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2024 V2 1001022024 V3 1001022024 V4 1001022024 V6 1001022024 V8 100102

2024V2100102

B. Tech. Ist Semester Examination, 2024

03 Hours70 marks

Instructions

  • The marks are indicated in the right-hand margin.
  • There are NINE questions in this paper.
  • Attempt FIVE questions in all.
  • Question No. 1 is compulsory.

Q.1 Choose the correct option the following (Any seven question only):

Ask AI

  1. Q1.1

    Which operation is not an elementary row operation?

    a)

    Swapping two rows

    b)

    Adding a multiple of one row to another

    c)

    Multiplying a row by zero.

    d)

    Multiplying a row by a non-zero constant

    Ask AI

  2. Q1.2

    The rank of a matrix is:

    a)

    Number of non-zero rows in echelon form

    b)

    Number of columns

    c)

    Number of rows

    d)

    None above

    Ask AI

  3. Q1.3

    The inverse of a matrix using Gauss-Jordan:

    a)

    only determinant calculation

    b)

    Reducing matrix to diagonal form

    c)

    Augmenting with identity matrix and applying row operations

    d)

    None of the above

    Ask AI

  4. Q1.4

    A matrix is diagonalizable:

    a)

    It has repeated eigenvalues only

    b)

    It is symmetric

    c)

    It has a full set of linearly independent eigenvectors

    d)

    It is square

    Ask AI

  5. Q1.5

    A matrix is similar to a diagonal matrix if:

    a)

    It has complex entries

    b)

    It has n linearly independent eigenvectors

    c)

    It is invertible

    d)

    None of the above

    Ask AI

  6. Q1.6

    A function is Riemann integrable if:

    a)

    It is continuous

    b)

    It has infinite discontinuities

    c)

    It is discontinuous everywhere

    d)

    None of the above

    Ask AI

  7. Q1.7

    Jacobian is:

    a)

    A scalar

    b)

    A vector

    c)

    A matrix of partial derivatives

    d)

    A function

    Ask AI

  8. Q1.8

    Taylor's expansion for multivariable function includes:

    a)

    Only first order terms

    b)

    Only second order

    c)

    All orders

    d)

    Only constant term

    Ask AI

  9. Q1.9

    Change of variables in double integral involves:

    a)

    Matrix algebra

    b)

    Laplace transforms

    c)

    Jacobian

    d)

    Only constant term

    Ask AI

  10. Q1.10

    Triple integral over a region gives:

    a)

    Area

    b)

    Length

    c)

    Volume

    d)

    Angle

    Ask AI

Q.2 Solve both questions :

Ask AI

  1. Q2.1

    What is the difference between a vector space and a subspace? Illustrate with examples.

    Ask AI

  2. Q2.2

    Define and explain rank, row space, and column space of a matrix with examples.

    Ask AI

Q.3 Solve both questions :

Ask AI

  1. Q3.1

    Explain the Cayley-Hamilton Theorem and verify it for a 2x2 matrix.

    Ask AI

  2. Q3.2

    Define and compute the Jacobian for transformation x=u+vx = u + v of u−vu - v.

    Ask AI

Q.4 Solve both questions :

Ask AI

  1. Q4.1

    Explain the Gauss-Jordan method for finding the inverse of a matrix with an example.

    Ask AI

  2. Q4.2

    Define Hermitian, Skew-Hermitian, and Unitary matrices. Provide examples for each.

    Ask AI

Q.5 Solve both questions :

Ask AI

  1. Q5.1

    Explain and prove the Rank-Nullity theorem.

    Ask AI

  2. Q5.2

    Describe the method of finding eigenvalues and eigenvectors of a matrix.

    Ask AI

Q.6 Solve both questions :

Ask AI

  1. Q6.1

    State and prove Rolle's Theorem with a graphical example.

    Ask AI

  2. Q6.2

    Define Beta and Gamma functions. Derive the relation between them.

    Ask AI

Q.7 Solve both questions :

Ask AI

  1. Q7.1

    Derive the Taylor series for a function of two variables.

    Ask AI

  2. Q7.2

    Solve a maxima-ratum problem using second derivative test.

    Ask AI

Q.8 Solve both questions :

Ask AI

  1. Q8.1

    Evaluate a double integral to find area under a curve.

    Ask AI

  2. Q8.2

    Convert a double integral into polar coordinates and evaluate.

    Ask AI

Q.9 Write short notes on any two of the following:

Ask AI

2024V3100102

B. Tech. Ist Semester Examination, 2024

03 Hours70 marks

Instructions

  • The marks are indicated in the right-hand margin.
  • There are NINE questions in this paper.
  • Attempt FIVE questions in all.
  • Question No. 1 is compulsory.

