Careers360 Logo

Popular Searches

    NCERT Solutions for Exercise 4.6 Class 12 Maths Chapter 4 - Determinants

    Access premium articles, webinars, resources to make the best decisions for career, course, exams, scholarships, study abroad and much more with

    Plan, Prepare & Make the Best Career Choices

    NCERT Solutions for Exercise 4.6 Class 12 Maths Chapter 4 - Determinants

    Edited By Ramraj Saini | Updated on Dec 03, 2023 04:15 PM IST | #CBSE Class 12th

    NCERT Solutions For Class 12 Maths Chapter 4 Exercise 4.6

    NCERT Solutions for Exercise 4.6 Class 12 Maths Chapter 4 Determinants are discussed here. These NCERT solutions are created by subject matter expert at Careers360 considering the latest syllabus and pattern of CBSE 2023-24. In this article, you will get NCERT solutions for Class 12 Maths chapter 4 exercise 4.6 consists of questions related to applications of matrix and determinants. There are a lot of applications of matrices and determinants in the field of research, statistics, computer graphics, business, economics, and mathematics. In exercise 4.6 Class 12 Maths you will learn the specific application of matrix and determinant i.e. solving system of linear equation using the inverse of the matrix. All the questions in Class 12 Maths ch 4 ex 4.6 are related to solving the system of linear equations having unique solutions.

    In this Class 12 Maths chapter 4 exercise 4.6 solutions you will get questions related to finding consistency of linear equations. 12th class Maths exercise 4.6 answers are designed as per the students demand covering comprehensive, step by step solutions of every problem. Practice these questions and answers to command the concepts, boost confidence and in depth understanding of concepts. Students can find all exercise together using the link provided below.

    Apply to Aakash iACST Scholarship Test 2024

    Applications for Admissions are open.

    Also, see

    Aakash iACST Scholarship Test 2024

    Get up to 90% scholarship on NEET, JEE & Foundation courses

    Assess NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.6

    Download PDF

    Determinants Exercise: 4.6

    Question:1 Examine the consistency of the system of equations.

    \small x+2y=2

    \small 2x+3y=3

    Answer:

    We have given the system of equations:18967

    \small x+2y=2

    \small 2x+3y=3

    The given system of equations can be written in the form of the matrix; AX =B

    where A= \begin{bmatrix} 1 &2 \\ 2&3 \end{bmatrix}, X= \begin{bmatrix} x\\y \end{bmatrix} and B = \begin{bmatrix} 2\\3 \end{bmatrix}.

    So, we want to check for the consistency of the equations;

    |A| = 1(3) -2(2) = -1 \neq 0

    Here A is non -singular therefore there exists A^{-1}.

    Hence, the given system of equations is consistent.

    Question:2 Examine the consistency of the system of equations

    \small 2x-y=5

    \small x+y=4

    Answer:

    We have given the system of equations:

    \small 2x-y=5

    \small x+y=4

    The given system of equations can be written in the form of matrix; AX =B

    where A= \begin{bmatrix} 2 &-1 \\ 1&1 \end{bmatrix}, X= \begin{bmatrix} x\\y \end{bmatrix} and B = \begin{bmatrix} 5\\4 \end{bmatrix}.

    So, we want to check for the consistency of the equations;

    |A| = 2(1) -1(-1) = 3 \neq 0

    Here A is non -singular therefore there exists A^{-1}.

    Hence, the given system of equations is consistent.

    Question:3 Examine the consistency of the system of equations.

    \small x+3y=5

    \small 2x+6y=8

    Answer:

    We have given the system of equations:

    \small x+3y=5

    \small 2x+6y=8

    The given system of equations can be written in the form of the matrix; AX =B

    where A= \begin{bmatrix} 1 &3 \\ 2&6 \end{bmatrix}, X= \begin{bmatrix} x\\y \end{bmatrix} and B = \begin{bmatrix} 5\\8 \end{bmatrix}.

    So, we want to check for the consistency of the equations;

    |A| = 1(6) -2(3) = 0

    Here A is singular matrix therefore now we will check whether the (adjA)B is zero or non-zero.

    adjA= \begin{bmatrix} 6 &-3 \\ -2& 1 \end{bmatrix}

    So, (adjA)B= \begin{bmatrix} 6 &-3 \\ -2& 1 \end{bmatrix}\begin{bmatrix} 5\\8 \end{bmatrix} = \begin{bmatrix} 30-24\\-10+8 \end{bmatrix}=\begin{bmatrix} 6\\-2 \end{bmatrix} \neq 0

    As, (adjA)B \neq 0 , the solution of the given system of equations does not exist.

    Hence, the given system of equations is inconsistent.

    Question:4 Examine the consistency of the system of equations.

    \small x+y+z=1

    \small 2x+3y+2z=2

    \small ax+ay+2az=4

    Answer:

    We have given the system of equations:

    \small x+y+z=1

    \small 2x+3y+2z=2

    \small ax+ay+2az=4

    The given system of equations can be written in the form of the matrix; AX =B

    where A = \begin{bmatrix} 1& 1&1 \\ 2& 3& 2\\ a& a &2a \end{bmatrix}, X = \begin{bmatrix} x\\y \\ z \end{bmatrix} and B = \begin{bmatrix} 1\\2 \\ 4 \end{bmatrix}.

    So, we want to check for the consistency of the equations;

    |A| = 1(6a-2a) -1(4a-2a)+1(2a-3a)

    = 4a -2a-a = 4a -3a =a \neq 0

    [If zero then it won't satisfy the third equation]

    Here A is non- singular matrix therefore there exist A^{-1}.

    Hence, the given system of equations is consistent.

    Question:5 Examine the consistency of the system of equations.

    \small 3x-y-2z=2

    \small 2y-z=-1

    \small 3x-5y=3

    Answer:

    We have given the system of equations:

    \small 3x-y-2z=2

    \small 2y-z=-1

    \small 3x-5y=3

    The given system of equations can be written in the form of matrix; AX =B

    where A = \begin{bmatrix} 3& -1&-2 \\ 0& 2& -1\\ 3& -5 &0 \end{bmatrix}, X = \begin{bmatrix} x\\y \\ z \end{bmatrix} and B = \begin{bmatrix} 2\\-1 \\ 3 \end{bmatrix}.

    So, we want to check for the consistency of the equations;

    |A| = 3(0-5) -(-1)(0+3)-2(0-6)

    = -15 +3+12 = 0

    Therefore matrix A is a singular matrix.

    So, we will then check (adjA)B,

    (adjA) = \begin{bmatrix} -5 &10 &5 \\ -3& 6 & 3\\ -6& 12 & 6 \end{bmatrix}

    \therefore (adjA)B = \begin{bmatrix} -5 &10 &5 \\ -3& 6 & 3\\ -6& 12 & 6 \end{bmatrix}\begin{bmatrix} 2\\-1 \\ 3 \end{bmatrix} = \begin{bmatrix} -10-10+15\\ -6-6+9 \\ -12-12+18 \end{bmatrix} = \begin{bmatrix} -5\\-3 \\ -6 \end{bmatrix} \neq 0

    As, (adjA)B is non-zero thus the solution of the given system of the equation does not exist. Hence, the given system of equations is inconsistent.

    Question:6 Examine the consistency of the system of equations.

    \small 5x-y+4z=5

    \small 2x+3y+5z=2

    \small 5x-2y+6z=-1

    Answer:

    We have given the system of equations:

    \small 5x-y+4z=5

    \small 2x+3y+5z=2

    \small 5x-2y+6z=-1

    The given system of equations can be written in the form of the matrix; AX =B

    where A = \begin{bmatrix} 5& -1&4 \\ 2& 3& 5\\ 5& -2 &6 \end{bmatrix}, X = \begin{bmatrix} x\\y \\ z \end{bmatrix} and B = \begin{bmatrix} 5\\2 \\ -1 \end{bmatrix}.

