Explore topic-wise InterviewSolutions in .

Let B = A + A¹ then 

B¹ = (A + A¹)¹ = A¹ + (A¹)¹ 

= A¹ + A= A + A¹ = B 

∴ B¹ = B ∴B is symmetric matrix 

∴ A + A¹ is a symmetric matrix. 

C = A – A¹ 

C¹ = (A – A¹)¹ = A¹ – (A¹)¹ 

= A¹ – A = -(A – A¹) = -C 

C¹ = -C is a skew-symmetric matrix. 

∴ A – A¹ is a skew-symmetric matrix.

Given relation is R = {(a₁, b₁ ), (a₁, b₂ ), (a₂, b₁ ), (a₃, b₃ ), (a₄, b₂ ), (a₅, b₂ )}.

Since, R(a₁ ) = b₁ and R(a₂ ) = b₁.

Therefore, relation R is not one-one.

Now, range of relation R is {b₁, b₂, b₃ }. And codomain of relation R is B = {b₁, b₂, b₃, b₄ } ≠ the range of relation R.

Therefore, the relation R is not onto.

Hence, relation R is neither one-one nor onto.

f(x) is a polynomial in x. Hence it is continuous over [-4, 2] and differentiable over (-4, 2).

f(-4) = (-4)² + 2 (-4) - 8 

= 16 - 8 - 8 = 0

f(2) = 4 + 4 - 8 = 0

∴ f(-4) = f(2)

∴ All the conditions of the Rolle's theorem are satisfied.

∴ there exists a c ∈[-4, 2] such that

f'(c) = 0 f'(x) = 2x + 2

f(c) = 2c + 2

f(c) = 0

⇒ 2c + 2 = 0

⇒ 2c = -2

⇒ c = -1 ∈[-4, 2]

∴ Rolle's theorem is verified.

P₁ = 2 bar ⇒ 2 x 10⁵ pascal

P₂ = 10 bar = 10 x 10⁵ pascal

T₁ = 400 i

T₁ = 673 k

T₂ = ?

First law of thermodynamics

\(\Delta Q=\Delta U + \Delta W\)

For adiabatic process \(\Delta Q = 0\)

Then work done \(\Delta W = \Delta U\)

\(\frac{P_1}{T_1}=\frac{P_2}{T_2}\)

\(\frac{2\times10}{673}=\frac{10\times10}{T_2}\) 

T₂ = 5 x 673

T₂ = 3365 k

(a) Work done

\(\Delta W=\frac{rR}{r-1}(T_2-T_1)\)

\(\Delta W=\frac{1.4\times8.3}{1.4-1}(3365-673)\) 

\(\Delta W=\frac{11.62}{0.4}(2692)\) 

\(\Delta W = 78.20 KJ\)

(b) Change in internal energy is equal to work done

\(\Delta U=\Delta W\)

\(\Delta U=\Delta W\)

(c) Heat transfer in the adiabatic process 

\(\Delta Q=0\)

(2/3, -1/3, -2/3)

x(î + ĵ + k̂) = 1 

⇒ xî + xĵ + xk̂ = 1

⇒ √(x² + x² + x²) = 1

⇒ √3x² = 1

⇒ x = 1/√3

1. Do they hack the trees Into pieces? 

2. Did he spring like a buck and disappear? 

3. Does Mara want to grow fast and strong? 

4. Did Mara build the lake?

5. Did Mara go to the edge of the lake?

6. Does it take a moment to die?

7. Do they keep looking at the sky’?

8. Does the woman stick to you like a burr?

9. Did Nicola answer seriously?

10. Did we drive to the tiny village?

11. Do they know Verona very well?

12. Did her beauty give the spring everlasting youth?

1. Does the medicinal creeper grow in the wild? 

2. Did the narrator carry on a profession in a big city? 

3. Does he put it into his pocket? 

4. Does fear become a delirium?

5. Did Nasiruddin Sheikh support his son’s venture?

6. Do the boys help their families by working as mechanics? 

7. Do the girls work as maidservants in the village?

8. Did Babar Ali want to change the situation? 

9. Does he teach his students under the open sky? 1

10. Does Babar Ali live in West Bengal?

• Proximity to water bodies or rivers
• Uninterrupted power supply
• Availability of capital for investment
• Entrepreneurship
• Proximity to market

Raw material and power: 

In determining the location of an industry, nearness to sources of raw material is of vital importance. Nearness to the sources of raw materials would reduce the cost of production of the industry.

