NCERT Solutions Class 12
-
NCERT Solutions-Mathematics
- Relations and Functions : NCERT Solutions – Class 12 Maths (Ex 1)
- Relations and Functions : NCERT Solutions – Class 12 Maths (Ex 2)
- Relations and Functions : NCERT Solutions – Class 12 Maths (Ex 3)
- Relations and Functions : NCERT Solutions – Class 12 Maths (Ex 4)
- Relations and Functions : NCERT Solutions – Class 12 Maths (Ex 5)
- Inverse Trigonometric Function : NCERT Solutions – Class 12 Maths (Ex 1)
- Inverse Trigonometric Function : NCERT Solutions – Class 12 Maths (Ex 2)
- Inverse Trigonometric Function : NCERT Solutions – Class 12 Maths (Ex 3)
- Matrices : NCERT Solutions – Class 12 Maths (Ex 1)
- Matrices : NCERT Solutions – Class 12 Maths (Ex 2)
- Matrices : NCERT Solutions – Class 12 Maths (Ex 3)
- Matrices : NCERT Solutions – Class 12 Maths (Ex 4)
- Matrices : NCERT Solutions – Class 12 Maths (Ex 5)
- Determinants : NCERT Solutions – Class 12 Maths (Ex 1)
- Determinants : NCERT Solutions – Class 12 Maths (Ex 2)
- Determinants : NCERT Solutions – Class 12 Maths (Ex 3)
- Determinants : NCERT Solutions – Class 12 Maths (Ex 4)
- Determinants : NCERT Solutions – Class 12 Maths (Ex 5)
- Determinants : NCERT Solutions – Class 12 Maths (Ex 6)
- Determinants : NCERT Solutions – Class 12 Maths (Ex 7)
- Continuity and Differentiability : NCERT Solutions – Class 12 Maths (Ex 1)
- Continuity and Differentiability : NCERT Solutions – Class 12 Maths (Ex 2)
- Continuity and Differentiability : NCERT Solutions – Class 12 Maths (Ex 3)
- Continuity and Differentiability : NCERT Solutions – Class 12 Maths (Ex 4)
- Continuity and Differentiability : NCERT Solutions – Class 12 Maths (Ex 5)
- Continuity and Differentiability : NCERT Solutions – Class 12 Maths (Ex 6)
- Continuity and Differentiability : NCERT Solutions – Class 12 Maths (Ex 7)
- Continuity and Differentiability : NCERT Solutions – Class 12 Maths (Ex 8)
- Continuity and Differentiability : NCERT Solutions – Class 12 Maths (Ex 9)
-
NCERT Solutions-Chemistry
- Aldehydes, Ketones and Carboxylic Acids : NCERT Solutions – Class 12 Chemistry
- Alcohols, Phenols and Ethers : NCERT Solutions – Class 12 Chemistry
- Amines : NCERT Solutions – Class 12 Chemistry
- Biomolecules : NCERT Solutions – Class 12 Chemistry
- Chemical Kinetics : NCERT Solutions – Class 12 Chemistry
- Chemistry in Everyday Life : NCERT Solutions – Class 12 Chemistry
- Coordination Compounds : NCERT Solutions – Class 12 Chemistry
- Electrochemistry : NCERT Solutions – Class 12 Chemistry
- General Principles and Processes of Isolation of Elements : NCERT Solutions – Class 12 Chemistry
- Haloalkanes and Haloarenes : NCERT Solutions – Class 12 Chemistry
- Polymers : NCERT Solutions – Class 12 Chemistry
- Surface Chemistry : NCERT Solutions – Class 12 Chemistry
- The d-and f-Block Elements : NCERT Solutions – Class 12 Chemistry
- The p-Block Elements : NCERT Solutions – Class 12 Chemistry
- The Solid State : NCERT Solutions – Class 12 Chemistry
- Solutions : NCERT Solutions – Class 12 Chemistry
-
NCERT Solutions-Biology
-
NCERT Solutions-Physics
- Electrostatic Potential And Capacitance : NCERT Solutions – Class 12 Physics
- Electric Charges And Fields : NCERT Solutions – Class 12 Physics
- Semiconductor Electronics: Materials, Devices And Simple Circuits : NCERT Solutions – Class 12 Physics
- Ray Optics And Optical Instruments : NCERT Solutions – Class 12 Physics
- Nuclei : NCERT Solutions – Class 12 Physics
- Moving Charges And Magnetism : NCERT Solutions – Class 12 Physics
- Magnetism And Matter : NCERT Solutions – Class 12 Physics
- Electromagnetic Induction : NCERT Solutions – Class 12 Physics
- Dual Nature Of Radiation And Matter : NCERT Solutions – Class 12 Physics
- Current Electricity : NCERT Solutions – Class 12 Physics
- Communication Systems : NCERT Solutions – Class 12 Physics
- Atoms : NCERT Solutions – Class 12 Physics
- Alternating Current : NCERT Solutions – Class 12 Physics
Inverse Trigonometric Function : NCERT Solutions – Class 12 Maths (Ex 3)
Miscellaneous
Find the value of the following:
1.
Ans.
=
=
=
= i.e.,
, value of
lies in I quadrant.
= =
2.
Ans.
=
=
=
= i.e.,
, value of
lies in I quadrant.
= =
3. Prove that:
Ans. Let so that
Since
= =
=
4. Prove that:
Ans. Let so that
Again, Let so that
Since
=
=
5. Prove that:
Ans. Let so that
Again, Let so that
Since =
=
6. Prove that:
Ans. Let so that
Again, Let so that
Since =
=
7. Prove that:
Ans. Let so that
Again, Let so that
Since =
=
8. Prove that:
Ans. L.H.S. =
=
=
=
=
=
=
R.H.S.
9. Prove that:
Ans. Let so that
=
=
=
=
10. Prove that:
Ans. We know that =
Again,
=
L.H.S. =
=
=
=
11. Prove that:
Ans. Putting so that
L.H.S. =
=
=
=
Dividing every term by
=
=
= =
= = R.H.S.
12. Prove that:
Ans. L.H.S. =
=
= …(i)
Now, let so that
From eq. (i),
= R.H.S.
13. Solve the equation:
Ans.
14. Solve the equation:
Ans. Putting
15. is equal to:
(A)
(B)
(C)
(D)
Ans. Let where
so that
Putting
Therefore, option (D) is correct.
16. then
is equal to:
(A)
(B)
(C) 0
(D)
Ans. Putting so that
or
or
But does not satisfy the given equation.
Therefore, option (C) is correct.
17. is equal to:
(A)
(B)
(C)
(D)
Ans.
=
=
=
=
=
=
Therefore, option (C) is correct.