    So, we want to check for the consistency of the equations;

    |A| = 5(18+10) +1(12-25)+4(-4-15)

    = 140-13-76 = 51 \neq 0

    Here A is non- singular matrix therefore there exist A^{-1}.

    Hence, the given system of equations is consistent.

    Question:7 Solve system of linear equations, using matrix method.

    \small 5x+2y=4

    \small 7x+3y=5

    Answer:

    The given system of equations

    \small 5x+2y=4

    \small 7x+3y=5

    can be written in the matrix form of AX =B, where

    A = \begin{bmatrix} 5 &4 \\ 7& 3 \end{bmatrix}, X = \begin{bmatrix} x\\y \end{bmatrix} and B = \begin{bmatrix} 4\\5 \end{bmatrix}

    we have,

    |A| = 15-14=1 \neq 0.

    So, A is non-singular, Therefore, its inverse A^{-1} exists.

    as we know A^{-1} = \frac{1}{|A|} (adjA)

    A^{-1} = \frac{1}{|A|} (adjA) = (adjA) = \begin{bmatrix} 3 &-2 \\ -7& 5 \end{bmatrix}

    So, the solutions can be found by X = A^{-1}B = \begin{bmatrix} 3 &-2 \\ -7 & 5 \end{bmatrix}\begin{bmatrix} 4\\5 \end{bmatrix}

    \Rightarrow \begin{bmatrix} x\\y \end{bmatrix} = \begin{bmatrix} 12-10\\ -28+25 \end{bmatrix} = \begin{bmatrix} 2\\-3 \end{bmatrix}

    Hence the solutions of the given system of equations;

    x = 2 and y =-3.

    Question:8 Solve system of linear equations, using matrix method.

    2x-y=-2

    3x+4y=3

    Answer:

    The given system of equations

    2x-y=-2

    3x+4y=3

    can be written in the matrix form of AX =B, where

    A = \begin{bmatrix} 2 &-1 \\ 3& 4 \end{bmatrix}, X = \begin{bmatrix} x\\y \end{bmatrix} and B = \begin{bmatrix} -2\\3 \end{bmatrix}

    we have,

    |A| = 8+3=11 \neq 0.

    So, A is non-singular, Therefore, its inverse A^{-1} exists.

    as we know A^{-1} = \frac{1}{|A|} (adjA)

    A^{-1} = \frac{1}{|A|} (adjA) = \frac{1}{11}\begin{bmatrix} 4 &1 \\ -3& 2 \end{bmatrix}

    So, the solutions can be found by X = A^{-1}B = \frac{1}{11}\begin{bmatrix} 4 &1 \\ -3 & 2 \end{bmatrix}\begin{bmatrix} -2\\3 \end{bmatrix}

    \Rightarrow \begin{bmatrix} x\\y \end{bmatrix} = \frac{1}{11}\begin{bmatrix} -8+3\\ 6+6 \end{bmatrix} = \frac{1}{11}\begin{bmatrix} -5\\12 \end{bmatrix}= \begin{bmatrix} -\frac{5}{11}\\ \\-\frac{12}{11} \end{bmatrix}

    Hence the solutions of the given system of equations;

    x =\frac{-5}{11} \ and\ y =\frac{12}{11}.

    Question:9 Solve system of linear equations, using matrix method.

    \small 4x-3y=3

    \small 3x-5y=7

    Answer:

    The given system of equations

    \small 4x-3y=3

    \small 3x-5y=7

    can be written in the matrix form of AX =B, where

    A = \begin{bmatrix} 4 &-3 \\ 3& -5 \end{bmatrix}, X = \begin{bmatrix} x\\y \end{bmatrix} and B = \begin{bmatrix} 3\\7 \end{bmatrix}

    we have,

    |A| = -20+9=-11 \neq 0.

    So, A is non-singular, Therefore, its inverse A^{-1} exists.

    as we know A^{-1} = \frac{1}{|A|} (adjA)

    A^{-1} = \frac{1}{|A|} (adjA) = \frac{-1}{11}\begin{bmatrix} -5 &3 \\ -3& 4 \end{bmatrix} = \frac{1}{11} \begin{bmatrix} 5 &-3 \\ 3& -4 \end{bmatrix}

    So, the solutions can be found by X = A^{-1}B = \frac{1}{11}\begin{bmatrix} 5 &-3 \\ 3 & -4 \end{bmatrix}\begin{bmatrix} 3\\7 \end{bmatrix}

    \Rightarrow \begin{bmatrix} x\\y \end{bmatrix} = \frac{1}{11}\begin{bmatrix} 15-21\\ 9-28 \end{bmatrix} = \frac{1}{11}\begin{bmatrix} -6\\-19 \end{bmatrix}= \begin{bmatrix} -\frac{6}{11}\\ \\-\frac{19}{11} \end{bmatrix}

    Hence the solutions of the given system of equations;

    x =\frac{-6}{11} \ and\ y =\frac{-19}{11}.

    Question:10 Solve system of linear equations, using matrix method.

    \small 5x+2y=3

    \small 3x+2y=5

    Answer:

    The given system of equations

    \small 5x+2y=3

    \small 3x+2y=5

    can be written in the matrix form of AX =B, where

    A = \begin{bmatrix} 5 &2 \\ 3& 2 \end{bmatrix}, X = \begin{bmatrix} x\\y \end{bmatrix} and B = \begin{bmatrix} 3\\5 \end{bmatrix}

    we have,

    |A| = 10-6=4 \neq 0.

    So, A is non-singular, Therefore, its inverse A^{-1} exists.

    as we know A^{-1} = \frac{1}{|A|} (adjA)

    A^{-1} = \frac{1}{|A|} (adjA) = \frac{1}{4}\begin{bmatrix} 2 &-2 \\ -3& 5 \end{bmatrix}

    So, the solutions can be found by X = A^{-1}B = \frac{1}{4}\begin{bmatrix} 2 &-2 \\ -3 & 5 \end{bmatrix}\begin{bmatrix} 3\\5 \end{bmatrix}

    \Rightarrow \begin{bmatrix} x\\y \end{bmatrix} = \frac{1}{4}\begin{bmatrix} 6-10\\ -9+25 \end{bmatrix} = \frac{1}{4}\begin{bmatrix} -4\\16 \end{bmatrix}= \begin{bmatrix} -1\\4 \end{bmatrix}

    Hence the solutions of the given system of equations;

    x =-1 \ and\ y =4.

    Question:11 Solve system of linear equations, using matrix method.

    \small 2x+y+z=1

    \small x-2y-z= \frac{3}{2}

    \small 3y-5z=9

    Answer:

    The given system of equations

    \small 2x+y+z=1

    \small x-2y-z= \frac{3}{2}

    \small 3y-5z=9

    can be written in the matrix form of AX =B, where

    A = \begin{bmatrix} 2 &1 &1 \\ 1 & -2 &-1 \\ 0& 3 &-5 \end{bmatrix}, X = \begin{bmatrix} x\\y \\z \end{bmatrix} and B =\begin{bmatrix} 1\\ \\ \frac{3}{2} \\ \\ 9 \end{bmatrix}

    we have,

    |A| =2(10+3)-1(-5-0)+1(3-0) = 26+5+3 = 34 \neq 0.

