Math Chapter Wise

EnglishLT 2018

Q141.If A is a 2× × ×2 matrix such that adj A=6, |A|=12, then trace (A–1) is

A1/2 B1/3 C1/6 D1

Show answer

EnglishLT 2018

Q142.Consider the following statements: I. If A is skew-symmetric matrix, then A2 is symmetric. II. Trace of a skew-symmetric matrix of an odd order is always zero. Which of the above statements is/are true?

AOnly I BOnly II CBoth I and II DNeither I nor II

Show answer

EnglishLT 2018

Q143.The system of equations x 2y 3z 1 2x y 3z 2 x y 2z 3 + + = + + = + + = + + = + + = + + = + + = + + = + + = + + = + + = + + = has

Ano solution Bunique solution Cinfinite solution DNone of the above

Show answer

EnglishDSSSB TGT (SECTION-B) 28 DEC 2014

Q144.If 2 1 4 2A 3B 3 2 5 and 5 0 3 A 2B 1 6 2 then B is equal to –

A8 1 2/1 10 1 B8 1 2/1 10 1 C8 1 2/1 10 1 DNone of these

Show answer

EnglishDSSSB TGT (SECTION-B) 28 DEC 2014

Q145.If 1 3 A 2 K and 2 A 4A 10 A, then K is equal to –

A1 or 4 B4 and not 1 C–4 D0

Show answer

EnglishDSSSB TGT (SECTION-B) 28 DEC 2014

Q146.If 1 2 x 2x 3 0, 3 0 8 value of x is–

A23/2 B13/2 C13/2 D23/2

Show answer

EnglishDSSSB TGT (SECTION-B) 28 DEC 2014

Q147.The matrix 1 2 4 3 0 6 1 1 P has one eigen value equal to 3. The sum of the other two eigen values is–

Ap – 2 Bp – 1 Cp DNone of these

Show answer

EnglishDSSSB TGT & PGT (SECTION-B) 28 DEC 2014

Q148.If A is skew symmetric matrix, then A2 is a–

ANull matrix BUnitary matrix CSkew symmetric DSymmertric

Show answer

EnglishSECTION B TGT & PGT TIER-I 31.11.2014

Q149.If A and B are matrices of same order, then (ABt –BAt) is a–

Askew symmetric matrix Bnull matrix Csymmetric matrix Dunit matrix

Show answer

EnglishSECTION B PGT TIER-I 31.11.2014

Q150.If A and B are square matrices of the same order, then (A+B) (A–B) is–

AA2/– B2 BA2/– BA – AB – B2 CA2 – B2 + BA – AB DA2 –BA + B2 + AB

Show answer

EnglishSECTION B PGT TIER-I 31.11.2014

Q151.If matrix ij 3 3 A a where ij 1 if i j a 0 if i j then A2 is equal to –

AI BA C0 DNone of these

Show answer

EnglishSECTION B PGT TIER-I 31.11.2014

Q152.If A and B are invertible matrices, then which of the following is not correct?

A1/adjA A A B1 1/det(A) [det(A)] C1 1 1/(AB) B A D1 1 1/(A B) B A

Show answer

EnglishSECTION B PGT TIER-I 31.11.2014

Q153.If A, B and C are angles of a triangle, then the determinant 1 cosC cosB cosC 1 cos A cosB cos A 1 is equal to–

A1 B0 C–1 DNone of these

Show answer

EnglishSECTION B PGT TIER-I 31.11.2014

Q154.If A is a square matrix such that 2 A, then 3 3 (A) (A) 7A is–

AA BA CA D3A

Show answer

EnglishSECTION B PGT TIER-I 31.11.2014

Q155.The rank of a matrix 1 2 3 2 4 7 3 6 10 is–

A1 B2 C3 DNone of these

Show answer

EnglishSECTION B PGT TIER-I 31.11.2014

Q156.The dimension of the vector space of all 3× × ×3 real matrices is–

A3 B9 C6 D4

Show answer

EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q157.Let U be a 3×3 complex Hermitian matrix which is unitary. Then the distinct eigen values of U are–

A± i B1 ± i C± 1 D1 (1 i) 2 ±

Show answer

EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q158.The eigen values of 3×3 real matrix P are 1, –2, 3. Then–

A1 2 1 P (5 2P P) 6 B1 2 1 P (5 2P P) 6 C1 2 1 P (5 2P P) 6 D1 2 1 P (5 2P P) 6

Show answer

EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q159.Eigen values of a real symmetric matrix are always–

Apositive Bnegative Creal Dcomplex

Show answer

EnglishJDD-75-PGT TIER II-X-15 28.06.2015

Q160.If scalar λ is a characteristic root of the matrix A then the matrix (A–λ) is–

ANon singular BDiagonal CSingular DNone of these

Show answer