Regular supply of power is a pre-requisite for the localization of industries. Coal, mineral oil and hydro-electricity are the three important conventional sources of power. Most of the industries tend to concentrate at the source of power.

Transport and man power: 

Transport facilities, generally, influence the location of industry. The transportation with its three modes, i.e., water, road, and rail collectively plays an important role. So the junction points of water-ways, roadways and railways become humming centres of industrial activity. Further, the modes and rates of transport and transport policy of Government considerably affect the location of industrial units.

Adequate supply of cheap and skilled labour is necessary for and industry. The attraction of an industry towards labour centers depends on the ratio of labour cost to the total cost of production which Weber calls ‘Labour cost of Index’.

Water, market and government policies: 

Water is another important require­ment for industries. Many industries are established near rivers, canals and lakes, because of this reason. Iron and steel industry, textile industries and chemical industries require large quantities of water, for their proper functioning.

The entire process of manufacturing is useless until the finished goods reach the market. Nearness to market is essential for quick disposal of manufactured goods. It helps in reducing the transport cost and enables the consumer to get things at cheaper rates.

Government activity in planning the future distribution of industries, for reducing regional disparities, elimination of pollution of air and water and for avoiding their heavy clustering in big cities, has become no less an important location factor.

f₁ =80 N 

f₂ = 70N 

F=√f₁² +f₂²+f₁. f₂ cosΦ

F=√6400+4900+5600cos 150° 

F=√ 11300+5600 . -√3/2 

F =√11300+2800.-√3 

F=10√113-28√3 

F=10√113-(28x1.73) 

F=10√113-48.44 

F=10√64.56 

F=10×8.034 

F 80.34N

1. b. 1921

2. b. 24.80

3. a. 2001

4. d) 971797095

1. a) Birth Rate – Death Rate

2. b) Shift from Rural Agrarian economy to Urban Industrial economy

3. c) High Birth Rate and Low Death Rate

4. b) Stage II

1. a). Climate Change

2. d). Not concerned with food security and livelihood of the people

3. c). Mixing modern technology with traditional knowledge

4. c). Per capita availability of water

(A) 1. (a) 2. (d) 3. (b) 4. (c)

b. Semi-clustered or fragmented

Dignitaries on the dais and off the dais, College Day is the most important day on the calendar ofevents of an educational institution and it is with great pleasure that I take the mike to introduce to you the Chief Guest. Since ours is a women’s college, it is with added pride that I place before you the impressive details of Ms. Sheela Patil, District Superintendent of Police. Ms. Patil hails from Gulbarga and has an M.A. from Gulbarga University. When it comes to the coveted IPS, I’m glad to announce that she is a rank holder of 2005 batch.

The way she has ascended the career chart is remarkable. From the position of a lecturer she steadily rose to the level of IPS officer and became the favourite of all law – abiding citizens of Haveri but a nightmare for anti – social elements. Her fearlessness and fairness have made her the most popular leader. Her courage and honesty are exemplary. I’m sure many students will take her as their role model after listening to her message. May I request you to address the audience?

(b) Both statements are correct and statement II correctly explains statement I

c) Both statements 1 and 2 are correct

The correct answer is Director General of Police Rajasthan.

• Director General of Police Rajasthan is the chief of Rajasthan Police.
  • Shri. Ajit Singh holds this position.
• The Rajasthan Police is the law enforcement agency for the state of Rajasthan in India.
  • HQ- Jaipur
  • motto-committed to serve
• In India, the Director General of Police is the highest ranking police officer in an Indian State or Union Territory.
• DGP is appointed by the Cabinet from the Indian Police Service and they hold a three-star rank.
• The rank insignia of a Director General of Police or Commissioner of Police (in Delhi) is the national emblem over crossed sword and baton.
• DGP-ranked officers wear Gorget patches on their collar which have a dark blue background with an oak leaf pattern stitched on it, similar to ADGs and IGs

b. Both 1 and 2 are correct

a) Skill development and entrepreneurship

The roots of the equation x² + 2x + 9 =0 are imaginary  as the discriminant D= 4-36= -32 , which is negative.

As the imaginary roots of a quadratic equation are conjugate to each other, so both the roots of the equations will be common.

