The GCD of x5+ x4+ x3– x2 – x + 1 and x3 + x2+ x + 1 over GF(3) is

Let x̅1 and x̅2 (where x̅2 > x̅1) be the means of two sets comprising n1 and n2 (where n2 < n1) observations respectively. If x̅ is the mean when they are pooled, then which one of the following is correct?

A

x̅₁ < x̅ < x̅₂

B

x̅ > x̅₂

C

x̅ < x̅₁

D

(x̅₁ – x̅) + (x̅₂ – x̅) = 0

Simplify : $${{{5 \over 3} \times {7 \over {51}}{\text{ of }}{{17} \over 5} - {1 \over 3}} \over {{2 \over 9} \times {5 \over 7}{\text{ of }}{{28} \over 5} - {2 \over 3}}}$$

A

$$\frac{1}{2}$$

B

4

C

2

D

$$\frac{1}{4}$$

If 4 is the GCD of 16 and 12, What is the GCD of 12 and 4?

A

12

B

6

C

4

D

2

GCD(a,b) is the same as GCD(|a|,|b|).

A

True

B

is the same as GCD(|a|,|b|). a) True [ False

GCD(a,b) = GCD(b,a mod b)

A

True

B

= GCD(b,a mod [ a) True [ False

The transfer function of a discrete time LTI system is given by
$$H\left( z \right) = {{2 - {3 \over 4}{z^{ - 1}}} \over {1 - {3 \over 4}{z^{ - 1}} + {1 \over 8}{z^{ - 2}}}}$$
Consider the following statements:
S₁ : The system is stable and causal for
$$ROC:\left| z \right| > {1 \over 2}$$
S₂ : The system is stable but not causal for
$$ROC:\left| z \right| S₃ : The system is neither stable nor causal for
$$ROC:{1 \over 4} Which one of the following statements is valid?

A

Both S₁ and S₂ are true

B

Both S₂ and S₃ true

C

Both S₁ and S₃ are true

D

S₁, S₂ and S₃ are all true

A charged particle q moving with a velocity $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over v} $ in a magnetic field $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over B} $ experiences a force given by $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over F} = q\left( {\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over v} \times \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over B} } \right).$ What is the work done by the force during a displacement $\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptstyle\rightharpoonup$}} \over{\Delta r}}$ of the charged particle?

A

qvBΔr

B

qvrΔB

C

Zero

D

qΔvBr

The complex envelope of the bandpass signal $$x\left( t \right) = \sqrt 2 \left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}} \right)\sin \left( {\pi t - {\pi \over 4}} \right),$$ centered about $$f = {1 \over 2}Hz,$$ is

A

$$\left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}{e^{j{\pi \over 4}}}} \right)$$

B

$$\left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}{e^{ - j{\pi \over 4}}}} \right)$$

C

$$\sqrt 2 \left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}{e^{j{\pi \over 4}}}} \right)$$

D

$$\sqrt 2 \left( {{{\sin \left( {{{\pi t} \over 5}} \right)} \over {{{\pi t} \over 5}}}{e^{ - j{\pi \over 4}}}} \right)$$

The GCD of x3+ x + 1 and x2 + x + 1 over GF(2) is

A

1

B

x + 1

C

x2

D

x2 + 1

The GCD of x5+x4+x3 – x2 – x + 1 and x3 + x2 + x + 1 over GF(3) is

A

1

B

x

C

x + 1

D

x2 + 1

The GCD of x5+ x4+ x3– x2 – x + 1 and x3 + x2+ x + 1 over GF(3) is

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