11th Maths Weekly Test - 1 ( Differential Calculus - Differentiability and Methods of Differentiatio

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 1 ( Differential Calculus - Differentiability and Methods of Differentiatio-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

Choose the correct statement

Derivative of odd functionis odd
Derivative of even function is even
Inverse of odd function is even
Inverse function of sin x is sin^-1 x

Choose the correct or the most suitable answer from the given four alternatives.
If \(f\left( x \right) =x+1\), then \(\frac { d }{ dx } ({ f }_{ 0 }f\left( x \right) )\) is

If g(x)=(x²+2x+3) f(x) and f(0)=5 and \(\underset{x \rightarrow 0}{lim}{f(x)-5\over x}=4\),then g'(0) is

Choose the correct or the most suitable answer from the given four alternatives.
For the curve \(\sqrt { x } +\sqrt { y } =1,\quad \frac { dy }{ dx } at\left( \frac { 1 }{ 4 } ,\frac { 1 }{ 4 } \right) is\)

\(\frac { 1 }{ 2 } \)
1
-1
2

If pv=81,then \({dp\over dv}\) at v=9 is

1
-1
2
-2

If y=mx+c and f(0)=\(f'(0)=1\),then f(2) is

1
2
3
-3

Choose the correct or the most suitable answer from the given four alternatives.
If, \(y=a+b{ x }^{ 2 }\) where a, b are arbitrary constants, then

\(\frac { d^{ 2 }y }{ d{ x }^{ 2 } } =2xy\)
\(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } ={ y }_{ 1 }\)
\(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } -\frac { dy }{ dx } +y=0\)
\(x\frac { d^{ 2 }y }{ d{ x }^{ 2 } } =2xy\)

The derivative of f(x)=x|x| at x =−3 is

6
-6
does not exist
0

If f(x)=x²-3x, then the points at which f(x)=f'(x) are

both positive integers
both negative integers
both irrational
one rational and another irrational

If the derivative of (ax - 5)e^3x at x=0 is -13, then the value of a is

8
-2
5
2

Part - B

Generic 2 - Answer All Question

Differentiate the following:\(y={3\sqrt{1+x^3}}\)

Find \({dy\over dx}\) if x = a(t - sin t), y = a(1 - cos t).

Find y''' if y=\({1\over x}\)

Find the derivation
3 sin x + 4 cos x - e^x

Part - C

Generic 3 - Answer All Question

Differentiate the following:\(s(t)=\sqrt[4]{t^3+1\over t^3-1}\)

Find the derivatives of the following functions with respect to corresponding independent variables:\(y=tan \theta (sin \theta +cos \theta)\).

Differentiate the following:\(y=(x^2+1)\sqrt[3]{x^2+2}\)

Find the derivative of tan^-1(1+x²) with respect to x²+x+1.

Part - D

Generic 5 - Answer All Question

If u= \(tan^{-1}{\sqrt{1+x^2}-1\over x}\) and v=tan ^-1 x, find \({du\over dv}\)

Differentiate x^x with respect to \(x\log { x } \)

Examine the differentiability of functions in R by drawing the diagrams | cos| x

\(If\quad x=4{ z }^{ 2 }+5,y=6{ z }^{ 2 }+7z+3,\quad find\quad \frac { d^{ 2 }y }{ dx^{ 2 } } \)

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11th Maths Weekly Test - 1 ( Differential Calculus - Differentiability and Methods of Differentiatio

St. Britto Hr. Sec. School - Madurai

11th Maths Weekly Test - 1 ( Differential Calculus - Differentiability and Methods of Differentiatio-Aug 2020

Part - A

Multiple Choice Question - Answer All Question

Choose the correct statement

Choose the correct or the most suitable answer from the given four alternatives. If \(f\left( x \right) =x+1\), then \(\frac { d }{ dx } ({ f }_{ 0 }f\left( x \right) )\) is

If g(x)=(x2+2x+3) f(x) and f(0)=5 and \(\underset{x \rightarrow 0}{lim}{f(x)-5\over x}=4\),then g'(0) is

Choose the correct or the most suitable answer from the given four alternatives. For the curve \(\sqrt { x } +\sqrt { y } =1,\quad \frac { dy }{ dx } at\left( \frac { 1 }{ 4 } ,\frac { 1 }{ 4 } \right) is\)

If pv=81,then \({dp\over dv}\) at v=9 is

If y=mx+c and f(0)=\(f'(0)=1\),then f(2) is

Choose the correct or the most suitable answer from the given four alternatives. If, \(y=a+b{ x }^{ 2 }\) where a, b are arbitrary constants, then

The derivative of f(x)=x|x| at x =−3 is

If f(x)=x2-3x, then the points at which f(x)=f'(x) are

If the derivative of (ax - 5)e3x at x=0 is -13, then the value of a is

Part - B

Generic 2 - Answer All Question

Differentiate the following:\(y={3\sqrt{1+x^3}}\)

Find \({dy\over dx}\) if x = a(t - sin t), y = a(1 - cos t).

Find y''' if y=\({1\over x}\)

Find the derivation 3 sin x + 4 cos x - ex

Part - C

Generic 3 - Answer All Question

Differentiate the following:\(s(t)=\sqrt[4]{t^3+1\over t^3-1}\)

Find the derivatives of the following functions with respect to corresponding independent variables:\(y=tan \theta (sin \theta +cos \theta)\).

Differentiate the following:\(y=(x^2+1)\sqrt[3]{x^2+2}\)

Find the derivative of tan-1(1+x2) with respect to x2+x+1.

Part - D

Generic 5 - Answer All Question

If u= \(tan^{-1}{\sqrt{1+x^2}-1\over x}\) and v=tan -1 x, find \({du\over dv}\)

Differentiate xx with respect to \(x\log { x } \)

Examine the differentiability of functions in R by drawing the diagrams | cos| x

\(If\quad x=4{ z }^{ 2 }+5,y=6{ z }^{ 2 }+7z+3,\quad find\quad \frac { d^{ 2 }y }{ dx^{ 2 } } \)

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Choose the correct or the most suitable answer from the given four alternatives.
If \(f\left( x \right) =x+1\), then \(\frac { d }{ dx } ({ f }_{ 0 }f\left( x \right) )\) is

If g(x)=(x²+2x+3) f(x) and f(0)=5 and \(\underset{x \rightarrow 0}{lim}{f(x)-5\over x}=4\),then g'(0) is

Choose the correct or the most suitable answer from the given four alternatives.
For the curve \(\sqrt { x } +\sqrt { y } =1,\quad \frac { dy }{ dx } at\left( \frac { 1 }{ 4 } ,\frac { 1 }{ 4 } \right) is\)

Choose the correct or the most suitable answer from the given four alternatives.
If, \(y=a+b{ x }^{ 2 }\) where a, b are arbitrary constants, then

If f(x)=x²-3x, then the points at which f(x)=f'(x) are

If the derivative of (ax - 5)e^3x at x=0 is -13, then the value of a is

Find the derivation
3 sin x + 4 cos x - e^x

Find the derivative of tan^-1(1+x²) with respect to x²+x+1.

If u= \(tan^{-1}{\sqrt{1+x^2}-1\over x}\) and v=tan ^-1 x, find \({du\over dv}\)

Differentiate x^x with respect to \(x\log { x } \)