Q.1 Choose the correct option the following (Any seven question only):

Ask AI

  1. Q1.1

    Which operation is not an elementary row operation?

    a)

    Swapping two rows

    b)

    Adding a multiple of one row to another

    c)

    Multiplying a row by zero.

    d)

    Multiplying a row by a non-zero constant

    Ask AI

  2. Q1.2

    The rank of a matrix is:

    a)

    Number of non-zero rows in echelon form

    b)

    Number of columns

    c)

    Number of rows

    d)

    None above

    Ask AI

  3. Q1.3

    The inverse of a matrix using Gauss-Jordan:

    a)

    only determinant calculation

    b)

    Reducing matrix to diagonal form

    c)

    Augmenting with identity matrix and applying row operations

    d)

    None of the above

    Ask AI

  4. Q1.4

    A matrix is diagonalizable:

    a)

    It has repeated eigenvalues only

    b)

    It is symmetric

    c)

    It has a full set of linearly independent eigenvectors

    d)

    It is square

    Ask AI

  5. Q1.5

    A matrix is similar to a diagonal matrix if:

    a)

    It has complex entries

    b)

    It has n linearly independent eigenvectors

    c)

    It is invertible

    d)

    None of the above

    Ask AI

  6. Q1.6

    A function is Riemann integrable if:

    a)

    It is continuous

    b)

    It has infinite discontinuities

    c)

    It is discontinuous everywhere

    d)

    None of the above

    Ask AI

  7. Q1.7

    Jacobian is:

    a)

    A scalar

    b)

    A vector

    c)

    A matrix of partial derivatives

    d)

    A function

    Ask AI

  8. Q1.8

    Taylor's expansion for multivariable function includes:

    a)

    Only first order terms

    b)

    Only second order

    c)

    All orders

    d)

    Only constant term

    Ask AI

  9. Q1.9

    Change of variables in double integral involves:

    a)

    Matrix algebra

    b)

    Laplace transforms

    c)

    Jacobian

    d)

    Only constant term

    Ask AI

  10. Q1.10

    Triple integral over a region gives:

    a)

    Area

    b)

    Length

    c)

    Volume

    d)

    Angle

    Ask AI

Q.2 Solve both questions :

Ask AI

  1. Q2.1

    What is the difference between a vector space and a subspace? Illustrate with examples.

    Ask AI

  2. Q2.2

    Define and explain rank, row space, and column space of a matrix with examples.

    Ask AI

Q.3 Solve both questions :

Ask AI

  1. Q3.1

    Explain the Cayley-Hamilton Theorem and verify it for a 2x2 matrix.

    Ask AI

  2. Q3.2

    Define and compute the Jacobian for transformation $ x = u + v $ of $ u - v $.

    Ask AI

Q.4 Solve both questions :

Ask AI

  1. Q4.1

    Explain the Gauss-Jordan method for finding the inverse of a matrix with an example.

    Ask AI

  2. Q4.2

    Define Hermitian, Skew-Hermitian, and Unitary matrices. Provide examples for each.

    Ask AI

Q.5 Solve both questions :

Ask AI

  1. Q5.1

    Explain and prove the Rank-Nullity theorem.

    Ask AI

  2. Q5.2

    Describe the method of finding eigenvalues and eigenvectors of a matrix.

    Ask AI

Q.6 Solve both questions :

Ask AI

  1. Q6.1

    State and prove Rolle's Theorem with a graphical example.

    Ask AI

  2. Q6.2

    Define Beta and Gamma functions. Derive the relation between them.

    Ask AI

Q.7 Solve both questions :

Ask AI

  1. Q7.1

    Derive the Taylor series for a function of two variables.

    Ask AI

  2. Q7.2

    Solve a maxima-ratum problem using second derivative test.

    Ask AI

Q.8 Solve both questions :

Ask AI

  1. Q8.1

    Evaluate a double integral to find area under a curve.

    Ask AI

  2. Q8.2

    Convert a double integral into polar coordinates and evaluate.

    Ask AI

Q.9 Write short notes on any two of the following:

Ask AI

  1. Q9.1

    a)

    Properties of Eigen vectors

    b)

    Riemann Integration & Riemann Sum

    c)

    Application to area and volume using double and triple integral

    d)

    Scalar and vector fields

    Ask AI

2024V4100102

B. Tech. Ist Semester Examination, 2024

03 Hours70 marks

Instructions

  • The marks are indicated in the right-hand margin.
  • There are NINE questions in this paper.
  • Attempt FIVE questions in all.
  • Question No. 1 is compulsory.

