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Question Bank

Question for GATE Statistics - Quiz / Questions / MCQ in English

Last Update on : October 10, 2026

Duration: 180 · Questions: 55 · Max Marks: 55

View GATE Statistics 2027 Exam Page

To boost your performance in GATE Statistics exam, practice each question regularly and with focus. Every question tests your subject understanding, so solve them one at a time. Taking a quiz improves your speed and accuracy. Practicing topic-wise MCQs. Students benefit greatly from reviewing questions with answer keys, which help clarify concepts and strengthen Questions knowledge for success in GATE Statistics exams.

Latest GATE Statistics Exam Question (Objective Questions), MCQ in English

Subjects : Statistics

Question Bank GATE Statistics Exam (Only MCQ) - English

Statistics

Q 1 :
The trace of a nilpotent matrix is:
  1. A.Negative
  2. B.Positive
  3. C.Zero
  4. D.Non-zero
Q 2 :
The singular value decomposition of a matrix A is unique up to:
  1. A.The determinant of A
  2. B.The eigenvalues of A
  3. C.The trace of A
  4. D.The ordering of singular values and signs of singular vectors
Q 3 :
The rank of a matrix A is invariant under:
  1. A.Orthogonal transformations
  2. B.Similarity transformations
  3. C.Elementary row operations
  4. D.Singular value decomposition
Q 4 :
The eigenvalues of a skew-symmetric matrix are:
  1. A.Purely imaginary or zero
  2. B.Always real
  3. C.Always positive
  4. D.Always complex
Q 5 :
The condition number of a matrix A is defined as:
  1. A.The determinant of A
  2. B.The ratio of the largest to smallest eigenvalue
  3. C.The trace of A
  4. D.The ratio of the largest to smallest singular value
Q 6 :
A matrix A is diagonalizable if and only if:
  1. A.Its determinant is zero
  2. B.Its eigenvalues are all distinct
  3. C.Its rank is zero
  4. D.Its algebraic and geometric multiplicities are equal for each eigenvalue
Q 7 :
The trace of a matrix A is equal to:
  1. A.The product of its singular values
  2. B.The sum of its eigenvalues
  3. C.The determinant of A
  4. D.The rank of A
Q 8 :
A matrix A is positive definite if:
  1. A.All its principal minors are negative
  2. B.All its eigenvalues are zero
  3. C.All its singular values are zero
  4. D.All its principal minors are positive
Q 9 :
The rank of a matrix A is equal to:
  1. A.The dimension of the null space of A
  2. B.The dimension of the column space of A
  3. C.The number of non-zero eigenvalues
  4. D.The trace of A
Q 10 :
The determinant of a matrix A is non-zero if:
  1. A.A is skew-symmetric
  2. B.A is singular
  3. C.A is invertible
  4. D.A is nilpotent
Q 11 :
A matrix A is orthogonal if:
  1. A.Its determinant is zero
  2. B.Its columns are linearly dependent
  3. C.Its rows are parallel
  4. D.Its columns are orthonormal
Q 12 :
The rank-nullity theorem for a matrix A implies:
  1. A.The rank equals the determinant
  2. B.The sum of the rank and nullity equals the number of rows
  3. C.The sum of the rank and nullity equals the number of columns
  4. D.The nullity equals the trace
Q 13 :
The eigenvalues of a Hermitian matrix are:
  1. A.Always complex
  2. B.Always real
  3. C.Always positive
  4. D.Always zero
Q 14 :
The singular value decomposition of a matrix A provides:
  1. A.A factorization into nilpotent matrices
  2. B.A factorization into symmetric matrices
  3. C.A factorization into unitary and diagonal matrices
  4. D.A factorization into skew-symmetric matrices
Q 15 :
The trace of a matrix A is invariant under:
  1. A.Orthogonal transformations
  2. B.Similarity transformations
  3. C.Singular value decomposition
  4. D.Row reduction
Q 16 :
A matrix A is positive definite if:
  1. A.All its singular values are zero
  2. B.All its eigenvalues are negative
  3. C.All its eigenvalues are zero
  4. D.All its eigenvalues are positive
Q 17 :
The orthogonal projection matrix P onto a subspace is:
  1. A.Idempotent and symmetric
  2. B.Invertible and symmetric
  3. C.Nilpotent and orthogonal
  4. D.Unitary and skew-symmetric
Q 18 :
The determinant of a unitary matrix is:
  1. A.Zero
  2. B.Magnitude 1
  3. C.Positive
  4. D.Negative
Q 19 :
The eigenvalues of a matrix A are preserved under:
  1. A.Orthogonal transformations
  2. B.Similarity transformations
  3. C.Singular value decomposition
  4. D.Row reduction
Q 20 :
The trace of a nilpotent matrix is:
  1. A.Zero
  2. B.Positive
  3. C.Negative
  4. D.Non-zero
Q 21 :
The singular value decomposition of a matrix A is unique up to:
  1. A.The ordering of singular values and signs of singular vectors
  2. B.The eigenvalues of A
  3. C.The trace of A
  4. D.The determinant of A
Q 22 :
The rank of a matrix A is invariant under:
  1. A.Orthogonal transformations
  2. B.Similarity transformations
  3. C.Elementary row operations
  4. D.Singular value decomposition
Q 23 :
The condition number of a matrix A is defined as:
  1. A.The trace of A
  2. B.The ratio of the largest to smallest eigenvalue
  3. C.The ratio of the largest to smallest singular value
  4. D.The determinant of A
Q 24 :
A matrix A is diagonalizable if and only if:
  1. A.Its eigenvalues are all distinct
