11th Standard Syllabus & Materials

11th Standard

TN 11th Tamil இயற்கை வேளாண்மை,சுற்றுச்சூழல் -செய்யுள் - மனோன்மணீயம் Important Questions And Answers Study Material - QB365 Set A

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TN 11th Tamil என்னுயிர் என்பேன் -துணைப்பாடம் - இசைத்தமிழர் இருவர் Important Questions And Answers Study Material - QB365 Set A

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11th Standard

TN 11th Tamil மொழி கலை -செய்யுள் - ஒவ்வொரு புல்லையும் Important Questions And Answers Study Material - QB365 Set A

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TN 11th Tamil பீடு பெற நில் - இலக்கணம் - பகுபத உறுப்புகள் Important Questions And Answers Study Material - QB365 Set A

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TN 11th Tamil பீடு பெற நில் - துணைப்பாடம் - வாடிவாசல் Important Questions And Answers Study Material - QB365 Set A

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TN 11th Tamil பீடு பெற நில் - செய்யுள் - குறுந்தொகை Important Questions And Answers Study Material - QB365 Set A

11th Standard Maths Binomial Theorem, Sequences and Series English Medium Free Online Test One Mark Questions with Answer Key 2020 - 2021

Published on: 10/11/2020

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.

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Std: 11th Standard - Maths

chapter: - Model Question paper

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Questions:

Multiple Choice Question

10 x 1 = 10

The sum of the series C₀²- C₁² + C₂² .....+ (- 1)ⁿC²_n where n is an even integer is ______________

(a)

2nC_n

(b)

(-1)ⁿ2nC_n

(c)

(-1)ⁿ2nC_n-1

(d)

(-1)^n/2nC_n/2

The value of 2 + 4 + 6 + + 2n is

(a)

\(\frac { n\left( n-1 \right) }{ 2 } \)

(b)

\(\frac { n\left( n+1 \right) }{ 2 } \)

(c)

\(\frac { 2n\left( 2n+1 \right) }{ 2 } \)

(d)

n(n + 1)

The series 1+4x+8x²+ \(\frac { 32 }{ 3 } { x }^{ 3 }+.....+\infty \ is\) ______________

(a)

e^x

(b)

e^4x

(c)

e^2x

(d)

e^8x

The value of \({ 9 }^{ \frac { 1 }{ 3 } }\) ,\({ 9 }^{ \frac { 1 }{ 9 } }\)\({ 9 }^{ \frac { 1 }{ 27}}\),\(\infty \) is ______________

(a)

(b)

(c)

(d)

none of these

If in an infinite G. P. first term is equal to 10 times the sum of all successive terms, then its common ratio is ______________

(a)

\(\frac { 1 }{ 10 } \)

(b)

\(\frac { 1 }{ 11 } \)

(c)

\(\frac { 1 }{ 9 } \)

(d)

\(\frac { 1 }{ 20 } \)

The first and last term of an A.P. are 1 and 11. If the sum of its terms is 36, then the number of terms will be ______________

(a)

(b)

(c)

(d)

The value of \(\frac { 1 }{ 2! } +\frac { 1 }{ 4! } +\frac { 1 }{ 6! } +....is\)

(a)

\(\frac { { e }^{ 2 }+1 }{ 2e } \)

(b)

\(\frac { { (e+1) }^{ 2 } }{ 2e } \)

(c)

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

(d)

\(\frac { { e }^{ 2 }+1 }{ 2e } \)

The sum of an infinite GP is 18. If the first term is 6, the common ratio is

(a)

\(\frac { 1 }{ 3 } \)

(b)

\(\frac { 2 }{ 3 } \)

(c)

\(\frac { 1 }{ 6 } \)

(d)

\(\frac { 3 }{ 4 } \)

The sum up to n terms of the series \(\sqrt { 2 } +\sqrt { 8 } +\sqrt { 18 } +\sqrt { 32 } +\).....is

(a)

\(\frac { n(n+1) }{ 2 } \)

(b)

2n(n+1)

(c)

\(\frac { n(n+1) }{ \sqrt { 2 } } \)

(d)

10.

The HM of two positive numbers whose AM and GM are 16, 8 respectively is

(a)

(b)

(c)

(d)

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Answers Key:

Multiple Choice Question

10 x 1 = 10

(d)
(-1)^n/2nC_n/2

(d)
n(n + 1)

(b)
e^4x

(b)
3

(b)
\(\frac { 1 }{ 11 } \)

(b)
6

\(e=1+\frac{1}{\lfloor 1}+\frac{1}{\lfloor 2}+\frac{1}{\lfloor 3}+\frac{1}{\lfloor 4}+\ldots \ldots\)
\(e^{-1}=1-\frac{1}{\lfloor 1}+\frac{1}{\lfloor 2}-\frac{1}{\lfloor 3}+\frac{1}{4}-\ldots\)
\(\frac{e+e^{-1}}{2}=1+\frac{1}{\lfloor 2}+\frac{1}{\lfloor 4}+\ldots\)
\(\frac{1}{\lfloor 2}+\frac{1}{\lfloor 4}+\ldots . \quad=\frac{e+e^{-1}}{2}-1\)
\(=\frac{\mathrm{e}-2+\mathrm{e}^{-1}}{2} \)
\(=\frac{(\mathrm{e}-1)^{2}}{2 \mathrm{e}} \)

\(a=6, S_{\infty}=18, r=? \)
\(S_{\infty} =\frac{a}{1-r}=\frac{6}{1-r}=18 \)
\(6 =18-18 r \)
\(18 r =12 \)
\(r =\frac{2}{3} \)

\(\sqrt{2}+\sqrt{8}+\sqrt{18}+\sqrt{32} \ldots . . =\sqrt{2}+2 \sqrt{2}+3 \sqrt{2}+4 \sqrt{2} . \)
\(=\sqrt{2}[1+2+3+\ldots .] \)
\(S_{n} =\frac{\sqrt{2}[n(n+1)]}{2} \)
\(=\frac{n(n+1)}{\sqrt{2}} \)

10.

\(\mathrm{AM}=16, \quad \mathrm{GM}=8, \quad \mathrm{HM}=?\)
\(\frac{a+b}{2}=16 \Rightarrow a+b=32\)
\(\sqrt{a b}=8 \Rightarrow a b=64\)
\(\therefore \mathrm{HM} =\frac{2 a b}{a+b} \)
\(=\frac{2(64)}{32}= 4 \)