Q.1 Choose the correct option the following (Any seven question only):

Ask AI

  1. Q1.1

    Which operation is not an elementary row operation?

    a)

    Swapping two rows

    b)

    Adding a multiple of one row to another

    c)

    Multiplying a row by zero.

    d)

    Multiplying a row by a non-zero constant

    Ask AI

  2. Q1.2

    The rank of a matrix is:

    a)

    Number of non-zero rows in echelon form

    b)

    Number of columns

    c)

    Number of rows

    d)

    None above

    Ask AI

  3. Q1.3

    The inverse of a matrix using Gauss-Jordan:

    a)

    only determinant calculation

    b)

    Reducing matrix to diagonal form

    c)

    Augmenting with identity matrix and applying row operations

    d)

    None of the above

    Ask AI

  4. Q1.4

    A matrix is diagonalizable:

    a)

    It has repeated eigenvalues only

    b)

    It is symmetric

    c)

    It has a full set of linearly independent eigenvectors

    d)

    It is square

    Ask AI

  5. Q1.5

    A matrix is similar to a diagonal matrix if:

    a)

    It has complex entries

    b)

    It has n linearly independent eigenvectors

    c)

    It is invertible

    d)

    None of the above

    Ask AI

  6. Q1.6

    A function is Riemann integrable if:

    a)

    It is continuous

    b)

    It has infinite discontinuities

    c)

    It is discontinuous everywhere

    d)

    None of the above

    Ask AI

  7. Q1.7

    Jacobian is:

    a)

    A scalar

    b)

    A vector

    c)

    A matrix of partial derivatives

    d)

    A function

    Ask AI

  8. Q1.8

    Taylor's expansion for multivariable function includes:

    a)

    Only first order terms

    b)

    Only second order

    c)

    All orders

    d)

    Only constant term

    Ask AI

  9. Q1.9

    Change of variables in double integral involves:

    a)

    Matrix algebra

    b)

    Laplace transforms

    c)

    Jacobian

    d)

    Only constant term

    Ask AI

  10. Q1.10

    Triple integral over a region gives:

    a)

    Area

    b)

    Length

    c)

    Volume

    d)

    Angle

    Ask AI

Q.2 Solve both questions :

Ask AI

  1. Q2.1

    What is the difference between a vector space and a subspace? Illustrate with examples.

    Ask AI

  2. Q2.2

    Define and explain rank, row space, and column space of a matrix with examples.

    Ask AI

Q.3 Solve both questions :

Ask AI

  1. Q3.1

    Explain the Cayley-Hamilton Theorem and verify it for a 2x2 matrix.

    Ask AI

  2. Q3.2

    Define and compute the Jacobian for transformation x=u+vx = u + v of u−vu - v.

    Ask AI

Q.4 Solve both questions :

Ask AI

  1. Q4.1

    Explain the Gauss-Jordan method for finding the inverse of a matrix with an example.

    Ask AI

  2. Q4.2

    Define Hermitian, Skew-Hermitian, and Unitary matrices. Provide examples for each.

    Ask AI

Q.5 Solve both questions :

Ask AI

  1. Q5.1

    Explain and prove the Rank-Nullity theorem.

    Ask AI

  2. Q5.2

    Describe the method of finding eigenvalues and eigenvectors of a matrix.

    Ask AI

Q.6 Solve both questions :

Ask AI

  1. Q6.1

    State and prove Rolle's Theorem with a graphical example.

    Ask AI

  2. Q6.2

    Define Beta and Gamma functions. Derive the relation between them.

    Ask AI

Q.7 Solve both questions :

Ask AI

  1. Q7.1

    Derive the Taylor series for a function of two variables.

    Ask AI

  2. Q7.2

    Solve a maxima-ratum problem using second derivative test.

    Ask AI

Q.8 Solve both questions :

Ask AI

  1. Q8.1

    Evaluate a double integral to find area under a curve.

    Ask AI

  2. Q8.2

    Convert a double integral into polar coordinates and evaluate.

    Ask AI

Q.9 Write short notes on any two of the following:

Ask AI

  1. Q9.1

    • Properties of Eigen vectors
    • Riemann Integration & Riemann Sum
    • Application to area and volume using double and triple integral
    • Scalar and vector fields
    a)

    Properties of Eigen vectors

    b)

    Riemann Integration & Riemann Sum

    c)

    Application to area and volume using double and triple integral

    d)

    Scalar and vector fields

    Ask AI

2024V6100102

B. Tech. Ist Semester Examination, 2024

03 Hours70 marks

Instructions

  • The marks are indicated in the right-hand margin.
  • There are NINE questions in this paper.
  • Attempt FIVE questions in all.
  • Question No. 1 is compulsory.

