1 and 1

C. not derivable at – 1 and 1

D. derivable at all x ∈ R

Answer : Option C
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q2. If x = f(t) and y = g (t), then

\frac{d^{2} y}{d x^{2}}

is qual to

A. f′(t).g′′(t)g′(t).f′′(t)

B. g′′(t)f′′(t)

C. g′′(t)f′(t)−g′(t)f′′(t)(f′(t))2

Answer : Option D
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q3.

f (x) = | [x] x | in - 1

\leq

\leq

2 is

A. continuous at x = 0

B. discontinuous at x = 0

C. continuous at x = 2

D. differentiable at x = 0

Answer : Option A
Explaination / Solution:

function is continuous at x=0 but discontinuous at x=1

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q4.

\frac{d}{d x} (\tan^{- 1} (\frac{\sqrt{x} - \sqrt{a}}{1 + \sqrt{x a}})), x, a > 0, i s

A. tan1x−−√−tan−1a−−√

B. 11+x

C. 11+x−11+a

Answer : Option D
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q5.

\underset{h \to 0}{L t} \frac{\sqrt[3]{8 + h} - 2}{h}

is equal to

A. 1/24

B. 1/3

C. 1/12

D. 2

Answer : Option C
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q6. If f (x) =

\sqrt{1 - x^{2}}, x \in (0, 1), t h e n f^{'} (x)

is equal to

A. 11−x2√

B. -x1−x2√

C. x2−1−−−−−√

D. √1-x²

Answer : Option B
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q7. If

y = \sin^{- 1}

x and z =

\cos^{- 1} \sqrt{1 - x^{2}},

then

\frac{d y}{d z} =

A. tan−1x1−x2√

B. 0

C. 1

D. -1

Answer : Option C
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q8.

is equal to

A. 31+9x2

B. 11+x2

C. sec23x

D. 31+x2

Answer : Option D
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q9.

\frac{d}{d x} (\cos^{- 1} (\frac{x^{- 1} - x}{x^{- 1} + x}))

is equal to

A. 41+x2,x>0

B. −21+x2√

C. 1−x2

21+x2,x>0

Answer : Option D
Explaination / Solution:

# Limits and Derivatives # CBSE 11th Mathematics Prepare / Learn

Q10.

\frac{d}{d x} (\sin^{- 1} (\frac{2}{x^{- 1} + x}))

is equal to

A. 1−x2−−−−−√

21+x2;0<|x|<1

C. 21+x2√,|x|<1

D. 1x+x2√

Answer : Option B
Explaination / Solution:

Total Question/Mark :
Scored Mark :
Mark for Correct Answer : 1
Mark for Wrong Answer : -0.5
Mark for Left Answer : 0

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