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# GATE EC 2021: Subject Revision Quiz 8 (App update required to attempt this test)

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Question 1

Consider the series,
obtained from the Newton-Raphson method. The series converges to _____.

Question 2

If the characteristics polynomial of matrix M over R (the set of real numbers) is and one eigenvalue of M is 2, then the largest among the absolute values of the eigenvalues of M is _____.

Question 3

The solution of differential equation y’ – 2y = 0 is given by:

Question 4

The differential equation is valid in the domain 0 ≤ x ≤ 1 with y(0) = 2.25. The solution of the differential equation is

Question 5

For the vector  ï the value of ____________

Question 6

Consider a quadratic equation with coefficients in a base b. The solutions of this equation in the same base b are and Then b = _____.

Question 7

A scalar potential φ has the following gradient.
Consider the integral

The curve C is parameterized as follows

Question 8

Let X be a random variable that is uniformly distributed on [–1, +1]. If Find the variance of Y. (Round the answer upto two decimal places)

Question 9

____________.

Question 10

Let S be a sample space and two mutually exclusive events A and B be such that =S. If P(.) denotes the probability of the event, the maximum value of P(A)P(B) is __________.

Question 11

Let    and
be two matrices.
Then the rank of P + Q is ____.

Question 12

The minimum number of equal length subintervals needed to approximate  to an accuracy of at least  ousing the trapezoidal rule is

Question 13

E1 and E2 are events in a probability space satisfying the following constraints:
* Pr(E1) = Pr(E2)
* Pr(E1E2) = 1
* E1 and E2 are independent
The value of Pr(E1), the probability of the event E1, is

Question 14

In the LU decomposition of the matrix if the diagonal elements of U are both 1, then the lower diagonal entry l22 of Lis_________.

Question 15

The value of c of Lagrange’s mean value theorem if f(x) = x(x – 1) (x –2) over the interval __________.
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