NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.3

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NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.3 is given in this article. Chapter 4 Exercise 4.2 includes questions on calculating the area of a triangle using determinants when the coordinates of 3 vertices have been given and the points are converted into the form of determinants.

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Class 12 Chapter 4 Determinants Topics:

Inverse Laplace Transform	Determinants and Matrices	Applications of determinants and matrices
Properties of Determinants	Minors and Cofactors	Difference between rows and columns
Elementary Matrix Operations	Non-singular matrix	Consistent and inconsistent system of equations
Consistent System of Linear Equations	Determinant Formula	Jacobian Method

CBSE Class 12 Mathematics Study Guides:

Math MCQs	Math Study Notes	Math Formula
Calculus	Arithmetic	NCERT Solutions for Class 12 Maths
Mensuration	Trigonometry	Difference between in Maths

CBSE CLASS XII Related Questions

1.
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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2.
The least value of \[ f(x)=e^{-x} \] in the interval \[ [0,3] \] is:
- \( e^{-3} \)
- \( -1 \)
- \( 1 \)
- \( -e^3 \)
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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.
Assertion (A) : In an experiment of throwing an unbiased die, the probability of getting a prime number given that number appearing on the die being odd is \( \frac{2}{3} \).
Reason (R) : For any two events \( A \) and \( B \), \( P(A|B) = \frac{P(A \cup B)}{P(B)} \).
- 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 and Reason (R) is false.
- Assertion (A) is false and Reason (R) is true.
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5.
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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6.
Find the domain of \[ q(x)=\cos^{-1}(4x^2-3). \] Hence, find the value of \(x\) for which \[ q(x)=0. \] Also, write the range of \[ 3q(x)-\pi. \]
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