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: 26/08/2019
Trigonometry
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.
Number of solutions of the equation tan x + sec x = 2 cos x lying in the interval [0, 2π] is _______________
0
1
2
3
2.
If (A + B) = \(\frac{\pi}{4}\), (cot A - 1) (cot B - 1) = _______________
0
-2
2
1
3.
If 2 sin θ + 1 = 0 and \(\sqrt{3}\) tan θ = 1, then the most general value of θ is _______________
\(n\pi\pm\frac{\pi}{6}\)
\(n\pi+(-1)^n\frac{7\pi}{6}\)
\(2n\pi+\frac{7\pi}{6}\)
\(2n\pi+\frac{11\pi}{6}\)
4.
If sin(45 ° + 10°) - sin(45° -10°) = \(\sqrt{2}\)sin x then x is ___________
0o
5°
10°
15°
5.
2tan-1\(\left( \frac { 1 }{ 5 } \right) \) is equal to _______________
tan\(\left( \frac { 5 }{ 12 } \right) \)
\(\frac { 5 }{ 12 } \)
\(\tan^{-1}\left({5 \over 12}\right)\)
tan-1\(\frac { 2 }{ 5 } \)
6.
If cosec x + cot x = \(\frac { 11 }{ 2 } \) then tan x = ___________
\(\frac { 21 }{ 22 } \)
\(\frac { 15 }{ 16 } \)
\(\frac { 44 }{ 117 } \)
\(\frac { 117 }{ 44 } \)
7.
If tan x = \(\frac { -1 }{ \sqrt { 5 } } \) and x lies in the IV quadrant, then the value of cos x is ___________
\(\sqrt { \frac { 5 }{ 6 } } \)
\(\frac { 2 }{ \sqrt { 6 } } \)
\(\frac { 1 }{ 2 } \)
\(\frac { 1 }{ \sqrt { 6 } } \)
8.
In a ΔABC, if
(i) \(sin\frac { A }{ 2 } sin\frac { B }{ 2 } sin\frac { C }{ 2 } \) > 0
(ii) sin A sin B sin C > 0, Then
Both (i) and (ii) are true
Only (i) is true
Only (ii) is true
Neither (i) nor (ii) is true
9.
A wheel is spinning at 2 radians/second. How many seconds will it take to make 10 complete rotations?
10\(\pi \) seconds
20\(\pi \) seconds
5\(\pi \) seconds
15\(\pi \) seconds
10.
If f(ፀ) = |sin ፀ| + |cos ፀ|, ፀ\(\in \)R, then f(ፀ) is in the interval
[0, 2]
[1,\(\sqrt { 2 } \)]
[1, 2]
[0, 1]
11.
If tan α and tan β are the roots of x2 + ax + b = 0; then \(\frac { sin(\alpha +\beta ) }{ sin\alpha sin\beta } \) is equal to
\(\frac { b }{ a } \)
\(\frac { a }{ b } \)
\(-\frac { a }{ b } \)
\(-\frac { b}{ a } \)
12.
cos 2ፀ cos 2ф + sin2(ፀ - ф) - sin2(ፀ + ф) is equal to
sin2(ፀ+\(\phi \))
cos2(ፀ+\(\phi \))
sin2(ፀ-\(\phi \))
cos2(ፀ-\(\phi \))
13.
cos10 + cos20 + cos30 +: : : + cos1790 =
0
1
-1
89
14.
The maximum value of 4sin2x + 3 cos2x + \(sin\frac { x }{ 2 } +cos\frac { x }{ 2 } \) is
\(4 + \sqrt{2}\)
\(3+ \sqrt{2}\)
9
4
15.
\(\frac { 1 }{ cos{ 80 }^{ 0 } } -\frac { \sqrt { 3 } }{ sin{ 80 }^{ 0 } } \)=
\(\sqrt{2}\)
\(\sqrt{3}\)
2
4
1.
(c)
2
2.
(c)
2
3.
(c)
\(2n\pi+\frac{7\pi}{6}\)
4.
(c)
10°
5.
(c)
\(\tan^{-1}\left({5 \over 12}\right)\)
6.
(c)
\(\frac { 44 }{ 117 } \)
7.
(a)
\(\sqrt { \frac { 5 }{ 6 } } \)
8.
\(\text { We know that in } \Delta \mathrm{ABC}\)
\(\sin \frac{A}{2} \sin \frac{B}{2} \sin \frac{C}{2}>0\)
\(\text { And also } \sin A \sin B \sin C>0\)
Both are true..
Since sine is positive in I and II quadrant.
Both (i) and (ii) are true.
9.
