Let f1(z) = z2 and f2(z) = $$\overline {\text{z}} $$ be two complex variable function. Here $$\overline {\text{z}} $$ is the complex conjugate of z. Choose the correct answer.

The following Boolean expression $$Y = A \cdot \overline B \cdot \overline C \cdot \overline D + \overline A \cdot B \cdot \overline C \cdot D + \overline A \cdot \overline B \cdot \overline C \cdot D + \overline A \cdot \overline B \cdot \overline C \cdot D + \overline A \cdot B \cdot C \cdot D + A \cdot \overline B \cdot \overline C \cdot D$$ can be simplified to

A

$$\overline A \cdot \overline B \cdot C + A \cdot \overline D $$

B

$$\overline A \cdot B \cdot \overline C + A \cdot \overline D $$

C

$$A \cdot \overline B \cdot \overline C + \overline A \cdot D$$

D

$$A \cdot \overline B \cdot C + \overline A \cdot D$$

Let the average temperatures in Centigrade (C) and Fahrenheit (F) be $$\overline C $$ and $$\overline F $$. If $$\overline C $$ and $$\overline F $$ are related to $$F = \frac{9}{2}C + 32,$$ then $$\overline F $$ and $$\overline C $$ have the relation

A

$$\overline F = \frac{9}{2}\overline C + 32$$

B

$$\overline F = \overline C + 32$$

C

$$\overline F = \frac{9}{2}\overline C $$

D

$$\overline F = \frac{9}{5}\overline C - 32$$

ABCD is a parallelogram and the diagonals $\overline {AC} $ and $\overline {BD} $ intersect at 'O'. If E, F, G and H are the mid-point of $\overline {AO}$, $\overline {DO}$, $\overline {CO}$ and $\overline {BO} $ respectively, then what is the ratio of (EF + FG + GH + HE) and (AD + DC + CB + BA)?

A

1 ∶ 2

B

2 ∶ 3

C

3 ∶ 4

D

4 ∶ 5

ΔABC is an isosceles triangle and $$\overline {AB} $$ = $$\overline {AC} $$ = 2a unit, $$\overline {BC} $$ = a unit. Draw $$\overline {AD} $$ ⊥ $$\overline {BC} $$ , and find the length of $$\overline {AD} $$

A

$$\sqrt {15} $$ a unit

B

$$\frac{{\sqrt {15} }}{2}$$ a unit

C

$$\sqrt {17} $$ a unit

D

$$\frac{{\sqrt {17} }}{2}$$ a unit

In the given circle, line $\rm\overline{AB}$ is produced to meet tangent $\rm\overline{DE}$ at point D. If $\rm\overline{AB}$ = 7 cm and $\rm\overline{DE}$ = 12 cm, then what will be the length of $\rm\overline{BD}$?

A

7 cm

B

9 cm

C

$2\sqrt{21}$ cm

D

8 cm

In the circle below, chord $\overline {AB}$ is extended to meet the tangent $\overline {DE}$ at D. If $\overline {AB}$ = 24 cm $\overline {DE}$ = 9 cm, what is the length of $\overline {BD}$?

A

4√6 cm

B

3 cm

C

5 cm

D

4 cm

The Boolean expression Y = $$\overline {{\text{ABC}}} $$ D + $$\overline {{\text{AB}}} $$ CD + $$\overline {\text{A}} $$B$$\overline {\text{C}} $$ D + $$\overline {\text{A}} $$BCD reduces to

A

AB

B

D

C

$$\overline {\text{A}} $$

D

$$\overline {\text{A}} $$D

In the given circle, chord $\overline {AB}$ is extended to meet the tangent $\overline {DE}$ at D. If $\overline {AB}$ = 10 cm and $\overline {DE}$ 12 cm, what is the length of B̅D̅?

A

7 cm

B

8 cm

C

9 cm

D

$2\sqrt {21} \;cm$

A point z has been plotted in the complex plane, as shown in figure below.
Complex Variable mcq question image

The plot for point $$\frac{1}{{\text{z}}}$$ is

A

B

C

D

Which of the following statements are true?
1. The coefficient of rank correlation has the same limits as the Karl Pearson's coefficient of correlation.
2. The coefficient of correlation is independent of the change of origin but not of scale.
3. The covariance between $$X$$ and $$Y$$ is defined as $$\frac{{\sum {xy} }}{n}$$ where, $$x = \left( {X - \overline X } \right),y = \left( {Y - \overline Y } \right)$$ and $$n = $$ no. of paired observations.
4. $${b_{xy}}$$ is called regression coefficient of $$X$$ variable on $$Y$$ variable.
5. If $${b_{xy}}$$ is 0.4 and $${b_{yx}}$$ is 1.6, coefficient of determination would be 0.8.
Select the correct answer:

A

1, 2 and 3

B

1, 3 and 4

C

3, 4 and 5

D

2, 3 and 5

Let f₁(z) = z² and f₂(z) = $$\overline {\text{z}} $$ be two complex variable function. Here $$\overline {\text{z}} $$ is the complex conjugate of z. Choose the correct answer.

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