    So, A is non-singular, Therefore, its inverse A^{-1} exists.

    as we know A^{-1} = \frac{1}{|A|} (adjA)

    Now, we will find the cofactors;

    A_{11} =(-1)^{1+1}(10+3) = 13 A_{12} =(-1)^{1+2}(-5-0) = 5

    A_{13} =(-1)^{1+3}(3-0) = 3 A_{21} =(-1)^{2+1}(-5-3) = 8

    A_{22} =(-1)^{2+2}(-10-0) = -10 A_{23} =(-1)^{2+3}(6-0) = -6

    A_{31} =(-1)^{3+1}(-1+2) = 1 A_{32} =(-1)^{3+2}(-2-1) = 3

    A_{33} =(-1)^{3+3}(-4-1) = -5

    (adjA) =\begin{bmatrix} 13 &8 &1 \\ 5& -10 & 3\\ 3& -6 & -5 \end{bmatrix}

    A^{-1} = \frac{1}{|A|} (adjA) = \frac{1}{34}\begin{bmatrix} 13 &8 &1 \\ 5& -10 & 3\\ 3& -6 & -5 \end{bmatrix}

    So, the solutions can be found by X = A^{-1}B = \frac{1}{34}\begin{bmatrix} 13 &8 &1 \\ 5& -10 & 3\\ 3& -6 & -5 \end{bmatrix}\begin{bmatrix} 1\\\frac{3}{2} \\ 9 \end{bmatrix}

    \Rightarrow\begin{bmatrix} x\\y \\ z \end{bmatrix} = \frac{1}{34}\begin{bmatrix} 13+12+9\\5-15+27 \\ 3-9-45 \end{bmatrix} = \frac{1}{34}\begin{bmatrix} 34\\17 \\ -51 \end{bmatrix}= \begin{bmatrix} 1\\\frac{1}{2} \\ -\frac{3}{2} \end{bmatrix}

    Hence the solutions of the given system of equations;

    x =1,\ y =\frac{1}{2},\ and\ \ z=-\frac{3}{2}.

    Question:12 Solve system of linear equations, using matrix method.

    \small x-y+z=4

    \small 2x+y-3z=0

    \small x+y+z=2

    Answer:

    The given system of equations

    \small x-y+z=4

    \small 2x+y-3z=0

    \small x+y+z=2

    can be written in the matrix form of AX =B, where

    A = \begin{bmatrix} 1 &-1 &1 \\ 2 & 1 &-3 \\ 1& 1 &1 \end{bmatrix}, X = \begin{bmatrix} x\\y \\z \end{bmatrix} and\ B =\begin{bmatrix} 4\\ 0 \\ 2 \end{bmatrix}.

    we have,

    |A| =1(1+3)+1(2+3)+1(2-1) = 4+5+1= 10 \neq 0.

    So, A is non-singular, Therefore, its inverse A^{-1} exists.

    as we know A^{-1} = \frac{1}{|A|} (adjA)

    Now, we will find the cofactors;

    A_{11} =(-1)^{1+1}(1+3) = 4 A_{12} =(-1)^{1+2}(2+3) = -5

    A_{13} =(-1)^{1+3}(2-1) = 1 A_{21} =(-1)^{2+1}(-1-1) = 2

    A_{22} =(-1)^{2+2}(1-1) = 0 A_{23} =(-1)^{2+3}(1+1) = -2

    A_{31} =(-1)^{3+1}(3-1) = 2 A_{32} =(-1)^{3+2}(-3-2) = 5

    A_{33} =(-1)^{3+3}(1+2) = 3

    (adjA) =\begin{bmatrix} 4 &2 &2 \\ -5& 0 & 5\\ 1& -2 & 3 \end{bmatrix}

    A^{-1} = \frac{1}{|A|} (adjA) = \frac{1}{10}\begin{bmatrix} 4 &2 &2 \\ -5& 0 & 5\\ 1& -2 & 3 \end{bmatrix}

    So, the solutions can be found by X = A^{-1}B =\frac{1}{10}\begin{bmatrix} 4 &2 &2 \\ -5& 0 & 5\\ 1& -2 & 3 \end{bmatrix}\begin{bmatrix} 4\\0 \\ 2 \end{bmatrix}

    \Rightarrow\begin{bmatrix} x\\y \\ z \end{bmatrix} = \frac{1}{10}\begin{bmatrix} 16+0+4\\-20+0+10 \\ 4+0+6 \end{bmatrix} = \frac{1}{10}\begin{bmatrix} 20\\-10 \\ 10 \end{bmatrix}= \begin{bmatrix} 2\\-1 \\ 1 \end{bmatrix}

    Hence the solutions of the given system of equations;

    x =2,\ y =-1,\ and\ \ z=1.

    Question:13 Solve system of linear equations, using matrix method.

    \small 2x+3y+3z=5

    \small x-2y+z=-4

    \small 3x-y-2z=3

    Answer:

    The given system of equations

    \small 2x+3y+3z=5

    \small x-2y+z=-4

    \small 3x-y-2z=3

    can be written in the matrix form of AX =B, where

    A = \begin{bmatrix} 2 &3 &3 \\ 1 & -2 &1 \\ 3& -1 &-2 \end{bmatrix}, X = \begin{bmatrix} x\\y \\z \end{bmatrix} and\ B =\begin{bmatrix} 5\\ -4 \\ 3 \end{bmatrix}.

    we have,

    |A| =2(4+1) -3(-2-3)+3(-1+6) = 10+15+15 = 40.

    So, A is non-singular, Therefore, its inverse A^{-1} exists.

    as we know A^{-1} = \frac{1}{|A|} (adjA)

    Now, we will find the cofactors;

    A_{11} =(-1)^{1+1}(4+1) = 5 A_{12} =(-1)^{1+2}(-2-3) = 5

    A_{13} =(-1)^{1+3}(-1+6) = 5 A_{21} =(-1)^{2+1}(-6+3) = 3

    A_{22} =(-1)^{2+2}(-4-9) = -13 A_{23} =(-1)^{2+3}(-2-9) = 11

    A_{31} =(-1)^{3+1}(3+6) = 9 A_{32} =(-1)^{3+2}(2-3) = 1

    A_{33} =(-1)^{3+3}(-4-3) = -7

    (adjA) =\begin{bmatrix} 5 &3 &9 \\ 5& -13 & 1\\ 5&11 & -7 \end{bmatrix}

    A^{-1} = \frac{1}{|A|} (adjA) = \frac{1}{40}\begin{bmatrix} 5 &3 &9 \\ 5& -13 & 1\\ 5& 11 & -7 \end{bmatrix}

    So, the solutions can be found by X = A^{-1}B =\frac{1}{40}\begin{bmatrix} 5 &3 &9 \\ 5& -13 & 1\\ 5& 11 & -7 \end{bmatrix}\begin{bmatrix} 5\\-4 \\ 3 \end{bmatrix}

    \Rightarrow\begin{bmatrix} x\\y \\ z \end{bmatrix} = \frac{1}{40}\begin{bmatrix} 25-12+27\\25+52+3 \\ 25-44-21 \end{bmatrix} = \frac{1}{40}\begin{bmatrix} 40\\80 \\ -40 \end{bmatrix}= \begin{bmatrix} 1\\2 \\ -1 \end{bmatrix}

    Hence the solutions of the given system of equations;

    x =1,\ y =2,\ and\ \ z=-1.

    Question:14 Solve system of linear equations, using matrix method.

    \small x-y+2z=7

    \small 3x+4y-5z=-5

    \small 2x-y+3z=12

    Answer:

    The given system of equations

    \small x-y+2z=7

    \small 3x+4y-5z=-5

    \small 2x-y+3z=12

    can be written in the matrix form of AX =B, where

    A = \begin{bmatrix} 1 &-1 &2 \\ 3 & 4 &-5 \\ 2& -1 &3 \end{bmatrix}, X = \begin{bmatrix} x\\y \\z \end{bmatrix} and\ B =\begin{bmatrix} 7\\ -5 \\ 12 \end{bmatrix}.

    we have,

    |A| =1(12-5) +1(9+10)+2(-3-8) = 7+19-22 = 4 \neq0.

