InstaQB

Home
Institutions
- Institutions
  
  Polytechnic Colleges
  
  Medical Colleges
  
  Arts & Science Colleges
  
  Universities
  
  Engineering Colleges
  
  Agricultural Colleges
  
  Research Institute
  
  Law Colleges
  
  Audiology and Speech Colleges
  
  Business & Management colleges
  
  Nursing colleges
  
  Hotel Management institutes
  
  Aeronautical Colleges
  
  Bachelor's Degree
Syllabus
Courses
Stateboard
- 12th Standard English Medium
  
  Maths
  
  Physics
  
  Chemistry
  
  Biology
  
  Computer Science
  
  Business Maths
  
  Economics
  
  Commerce
  
  Accountancy
  
  History
  
  Computer Applications
  
  Computer Technology
  12th Standard Tamil Medium
  
  உயிரியல்
  
  கணினி பயன்பாடுகள்
  
  கணினி அறிவியல்
  
  வணிகக் கணிதம்
  
  வணிகவியல்
  
  பொருளியல்
  
  கணிதவியல்
  
  வேதியியல்
  
  இயற்பியல்
  
  கணினி தொழில்நுட்பம்
  
  வரலாறு
  
  கணக்குப்பதிவியல்
  11th Standard English Medium
  
  Maths
  
  Commerce
  
  Economics
  
  Biology
  
  Business Maths
  
  Accountancy
  
  Computer Science
  
  Physics
  
  Chemistry
  
  Computer Applications
  
  History
  
  Computer Technology
  
  Bio - Zoology
  11th Standard Tamil Medium
  
  கணிதவியல்
  
  உயிரியல்
  
  பொருளியல்
  
  இயற்பியல்
  
  வேதியியல்
  
  வணிகக் கணிதம்
  
  கணினி அறிவியல்
  
  கணக்குப்பதிவியல்
  
  வணிகவியல்
  
  கணினி பயன்பாடுகள்
  10th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  
  9th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  
  8th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
  7th Standard English Medium
  
  Mathematics
  
  Science
  
  Social Science
ICSE/ISC
- Class XII
  
  Mathematics
  
  Physics
  
  Accountancy
  
  Biology
  
  History
  
  Geography
  
  Psychology
  
  chemistry
  
  Economics
  
  Computer Science
  
  Political Science
  
  Business Studies
  Class XI
  
  Accountancy
  
  Chemistry
  
  Mathematics
  
  Biology
  
  Geography
  
  Physics
  
  History
CBSE
- 12Th Standard
  
  Physics
  
  Chemistry
  
  Maths
  
  Biology
  
  History
  
  Economics
  
  Commerce
  
  Geography
  
  Socialogy
  
  Business Studies
  
  Computer Science
  
  Biotechnology Class
  
  Political Science
  
  Home Science
  11Th Standard
  
  Physics
  
  Chemistry
  
  Maths
  
  Biology
  
  History
  
  Economics
  
  Commerce
  
  Socialogy
  
  Business Studies
  
  Geography
  
  Home Science
  
  Computer Science
  
  Biotechnology Class
  
  Political Science
  10Th Standard
  
  Physics
  
  Chemistry
  
  Biology
  
  Mathematics
  
  Economics
  
  Geography
  
  History & Civics
  
  Computer Application
  9Th Standard
  
  Physics
  
  Chemistry
  
  Biology
  
  mathematics
  
  Computer Application
  
  Economics
  
  Geography
  
  History & Civics

12th Maths Weekly Test -3 (Inverse Trigonometric Functions)

St. Britto Hr. Sec. School - Madurai

12th Maths Weekly Test -3 (Inverse Trigonometric Functions)-Aug 2020

Time : 1.30 Hours

Part - A

Multiple Choice Question - Answer All Question

If sin^-1 x+sin^-1 y=\(\frac{2\pi}{3};\)then cos^-1x+cos^-1 y is equal to

\(\frac{2\pi}{3}\)
\(\frac{\pi}{3}\)
\(\frac{\pi}{6}\)
\(\pi\)