  2. B.Its algebraic and geometric multiplicities are equal for each eigenvalue
  3. C.Its rank is zero
  4. D.Its determinant is zero
Q 25 :
The trace of a matrix A is equal to:
  1. A.The determinant of A
  2. B.The product of its singular values
  3. C.The sum of its eigenvalues
  4. D.The rank of A
Q 26 :
A matrix A is positive definite if:
  1. A.All its principal minors are positive
  2. B.All its eigenvalues are zero
  3. C.All its singular values are zero
  4. D.All its principal minors are negative
Q 27 :
The rank of a matrix A is equal to:
  1. A.The dimension of the null space of A
  2. B.The dimension of the column space of A
  3. C.The number of non-zero eigenvalues
  4. D.The trace of A
Q 28 :
The determinant of a matrix A is non-zero if:
  1. A.A is skew-symmetric
  2. B.A is singular
  3. C.A is invertible
  4. D.A is nilpotent
Q 29 :
A matrix A is orthogonal if:
  1. A.Its rows are parallel
  2. B.Its columns are linearly dependent
  3. C.Its columns are orthonormal
  4. D.Its determinant is zero
Q 30 :
The rank-nullity theorem for a matrix A implies:
  1. A.The nullity equals the trace
  2. B.The sum of the rank and nullity equals the number of rows
  3. C.The rank equals the determinant
  4. D.The sum of the rank and nullity equals the number of columns
Q 31 :
The eigenvalues of a Hermitian matrix are:
  1. A.Always complex
  2. B.Always real
  3. C.Always positive
  4. D.Always zero
Q 32 :
The singular value decomposition of a matrix A provides:
  1. A.A factorization into symmetric matrices
  2. B.A factorization into unitary and diagonal matrices
  3. C.A factorization into nilpotent matrices
  4. D.A factorization into skew-symmetric matrices
Q 33 :
The trace of a matrix A is invariant under:
  1. A.Similarity transformations
  2. B.Orthogonal transformations
  3. C.Singular value decomposition
  4. D.Row reduction
Q 34 :
A matrix A is positive definite if:
  1. A.All its eigenvalues are negative
  2. B.All its eigenvalues are positive
  3. C.All its eigenvalues are zero
  4. D.All its singular values are zero
Q 35 :
The determinant of a unitary matrix is:
  1. A.Magnitude 1
  2. B.Zero
  3. C.Positive
  4. D.Negative
Q 36 :
The eigenvalues of a matrix A are preserved under:
  1. A.Singular value decomposition
  2. B.Orthogonal transformations
  3. C.Similarity transformations
  4. D.Row reduction
Q 37 :
The rank of a matrix A is invariant under:
  1. A.Orthogonal transformations
  2. B.Similarity transformations
  3. C.Elementary row operations
  4. D.Singular value decomposition
Q 38 :
The condition number of a matrix A is defined as:
  1. A.The ratio of the largest to smallest singular value
  2. B.The ratio of the largest to smallest eigenvalue
  3. C.The trace of A
  4. D.The determinant of A
Q 39 :
A matrix A is diagonalizable if and only if:
  1. A.Its algebraic and geometric multiplicities are equal for each eigenvalue
  2. B.Its eigenvalues are all distinct
  3. C.Its rank is zero
  4. D.Its determinant is zero
Q 40 :
The rank of a matrix A is equal to:
  1. A.The trace of A
  2. B.The dimension of the null space of A
  3. C.The number of non-zero eigenvalues
  4. D.The dimension of the column space of A
Q 41 :
The determinant of a matrix A is non-zero if:
  1. A.A is skew-symmetric
  2. B.A is singular
  3. C.A is invertible
  4. D.A is nilpotent
Q 42 :
A matrix A is orthogonal if:
  1. A.Its columns are linearly dependent
  2. B.Its columns are orthonormal
  3. C.Its rows are parallel
  4. D.Its determinant is zero
Q 43 :
The rank-nullity theorem for a matrix A implies:
  1. A.The sum of the rank and nullity equals the number of columns
  2. B.The sum of the rank and nullity equals the number of rows
  3. C.The rank equals the determinant
  4. D.The nullity equals the trace
Q 44 :
The eigenvalues of a Hermitian matrix are:
  1. A.Always zero
  2. B.Always complex
  3. C.Always positive
  4. D.Always real
Q 45 :
The singular value decomposition of a matrix A provides:
  1. A.A factorization into nilpotent matrices
  2. B.A factorization into symmetric matrices
  3. C.A factorization into unitary and diagonal matrices
  4. D.A factorization into skew-symmetric matrices
Q 46 :
A matrix A is positive definite if:
  1. A.All its eigenvalues are positive
  2. B.All its eigenvalues are negative
  3. C.All its eigenvalues are zero
  4. D.All its singular values are zero
Q 47 :
The eigenvalues of a matrix A are preserved under:
  1. A.Orthogonal transformations
  2. B.Similarity transformations
  3. C.Singular value decomposition
  4. D.Row reduction
Q 48 :
The rank of a matrix A is invariant under:
  1. A.Similarity transformations
  2. B.Elementary row operations
  3. C.Orthogonal transformations
  4. D.Singular value decomposition
Q 49 :
The trace of a matrix A is equal to:
  1. A.The determinant of A
  2. B.The product of its singular values
  3. C.The sum of its eigenvalues
  4. D.The rank of A
Q 50 :
The rank of a matrix A is equal to:
  1. A.The dimension of the null space of A
  2. B.The dimension of the column space of A
  3. C.The number of non-zero eigenvalues
  4. D.The trace of A

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