    So, A is non-singular, Therefore, its inverse A^{-1} exists.

    as we know A^{-1} = \frac{1}{|A|} (adjA)

    Now, we will find the cofactors;

    A_{11} =(-1)^{12-5} = 7 A_{12} =(-1)^{1+2}(9+10) = -19

    A_{13} =(-1)^{1+3}(-3-8) = -11 A_{21} =(-1)^{2+1}(-3+2) = 1

    A_{22} =(-1)^{2+2}(3-4) = -1 A_{23} =(-1)^{2+3}(-1+2) = -1

    A_{31} =(-1)^{3+1}(5-8) = -3 A_{32} =(-1)^{3+2}(-5-6) = 11

    A_{33} =(-1)^{3+3}(4+3) = 7

    (adjA) =\begin{bmatrix} 7 &1 &-3 \\ -19& -1 & 11\\ -11&-1 & 7 \end{bmatrix}

    A^{-1} = \frac{1}{|A|} (adjA) = \frac{1}{4}\begin{bmatrix} 7 &1 &-3 \\ -19& -1 & 11\\ -11&-1 & 7 \end{bmatrix}

    So, the solutions can be found by X = A^{-1}B =\frac{1}{4}\begin{bmatrix} 7 &1 &-3 \\ -19& -1 & 11\\ -11&-1 & 7 \end{bmatrix}\begin{bmatrix} 7\\-5 \\ 12 \end{bmatrix}

    \Rightarrow\begin{bmatrix} x\\y \\ z \end{bmatrix} = \frac{1}{4}\begin{bmatrix} 49-5-36\\-133+5+132 \\ -77+5+84 \end{bmatrix} = \frac{1}{4}\begin{bmatrix} 8\\4 \\ 12 \end{bmatrix}= \begin{bmatrix} 2\\1 \\ 3 \end{bmatrix}

    Hence the solutions of the given system of equations;

    x =2,\ y =1,\ and\ \ z=3.

    Question:15 If A=\begin{bmatrix} 2 &-3 &5 \\ 3 & 2 &-4 \\ 1 &1 &-2 \end{bmatrix} , find A^-^1. Using A^-^1 solve the system of equations

    2x-3y+5z=11

    3x+2y-4z=-5

    x+y-2z=-3

    Answer:

    The given system of equations

    2x-3y+5z=11

    3x+2y-4z=-5

    x+y-2z=-3

    can be written in the matrix form of AX =B, where

    A=\begin{bmatrix} 2 &-3 &5 \\ 3 & 2 &-4 \\ 1 &1 &-2 \end{bmatrix}, X = \begin{bmatrix} x\\y \\z \end{bmatrix} and\ B =\begin{bmatrix} 11\\ -5 \\ -3 \end{bmatrix}.

    we have,

    |A| =2(-4+4) +3(-6+4)+5(3-2) = 0-6+5 = -1 \neq0.

    So, A is non-singular, Therefore, its inverse A^{-1} exists.

    as we know A^{-1} = \frac{1}{|A|} (adjA)

    Now, we will find the cofactors;

    A_{11} =(-1)^{-4+4} = 0 A_{12} =(-1)^{1+2}(-6+4) = 2

    A_{13} =(-1)^{1+3}(3-2) = 1 A_{21} =(-1)^{2+1}(6-5) = -1

    A_{22} =(-1)^{2+2}(-4-5) = -9 A_{23} =(-1)^{2+3}(2+3) = -5

    A_{31} =(-1)^{3+1}(12-10) = 2 A_{32} =(-1)^{3+2}(-8-15) = 23

    A_{33} =(-1)^{3+3}(4+9) = 13

    (adjA) =\begin{bmatrix} 0 &-1 &2 \\ 2& -9 & 23\\ 1&-5 & 13 \end{bmatrix}

    A^{-1} = \frac{1}{|A|} (adjA) = -1\begin{bmatrix} 0 &-1 &2 \\ 2& -9 & 23\\ 1&-5 & 13 \end{bmatrix} = \begin{bmatrix} 0 &1 &-2 \\ -2& 9 & -23\\ -1&5 & -13 \end{bmatrix}

    So, the solutions can be found by X = A^{-1}B = \begin{bmatrix} 0 &1 &-2 \\ -2& 9 & -23\\ -1&5 & -13 \end{bmatrix}\begin{bmatrix} 11\\-5 \\ -3 \end{bmatrix}

    \Rightarrow\begin{bmatrix} x\\y \\ z \end{bmatrix} = \begin{bmatrix} 0-5+6\\-22-45+69 \\ -11-25+39 \end{bmatrix} = \begin{bmatrix} 1\\2 \\ 3 \end{bmatrix}

    Hence the solutions of the given system of equations;

    x =1,\ y =2,\ and\ \ z=3.

    Question:16 The cost of 4 kg onion, 3 kg wheat and 2 kg rice is Rs 60. The cost of 2 kg onion, 4 kg wheat and 6 kg rice is Rs 90. The cost of 6 kg onion 2 kg wheat and 3 kg rice is Rs 70. Find cost of each item per kg by matrix method.

    Answer:

    So, let us assume the cost of onion, wheat, and rice be x, y and z respectively.

    Then we have the equations for the given situation :

    4x+3y+2z = 60

    2x+4y+6z = 90

    6x+2y+3y = 70

    We can find the cost of each item per Kg by the matrix method as follows;

    Taking the coefficients of x, y, and z as a matrix A.

    We have;

    A = \begin{bmatrix} 4 &3 &2 \\ 2& 4 &6 \\ 6 & 2 & 3 \end{bmatrix}, X= \begin{bmatrix} x\\y \\ z \end{bmatrix} and\ B = \begin{bmatrix} 60\\90 \\ 70 \end{bmatrix}.

    |A| = 4(12-12) -3(6-36)+2(4-24) = 0 +90-40 = 50 \neq 0

    Now, we will find the cofactors of A;

    A_{11} = (-1)^{1+1}(12-12) = 0 A_{12} = (-1)^{1+2}(6-36) = 30

    A_{13} = (-1)^{1+3}(4-24) = -20 A_{21} = (-1)^{2+1}(9-4) = -5

    A_{22} = (-1)^{2+2}(12-12) = 0 A_{23} = (-1)^{2+3}(8-18) = 10

    A_{31} = (-1)^{3+1}(18-8) = 10 A_{32} = (-1)^{3+2}(24-4) = -20

    A_{33} = (-1)^{3+3}(16-6) = 10

    Now we have adjA;

    adjA = \begin{bmatrix} 0 &-5 &10 \\ 30 & 0 &-20 \\ -20 & 10 & 10 \end{bmatrix}

    A^{-1} = \frac{1}{|A|} (adjA) = \frac{1}{50}\begin{bmatrix} 0 &-5 &10 \\ 30 & 0 &-20 \\ -20 & 10 & 10 \end{bmatrix}s

    So, the solutions can be found by X = A^{-1}B = \frac{1}{50}\begin{bmatrix} 0 &-5 &10 \\ 30 & 0 &-20 \\ -20 & 10 & 10 \end{bmatrix}\begin{bmatrix} 60\\90 \\ 70 \end{bmatrix}

    \Rightarrow\begin{bmatrix} x\\y \\ z \end{bmatrix} = \begin{bmatrix} 0-450+700\\1800+0-1400 \\ -1200+900+700 \end{bmatrix} =\frac{1}{50} \begin{bmatrix} 250\\400 \\ 400 \end{bmatrix} = \begin{bmatrix} 5\\8 \\ 8 \end{bmatrix}

    Hence the solutions of the given system of equations;

    x =5,\ y =8,\ and\ \ z=8.

    Therefore, we have the cost of onions is Rs. 5 per Kg, the cost of wheat is Rs. 8 per Kg, and the cost of rice is Rs. 8 per kg.

