For an analytic function, f(x + iy) = u(i, y) + iv(i, y), u is given by u = 3x2 - 3y. The expression for v, considering K to be a constant is

For an analytic function, f(x + iy) = u(i, y) + iv(i, y), u is given by u = 3x<sup>2</sup> - 3y. The expression for v, considering K to be a constant is

Consider the following assertions.
1. Synthetic apirori judgment is the standard of knowledge.
2. Synthetic a posteriori judgement is the standard of knowledge.
3. Analytic apriori judgement is the standard of knowledge.
4. Analytic a posteriori judgement is the standard of knowledge.
Select the correct answer:

A

Only 1 is correct

B

Only 2 is correct

C

1 and 4 are correct

D

Only 3 is correct

Consider the following assertions
1. Synthetic apriori judgement is the standard of knowledge
2. Synthetic a posteriori judgement is the standard of knowledge.
3. Analytic apriori judgement is the standard of knowledge.
4. Analytic a posteriori judgement is the standard of knowledge

A

Only 1 is correct

B

Only 1 and 4 are correct

C

Only 2 is correct

D

Only 3 is correct

In August 2021, the International Vaccine Institute (IVI) has announced that the first participant received Bharat Biotech's Chikungunya vaccine candidate (BBV87) in a Phase 2/3 clinical trial in which country?

A

Costa Rica

B

Nicaragua

C

Honduras

D

Panama

E

Belize

An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y), where $${\text{i}} = \sqrt { - 1} .$$ If u(x, y) = x² - y², then expression for v(x, y) in terms of x, y and a general constant c would be

A

xy + c

B

$$\frac{{{{\text{x}}^2} + {{\text{y}}^2}}}{2} + {\text{c}}$$

C

2xy + c

D

$$\frac{{{{\left( {{\text{x}} - {\text{y}}} \right)}^2}}}{2} + {\text{c}}$$

Group I shows different heat addition processes in power cycles. Likewise, Group II shows different heat removal processes. Group III lists power cycles. Match items from Groups I, II and III. Group I Group II Group III P. Pressure constant S. Pressure constant 1. Rankine cycle Q. Volume constant T. Volume constant 2. Otto cycle R. Temperature constant U. Temperature constant 3. Carnot cycle 4. Diesel cycle 5. Brayton cycle

A

P – S – 5, R – U – 3, P – S – 1, Q – T - 2

B

P – S – 1, R – U – 3, P – S – 4, P – T - 2

C

R – T – 3, P – S – 1, P – T – 4, Q – S - 5

D

P – T – 4, R – S – 3, P – S – 1, P – S - 5

A harmonic function is analytic if it satisfies the Laplace equation. If u(x, y) = 2x² - 2y² + 4xy is a harmonic function, then its conjugate harmonic function v(x, y) is

A

4y² - 4xy + constant

B

-4xy + 2y² - 2x² + constant

C

2x² - 2y² + xy + constant

D

4xy - 2x² + 2y² + constant

Which of the following statements about Regular Expression is/are incorrect? A. The union of two regular expressions is also a regular expression B. The concatenation of two regular expressions is also a regular expression C. The iteration of a regular expression is also a regular expression

A

Only C

B

Only A

C

Both A and C

D

A, B and C

An analytic function of a complex variable z = x + iy is expressed as f(z) = u(x, y) + iv(x, y) where $${\text{i}} = \sqrt { - 1} .$$ If u = xy, the expression for v should be

A

$$\frac{{{{\left( {{\text{x}} + {\text{y}}} \right)}^2}}}{2} + {\text{k}}$$

B

$$\frac{{{{\text{x}}^2} - {{\text{y}}^2}}}{2} + {\text{k}}$$

C

$$\frac{{{{\text{y}}^2} - {{\text{x}}^2}}}{2} + {\text{k}}$$

D

$$\frac{{{{\left( {{\text{x}} - {\text{y}}} \right)}^2}}}{2} + {\text{k}}$$

A complex function f(z) = u(x, y) + iv(x, y) and its complex conjugate, f'(z) = u(x, y) - iv(x, y) are both analytic in the entire complex plane, where z = x + iy and $${\text{i}} = \sqrt { - 1} .$$ The function f is then given by

A

f(z) = x + iy

B

f(z) = x² - y² + i2xy

C

f(z) = constant

D

f(z) = x² + y²

The statement concern psychrometric chart. 1. Constant relative humidity lines are uphill straight lines to the right 2. Constant wet bulb temperature lines are downhill straight lines to the right. 3. Constant specific volume lines are downhill straight lines to the right. 4. Constant enthalpy lines are coincident with constant wet bulb temperature lines. Which of the statements are correct?

A

2 and 3

B

1 and 2

C

1 and 3

D

2 and 4

For an analytic function, f(x + iy) = u(i, y) + iv(i, y), u is given by u = 3x² - 3y. The expression for v, considering K to be a constant is

Related Questions