Math Chapter Wise

EnglishJSSC PGT 2018

Q61.Which one of the following statements is false?

AFor any vector space, basis set gives a minimal spanning set. BBasis set for a vector space is not unique. CAny set of vectors with null vector is linearly dependent. DFor any linear transformation T: V → V and for any basis set {v1...,vk} of V, set {T(v1):1≤ i ≤ k} also gives a basis set.

Show answer

EnglishJSSC PGT 2018

Q62.Which one of the following is NOT a subspace?

A{(x, 2x): x ∈ ℝ } over ℝ. Bℚ over ℚ C{(x, y): x × y = 0} over ℝ. D{(x, y): 2x + 3y = 0} over ℝ.

Show answer

EnglishJSSC PGT 2018

Q63.What is the dimension of the vector space of all 2 × 2 symmetric real-valued matrices?

A3 B1 C2 D4

Show answer

EnglishJSSC PGT 2018

Q64.A is an n × n non-singular matrix. Which one of the following statements is true?

AThe eigenvectors of A are orthogonal to each other. BAll the eigenvalues are positive. C0 cannot be an eigenvalue of A. D() n ii i 1 tr A a 0 = ≠ ∑

Show answer

EnglishJSSC PGT 2018

Q65.Consider the vector space of all polynomials with real coefficients with degree bounded by 2 and define the linear functional T as T (f) = f (0). Find the dimension of null space of T.

A2 B4 C1 D3

Show answer

EnglishJSSC PGT 2018

Q66.For any subset U of a vector space V, we have U⊥ ⊥ = {v: v is orthogonal to x for some x ∈ U}. Find (U⊥ ⊥) where U = {(2, 0, 0)}, (1, 0, 3).

Aℝ B{(2, 0, 0), (1, 0, 3)} C{(x, y, z): y = 0} D{0, 0, 0}

Show answer

EnglishOAVS TGT 2017

Q67.If x x 3 4 = 1 x 1 2 the value of x is.

A1, –2 B–1, 2 C1, 2 D–1,–2

Show answer

EnglishOAVS TGT 2017

Q68.If A = 1 1 –2 2 1 –3,find A. 5 4 –9

A3 B1 C0 D2

Show answer

EnglishOAVS TGT 2017

Q69.If λ is an eigen value of a matrix A then the eigen value of A–1 is:

A1/λ B–λ Cλ Dλ2

Show answer

EnglishOAVS TGT 2017

Q70.() tan64º×sin72º cos18º×cot26º

Atan2/64º B2 Csin2/72º D1

Show answer

EnglishOAVS TGT 2017

Q71.If A2 = A then the matrix A is:

ASymmetric BIdempotent CSingular DSkew Symmetric

Show answer

EnglishOAVS TGT 2017

Q72.The sum of the eigen values of a matrix is the sum of:

AAll the elements of the matrix BElements in the principle diagonal CElements in the first row DElements in the last column

Show answer

EnglishOAVS TGT 2017

Q73.If 3x + 2y = 6, 6x + 4y = 12 are two linear equations, then which of the following is true?

AThe pair of equations have only one solution BThe pair of equations have finite solution CThe pair of equations have infinite solution DThe pair of equations have no solution

Show answer

EnglishKVS TGT 2017

Q74.If 3 5 A 4 2, then A2 –5A =

AI B4 I C14I D0

Show answer

EnglishKVS TGT 2017

Q75.Matrix A is such that A2 = 2A – I, where I is the identity matrix. Then for n 2, An is equal to–

AnA (n 1)I/− − BnA 1 Cn 1/2 A (n 1)I Dn 1/2 A I

Show answer

EnglishKVS TGT 2017

Q76.If 5 15 25 7 21 30 8 24 42 − ∆ = ∆ = then

A0 B1 C1 D5

Show answer

EnglishKVS TGT 2017

Q77.The value of b c a a b c a b c c a b is–

Aabc B(a + b)(b + c)(c + a) C4 abc D(a + b + c)

Show answer

EnglishKVS TGT 2017

Q78.Which of the following sets of vectors is linearly independent?

A0 1 1 2, 1, 1 2 0 0 B0 2 2 1, 1, 0 1 1 0 C2 2 1 0, 2, 1 0 2 1 − D0 2 2 1, 1, 0 1 1 0

Show answer

EnglishKVS TGT 2017

Q79.Let P2(t) denote the set of real polynomials of the form p(t) = a0 + a1t + a2t2, where the co- efficient ai∈R, i = 0, 1, 2. Which of the following form a basis for P2(t)?

A1, 4t, 4y2 B1–4t + t2, – 2 + t – t2, – 7t + t2 C1, t, t2, t3 D1, 1 – 4t, 1 – 4t2

Show answer

EnglishKVS TGT 2017

Q80.Given two vectors 15 x 3 9 and 15 y 9 k. For x and y to be orthogonal, value of k is–

A22 B–22 C17.75 D–17.75

Show answer