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GATE Exam: Engineering Mathematics Quiz 24

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Question 1

The probability that a given positive integer lying between 1 and 100 (both inclusive) is NOT divisible by 2, 3 or 5 is ______ .

Question 2

In the given matrix

one of the Eigen values is 1. The Eigen vectors corresponding to the Eigen value1are

Question 3

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 4

Let A be real valued square symmetric matrix of rank 2 with

Consider the following statements.
(I) One eigen value must be in [-5, 5]
(II) The eigen value with the largest magnitude must be strictly greater than 5.
Which of the above statements about eigen values of A is/are necessarily CORRECT?

Question 5

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 6

Consider the following function.

F(x)= (1/3)x³ + (1/2)x²-6x+1000

Find the value at which f has a relative minimum.

Question 7

If the proportion of handicapped people in a large population is 0.006, then what is the probability that there will be atmost one handicapped person in a randomly chosen group of 500 people. Use poisson approximation to compute the probability.

Question 8

Find the value by evaluating the following integral.

Question 9

Find the standard deviation of 2,4,6 and 8. (Round upto two decimal places)

Question 10

How many solutions does the following system of linear equations have?
-x + 5y = -1
x - y = 2
x + 3y = 3

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ESE & GATE CE Engineering Mathematics

Mar 22ESE & GATE CE