NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.1

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Class 12 Maths NCERT Solutions Chapter 4 Determinants Exercise 4.1 is given in this article. Chapter 4 Determinants Exercise includes questions on determinant of a matrix, determinants of a matrix of order one, determinants of a matrix of order two, and determinants of a matrix of order 3 × 3.

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Class 12 Chapter 4 Determinants Topics:

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

CBSE Class 12 Mathematics Study Guides:

Algebra	Arithmetic	Trigonometry
Geometry	Calculus	Math Formula
Math MCQs	Mensuration	Math Study Notes
Permutation and Combination	Difference between in Maths	NCERT Solutions for Class 12 Maths

CBSE CLASS XII Related Questions

1.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]
View Solution
2.
A line passing through the points \(A(1,2,3)\) and \(B(6,8,11)\) intersects the line \[ \vec r = 4\hat i + \hat j + \lambda(6\hat i + 2\hat j + \hat k) \] Find the coordinates of the point of intersection. Hence write the equation of a line passing through the point of intersection and perpendicular to both the lines.
View Solution
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 \[ x^{-1} + y^{-1} + z^{-1} = -1 \]
View Solution
4.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]
View Solution
5.
Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).
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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NCERT Solutions for Class 12 Maths Chapter 4 Determinants

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Important Questions for Class 12 Math Chapter 4 Determinants

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.3

NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.4

CBSE CLASS XII Previous Year Papers

Mathematics

Mathematics Preparation Guides

Matrices: Types, Properties, Formulas & Examples

Relations and Functions: Explanation, Types, and Representation

Types of Matrices: Row, Column, Zero, Symmetric, Skew Symmetric

Minors and Cofactors of Determinant: Definition, Formula and Solved Examples

Operations on Matrices: Addition, Subtraction, Multiplication and Solved Examples

Determinants: Types, Properties & Examples

Types of Relations: Definition, Classification and Examples

Properties of Determinants: Explanation, Important Properties and Examples

Plane: Equation of a Plane in Three-Dimensional Space

Invertible Matrices: Theorems, Properties and Examples

Symmetric and Skew Symmetric Matrices: Definition and Properties

Types of Functions: Elements, Equations, Range, and Domain

Introduction to Three-Dimensional Geometry: Distance, Important Formulae

Angle between Two Lines: Formula, Derivation & Calculation

Binary Operations: Types, Properties and Examples

Addition of Vectors: Definition, Formula, Laws and Properties

Types of Vectors: Definition, Properties & Examples

Definite Integral: Formula, Properties, Application & Examples

Integration by Partial Fractions: Formula, Steps & Examples

Angle Between a Line and a Plane: Formulas and Solved Examples

Mathematics NCERT Solutions

NCERT Solutions For Class 12 Mathematics Chapter 13: Probability

NCERT Solutions For Class 12 Mathematics Chapter 9: Differential Equations

NCERT Solutions For Class 12 Mathematics Chapter 7 Integrals

NCERT Solutions For Class 12 Mathematics Chapter 12: Linear Programming

NCERT Solutions for Class 12 Maths Chapter 3 Matrices

NCERT Solutions For Class 12 Mathematics Chapter 6 Applications of Derivatives

NCERT Solutions For Class 12 Mathematics Chapter 2 Inverse Trigonometric Functions

NCERT Solutions for Class 12 Maths Chapter 4 Determinants

NCERT Solutions for Class 12 Maths Chapter 5 Continuity and Differentiability

NCERT Solutions for Class 12 Maths Chapter 10 Vector Algebra

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NCERT Solutions for Class 12 Maths Chapter 4 Determinants Exercise 4.1

CBSE CLASS XII Related Questions

1.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

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.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]

5.
Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

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 4 Determinants Exercise 4.1

CBSE CLASS XII Related Questions

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

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.Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]

5.Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

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

1.
Find the general solution of the differential equation \[ y\log y\,\frac{dx}{dy}+x=\frac{2}{y}. \]

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.
Evaluate : \[ \int_{\frac{1}{12}}^{\frac{5}{12}} \frac{dx}{1+\sqrt{\cot x}} \]

5.
Mother, Father and Son line up at random for a family picture. Let events \(E\): Son on one end and \(F\): Father in the middle. Find \(P(E/F)\).

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 \(2p(x)+\frac{\pi}{2}\).