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Answer is (1)

(3) T, T, F

(p ∧ q) → (~q \(\lor\) r) = false

when (p ∧ q) = T

and  (~q \(\lor\) r) = F

So (p ∧ q) = T is possible when p = q = true 

\(\therefore\)  ~q = False (q = true) 

So (~q \(\lor\) r) = False is possible if r is false

\(\therefore\) p = T, q = T, r = F

The lines represented by x² − 5xy + 6y2 = 0 are x − 2y = 0 and x − 3y = 0.

we get the following:

1.  Equation of the pair of lines passing through (1, 1) and parallel to the lines x − 2y = 0 and x − 3y = 0 is 

(x − 1)² −5 (x − 1) (y − 1) + 6(y − 1)² = 0

x² − 5xy + 6y² + 3x − 7y + 2 = 0

2.  Equation of the pair of lines passing through (1, 1) and perpendicular to the lines

6(x − 1)² + 5 (x − 1) (y − 1) + (y − 1)² = 0

6x² + 5xy + y² − 17x − 7y + 12 = 0

Answer is (B)

Correct option (c),(d)

Explanation :

Let x/b + y/b = 1

be the equation of the line which forms a triangle with the coordinate axes of area α sq. unit. Since the line passes through (2, 2), we have

2/a + 2/b = 1 ...(1)

We have 1/2|ab| = α so that

ab = ±2α  ....(2)

now, from Eq.(2)

2a + 2b = ab = 2α

Therefore

a + b = α  ...(3)

Hence, from Eqs. (2) and (3), a and b are the roots of the equation  x² - αx + 2α = 0. Therefore 

2a + 2b = -2α

a + b = -α

Hence a and b are roots of the equation

x² + αx - 2α = 0

It, the required line is of the form

(2x − y + 5 = 0) + λ (x + y + 1) = 0

Since this also passes through (0, 0), we have λ =  −5.

Hence the required line is

(2x − y + 5) − 5 (x + y + 1) = 0

-3x - 6y = 0

x + 2y = 0

Direct Method: 

Solving the equations 2x − y + 5 = 0 and x + y + 1 = 0,

we get the point of intersection (−2, 1). Therefore, the equation of the line joining (−2, 1) and (0,0) is

y = 0 -1/0 + 2 x 

or x + 2y = 0

(C)  Request

(D) Offering help

Correct option  (a),(b)

Explanation :

It is clear that the vertical line x = 1 passes through (1, 1) and its distance from the origin is 1.

Hence, y =1 is the other line.

7 – periods.

Carlyle had adopted a trick for perfection in letter writing. He used the lightest and most casual way to give a personal touch in letter writing. He described things in such an intimate way that the reader found scenes before his eyes. In other words, his description in letter was lively.

(a) They haven't told us how to put clothes. 

(b) He doesn't know how to turn the water off.  

(c) He doesn't know how to reach the railway station.

(d) The instruction doesn't tell us how to start the engine.

(e) The coach doesn't tell us how to play cricket

The photographer did not like the face and posture of the author. He was adjusting and adjusting his camera for the face and posture of the author. This is why the photographer took too much time.

(a) reconstruct

(b) filtered

(c) worthless

(d) reconcile

(e) enthusiasm

(f) privacy

(g) trifle

Pure – Impure

Hope – Despair

Reject – Accept

Sharp – Blunt

Noisy – Quiet

(a) Simile

(b) Simile

(c) Metaphor 

Simile is a figure of speech in which likeness between two different objects is expressed directly using words such as 'like', 'so' and 'as'.

For example :My love is like a red red rose. 

The word 'like' shows the smilarity between love and rose. 

On observing data

(a) When s = 16 x 4.9 m

∴16 x 4.9 = 4.9 x t²

∴ t² = 16

t = 4 sec

(b) When t = 10

s = 4.9 x t²

= 4.9 x (10)²

s = 490 m

(c) s ∝ t²

s = kt²

where k = 4.9 m/sec²

(d) Distance is proportional to the square of time taken to the freely falling body constant of proportionality is 4.9 m/sec².

Man should should his time and energy in making beautiful things, finding out more and more about the universe, setting disputes and differences between warring nations and discovering new ways to prevent poverty.

(a) |x| + |y|

∴ |x| + |y| = 4 + 3 = 7

|x + y| = |4 + 3| = 7

(b) |x| + |y|

∴ |x| + |y| = 4 + 3 = 7

|x + y| = |4 – 3| = 1

(c) |x| + |y| ≥ |x + y|

Concept:

If a,b, c are in AP, then 2b = a + c or b - a = c - b

Calculation:

Let, 1/ab, 1/ca and 1/bc are in AP

⇒\(\rm \frac{1}{ca}\rm -\frac{1}{ab}=\rm \frac{1}{bc}-\rm \frac{1}{ca}\)

\(\rm \frac{1}{a}( \frac{1}{a}- \frac{1}{a})= \frac{1}{a}( \frac{1}{a}- \frac{1}{a})\\ ⇒ \frac{b-c}{abc}= \frac{a-b}{abc}\)

⇒ b-c = a-b 

⇒2b = a+c

⇒ a,b, c are in AP, which is true.

Now, let 1/(b+c) ,1/(c+a) and 1/(a+b) are in AP

\(\rm \frac{2}{c+a}=\frac{1}{b+c}+\frac{1}{a+b}\)

⇒ 2(a+b)(b+c) = (a+b+b+c)(c+a)

⇒2(ab + ac + b² + bc) = (ac + a² + 2bc + 2ab + c² + ca)

⇒2ab + 2ac + 2b² + 2bc = ac + a² + 2bc + 2ab + ac + c²

⇒ 2b² = a² + c²

a, b, c are not in AP, so this is not true.