If sin⁻¹x = 2sin⁻¹\(\alpha\) has a solution, then

\(|\alpha |\le \frac { 1 }{ \sqrt { 2 } } \)
\(|\alpha |\ge \frac { 1 }{ \sqrt { 2 } } \)
\(|\alpha |<\frac { 1 }{ \sqrt { 2 } } \)
\(|\alpha |>\frac { 1 }{ \sqrt { 2 } } \)

If sin^-1 x+sin^-1 y+sin^-1 z=\(\frac{3\pi}{2}\), the value of x²⁰¹⁷+y²⁰¹⁸+z²⁰¹⁹\(-\frac { 9 }{ { x }^{ 101 }+{ y }^{ 101 }+{ z }^{ 101 } } \)is

0
1
2
3

The domain of the function defined by f(x)=sin⁻¹\(\sqrt{x-1} \) is

[1,2]
[-1,1]
[0,1]
[-1,0]

\({ tan }^{ -1 }\left( \frac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \frac { 2 }{ 9 } \right) \)is equal to

\(\frac { 1 }{ 2 } { cos }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)
\(\frac { 1 }{ 2 } { sin }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)
\(\frac { 1 }{ 2 } {tan }^{ -1 }\left( \frac { 3 }{ 5 } \right) \)
\({ tan}^{ -1 }\left( \frac { 1}{ 2 } \right) \)

If cot^-1 2 and cot^-1 3 are two angles of a triangle, then the third angle is

\(\frac{\pi}{4}\)
\(\frac{3\pi}{4}\)
\(\frac{\pi}{6}\)
\(\frac{\pi}{3}\)

sin^-1(2cos²x-1)+cos^-1(1-2sin²x)=

\(\frac{\pi}{2}\)
\(\frac{\pi}{3}\)
\(\frac{\pi}{4}\)
\(\frac{\pi}{6}\)

If |x|\(\le\)1, then 2tan^-1 x-sin^-1 \(\frac{2x}{1+x^2}\) is equal to

tan^-1x
sin^-1x
0
\(\pi\)

If sin^-1 x+cot^-1\((\frac{1}{2})=\frac{\pi}{2}\), then x is equal to

\(\frac{1}{2}\)
\(\frac{1}{\sqrt{5}}\)
\(\frac{2}{\sqrt{5}}\)
\(\frac{\sqrt3}{2}\)

sin(tan^-1x), |x|<1 ia equal to

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

The number of solutions of the equation \({ tan }^{ -1 }2x+{ tan }^{ -1 }3x=\cfrac { \pi }{ 4 } \)

2
3
1
none

The number of real solutions of the equation \(\sqrt { 1+cos2x } ={ 2sin }^{ -1 }\left( sinx \right) ,-\pi<x<\pi\) is

0
1
2
infinte

\({ tan }^{ -1 }\left( \cfrac { 1 }{ 4 } \right) +{ tan }^{ -1 }\left( \cfrac { 2 }{ 11 } \right) \) =

0
\(\cfrac { 1 }{ 2 } \)
-1
none

The value of \({ cos }^{ -1 }\left( \cfrac { cos5\pi }{ 3 } \right) +sin^{ -1 }\left( \cfrac { sin5\pi }{ 3 } \right) \) is

\(\cfrac { \pi }{ 2 } \)
\(\cfrac { 5\pi }{ 3 } \)
\(\cfrac { 10\pi }{ 3 } \)
0

If \(4{ cos }^{ -1 }x+{ sin }^{ -1 }x=\pi \) then x is

\(\cfrac { 3 }{ 2 } \)
\(\cfrac { 1 }{ \sqrt { 2 } } \)
\(\cfrac { \sqrt { 3 } }{ 2 } \)
\(\cfrac { 2 }{ \sqrt { 3 } } \)

If \({ cos }^{ -1 }x>x>{ sin }^{ -1 }x\) then

\(\cfrac { 1 }{ \sqrt { 2 } } <x\le 1\)
\(0\le x<\cfrac { 1 }{ \sqrt { 2 } } \)
\(-1\le x<\cfrac { 1 }{ \sqrt { 2 } } \)
x>0

\(cot\left( \cfrac { \pi }{ 4 } -{ 2cot }^{ -1 }3 \right) \)