    More About NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.6:-

    In Class 12th Maths chapter 4 exercise 4.6 solutions, there are 16 long answer-type questions which you should try to solve by yourself. There are three solved examples given in the NCERT textbook before exercise 4.6 Class 12 Maths that you can solve. Solving these examples will help you in solving this exercise 4.6 Class 12 Maths. This chapter is important for the board exams as well as for the higher studies in engineering. Solving a system of linear equations is a must-be-know tool for any engineering branch. You are advised to go through these NCERT Solutions for Class 12 Maths chapter 4 Exercise 4.6 for conceptual clarity.

    Also Read| Determinants Class 12 Chapter 4 Notes

    Benefits of NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.6:-

    • This chapter is very important for board exams and competitive exams like JEE, SRMJEE, etc.
    • Class 12 Maths chapter 4 exercise 4.6 solutions are helpful for you in solving the system of linear equations and linear equations consistency problems.
    • NCERT Solutions for Class 12 Maths Chapter 4 Exercise 4.6 are helpful for the students who are not able to solve NCERT problems by themself.
    • In the Class 12th Maths chapter 4 exercise 4.6 solutions, you will learn the art of answering in board exams to get good marks.
    • You can take these Class 12 Maths chapter 4 exercise 4.6 solutions for reference.
    JEE Main Highest Scoring Chapters & Topics
    Just Study 40% Syllabus and Score upto 100%
    Download EBook

    Key Features Of NCERT Solutions for Exercise 4.6 Class 12 Maths Chapter 4

    • Comprehensive Coverage: The solutions encompass all the topics covered in ex 4.6 class 12, ensuring a thorough understanding of the concepts.
    • Step-by-Step Solutions: In this class 12 maths ex 4.6, each problem is solved systematically, providing a stepwise approach to aid in better comprehension for students.
    • Accuracy and Clarity: Solutions for class 12 ex 4.6 are presented accurately and concisely, using simple language to help students grasp the concepts easily.
    • Conceptual Clarity: In this 12th class maths exercise 4.6 answers, emphasis is placed on conceptual clarity, providing explanations that assist students in understanding the underlying principles behind each problem.
    • Inclusive Approach: Solutions for ex 4.6 class 12 cater to different learning styles and abilities, ensuring that students of various levels can grasp the concepts effectively.
    • Relevance to Curriculum: The solutions for class 12 maths ex 4.6 align closely with the NCERT curriculum, ensuring that students are prepared in line with the prescribed syllabus.

    Also see-

    NCERT Solutions of Class 12 Subject Wise

    Subject Wise NCERT Exampler Solutions

    Happy learning!!!

    Frequently Asked Question (FAQs)

    1. If A is a square matrix of order 2 and |A| = 2 then det( transpose(A)) ?​

    |A^T| = |A| = 2

    2. If three-point are collinear then find area of triangle formed by these points ?

    If three-point are collinear then the area of triangle formed by these points is zero.

    3. What is the definition of consistent system ?

    If solutions of a system of equations exist then it is called a consistent system.

    4. What is the definition of inconsistent system ?

    If the solution of a system of equations doesn't exist then it is called a inconsistent system.

    5. How many questions are there in the exercise 4.6 Class 12 Maths?

    There are 16 questions in the exercise 4.6 Class 12 Maths. The questions are solved with all the necessary steps. Students can follow the NCERT syllabus to get a good score in the board exam.

    6. The transpose of the row matrix is ?

    The transpose of the row matrix is the column matrix.

    7. The transpose of the column matrix is ?

    The transpose of the column matrix is the row matrix.

    8. If the determinant of matrix A is zero then matrix A is called ?

    If the determinant of matrix A is zero then matrix A is called singular matrix.

    Articles

    Upcoming School Exams

    Exam Date:05 February,2024 - 04 March,2024

    Exam Date:27 February,2024 - 10 March,2024

    Exam Date:27 February,2024 - 10 March,2024

    Exam Date:29 February,2024 - 29 February,2024

    Exam Date:29 February,2024 - 29 February,2024

    View All School Exams

    Explore Top Universities Across Globe

    Questions related to CBSE Class 12th

    Have a question related to CBSE Class 12th ?

    hello,

    Yes you can appear for the compartment paper again since CBSE gives three chances to a candidate to clear his/her exams so you still have two more attempts. However, you can appear for your improvement paper for all subjects but you cannot appear for the ones in which you have failed.

    I hope this was helpful!

    Good Luck

    Hello dear,

    If you was not able to clear 1st compartment and now you giving second compartment so YES, you can go for your improvement exam next year but if a student receives an improvement, they are given the opportunity to retake the boards as a private candidate the following year, but there are some requirements. First, the student must pass all of their subjects; if they received a compartment in any subject, they must then pass the compartment exam before being eligible for the improvement.


    As you can registered yourself as private candidate for giving your improvement exam of 12 standard CBSE(Central Board of Secondary Education).For that you have to wait for a whole year which is bit difficult for you.


    Positive side of waiting for whole year is you have a whole year to preparing yourself for your examination. You have no distraction or something which may causes your failure in the exams. In whole year you have to stay focused on your 12 standard examination for doing well in it. By this you get a highest marks as a comparison of others.


    Believe in Yourself! You can make anything happen


    All the very best.

    Hello Student,

    I appreciate your Interest in education. See the improvement is not restricted to one subject or multiple subjects  and  we cannot say if improvement in one subject in one year leads to improvement in more subjects in coming year.

    You just need to have a revision of all subjects what you have completed in the school. have a revision and practice of subjects and concepts helps you better.

    All the best.

    If you'll do hard work then by hard work of 6 months you can achieve your goal but you have to start studying for it dont waste your time its a very important year so please dont waste it otherwise you'll regret.

    Yes, you can take admission in class 12th privately there are many colleges in which you can give 12th privately.

    View All

    A block of mass 0.50 kg is moving with a speed of 2.00 ms-1 on a smooth surface. It strikes another mass of 1.00 kg and then they move together as a single body. The energy loss during the collision is

    Option 1)

    0.34\; J

    Option 2)

    0.16\; J

    Option 3)

    1.00\; J

    Option 4)

    0.67\; J

    A person trying to lose weight by burning fat lifts a mass of 10 kg upto a height of 1 m 1000 times.  Assume that the potential energy lost each time he lowers the mass is dissipated.  How much fat will he use up considering the work done only when the weight is lifted up ?  Fat supplies 3.8×107 J of energy per kg which is converted to mechanical energy with a 20% efficiency rate.  Take g = 9.8 ms−2 :

    Option 1)

    2.45×10−3 kg

    Option 2)

     6.45×10−3 kg

    Option 3)

     9.89×10−3 kg

    Option 4)

    12.89×10−3 kg

     

    An athlete in the olympic games covers a distance of 100 m in 10 s. His kinetic energy can be estimated to be in the range

    Option 1)

    2,000 \; J - 5,000\; J

    Option 2)

    200 \, \, J - 500 \, \, J

    Option 3)

    2\times 10^{5}J-3\times 10^{5}J

    Option 4)

    20,000 \, \, J - 50,000 \, \, J

    A particle is projected at 600   to the horizontal with a kinetic energy K. The kinetic energy at the highest point

    Option 1)

    K/2\,

    Option 2)

    \; K\;

    Option 3)

    zero\;

    Option 4)

    K/4

    In the reaction,

    2Al_{(s)}+6HCL_{(aq)}\rightarrow 2Al^{3+}\, _{(aq)}+6Cl^{-}\, _{(aq)}+3H_{2(g)}

    Option 1)

    11.2\, L\, H_{2(g)}  at STP  is produced for every mole HCL_{(aq)}  consumed

    Option 2)

    6L\, HCl_{(aq)}  is consumed for ever 3L\, H_{2(g)}      produced

    Option 3)

    33.6 L\, H_{2(g)} is produced regardless of temperature and pressure for every mole Al that reacts

    Option 4)

    67.2\, L\, H_{2(g)} at STP is produced for every mole Al that reacts .