So, a/1 = b/2 =c/9

or,  a:b:c = 1:2:9

Ans: 25

Suppose 1 worker does 1 unit work in a day

Assume 150 workers can finish the work in (n-8) days, if all workers work all the days.
Then, total work =150(n−8) ⋯(1)

Actually 150 workers work on day-1, 146 workers work on day-2, ... and work is completed in n days. Therefore,
total work = 150 + 146 + ...  (n terms)

This is an arithmetic progression with a = 150, d = -4. Therefore,
total work
=n/2[2×150+(n−1)(−4)]

=n/2[300−4n+4]

=n/2[304−4n]

=n(152−2n) ⋯(2)

From(1) and (2)
150(n−8)=n(152−2n)

75(n−8)=n(76−n)

75n−600=76n−n^2

n^2−n−600=0

(n−25)(n+24)=0

n=25

i.e., number of days in which the work was completed = 25

Solution:

Suppose the work is completed in n days.            

Since 4 workers went away on every day except the first day.

∴ Total number of worker who worked all the n days is the sum of n terms of A.P. with first term 150 and common difference – 4.

Total number of worker who worked all the n days = n/2[2 x 150 + (n-1) x -4 ] =  n (152 – 2n)

If the workers would not have went away, then the work would have finished in (n – 8) days with 150 workers working on every day.

∴ Total number of workers who would have worked all n days = 150 (n – 8)

∴ n (152 – 2n) = 150 (n – 8)  

⇒ 152n – 2n² = 150n – 1200     

 ⇒ 2n² – 2n – 1200 = 0

⇒ n² – n – 600 = 0                 

⇒ n² – 25n + 24n – 600 = 0        

⇒ n(n – 25) + 24 (n + 25) = 0

⇒ (n – 25) (n + 24) = 0 

⇒ n – 25 = 0 or n + 24 = 0                  

⇒ n = 25 or n = – 24

⇒ n = 25 ( Number of days cannot be negative)

Thus, the work is completed in 25 days.

We have given a,b,c,d,e,f are in A.P

So, let common difference = x

so, a+x=b

a+2x=c

a+3x = d

a+4x = e

a+5x = f

=> e-c = a+4x-a-2x = 2x ---------(1)

=> d-c = a+3x-a-2x = x --------(2)

so from 1 and 2 we get

e-c = 2(d-c)

Take the four numbers as (a-3d),(a-d),(a+d),(a+3d) in AP with common difference as 2d.

Now given that Sum of four numbers = 96

i.e (a-3d)+(a-d)+(a+d)+(a+3d) = 96

=> 4a = 96

=> a = 24 ----------(1)

Now to find d use the other condition.

i.e Product of means/Product of Extremes = 35/27

=> (a-d)(a+d) / (a-3d)(a+3d) = 35/27

=> a² - d² / a² -9d² = 35/27 ---------------(2)

Now find the value of d using equation (1) and (2)

You will get d = 4

So the four numbers are:

a-3d = 24-3*4 = 12

a-d = 24 - 4 = 20

a+d = 24+4 = 28

a+3d = 24+12 = 36

Hence the four numbers are 12,20,28,36

Your question is a bit not clear.But what I understand showing you.

Given  a1,a2,a3.............  be terms of an AP

Let common difference is d

(a1+a2+a3+a4...............ap)/(a1+a2+a3+a4................aq)=p^2/Q^2

p/2[2a₁ + (p-1)d] / q/2[2a₁+(q-1)d] = P²/Q²

^=> p[2a₁ + (p-1)d] / q[2a₁+(q-1)d] = P²/Q²  --------------------(1)

Now a6/a21 = a₁ + (6-1)d / a₁ + (21-1)d

=> a₆/a₂₁ = a₁ + 5d / a₁ + 20d  -------------(2)

Now find the ratio using equation (1) and (2)

The role of communication in NGO's is to share information, tell stories, protect the brand's reputation, and engage in conversations that inspire people to join their organization in fulfilling its mission.

Strong communication in local government creates trust in its citizens. The hope is that this trust will inspire citizens to become involved in their communities. As the relationship builds between governments and citizens, over time, citizens will come to realize that their concerns matter.

Performance norms: Performance norms are centered on how hard a person should work in a given group. They are informal cues, if you will, that tells a person or helps a person understand how hard they should work and what type of output they should have.This norm is centered on how we should act in social settings.