Explore topic-wise InterviewSolutions in Current Affairs.

Option : (c)

\(A^2=2A\)

\(\Rightarrow|A^2|=|2A|\)

\(\Rightarrow|A^2|=2^3|A|\)

\(as\,|kA|=k^n|A|\) for a matrix of order n

\(\Rightarrow\) either |A| = 0 or |A| = 8

But A is non-singular matrix

\(\therefore|2A|=2^3|A|=8^2=64 \)

Option : (a)

 \(tan^{-1}\left(\frac{\sqrt{1+cos\,x}+\sqrt{1-cos\,x}}{\sqrt{1+cos\,x}-\sqrt{1-cos\,x}}\right),\)

\(=tan^{-1}\left(\cfrac{-\sqrt2cos\frac{x}{2}+\sqrt2sin\frac{x}{2}}{-\sqrt2cos\frac{x}{2}-\sqrt2sin\frac{x}{2}}\right),\) \(\pi<x<\frac{3\pi}{2}\)

\(=tan^{-1}\left(\cfrac{cos\frac{x}{2}-sin\frac{x}{2}}{cos\frac{x}{2}+sin\frac{x}{2}}\right)\)

\(=tan^{-1}\left(\cfrac{1-tan\frac{x}{2}}{1+tan\frac{x}{2}}\right)\)

\(=tan^{-1}\left(\cfrac{tan\frac{\pi}{4}-tan\frac{x}{2}}{1+tan\frac{\pi}{4}tan\frac{x}{2}}\right)\)

\(=tan^{-1}\left(tan(\frac{\pi}{4}-\frac{x}{2})\right)\)

\(=\frac{\pi}{4}-\frac{x}{2}\)

Let the number be n = 12 m + 8, \(m\in Z\) 

(i) m = 0, then n = 8, \(\frac n {48} \) gives remainder 8.

(ii) m = 1, then n  = 20, \(\frac n {48} \) gives 20 as remainder.

(iii) m = 2, then n = 32, \(\frac n {48} \) gives 32 as remainder.

(iv) m = 3, then n = 44, \(\frac n {48} \) gives 44  as remainder.

(v) m = 4, then n = 56, \(\frac n {48} \) gives 8  as remainder.

Hence, when n is divides by 48 then possible remainder are 8, 20, 32 or 44.

I was scared. However, I managed to keep patience and I slowly came down the stairs. I was all alone at my home, my family were out. there was no electricity at that time. there was a little light coming from outside so i decided to open the door to see what was there. I slowly opened the door. Then the lights were on and there was a voice singing "Happy birthday to youuu" and when I opened my eyes....There was my family wishing me.All that happened later is a huge party. My younger brother fired a cracker it was the same which I heard before. 

\(f(x + y) = 2^x f(y) + 4^y f(x)\)  ......(1)

\(f(y + x) = 2^y f(x) + 4^x f(y)\)  .......(2)

Equation (1) - Equation (2), we obtain

\((2^x - 4^x) f(y) + (4y - 2y )f(x) = 0\)

⇒ \((26^x - 4^x) f(y) = (2^y - 4^y) = f(x)\)

⇒ \(\frac{f(x)}{2^x - 4^x} = \frac{f(y)}{2^y - 4^y} = k\)  (Let)

⇒ \(f(x) = k(2^x - 4^x)\)

\(\because f(2) = 3\)

\(\therefore k(2^3 - 4^3) = 3\)

⇒ \(k = \frac3{8 - 64} = \frac{3}{-56}\)

\(\therefore f(x) = \frac{-3}{56} (2^x-4^x)\)

\(f'(x) = \frac{-3}{56}(2^x log2 - 4^x log4)\)

\(= \frac{-3}{56}(2^x - 2^{2x + 1})log 2\)

\(f'(2) = \frac{-3}{56} (4 - 32) log2\)

\(= \frac{-3}{56} \times - 28\, log2\)

\(= 6 \,log2\)

\(f'(4) = \frac{-3}{56}(16 - 512)\, log2\)