    How many moles of magnesium phosphate, Mg_{3}(PO_{4})_{2} will contain 0.25 mole of oxygen atoms?

    Option 1)

    0.02

    Option 2)

    3.125 × 10-2

    Option 3)

    1.25 × 10-2

    Option 4)

    2.5 × 10-2

    If we consider that 1/6, in place of 1/12, mass of carbon atom is taken to be the relative atomic mass unit, the mass of one mole of a substance will

    Option 1)

    decrease twice

    Option 2)

    increase two fold

    Option 3)

    remain unchanged

    Option 4)

    be a function of the molecular mass of the substance.

    With increase of temperature, which of these changes?

    Option 1)

    Molality

    Option 2)

    Weight fraction of solute

    Option 3)

    Fraction of solute present in water

    Option 4)

    Mole fraction.

    Number of atoms in 558.5 gram Fe (at. wt.of Fe = 55.85 g mol-1) is

    Option 1)

    twice that in 60 g carbon

    Option 2)

    6.023 × 1022

    Option 3)

    half that in 8 g He

    Option 4)

    558.5 × 6.023 × 1023

    A pulley of radius 2 m is rotated about its axis by a force F = (20t - 5t2) newton (where t is measured in seconds) applied tangentially. If the moment of inertia of the pulley about its axis of rotation is 10 kg m2 , the number of rotations made by the pulley before its direction of motion if reversed, is

    Option 1)

    less than 3

    Option 2)

    more than 3 but less than 6

    Option 3)

    more than 6 but less than 9

    Option 4)

    more than 9

    Data Administrator

    Database professionals use software to store and organise data such as financial information, and customer shipping records. Individuals who opt for a career as data administrators ensure that data is available for users and secured from unauthorised sales. DB administrators may work in various types of industries. It may involve computer systems design, service firms, insurance companies, banks and hospitals.

    4 Jobs Available
    Bio Medical Engineer

    The field of biomedical engineering opens up a universe of expert chances. An Individual in the biomedical engineering career path work in the field of engineering as well as medicine, in order to find out solutions to common problems of the two fields. The biomedical engineering job opportunities are to collaborate with doctors and researchers to develop medical systems, equipment, or devices that can solve clinical problems. Here we will be discussing jobs after biomedical engineering, how to get a job in biomedical engineering, biomedical engineering scope, and salary. 

    4 Jobs Available
    Database Architect

    If you are intrigued by the programming world and are interested in developing communications networks then a career as database architect may be a good option for you. Data architect roles and responsibilities include building design models for data communication networks. Wide Area Networks (WANs), local area networks (LANs), and intranets are included in the database networks. It is expected that database architects will have in-depth knowledge of a company's business to develop a network to fulfil the requirements of the organisation. Stay tuned as we look at the larger picture and give you more information on what is db architecture, why you should pursue database architecture, what to expect from such a degree and what your job opportunities will be after graduation. Here, we will be discussing how to become a data architect. Students can visit NIT Trichy, IIT Kharagpur, JMI New Delhi

    3 Jobs Available
    Ethical Hacker

    A career as ethical hacker involves various challenges and provides lucrative opportunities in the digital era where every giant business and startup owns its cyberspace on the world wide web. Individuals in the ethical hacker career path try to find the vulnerabilities in the cyber system to get its authority. If he or she succeeds in it then he or she gets its illegal authority. Individuals in the ethical hacker career path then steal information or delete the file that could affect the business, functioning, or services of the organization.

    3 Jobs Available
    Data Analyst

    The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

    Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

    3 Jobs Available
    Water Manager

    A career as water manager needs to provide clean water, preventing flood damage, and disposing of sewage and other wastes. He or she also repairs and maintains structures that control the flow of water, such as reservoirs, sea defense walls, and pumping stations. In addition to these, the Manager has other responsibilities related to water resource management.

    3 Jobs Available
    Geothermal Engineer

    Individuals who opt for a career as geothermal engineers are the professionals involved in the processing of geothermal energy. The responsibilities of geothermal engineers may vary depending on the workplace location. Those who work in fields design facilities to process and distribute geothermal energy. They oversee the functioning of machinery used in the field.

    3 Jobs Available
    Geotechnical engineer

    The role of geotechnical engineer starts with reviewing the projects needed to define the required material properties. The work responsibilities are followed by a site investigation of rock, soil, fault distribution and bedrock properties on and below an area of interest. The investigation is aimed to improve the ground engineering design and determine their engineering properties that include how they will interact with, on or in a proposed construction. 

    The role of geotechnical engineer in mining includes designing and determining the type of foundations, earthworks, and or pavement subgrades required for the intended man-made structures to be made. Geotechnical engineering jobs are involved in earthen and concrete dam construction projects, working under a range of normal and extreme loading conditions. 

    3 Jobs Available
    Budget Analyst

    Budget analysis, in a nutshell, entails thoroughly analyzing the details of a financial budget. The budget analysis aims to better understand and manage revenue. Budget analysts assist in the achievement of financial targets, the preservation of profitability, and the pursuit of long-term growth for a business. Budget analysts generally have a bachelor's degree in accounting, finance, economics, or a closely related field. Knowledge of Financial Management is of prime importance in this career.

    4 Jobs Available
    Operations Manager

    Individuals in the operations manager jobs are responsible for ensuring the efficiency of each department to acquire its optimal goal. They plan the use of resources and distribution of materials. The operations manager's job description includes managing budgets, negotiating contracts, and performing administrative tasks.

    3 Jobs Available
    Finance Executive

    A career as a Finance Executive requires one to be responsible for monitoring an organisation's income, investments and expenses to create and evaluate financial reports. His or her role involves performing audits, invoices, and budget preparations. He or she manages accounting activities, bank reconciliations, and payable and receivable accounts.  

    3 Jobs Available
    Data Analyst

    The invention of the database has given fresh breath to the people involved in the data analytics career path. Analysis refers to splitting up a whole into its individual components for individual analysis. Data analysis is a method through which raw data are processed and transformed into information that would be beneficial for user strategic thinking.

    Data are collected and examined to respond to questions, evaluate hypotheses or contradict theories. It is a tool for analyzing, transforming, modeling, and arranging data with useful knowledge, to assist in decision-making and methods, encompassing various strategies, and is used in different fields of business, research, and social science.

    3 Jobs Available
    Product Manager

    A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

    3 Jobs Available
    Investment Banker

    An Investment Banking career involves the invention and generation of capital for other organizations, governments, and other entities. Individuals who opt for a career as Investment Bankers are the head of a team dedicated to raising capital by issuing bonds. Investment bankers are termed as the experts who have their fingers on the pulse of the current financial and investing climate. Students can pursue various Investment Banker courses, such as Banking and Insurance, and Economics to opt for an Investment Banking career path.

    3 Jobs Available
    Underwriter

    An underwriter is a person who assesses and evaluates the risk of insurance in his or her field like mortgage, loan, health policy, investment, and so on and so forth. The underwriter career path does involve risks as analysing the risks means finding out if there is a way for the insurance underwriter jobs to recover the money from its clients. If the risk turns out to be too much for the company then in the future it is an underwriter who will be held accountable for it. Therefore, one must carry out his or her job with a lot of attention and diligence.

    3 Jobs Available
    Fund Manager

    Are you searching for a fund manager job description? A fund manager is a stock market professional hired by a mutual fund company to manage the funds’ portfolio of numerous clients and oversee their trading activities. In an investment company, multiple managers oversee the clients’ money and make their respective decisions. 

