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

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

Q1.

\frac{d}{d x} (\frac{x}{2} \sqrt{x^{2} + a^{2}} + \frac{a^{2}}{2} \log (x + \sqrt{x^{2} + a^{2}}))

is equal to

A. 1x2+a2√

B. 1x+x2+a2√

C. x2−a2−−−−−−√

D. x2+a2−−−−−−√

Answer : Option D
Explaination / Solution:

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

Q2.

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

is equal to

A. a2−x2−−−−−−√

B. 2a2−x2−−−−−−√

C. 1logx

D. 1+x2

Answer : Option B
Explaination / Solution:

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

Q3.

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

is equal to

A. −x1−x2√for0<|x|<1

B. −x|x|1−x2√;for0<|x|<1

C. −11−x2√for|x|<1

D. 1+x2

Answer : Option B
Explaination / Solution:

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

Q4.

\frac{d}{d x} (\cos^{- 1} (\sqrt{1 - x^{2})})

is equal to

A. 11−x2√for0<|x|<1

B. 24−(2x)2√for|x|<1

C. 11+x2√for|x|<1

D. x|x|1−x2√for0<|x|<1

Answer : Option D
Explaination / Solution:

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

Q5.

\frac{d}{d x} (\sec^{- 1} x)

is equal to

A. 13xx2−x√for|x|>1

B. 11+x2

1|x|x2−1√for|x|>1

D. −1xx2−1√for|x|>1

Answer : Option C
Explaination / Solution:

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

Q6.

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

is equal to

A. 1xx2−1√for|x|>1

−1|x|x2−1√for|x|>1

C. 1xx3−2x√;for|x|>1

D. −12xx2−1√for|x|>1

Answer : Option B
Explaination / Solution:

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

Q7.

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

is equal to

A. −12x−x2√

B. 1x2−2x√

C. 12x−x2√

Answer : Option D
Explaination / Solution:

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

Q8.

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

is equal to

A. 12(2x−x2)3/2

B. x-12(2x−x2)3/2

C. 11−x2

D. 1−x(2x−x2)3/2

Answer : Option B
Explaination / Solution:

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

Q9. If y =

\sqrt{x + \sqrt{x + \sqrt{x + . . . + t o \infty}}}

then

\frac{d y}{d x} =

A. 12y-1

B. xy+1−−−√

C. 12y+1

D. xy+1

Answer : Option A
Explaination / Solution:

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

Q10.

f (x) is

A. continuous

B. not continuous

C. continuous on left and discontinuous on right.

D. continuous but not derivable

Answer : Option B
Explaination / Solution:

At x=1,

L.H.L. $\to$ 1

R.H.L. $\to$ 2

L.H.L. $\neq$ R.H.L.

Therefore function is not continuous at x=1 which is why it is not derivable at x=1

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