Hence, option (1) is correct. 

(a) Many aspire after wealth, but very few get it.

(b) You should not be afraid of mistakes.

(c) Marsha is absent from the class today.

Concept:

Arithmetic Progression (AP): The series of numbers where the difference of any two consecutive terms is the same, is called an Arithmetic Progression.

• If three numbers a, b and c are in AP, then b - a = c - b ⇒ 2b = a + c.

Geometric Progression (GP): The series of numbers where the ratio of any two consecutive terms is the same, is called a Geometric Progression.

• If three numbers a, b and c are in GP, then\(\rm \dfrac ba=\dfrac cb\) ⇒ b2 = ac.

Harmonic Progression (HP): The series of numbers where the reciprocals of the terms are in Arithmetic Progression, is called a Harmonic Progression.

• If three numbers a, b and c are in HP, then \(\rm \dfrac{1}{a}+\dfrac{1}{c}=\dfrac{2}{b}\).

Calculation:

Let's say that the second degree polynomial is f(x) = px² + qx + r.

From the given information:

f(1) = f(-1)

⇒ p(1)2 + q(1) + r = p(-1)2 + q(-1) + r

⇒ p + q = p - q

⇒ 2q = 0

⇒ q = 0

∴ f(x) = px2 + 0(x) + r

⇒ f(x) = px2 + r

And, f'(x) = 2px.

Now, f'(a) = 2pa, f'(b) = 2pb and f'(c) = 2pc.

Since a, b and c are in AP, we have:

2b = a + c.

Multiplying by 2p, we get:

(2p)2b = (2p)a + (2p)c

⇒ 2(2pb) = 2pa + 2pc

⇒ 2pa, 2pb and 2pc are in AP.

⇒ f'(a), f'(b) and f'(c) are in AP.

(a) Inshu shouted at the top of his voice

(b) He burst into tears.

(c) I agree with you.

(d) one cannot do anything without money.

Metaphor- It is a figure of speech in which likeness between two disimilar objects are implied but not clearly expressed. Example- Subhash Chandra Bose was the lion of India.

Delay - Haste, 

Accept-Reject, 

Soft-hard, 

Despair-Hope, 

Impure-Pure.

Management Principles Developed by Henri Fayol.

1. Division of Work: Division of work refers to dividing the work into compact jobs and allocating these compact jobs to different individuals. This Principle applies to both managerial as well as technical work. 

2. Discipline: Discipline refers to obedience to rules and regulations of the organization, which is necessary for systematic working of the organization. 

3. Unity of Command: Principles of unity of command is followed as subordinate receive orders and is accountable to only one superior. However, in the principle of unity of command is violated as subordinate get orders from two superiors. 

4. Unity of Direction: Unity of Direction implies that there should be one head and one plan for group of activities having same objectives. It ensures unity of action and coordination and avoids unnecessary duplication of efforts. 

5. Centralisation and Decentralisation: According to this principle, there should be proper balance between centralization and decentralization in the organization. Centralisation refers to concentration of decision-making authority, whereas decentralization refers to evenly distribution of authority at all levels of management.

Divisional Structure: When jobs related to one product are grouped under one department, it is termed as divisional structure. This type of structure is suitable for large organization, which have various product lines or several products.

Advantages of Divisonal Structure.

1. Product Specialization: The members of a division gain experience in all functions related to a particular product. Product specialization helps them in the development of varied skills and prepared them for higher positions. 

2. Greater Accountability: In divisional structure, each product department is treated as a profit Centre’ and is accountable for its own profit or loss. This provides a base for measuring performance and helps in fixing responsibility in case of poor performance. 

3. Flexibility: it promotes flexibility and initiative as each division functions as an autonomous unity. It leads to fast decision-making. 

4. Expansion and Growth: It facilitates expansion, diversification and growth as new divisions can be added without interrupting the existing operation.

Funcations of a Supervisor

The functions of a supervisor can be understood from the following points: 

1. Promotes Group Unity: Supervisor plays a key role in maintaining group unity among workers. He sorts out their internal differences and adopts a people-oriented approach to build harmonious relations in his department. 

2. Helps in Improving Performance: Supervisor ensures performance of work according to the targets set. He takes responsibility for achievement of task and motivates his workers effectively. 

3. Provides Training to the Employees: Supervisor provides good on-the-job training to the works. A skilled and knowledgeable supervisor can build efficient team of workers by arranging appropriate training programmes for the employees. 

4. Influences Workers: Supervisor plays a key role in influencing the workers in the organization. He builds up high morale among workers though good leadership. 

5. Provides Feedback: A good supervisor analyses the work performed and gives feedback to the workers. He suggests ways and means of developing work skills.

An exchange-traded fund as a mutual fund that trades like a stock.

The closing price on the day previous to the day of valuation.

The financial results of an organization depends on the performance of its Sales management.

Auto pilot for an aircraft is closed loop system and remaining all are open loop systems.

Under rolling settlement all open positions at the end of the day mandatorily result in payment/delivery „n‟ days later.

Currently trades in rolling settlement are settled on T+2 basis where T is the trade day.

Communication is said to be effective and complete when the receiver (a prospective customer/existing customer) understands it in the same sense what the sender (salesman) wished to communicate.

Rolling settlement refers to the settling of trades at a standard fixed period of days after the execution occurred (i.e. T+2).