    2 Jobs Available
    Welding Engineer

    Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

    5 Jobs Available
    Transportation Planner

    A career as Transportation Planner requires technical application of science and technology in engineering, particularly the concepts, equipment and technologies involved in the production of products and services. In fields like land use, infrastructure review, ecological standards and street design, he or she considers issues of health, environment and performance. A Transportation Planner assigns resources for implementing and designing programmes. He or she is responsible for assessing needs, preparing plans and forecasts and compliance with regulations.

    3 Jobs Available
    Naval Architect

    A Naval Architect is a professional who designs, produces and repairs safe and sea-worthy surfaces or underwater structures. A Naval Architect stays involved in creating and designing ships, ferries, submarines and yachts with implementation of various principles such as gravity, ideal hull form, buoyancy and stability. 

    2 Jobs Available
    Field Surveyor

    Are you searching for a Field Surveyor Job Description? A Field Surveyor is a professional responsible for conducting field surveys for various places or geographical conditions. He or she collects the required data and information as per the instructions given by senior officials. 

    2 Jobs Available
    Highway Engineer

    Highway Engineer Job Description: A Highway Engineer is a civil engineer who specialises in planning and building thousands of miles of roads that support connectivity and allow transportation across the country. He or she ensures that traffic management schemes are effectively planned concerning economic sustainability and successful implementation.

    2 Jobs Available
    Conservation Architect

    A Conservation Architect is a professional responsible for conserving and restoring buildings or monuments having a historic value. He or she applies techniques to document and stabilise the object’s state without any further damage. A Conservation Architect restores the monuments and heritage buildings to bring them back to their original state.

    2 Jobs Available
    Safety Manager

    A Safety Manager is a professional responsible for employee’s safety at work. He or she plans, implements and oversees the company’s employee safety. A Safety Manager ensures compliance and adherence to Occupational Health and Safety (OHS) guidelines.

    2 Jobs Available
    Team Lead

    A Team Leader is a professional responsible for guiding, monitoring and leading the entire group. He or she is responsible for motivating team members by providing a pleasant work environment to them and inspiring positive communication. A Team Leader contributes to the achievement of the organisation’s goals. He or she improves the confidence, product knowledge and communication skills of the team members and empowers them.

    2 Jobs Available
    Orthotist and Prosthetist

    Orthotists and Prosthetists are professionals who provide aid to patients with disabilities. They fix them to artificial limbs (prosthetics) and help them to regain stability. There are times when people lose their limbs in an accident. In some other occasions, they are born without a limb or orthopaedic impairment. Orthotists and prosthetists play a crucial role in their lives with fixing them to assistive devices and provide mobility.

    6 Jobs Available
    Veterinary Doctor

    A veterinary doctor is a medical professional with a degree in veterinary science. The veterinary science qualification is the minimum requirement to become a veterinary doctor. There are numerous veterinary science courses offered by various institutes. He or she is employed at zoos to ensure they are provided with good health facilities and medical care to improve their life expectancy.

    5 Jobs Available
    Pathologist

    A career in pathology in India is filled with several responsibilities as it is a medical branch and affects human lives. The demand for pathologists has been increasing over the past few years as people are getting more aware of different diseases. Not only that, but an increase in population and lifestyle changes have also contributed to the increase in a pathologist’s demand. The pathology careers provide an extremely huge number of opportunities and if you want to be a part of the medical field you can consider being a pathologist. If you want to know more about a career in pathology in India then continue reading this article.

    5 Jobs Available
    Speech Therapist
    4 Jobs Available
    Gynaecologist

    Gynaecology can be defined as the study of the female body. The job outlook for gynaecology is excellent since there is evergreen demand for one because of their responsibility of dealing with not only women’s health but also fertility and pregnancy issues. Although most women prefer to have a women obstetrician gynaecologist as their doctor, men also explore a career as a gynaecologist and there are ample amounts of male doctors in the field who are gynaecologists and aid women during delivery and childbirth. 

    4 Jobs Available
    Oncologist

    An oncologist is a specialised doctor responsible for providing medical care to patients diagnosed with cancer. He or she uses several therapies to control the cancer and its effect on the human body such as chemotherapy, immunotherapy, radiation therapy and biopsy. An oncologist designs a treatment plan based on a pathology report after diagnosing the type of cancer and where it is spreading inside the body.

    3 Jobs Available
    Audiologist

    The audiologist career involves audiology professionals who are responsible to treat hearing loss and proactively preventing the relevant damage. Individuals who opt for a career as an audiologist use various testing strategies with the aim to determine if someone has a normal sensitivity to sounds or not. After the identification of hearing loss, a hearing doctor is required to determine which sections of the hearing are affected, to what extent they are affected, and where the wound causing the hearing loss is found. As soon as the hearing loss is identified, the patients are provided with recommendations for interventions and rehabilitation such as hearing aids, cochlear implants, and appropriate medical referrals. While audiology is a branch of science that studies and researches hearing, balance, and related disorders.

    3 Jobs Available
    Cardiothoracic Surgeon

    Cardiothoracic surgeons are an important part of the surgical team. They usually work in hospitals, and perform emergency as well as scheduled operations. Some of the cardiothoracic surgeons also work in teaching hospitals working as teachers and guides for medical students aspiring to become a cardiothoracic surgeon. A career as a cardiothoracic surgeon involves treating and managing various types of conditions within their speciality that includes their presence at different locations such as outpatient clinics, team meetings, and ward rounds. 

    2 Jobs Available
    Actor

    For an individual who opts for a career as an actor, the primary responsibility is to completely speak to the character he or she is playing and to persuade the crowd that the character is genuine by connecting with them and bringing them into the story. This applies to significant roles and littler parts, as all roles join to make an effective creation. Here in this article, we will discuss how to become an actor in India, actor exams, actor salary in India, and actor jobs. 

    4 Jobs Available
    Acrobat

    Individuals who opt for a career as acrobats create and direct original routines for themselves, in addition to developing interpretations of existing routines. The work of circus acrobats can be seen in a variety of performance settings, including circus, reality shows, sports events like the Olympics, movies and commercials. Individuals who opt for a career as acrobats must be prepared to face rejections and intermittent periods of work. The creativity of acrobats may extend to other aspects of the performance. For example, acrobats in the circus may work with gym trainers, celebrities or collaborate with other professionals to enhance such performance elements as costume and or maybe at the teaching end of the career.

    3 Jobs Available
    Video Game Designer

    Career as a video game designer is filled with excitement as well as responsibilities. A video game designer is someone who is involved in the process of creating a game from day one. He or she is responsible for fulfilling duties like designing the character of the game, the several levels involved, plot, art and similar other elements. Individuals who opt for a career as a video game designer may also write the codes for the game using different programming languages.

    Depending on the video game designer job description and experience they may also have to lead a team and do the early testing of the game in order to suggest changes and find loopholes.

    3 Jobs Available
    Talent Agent

    The career as a Talent Agent is filled with responsibilities. A Talent Agent is someone who is involved in the pre-production process of the film. It is a very busy job for a Talent Agent but as and when an individual gains experience and progresses in the career he or she can have people assisting him or her in work. Depending on one’s responsibilities, number of clients and experience he or she may also have to lead a team and work with juniors under him or her in a talent agency. In order to know more about the job of a talent agent continue reading the article.

    If you want to know more about talent agent meaning, how to become a Talent Agent, or Talent Agent job description then continue reading this article.

    3 Jobs Available
    Radio Jockey

    Radio Jockey is an exciting, promising career and a great challenge for music lovers. If you are really interested in a career as radio jockey, then it is very important for an RJ to have an automatic, fun, and friendly personality. If you want to get a job done in this field, a strong command of the language and a good voice are always good things. Apart from this, in order to be a good radio jockey, you will also listen to good radio jockeys so that you can understand their style and later make your own by practicing.

