47. 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?

- Option : B
- Explanation :

ρ(A) = n|A| = 0 ⇒ one eigen value must be ‘0’ ∈ [-5, 5]

∴ (I) is true

but eigen values of A are 0, −5,5

∴ The eigen value with the largest magnitude is not greater than 5

For and Let ⇒ eigen values = 5,5

∴ One eigen value must be in [−5,5] and largest eigen value magnitude is not greater than 5

∴ (II) is false

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- Option : A
- Explanation :

‘X’ is Gaussian random variable

⇒ X ∼ N(0, σ^{2}) for -∞ < x < ∞

Given

Since median is positional average

Therefore, median of Y is '0'.

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50. Consider the Karnaugh map given below, where x represents “don’t care” and blank represents 0.

Assume for all inputs (a, b, c, d) the respective complements (a, b, c, d) are also available. The above logic is implemented 2-input NOR gates only. The minimum number of NOR gates required is _____.Note – Numerical Type question

- Option : B
- Explanation :

From K-map simplification we get the min-term as CA' . So We can simplify it for NOR gate expression

i.e. C' NOR A = (C'+A)' = CA'

Now complemented inputs are also given to us so for 2 input NOR gate we need only 1 NOR gate.

1 is correct answer

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