11th Standard Syllabus & Materials
11th Standard
TN 11th Tamil இயற்கை வேளாண்மை,சுற்றுச்சூழல் -செய்யுள் - மனோன்மணீயம் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil என்னுயிர் என்பேன் -துணைப்பாடம் - இசைத்தமிழர் இருவர் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil மொழி கலை -செய்யுள் - ஒவ்வொரு புல்லையும் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - இலக்கணம் - பகுபத உறுப்புகள் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - துணைப்பாடம் - வாடிவாசல் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - செய்யுள் - குறுந்தொகை Important Questions And Answers Study Material - QB365 Set A
Published on: 11/11/2020
11th Standard Maths Differential Calculus - Differentiability and Methods of Differentiation English Medium Free Online Test 1 Mark Question 2020-2021
Download Tamil Nadu 11th Standard Maths question papers, model tests, one-mark questions, important questions, and public exam papers in PDF format. Free study materials and answer keys for TN State Board students.
Questions + Answers key
Take MCQ Maths Test1.
Choose the correct or the most suitable answer from the given four alternatives.
If f(x) is an odd function, then f'(x) is an ______ function
even
odd
even or odd
neither even nor odd
2.
Choose the correct or the most suitable answer from the given four alternatives.
If \(y=\log \left(\frac{1-x^2}{1+x^2}\right)\) then \(\frac{dy}{dx}\) is ______
\(\frac { 4{ x }^{ 3 } }{ 1-{ x }^{ 4 } } \)
\(-\frac { 4x }{ 1-{ x }^{ 4 } } \)
\(\frac { 1 }{ 4-{ x }^{ 4 } } \)
\(\frac { -4{ x }^{ 3 } }{ 1-{ x }^{ 4 } } \)
3.
Choose the correct or the most suitable answer from the given four alternatives.
The derivative of \(\cos ^{ -1 }{ (2{ x }^{ 2 } } -1)\) with respect to \(\cos ^{ -1 }{ x } \) is _____
2
\(\frac { 1 }{ 2\sqrt { 1-{ x }^{ 2 } } } \)
\(\frac { 2 }{ x } \)
\(1-{ x }^{ 2 }\)
4.
Choose the correct or the most suitable answer from the given four alternatives.
If \(y=\log _{ a }{ x } \) then \(\frac { dy }{ dx } \) is ______
\(\frac { 1 }{ x } \)
\(\frac { 1 }{ x\log _{ e }{ a } } \)
\(\log { _{ e }^{ a } } \)
\(\frac { 1 }{ \log _{ a }{ x } } \)
5.
Choose the correct or the most suitable answer from the given four alternatives.
If f(x) = 4x8, then ________
\(f^{ ' }\left( \frac { 1 }{ 2 } \right) =f^{ ' }\left( \frac { -1 }{ 2 } \right) \)
\(f\left( \frac { 1 }{ 2 } \right) =-f^{ ' }\left( \frac { -1 }{ 2 } \right) \)
\(f\left( \frac { 1 }{ 2 } \right) =f\left( \frac { -1 }{ 2 } \right) \)
\(f\left( \frac { 1 }{ 2 } \right) =f^{ ' }\left( \frac { -1 }{ 2 } \right) \)
6.
0
2
3
4
7.
The differential coefficient of log10 x with respect to logx10 is
1
-(log10 x)2
(logx 10)2
\(x^2\over100\)
8.
\({d\over dx}(e^{x+5log \ x})\) is
ex.x4(x+5)
ex.x(x+5)
ex\(+{5\over x}\)
ex\(-{5\over x}\)
9.
If y = mx + c and f(0) =\(f '(0)=1\), then f(2) is
1
2
3
-3
10.
\(\frac{d}{d x}\left(\frac{2}{\pi} \sin x^{\circ}\right)\) is
\({\pi\over 180}cos \ x^o\)
\({1\over 90} cos \ x^o\)
\({\pi\over 90}cos \ x^o\)
\({2\over \pi}cos \ x^o\)
1.
(a)
even
2.
(b)
\(-\frac { 4x }{ 1-{ x }^{ 4 } } \)
3.
(a)
2
4.
(b)
\(\frac { 1 }{ x\log _{ e }{ a } } \)
5.
(c)
\(f\left( \frac { 1 }{ 2 } \right) =f\left( \frac { -1 }{ 2 } \right) \)
6.
\(\text { The right hand derivative of } f(x) \text { at } x=2 \text { is }\)
\(f^{\prime}\left(2^{+}\right) =\lim _{x \rightarrow 2^{+}} \frac{f(x)-f(2)}{x-2} \)
\(=\lim _{x \rightarrow 2^{+}} \frac{(3 x+4)-(3(2)+4)}{x-2} \)
\(=\lim _{x \rightarrow 2^{+}} \frac{3 x+4-6-4}{x-2} \)
\(=\lim _{x \rightarrow 2^{+}} \frac{3(x-2)}{(x-2)}=3 \)
7.
\( y=\log _{10} x=\frac{1}{\log _x 10}\)
Diff w. r. to \(\log _x 10\)
\(y^{\prime}=\frac{-1}{\left(\log _x 10\right)^2}=-\left(\log _{10} x\right)^2 \)
8.
\(\text { Given } e^{x+5 \log x}=e^{x} \cdot e^{5 \log x}=e^{x} \cdot e^{\log x^{5}}=x^{5} e^{x}\)
\(\frac{d}{d x}\left(e^{x+5 \log x}\right) =\frac{d}{d x}\left(x^{5} e^{x}\right)=e^{x} x^{5}+e^{x}\left(5 x^{4}\right) \)
\(=e^{x} x^{4}(x+5) \)
9.
\(y =m x+c \)
\(f(x) =m x+c \Rightarrow f(0)=c=1 \)
\(\therefore c =1 \)
\(f^{\prime}(x) =m \)
\(f^{\prime}(0) =1=m \)
\(\therefore m =1 \)
\(\therefore f(x) =x+1 \)
\(f(2) =2+1=3 \)
10.
\(\frac{d}{d x}\left(\frac{2}{\pi} \sin x\left(\frac{\pi^{\circ}}{180}\right)\right) =\frac{2}{\pi} \cos \frac{\pi x^{\circ}}{180^{\circ}} \frac{\pi}{180^{\circ}} \)
\(=\frac{1}{90} \cos x^{\circ} \)
11th Standard Syllabus & Materials
11th Standard
TN 11th Tamil பீடு பெற நில் - செய்யுள் - காவடிச்சிந்து Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil பீடு பெற நில் - உரைநடை - மலை இடப்பெயர்கள் : ஓர் ஆய்வு Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil மாமழை போற்றுதும் - துணைப்பாடம் - யானை டாக்டர் Important Questions And Answers Study Material - QB365 Set A
NEW11th Standard
TN 11th Tamil மாமழை போற்றுதும் - செய்யுள் - ஐங்குறுநூறு Important Questions And Answers Study Material - QB365 Set A
Tamilnadu Stateboard 11th Standard Subjects
Maths
Commerce
Economics
Biology
Business Maths and Statistics
Accountancy
Computer Science
Physics
Chemistry
Maths
Biology
Economics
Physics
Chemistry
History
Business Maths and Statistics
Computer Science
Accountancy
Computer Applications
History
Computer Technology
Commerce
Computer Applications
Computer Technology
Tamil
English
French
Tamilnadu Stateboard Standards