Q.1 Choose the correct option the following (Any seven question only):

Ask AI

  1. Q1.1

    Which operation is not an elementary row operation?

    a)

    Swapping two rows

    b)

    Adding a multiple of one row to another

    c)

    Multiplying a row by zero.

    d)

    Multiplying a row by a non-zero constant

    Ask AI

  2. Q1.2

    The rank of a matrix is:

    a)

    Number of non-zero rows in echelon form

    b)

    Number of columns

    c)

    Number of rows

    d)

    None above

    Ask AI

  3. Q1.3

    The inverse of a matrix using Gauss-Jordan:

    a)

    only determinant calculation

    b)

    Reducing matrix to diagonal form

    c)

    Augmenting with identity matrix and applying row operations

    d)

    None of the above

    Ask AI

  4. Q1.4

    A matrix is diagonalizable:

    a)

    It has repeated eigenvalues only

    b)

    It is symmetric

    c)

    It has a full set of linearly independent eigenvectors

    d)

    It is square

    Ask AI

  5. Q1.5

    A matrix is similar to a diagonal matrix if:

    a)

    It has complex entries

    b)

    It has n linearly independent eigenvectors

    c)

    It is invertible

    d)

    None of the above

    Ask AI

  6. Q1.6

    A function is Riemann integrable if:

    a)

    It is continuous

    b)

    It has infinite discontinuities

    c)

    It is discontinuous everywhere

    d)

    None of the above

    Ask AI

  7. Q1.7

    Jacobian is:

    a)

    A scalar

    b)

    A vector

    c)

    A matrix of partial derivatives

    d)

    A function

    Ask AI

  8. Q1.8

    Taylor's expansion for multivariable function includes:

    a)

    Only first order terms

    b)

    Only second order

    c)

    All orders

    d)

    Only constant term

    Ask AI

  9. Q1.9

    Change of variables in double integral involves:

    a)

    Matrix algebra

    b)

    Laplace transforms

    c)

    Jacobian

    d)

    Only constant term

    Ask AI

  10. Q1.10

    Triple integral over a region gives:

    a)

    Area

    b)

    Length

    c)

    Volume

    d)

    Angle

    Ask AI

Q.2 Solve both questions :

Ask AI

  1. Q2.1

    What is the difference between a vector space and a subspace? Illustrate with examples.

    Ask AI

  2. Q2.2

    Define and explain rank, row space, and column space of a matrix with examples.

    Ask AI

Q.3 Solve both questions :

Ask AI

  1. Q3.1

    Explain the Cayley-Hamilton Theorem and verify it for a 2x2 matrix.

    Ask AI

  2. Q3.2

    Define and compute the Jacobian for transformation x=u+vx = u + v of u−vu - v.

    Ask AI

Q.4 Solve both questions :

Ask AI

  1. Q4.1

    Explain the Gauss-Jordan method for finding the inverse of a matrix with an example.

    Ask AI

  2. Q4.2

    Define Hermitian, Skew-Hermitian, and Unitary matrices. Provide examples for each.

    Ask AI

Q.5 Solve both questions :

Ask AI

  1. Q5.1

    Explain and prove the Rank-Nullity theorem.

    Ask AI

  2. Q5.2

    Describe the method of finding eigenvalues and eigenvectors of a matrix.

    Ask AI

Q.6 Solve both questions :

Ask AI

  1. Q6.1

    State and prove Rolle's Theorem with a graphical example.

    Ask AI

  2. Q6.2

    Define Beta and Gamma functions. Derive the relation between them.

    Ask AI

Q.7 Solve both questions :

Ask AI

  1. Q7.1

    Derive the Taylor series for a function of two variables.

    Ask AI

  2. Q7.2

    Solve a maxima-ratum problem using second derivative test.

    Ask AI

Q.8 Solve both questions :

Ask AI

  1. Q8.1

    Evaluate a double integral to find area under a curve.

    Ask AI

  2. Q8.2

    Convert a double integral into polar coordinates and evaluate.

