NCERT Solutions Class 12

NCERT SolutionsMathematics
 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 SolutionsChemistry
 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 dand fBlock Elements : NCERT Solutions – Class 12 Chemistry
 The pBlock Elements : NCERT Solutions – Class 12 Chemistry
 The Solid State : NCERT Solutions – Class 12 Chemistry
 Solutions : NCERT Solutions – Class 12 Chemistry

NCERT SolutionsBiology

NCERT SolutionsPhysics
 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
Determinants : NCERT Solutions – Class 12 Maths (Ex 6)
Exercise 4.6
Examine the consistency of the system of equations in Exercises 1 to 3.
1.
Ans. Matrix form of given equations is AX = B
A = and B =
=
Therefore, Unique solution and hence equations are consistent.
2.
Ans. Matrix form of given equations is AX = B
A = and B =
=
Therefore, Unique solution and hence equations are consistent.
3.
Ans. Matrix form of given equations is AX = B
A = and B =
= 6 – 6 = 0
Now (adj. A) B = =
Therefore, given equations are inconsistent, i.e., have no common solution.
Examine the consistency of the system of equations in Exercises 4 to 6.
4.
Ans. Matrix form of given equations is AX = B
Here A =
= 0
Therefore, Unique solution and hence equations are consistent.
5.
Ans. Matrix form of given equations is AX = B
Here A =
= =
Now (adj. A) =
And (adj. A) B = = =
Therefore, given equations are inconsistent.
6.
Ans. Matrix form of given equations is AX = B
Here A =
=
Therefore, Unique solution and hence equations are consistent.
Solve the system of linear equations, using matrix method, in Exercise 7 to 10.
7.
Ans. Matrix form of given equations is AX = B
Here A = , X = and B =
=
Therefore, solution is unique and =
=
Therefore, and
8.
Ans. Matrix form of given equations is AX = B
Here A = , X = and B =
=
Therefore, solution is unique and =
=
=
Therefore, and
9.
Ans. Matrix form of given equations is AX = B
Here A = , X = and B =
=
Therefore, solution is unique and =
=
=
Therefore, and
10.
Ans. Matrix form of given equations is AX = B
Here A = , X = and B =
=
Therefore, solution is unique and =
=
Therefore, and
Solve the system of linear equations, using matrix method, in Exercise 11 to 14.
11.
Ans. Matrix form of given equations is AX = B
Here A = , X = and B =
= =
Therefore, solution is unique and =
=
=
Therefore, and
12.
Ans. Matrix form of given equations is AX = B
Here A = , X = and B =
=
=
Therefore, solution is unique and =
=
=
Therefore, and
13.
Ans. Matrix form of given equations is AX = B
Here A = , X = and B =
=
=
Therefore, solution is unique and =
=
=
Therefore, and
14.
Ans. Matrix form of given equations is AX = B
Here A = , X = and B =
=
=
Therefore, solution is unique and =
=
=
Therefore, and
15. If A = find Using solve the system of equations
Ans. Given: Matrix A =
=
exists and ……….(i)
Now, and and
adj. A = =
From eq. (i),
=
Now, Matrix form of given equations is AX = B
Here A = , X = and B =
Therefore, solution is unique and
=
=
Therefore, and
16. The cost of 4 kg onion, 3 kg wheat and 2 kg rice is ` 60. The cost of 2 kg onion, 4 kg wheat and 2 kg rice is ` 90. The cost of 6 kg onion, 2 k wheat and 3 kg rice is ` 70. Find cost of each item per kg by matrix method.
Ans. Let ` ` ` per kg be the prices of onion, wheat and rice respectively.
According to given data, we have three equations,
Matrix form of given equations is AX = B
Here A = , X = and B =
= =
Therefore, solution is unique and = …….(i)
Now,
adj. A =
From eq. (i),
=
=
Therefore, and
Hence, the cost of onion, wheat and rice are ` 5, ` 8 and ` 8 per kg.