Engineering Mathematics GATE Question Answers with Explanation.
Q1 – Consider the following two statements with respect to the matrices m n Amxn , Bnxm , Cnxn and Dnxn.
Statement 1: tr(AB) = tr(BA)
Statement 2: tr(CD) = tr(DC)
where tr() represents the trace of a matrix. Which one of the following holds? (GATE 2022)
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Statement 1 is correct and Statement 2 is wrong.
Statement 1 is wrong and Statement 2 is correct.
Both Statement 1 and Statement 2 are correct.
Both Statement 1 and Statement 2 are wrong.
Ans – (3)
Explanation –
Q2 – Which of the following statements is/are TRUE for a group G? (GATE 2022)
If for all x, y ϵ G, (xy)2 = x2 y2 , then G is commutative.
If for all x ϵ G, x2 = 1, then G is commutative. Here, 1 is the identity element of G.
If the order of G is 2, then G is commutative.
If G is commutative, then a subgroup of G need not be commutative.
Ans – (1, 2, 3)
Explanation –
Q3 – The number of arrangements of six identical balls in three identical bins is______. (GATE 2022)
Ans – (7)
Explanation –Â
Q4 – The value of the following limit is _____________. (GATE 2022)
Ans – (-0.5)
Explanation –
Q5 – Which one of the following is the closed form for the generating function of the sequence {an}n>=0 defined below? (GATE 2022)
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Ans – (1)
Explanation –
Q6 – Consider solving the following system of simultaneous equations using LU decomposition.
x1 + x2 – 2x3 = 4
x1 + 3x2 – x3 = 7
x1 + x2 – 5x3 = 7
where L and U are denoted as
Which one of the following is the correct combination of values for L32, U33, and x1? (GATE 2022)
L32 = 2, U33 = -(1/2), x1 = -1
L32 = 2, U33 = 2, x1 = -1
L32 = -(1/2), U33 = 2, x1 = 0
L32 = -(1/2), U33 = -(1/2), x1 = 0
Ans – (4)
Explanation –
Q7 – Which of the following is/are the eigenvector(s) for the matrix given below? (GATE 2022)
Ans – (1, 3, 4)
Explanation –