7
6
5
none

The domain of cos^-1(x² - 4) Is______

[3,5]
[-1. 1]
\(\left[ -\sqrt { 5 } ,-\sqrt { 3 } \right] \cup \left[ \sqrt { 3 } ,\sqrt { 5 } \right] \)
[0,1]

The value of sin(2(tan^-1 0.75) is___________

0.75
1.5
0.96
sin^-1(1.5)

If \(\theta ={ sin }^{ -1 }\left( sin(-{ 60 }^{ 0 }) \right) \) then one of the possible values of \(\theta\) is _________

\(\cfrac { \pi }{ 3 } \)
\(\cfrac { \pi }{ 2 } \)
\(\cfrac { 2\pi }{ 3 } \)
\(\cfrac { -2\pi }{ 3 } \)

Part - B

Generic 2 - Answer All Question

Find the period and amplitude of
y=sin 7x

Find the value of
\({ sin }^{ -1 }\left( sin\left( \frac { 2\pi }{ 3 } \right) \right) \)

Find the domain of the following
\({ sin }^{ -1 }\left( \frac { { x }^{ 2 }+1 }{ 2x } \right) \)

Find all values of x such that
-6\(\pi\le x \le 6\pi\) and cos x -0

Is cos^-1(-x)=\(\pi\)-cos⁻¹(x) true? Justify your answer.

Find the value of
\(2{ cos }^{ -1 }\left( \frac { 1 }{ 2 } \right) +{ sin }^{ -1 }\left( \frac { 1 }{ 2 } \right) \)

For what value of x , the inequality\(\cfrac { \pi }{ 2 } <{ cos }^{ -1 }(3x-1)<\pi \) holds?

Find the domain of the following functions :
\(tan^{-1}(\sqrt{9-x^{2}})\)

Find the value of
\(tan(tan^{-1}(\frac{7\pi}{4}))\)

Find the principal value of
sec^-1\((\frac{2}{\sqrt3})\)

Part - C

Generic 3 - Answer All Question

Prove that \({ cos }^{ -1 }\left( \cfrac { 4 }{ 5 } \right) +{ tan }^{ -1 }\left( \cfrac { 3 }{ 5 } \right) ={ tan }^{ -1 }\left( \cfrac { 27 }{ 11 } \right) \)

Prove that \({ tan }^{ -1 }\left( \cfrac { m }{ n } \right) -{ tan }^{ -1 }\left( \cfrac { m-n }{ m+n } \right) =\cfrac { \pi }{ 4 } \)

Solve \({ tan }^{ -1 }\left( \cfrac { 2x }{ 1-{ x }^{ 2 } } \right) +{ cot }^{ -1 }\left( \cfrac { 1-{ x }^{ 2 } }{ 2x } \right) =\cfrac { \pi }{ 3 } ,x>0\)

Prove that \({ tan }^{ -1 }\sqrt { x } =\cfrac { 1 }{ 2 } { cos }^{ -1 }={ \cfrac { 1 }{ 2 } { cos }^{ -1 }\left( \cfrac { 1-x }{ 1+x } \right) ,x\epsilon \left| 0,1 \right| }\)

Find the real solutions of the equation
\({ tan }^{ -1 }\sqrt { x(x+1) } +{ sin }^{ -1 }\sqrt { { x }^{ 2 }+x+1 } =\cfrac { \pi }{ 2 } \)

Find the domain of sin^-1(2−3x²)

Find the domain of the following

sin⁻¹\(\left(\frac{x^2 + 1}{2x} \right)\)

Find the domain of
f(x)=sin^-1\(\left(\frac{| x | − 2}{3} \right)\)+cos^-1\(\left(\frac{1-| x | }{4} \right)\)

Find the value of \(cos\left(cos^{-1}\left(\frac{4}{5} \right)+sin^{-1}\left(\frac{4}{5} \right)\right)\)

Find

i) tan^-1\( (-\sqrt3)\)

ii) tan^-1\((tan\frac{3\pi}{5})\)

iii) tan(tan^-1 −(2019))

Comment

Add Comment

Tamilnadu Stateboardszs - Class