Let S be the set of points in the complex plane corresponding to the unit circle. (That is, S = {z : |z| = 1}. Consider the function f(z) = zz∗ where z∗ denotes the complex conjugate of z. The f(z) maps S to which one of the following in the complex plane

horizontal axis line segment from origin to (1, 0)

Let S be the set of points in the complex plane corresponding to the unit circle. (That is, S = {z : |z| = 1}. Consider the function f(z) = zz<sup>∗</sup> where z<sup>∗</sup> denotes the complex conjugate of z. The f(z) maps S to which one of the following in the complex plane

The value of the expression:sin²1° + sin²11° + sin²21° + sin²31° + sin²41° + sin²45° + sin²49° + sin²59° + sin²69° + sin²79° + sin²89° is?

A

0

B

$${\text{5}}\frac{1}{2}$$

C

$${\text{4}}\frac{1}{2}$$

D

5

User level threads are threads that are visible to the programmer and are unknown to the kernel. The operating system kernel supports and manages kernel level threads. Three different types of models relate user and kernel level threads. Which of the following statements is/are true ? (a) (i) The Many - to - one model maps many user threads to one kernel thread (ii) The one - to - one model maps one user thread to one kernel thread (iii) The many - to - many model maps many user threads to smaller or equal kernel threads (b) (i) Many - to - one model maps many kernel threads to one user thread (ii) One - to - one model maps one kernel thread to one user thread (iii) Many - to- many model maps many kernel threads to smaller or equal user threads

A

(a) is true; (b) is false

B

(a) is false; (b) is true

C

Both (a) and (b) are true

D

Both (a) and (b) are false

Raw material purchased:
1^st January, 600 units @ Rs. 12 per unit
12^th January, 500 units @ Rs. 14 per unit
21^st January, 300 units @ Rs. 13 per unit
Raw material issued for manufacture:
3^rd January 300 units
5^th January 124 units
15^th January 250 units
16^th January 300 units
Raw material returned to stores from manufacturing department on 14^th January, 50 units. The material is issued on First-in-First out method.
The value of material remaining in store on 21^st January will be:

A

5,775

B

6,100

C

6,350

D

6,600

Silicon is doped with arsenic (concentration 10²⁰ atoms.m^-3). At room temperature, the electron and hole mobilities in Si are 0.14 m².v^-1.s^-1 and 0.05 m²v^-1.s^-1 respectively. The conductivity in (?m)^-1, at room temperature for Si doped with As is

A

0.11

B

0.96

C

2.24

D

2.72

If a² sec²x - b² tan²x = c², then the value of sec²x + tan²x is equal to (assume b² ≠ a²)

A

$$\frac{{{b^2} - {a^2} + 2{c^2}}}{{{b^2} + {a^2}}}$$

B

$$\frac{{{b^2} + {a^2} - 2{c^2}}}{{{b^2} - {a^2}}}$$

C

$$\frac{{{b^2} - {a^2} - 2{c^2}}}{{{b^2} + {a^2}}}$$

D

$$\frac{{{b^2} - {a^2}}}{{{b^2} + {a^2} + 2{c^2}}}$$

If the contents of exchangeable ions (cmol kg^-1) determined in soil are Na⁺ = 5, K⁺ = 5, Ca²⁺ = 10, Mg²⁺ = 2, H⁺ = 1, Al⁺³ = 1, Cl^- = 1.6 and HCO^-₃ =0.4, the CEC of soil is

A

26 cmol (P⁺) kg^-1

B

20 cmol (P⁺) kg^-1

C

24 cmol (P⁺) kg^-1

D

None of these

The short-run production function for a firm is as follows
Q = -L³ + 15L² + 10L
Where Q denotes total output in physical units and L denotes units of labour which are homogeneous, but are not perfectly divisible and change in labour does not tend to become zero.
Statement I In this production function, the marginal product of 5^th unit of labour is 85.
Statement II Similarly, in this production function, the average product of the 5^th unit of labour is 60.

A

Both the statements are true

B

Both the statements are false

C

Statement I is true, while Statement II is false

D

Statement I is false, but Statement II is true

Given that ( 1² + 2² + 3² + .......... + 10² ) = 385, then the value of ( 2² + 4² + 6² + .......... + 20² ) is equal to = ?

A

770

B

1155

C

1540

D

(385)²

In a mine ventilation system, the resistances of two splits A and B are 0.5 Ns²m^-8 and 2 Ns²m^-8 respectively. Combined resistance of two shafts and trunk airways is 0.7 Ns²m^-8. A quantity of 20 m³/s of air passes through split A. The total air quantity passing the mine in m³/s is

A

30

B

27

C

25

D

17

Given that (1² + 2² + 3² + ..... + 20²) = 2870, the value of (2² + 4² + 6² + ... + 40² ) is :

A

2870

B

5740

C

11480

D

28700

Let S be the set of points in the complex plane corresponding to the unit circle. (That is, S = {z : |z| = 1}. Consider the function f(z) = zz^∗ where z^∗ denotes the complex conjugate of z. The f(z) maps S to which one of the following in the complex plane

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