    A career as radio jockey has a lot to offer to deserving candidates. If you want to know more about a career as radio jockey, and how to become a radio jockey then continue reading the article.

    3 Jobs Available
    Producer

    An individual who is pursuing a career as a producer is responsible for managing the business aspects of production. They are involved in each aspect of production from its inception to deception. Famous movie producers review the script, recommend changes and visualise the story. 

    They are responsible for overseeing the finance involved in the project and distributing the film for broadcasting on various platforms. A career as a producer is quite fulfilling as well as exhaustive in terms of playing different roles in order for a production to be successful. Famous movie producers are responsible for hiring creative and technical personnel on contract basis.

    2 Jobs Available
    Fashion Blogger

    Fashion bloggers use multiple social media platforms to recommend or share ideas related to fashion. A fashion blogger is a person who writes about fashion, publishes pictures of outfits, jewellery, accessories. Fashion blogger works as a model, journalist, and a stylist in the fashion industry. In current fashion times, these bloggers have crossed into becoming a star in fashion magazines, commercials, or campaigns. 

    2 Jobs Available
    Photographer

    Photography is considered both a science and an art, an artistic means of expression in which the camera replaces the pen. In a career as a photographer, an individual is hired to capture the moments of public and private events, such as press conferences or weddings, or may also work inside a studio, where people go to get their picture clicked. Photography is divided into many streams each generating numerous career opportunities in photography. With the boom in advertising, media, and the fashion industry, photography has emerged as a lucrative and thrilling career option for many Indian youths.

    2 Jobs Available
    Copy Writer

    In a career as a copywriter, one has to consult with the client and understand the brief well. A career as a copywriter has a lot to offer to deserving candidates. Several new mediums of advertising are opening therefore making it a lucrative career choice. Students can pursue various copywriter courses such as Journalism, Advertising, Marketing Management. Here, we have discussed how to become a freelance copywriter, copywriter career path, how to become a copywriter in India, and copywriting career outlook. 

    5 Jobs Available
    Editor

    Individuals in the editor career path is an unsung hero of the news industry who polishes the language of the news stories provided by stringers, reporters, copywriters and content writers and also news agencies. Individuals who opt for a career as an editor make it more persuasive, concise and clear for readers. In this article, we will discuss the details of the editor's career path such as how to become an editor in India, editor salary in India and editor skills and qualities.

    3 Jobs Available
    Journalist

    Careers in journalism are filled with excitement as well as responsibilities. One cannot afford to miss out on the details. As it is the small details that provide insights into a story. Depending on those insights a journalist goes about writing a news article. A journalism career can be stressful at times but if you are someone who is passionate about it then it is the right choice for you. If you want to know more about the media field and journalist career then continue reading this article.

    3 Jobs Available
    Publisher

    For publishing books, newspapers, magazines and digital material, editorial and commercial strategies are set by publishers. Individuals in publishing career paths make choices about the markets their businesses will reach and the type of content that their audience will be served. Individuals in book publisher careers collaborate with editorial staff, designers, authors, and freelance contributors who develop and manage the creation of content.

    3 Jobs Available
    Vlogger

    In a career as a vlogger, one generally works for himself or herself. However, once an individual has gained viewership there are several brands and companies that approach them for paid collaboration. It is one of those fields where an individual can earn well while following his or her passion. 

    Ever since internet costs got reduced the viewership for these types of content has increased on a large scale. Therefore, a career as a vlogger has a lot to offer. If you want to know more about the Vlogger eligibility, roles and responsibilities then continue reading the article. 

    3 Jobs Available
    Travel Journalist

    The career of a travel journalist is full of passion, excitement and responsibility. Journalism as a career could be challenging at times, but if you're someone who has been genuinely enthusiastic about all this, then it is the best decision for you. Travel journalism jobs are all about insightful, artfully written, informative narratives designed to cover the travel industry. Travel Journalist is someone who explores, gathers and presents information as a news article.

    2 Jobs Available
    Videographer
    2 Jobs Available
    SEO Analyst

    An SEO Analyst is a web professional who is proficient in the implementation of SEO strategies to target more keywords to improve the reach of the content on search engines. He or she provides support to acquire the goals and success of the client’s campaigns. 

    2 Jobs Available
    Welding Engineer

    Welding Engineer Job Description: A Welding Engineer work involves managing welding projects and supervising welding teams. He or she is responsible for reviewing welding procedures, processes and documentation. A career as Welding Engineer involves conducting failure analyses and causes on welding issues. 

    5 Jobs Available
    QA Manager
    4 Jobs Available
    Production Manager
    3 Jobs Available
    Product Manager

    A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

    3 Jobs Available
    Quality Controller

    A quality controller plays a crucial role in an organisation. He or she is responsible for performing quality checks on manufactured products. He or she identifies the defects in a product and rejects the product. 

    A quality controller records detailed information about products with defects and sends it to the supervisor or plant manager to take necessary actions to improve the production process.

    3 Jobs Available
    Production Engineer

    A career as a Production Engineer is crucial in the manufacturing industry. He or she ensures the functionality of production equipment and machinery to improve productivity and minimise production costs to drive revenues and increase profitability. 

    2 Jobs Available
    Product Designer

    Individuals who opt for a career as product designers are responsible for designing the components and overall product concerning its shape, size, and material used in manufacturing. They are responsible for the aesthetic appearance of the product. A product designer uses his or her creative skills to give a product its final outlook and ensures the functionality of the design. 

    Students can opt for various product design degrees such as B.Des and M.Des to become product designers. Industrial product designer prepares 3D models of designs for approval and discusses them with clients and other colleagues. Individuals who opt for a career as a product designer estimate the total cost involved in designing.

    2 Jobs Available
    Commercial Manager

    A Commercial Manager negotiates, advises and secures information about pricing for commercial contracts. He or she is responsible for developing financial plans in order to maximise the business's profitability.

    2 Jobs Available
    AWS Solution Architect

    An AWS Solution Architect is someone who specializes in developing and implementing cloud computing systems. He or she has a good understanding of the various aspects of cloud computing and can confidently deploy and manage their systems. He or she troubleshoots the issues and evaluates the risk from the third party. 

    4 Jobs Available
    QA Manager
    4 Jobs Available
    Azure Administrator

    An Azure Administrator is a professional responsible for implementing, monitoring, and maintaining Azure Solutions. He or she manages cloud infrastructure service instances and various cloud servers as well as sets up public and private cloud systems. 

    4 Jobs Available
    Information Security Manager

    Individuals in the information security manager career path involves in overseeing and controlling all aspects of computer security. The IT security manager job description includes planning and carrying out security measures to protect the business data and information from corruption, theft, unauthorised access, and deliberate attack 

    3 Jobs Available
    Computer Programmer

    Careers in computer programming primarily refer to the systematic act of writing code and moreover include wider computer science areas. The word 'programmer' or 'coder' has entered into practice with the growing number of newly self-taught tech enthusiasts. Computer programming careers involve the use of designs created by software developers and engineers and transforming them into commands that can be implemented by computers. These commands result in regular usage of social media sites, word-processing applications and browsers.

    3 Jobs Available
    Product Manager

    A Product Manager is a professional responsible for product planning and marketing. He or she manages the product throughout the Product Life Cycle, gathering and prioritising the product. A product manager job description includes defining the product vision and working closely with team members of other departments to deliver winning products.  

    3 Jobs Available
    ITSM Manager
    3 Jobs Available
    .NET Developer

    .NET Developer Job Description: A .NET Developer is a professional responsible for producing code using .NET languages. He or she is a software developer who uses the .NET technologies platform to create various applications. Dot NET Developer job comes with the responsibility of  creating, designing and developing applications using .NET languages such as VB and C#. 

    2 Jobs Available
    Back to top