NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.3

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NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.3 is given in this article. The chapter carries a weightage of around 08 marks in CBSE Term 2 Exam 2022.

There are a total of four exercises in the NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions.
The exercise deals with functions and types of functions.

Download PDF of NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.3

CBSE CLASS XII Related Questions

1.
If \[ P = \begin{bmatrix} 1 & -1 & 0 \\ 2 & 3 & 4 \\ 0 & 1 & 2 \end{bmatrix} \quad \text{and} \quad Q = \begin{bmatrix} 2 & 2 & -4 \\ -4 & 2 & -4 \\ 1 & -1 & 5 \end{bmatrix} \] find \( QP \) and hence solve the following system of equations using matrix method:
\[ x - y = 3,\quad 2x + 3y + 4z = 13,\quad y + 2z = 7 \]
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2.
Sports car racing is a form of motorsport which uses sports car prototypes. The competition is held on special tracks designed in various shapes. The equation of one such track is given as

(i) Find \(f'(x)\) for \(0<x>3\).
(ii) Find \(f'(4)\).
(iii)(a) Test for continuity of \(f(x)\) at \(x=3\).
OR
(iii)(b) Test for differentiability of \(f(x)\) at \(x=3\).
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3.
Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]
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4.
Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.
View Solution
5.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]
View Solution
6.
Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).
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You can also check

Exercise 1.1 Solutions	16 Questions (14 Short Answers, 2 MCQ)
Exercise 1.2 Solutions	12 Questions (10 Short Answers, 2 MCQ)
Exercise 1.4 Solutions	13 Questions (12 Short Answers, 1 MCQ)
Miscellaneous Exercise Solutions	19 Questions (7 Long answers, 9 Short answer type, 3 MCQ)

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Onto Function	Types of Relations	Modulus Function
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NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.3

Download PDF of NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.3

Other Exercise Solutions of Class 12 Maths Chapter 1 Relations and Functions

CBSE CLASS XII Related Questions

3.
Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

4.
Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.

5.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

6.
Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).

Similar Mathematics Concepts

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NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.3

Download PDF of NCERT Solutions for Class 12 Maths Chapter 1 Relations and Functions Exercise 1.3

Other Exercise Solutions of Class 12 Maths Chapter 1 Relations and Functions

CBSE CLASS XII Related Questions

3.Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

4.Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.

5.Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

6.Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).

Similar Mathematics Concepts

Comments

SUBSCRIBE TO OUR NEWS LETTER

3.
Obtain the value of \[ \Delta = \begin{vmatrix} 1 + x & 1 & 1 \\ 1 & 1 + y & 1 \\ 1 & 1 & 1 + z \end{vmatrix} \] in terms of \(x, y, z\). Further, if \(\Delta = 0\) and \(x, y, z\) are non–zero real numbers, prove that \[ x^{-1} + y^{-1} + z^{-1} = -1 \]

4.
Find the sub–interval of \((0,\pi)\) in which the function \[ f(x)=\tan^{-1}(\sin x-\cos x) \] is increasing and decreasing.

5.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

6.
Find the domain of \(p(x)=\sin^{-1}(1-2x^2)\). Hence, find the value of \(x\) for which \(p(x)=\frac{\pi}{6}\). Also, write the range of \(2p(x)+\frac{\pi}{2}\).