In one second it rotates = 2 radians.
For 2 radians it takes 1 second.
\(\text { For } 2 \pi \text { ( } 1 \text { revolution) it will take } \frac{2 \pi}{2}=\pi \text { second. }\)
\(\therefore \text { For } 10 \text { revolutions it takes } 10 \pi \text { seconds. }\)
10.
\(\text { It lies in } \frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}} \text { and } 0+1\)
\(=\sqrt{2} \text { and } 1=[1, \sqrt{2}]\)
11.
\(x^{2}+a x+b=0\)
\(\text { Let } \tan \alpha \text { and } \tan \beta \text { be the roots. }\)
\(\tan \alpha+\tan \beta =-a \)
\(\tan \alpha \tan \beta =b \)
\(\frac{\sin (\alpha+\beta)}{\sin \alpha \sin \beta} =\frac{\sin \alpha \cos \beta+\cos \alpha \sin \beta}{\sin \alpha \sin \beta} \)
\(=\cot \beta+\cot \alpha \)
\(=\frac{1}{\tan \alpha}+\frac{1}{\tan \beta} \)
\(=\frac{\tan \alpha+\tan \beta}{\tan \alpha \tan \beta}=\frac{-a}{b} \)
12.
\(\cos 2 \theta \cos 2 \phi+\sin ^{2}(\theta-\phi)-\sin ^{2}(\theta+\phi) \)
\(=\cos 2 \theta \cos 2 \phi+\frac{1}{2}-\frac{1}{2} \cos (2 \theta-2 \phi)-\frac{1}{2}+\frac{1}{2} \cos (2 \theta+2 \phi) \)
\(=\cos 2 \theta \cos 2 \phi+\frac{1}{2}[\cos (2 \theta+2 \phi)-\cos (2 \theta-2 \phi)] \)
\(=\cos 2 \theta \cos 2 \phi-\sin 2 \theta \cos 2 \phi \)
\(=\cos (2 \theta+2 \phi) \)
\(=\cos 2(\theta+\phi) \)
13.
\(\cos 1^{\circ}+\cos 2^{\circ}+\cos 3^{\circ}+\ldots \ldots \ldots+\cos 179^{\circ} \)
\(=\left(\cos 1^{\circ}+\cos 179^{\circ}\right)+\left(\cos 2^{\circ}+\cos 178^{\circ}\right)+ ...\)
\(=2 \cos 90^{\circ} \cos 89^{\circ}+2 \cos 90^{\circ} \cos 80^{\circ}+\ldots \ldots . \)
\(=0+0+0 \ldots \ldots=0 \)
14.
\(4 \sin ^{2} x+3 \cos ^{2} x+\sin \frac{x}{2}+\cos \frac{x}{2} \)
\(=3\left(\sin ^{2} x+\cos ^{2} x\right)+\sin ^{2} x+\sin \frac{x}{2}+\cos \frac{x}{2} \)
\(=3+\sin ^{2} x+\sin \frac{x}{2}+\cos \frac{x}{2} \)
\(\text { Maximum of } \sin x=1\)
\(\text { Maximum value of } \sin ^{2} x=1\)
\(\text { Maximum value of } \sin \frac{x}{2} \text { occurs where } x=45^{\circ}\)
\(\text { Maximum value is } 3+1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}=4+\frac{2}{\sqrt{2}}=4+\sqrt{2}\)
15.
\(x =\frac{1}{\cos 80^{\circ}}-\frac{\sqrt{3}}{\sin 80^{\circ}} \)
\(=\frac{\sin 80^{\circ}-\sqrt{3} \cos 80^{\circ}}{\sin 80^{\circ} \cos 80^{\circ}} \)
\(\frac{x}{2} =\frac{\frac{1}{2} \sin 80^{\circ}-\frac{\sqrt{3}}{2} \cos 80^{\circ}}{\frac{1}{2} \sin 80^{\circ} \cos 80^{\circ}} \)
\(=\frac{\sin 80^{\circ} \cos 60^{\circ}-\cos 80^{\circ} \sin 60^{\circ}}{\frac{1}{2} \sin 80^{\circ} \cos 80^{\circ}} \)
\(=\frac{\sin 20^{\circ}}{\frac{1}{2} \sin 80^{\circ} \cos 80^{\circ}} \)
\(=\frac{\sin 160^{\circ}}{\frac{1}{2} \sin 80^{\circ} \cos 80^{\circ}} \)
\(=\frac{2 \sin 80^{\circ} \cos 80^{\circ}}{\frac{1}{2} \sin 80^{\circ} \cos 80^{\circ}}=4 \)
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
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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