    Ask AI

Q.9 Write short notes on any two of the following:

Ask AI

  1. Q9.1

    • Properties of Eigen vectors
    • Riemann Integration & Riemann Sum
    • Application to area and volume using double and triple integral
    • Scalar and vector fields
    a)

    Properties of Eigen vectors

    b)

    Riemann Integration & Riemann Sum

    c)

    Application to area and volume using double and triple integral

    d)

    Scalar and vector fields

    Ask AI

2024V8100102

B. Tech. Ist Semester Examination, 2024

03 Hours70 marks

Instructions

  • The marks are indicated in the right-hand margin.
  • There are NINE questions in this paper.
  • Attempt FIVE questions in all.
  • Question No. 1 is compulsory.

Q.1 Choose the correct option the following (Any seven question only):

Ask AI

  1. Q1.1

    Which operation is not an elementary row operation?

    a)

    Swapping two rows

    b)

    Adding a multiple of one row to another

    c)

    Multiplying a row by zero.

    d)

    Multiplying a row by a non-zero constant

    Ask AI

  2. Q1.2

    The rank of a matrix is:

    a)

    Number of non-zero rows in echelon form

    b)

    Number of columns

    c)

    Number of rows

    d)

    None above

    Ask AI

  3. Q1.3

    The inverse of a matrix using Gauss-Jordan:

    a)

    only determinant calculation

    b)

    Reducing matrix to diagonal form

    c)

    Augmenting with identity matrix and applying row operations

    d)

    None of the above

    Ask AI

  4. Q1.4

    A matrix is diagonalizable:

    a)

    It has repeated eigenvalues only

    b)

    It is symmetric

    c)

    It has a full set of linearly independent eigenvectors

    d)

    It is square

    Ask AI

  5. Q1.5

    A matrix is similar to a diagonal matrix if:

    a)

    It has complex entries

    b)

    It has n linearly independent eigenvectors

    c)

    It is invertible

    d)

    None of the above

    Ask AI

  6. Q1.6

    A function is Riemann integrable if:

    a)

    It is continuous

    b)

    It has infinite discontinuities

    c)

    It is discontinuous everywhere

    d)

    None of the above

    Ask AI

  7. Q1.7

    Jacobian is:

    a)

    A scalar

    b)

    A vector

    c)

    A matrix of partial derivatives

    d)

    A function

    Ask AI

  8. Q1.8

    Taylor's expansion for multivariable function includes:

    a)

    Only first order terms

    b)

    Only second order

    c)

    All orders

    d)

    Only constant term

    Ask AI

  9. Q1.9

    Change of variables in double integral involves:

    a)

    Matrix algebra

    b)

    Laplace transforms

    c)

    Jacobian

    d)

    Only constant term

    Ask AI

  10. Q1.10

    Triple integral over a region gives:

    a)

    Area

    b)

    Length

    c)

    Volume

    d)

    Angle

    Ask AI

Q.2 Solve both questions :

Ask AI

  1. Q2.1

    What is the difference between a vector space and a subspace? Illustrate with examples.

    Ask AI

  2. Q2.2

    Define and explain rank, row space, and column space of a matrix with examples.

    Ask AI

Q.3 Solve both questions :

Ask AI

  1. Q3.1

    Explain the Cayley-Hamilton Theorem and verify it for a 2x2 matrix.

    Ask AI

  2. Q3.2

    Define and compute the Jacobian for transformation $ x = u + v $ of $ u - v $.

    Ask AI

Q.4 Solve both questions :

Ask AI

  1. Q4.1

    Explain the Gauss-Jordan method for finding the inverse of a matrix with an example.

    Ask AI

  2. Q4.2

    Define Hermitian, Skew-Hermitian, and Unitary matrices. Provide examples for each.

    Ask AI

Q.5 Solve both questions :

Ask AI

  1. Q5.1

    Explain and prove the Rank-Nullity theorem.

    Ask AI

  2. Q5.2

    Describe the method of finding eigenvalues and eigenvectors of a matrix.

    Ask AI

Q.6 Solve both questions :

Ask AI

  1. Q6.1

    State and prove Rolle's Theorem with a graphical example.

    Ask AI

  2. Q6.2

    Define Beta and Gamma functions. Derive the relation between them.

    Ask AI

Q.7 Solve both questions :

Ask AI

  1. Q7.1

    Derive the Taylor series for a function of two variables.

    Ask AI

  2. Q7.2

    Solve a maxima-ratum problem using second derivative test.

    Ask AI

Q.8 Solve both questions :

Ask AI

  1. Q8.1

    Evaluate a double integral to find area under a curve.

    Ask AI

  2. Q8.2

    Convert a double integral into polar coordinates and evaluate.

    Ask AI

Q.9 Write short notes on any two of the following:

Ask AI

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