NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Exercise

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NCERT Solutions for Class 12 Maths Chapter 4 Determinants Miscellaneous Exercise is given in this article with a step by step explanation of concepts. Chapter 4 Determinants Miscellaneous Exercise covers all the concepts of the order of determinants of a matrix, properties of determinants, area of a triangle, adjoint of a matrix, etc.

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Class 12 Maths Chapter 4 Determinants Topics:

Applications of determinants and matrices	Non-singular matrix	Difference between rows and columns
Non-singular matrix	Elementary Matrix Operations	Consistent System of Linear Equations
Jacobian Method	Minors and Cofactors	Inverse Laplace Transform

CBSE Class 12 Maths Study Guides:

Math MCQs	Math Study Notes	Math Formula
NCERT Solutions for Class 12 Maths	Difference between in Maths	Algebra
Probability and Statistics	Trigonometry	Geometry

CBSE CLASS XII Related Questions

1.
For a square matrix \(A\), \[ (3A)^{-1}= \]

\( 3A^{-1} \)
\( 9A^{-1} \)
\( \frac{1}{3} A^{-1} \)
\( \frac{1}{9} A^{-1} \)

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2.
The domain of \[ f(x)=\cos^{-1}(2x-5) \] is:

\([-1, 1]\)
\([4, 6]\)
\([-7, -3]\)
\([2, 3]\)

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3.
A function \[ f:\mathbb{R}-\left\{\frac{3}{5}\right\} \to \mathbb{R}-\left\{\frac{3}{5}\right\} \] is defined as \[ f(x)=\frac{3x+2}{5x-3}. \] Show that \(f\) is one-one and onto.

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4.
For two vectors \(\vec{a}\) and \(\vec{b}\):

Assertion (A): \[ |\vec{a}\times\vec{b}|^2+(\vec{a}\cdot\vec{b})^2 = |\vec{a}|^2|\vec{b}|^2 \] Reason (R): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]

Both Assertion (A) and Reason (R) are true and the Reason (R) is the correct explanation of the Assertion (A).
Both Assertion (A) and Reason (R) are true, but Reason (R) is not the correct explanation of the Assertion (A).
Assertion (A) is true, but Reason (R) is false.
Assertion (A) is false, but Reason (R) is true.

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5.
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 a sports car racing track is given as: \[ f(x)= \begin{cases} x^4-4x^2+4, & 0\leq x<3,\\ x^2+40, & x\geq 3 \end{cases} \] Based on this information:

6.
For \[ f(x)=x+\frac{1}{x}, \quad x\neq 0. \]

local maximum value is 2
local minimum value is \( -2 \)
local maximum value is \( -2 \)
local minimum value \( < \) local maximum value

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NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Exercise

CBSE CLASS XII Related Questions

1.
For a square matrix \(A\), \[ (3A)^{-1}= \]

2.
The domain of \[ f(x)=\cos^{-1}(2x-5) \] is:

3.
A function \[ f:\mathbb{R}-\left\{\frac{3}{5}\right\} \to \mathbb{R}-\left\{\frac{3}{5}\right\} \] is defined as \[ f(x)=\frac{3x+2}{5x-3}. \] Show that \(f\) is one-one and onto.

4.
For two vectors \(\vec{a}\) and \(\vec{b}\):

Assertion (A): \[ |\vec{a}\times\vec{b}|^2+(\vec{a}\cdot\vec{b})^2 = |\vec{a}|^2|\vec{b}|^2 \] Reason (R): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]

6.
For \[ f(x)=x+\frac{1}{x}, \quad x\neq 0. \]

Comments

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NCERT Solutions for Class 12 Maths Chapter 4 Miscellaneous Exercise

CBSE CLASS XII Related Questions

1. For a square matrix \(A\), \[ (3A)^{-1}= \]

2.The domain of \[ f(x)=\cos^{-1}(2x-5) \] is:

3. A function \[ f:\mathbb{R}-\left\{\frac{3}{5}\right\} \to \mathbb{R}-\left\{\frac{3}{5}\right\} \] is defined as \[ f(x)=\frac{3x+2}{5x-3}. \] Show that \(f\) is one-one and onto.

4.For two vectors \(\vec{a}\) and \(\vec{b}\): Assertion (A): \[ |\vec{a}\times\vec{b}|^2+(\vec{a}\cdot\vec{b})^2 = |\vec{a}|^2|\vec{b}|^2 \] Reason (R): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]

6. For \[ f(x)=x+\frac{1}{x}, \quad x\neq 0. \]

Comments

SUBSCRIBE TO OUR NEWS LETTER

1.
For a square matrix \(A\), \[ (3A)^{-1}= \]

2.
The domain of \[ f(x)=\cos^{-1}(2x-5) \] is:

3.
A function \[ f:\mathbb{R}-\left\{\frac{3}{5}\right\} \to \mathbb{R}-\left\{\frac{3}{5}\right\} \] is defined as \[ f(x)=\frac{3x+2}{5x-3}. \] Show that \(f\) is one-one and onto.

4.
For two vectors \(\vec{a}\) and \(\vec{b}\):

Assertion (A): \[ |\vec{a}\times\vec{b}|^2+(\vec{a}\cdot\vec{b})^2 = |\vec{a}|^2|\vec{b}|^2 \] Reason (R): \[ |\vec{a}\times\vec{b}| = (\vec{a}\cdot\vec{b})\tan\theta, \quad \theta\neq\frac{\pi}{2}. \]

6.
For \[ f(x)=x+\frac{1}{x}, \quad x\neq 0. \]