\(= \frac{-3}{56}\times - 496\,log2\)

\( = \frac{-3}{7}\times{-62} \,log 2\)

\(= \frac{96}{7}log2\)

\(\therefore \frac{14f'(4)}{f'(2)} = \frac{14 \times \frac{96}{7}\,log2}{6\, log2}\)

\(= \frac{36 \times 2}{6}\)

\(= \frac{96}{3}\)

\(= 32\)

Sum of roots = 12sin a + 5cos a = -a

Product of roots = (12sin a)(5sin a) = b

⇒ 12sin a +5cos a = -a  .....(i)

and 60sin a cos a = b    .....(ii)

Squaring equation (1), we get

144sin²a + 25cos²a + 120sin a cos a = a²

⇒ 144sin²a + 25(1 -sin²a) + 2b = a²  (From(i))

⇒ 119 sin²a = a² - 2b - 25

⇒ sin²a = \(\frac{a^2 - 2b - 25}{119}\)

but 0 \(\le\) sin²a \(\le\) 1

⇒ 0 \(\le\) a² - 2b - 25 \(\le\) 119

⇒ 0 \(\le\) a² - 2b \(\le\) 144

Renu Garg
Marine beach,
Mumbai
400001

Feb 05, 2019

National daily
Paratha Gali,
Delhi

Subject: The downfall of educational interest of students in their studies

Sir,

I am Renu Garg studying in class .. in XYZ school, Mumbai. Every day I come across many students who were much good in their studies in past classes but they are loosing their interest in studies and their marks are going degraded each exam. I thought to write you a letter discussing the downfall of interest in studies of the students due to modern day technology.

In modern days as our technology is becoming advanced day by day, it is helping the mass as well as affecting in stacks. Students are wasting a lot of time in video games, social media, as these things grab their interest more than books and copies. But if all these factors are taken in a good way then the potential of students will increase to a greater extent. 

Sir, I want you to publish an editorial on this topic because a mass is getting affected by it. Hope you understand.

Yours truly,

Renu Garg
Student

(a) Do you have anything to read ?

(b) Do you know how did they look like ?

(c) aren't they ?

(d) I will tell you about them.

(e) Like to listen to it from you.

1. What a humble teacher Mr Desai is !

2. The man who is standing at the gate is the security guard of the society.

3. As soon as the sun rises, the birds leave their nests. OR When the sun rises, the birds leave their nests.

4. All the students of my class are well-behaved and obedient.

5. Would you please go and open the door ?

6. Our class is going to visit the Science City tomorrow.

Correct option is B) how much we’ll pay

Correct option is C) why she is crying

A. because she couldn’t find food for her young ones

(a) of 

(b) on

(c) by 

(d) to

(a) Got up 

(b) Turned up

(c) Made up his mind 

(d) Put across.

Radha is shorter than any other member in the family.

(c)  put up with

Chandra’s handwriting is better than that of Mangala.

a.  My clothes are being washed by me.

Don Anselmo wore the same faded cutaway and carried the same stick. He was accompanied by the boy again.

i) b 

ii) d 

iii) a 

iv) d

v) c 

vi) d

Don Anselmo was very much passionate about his land and the children. His land had come from his ancestors. He lived in that land from his birth. He took possession of his house from his mother. Everyone in the village were his relatives and the children are his nieces, nephews and grand children. Every time a child has been born in Rio en Medio, a tree was planted in its name.

Bangalore is the Capital city of Karnataka.

Correct option is A) beat

Voracious is one word for Very eager for knowledge.

Correct option is B) doing

Correct option is A) are caused

Refers to the below link

https://bit.ly/2TDki1Y

Suggest has two syllables

From

ABC No. 65, III Cross, II main,

Basavanagar,

Bellary

To 

The Divisional Officer, Bellary

Corporation,

Bellary.

Respected Sir,

Sub : Repair of bad roads.

I am compelled to write to you on behalf of our area ie., Basavanagara. Almost all the roads in our area had pot holes. During rainy season it is very difficult to walk or ride on the road. I and all our area people request you to take immediate remedial measures to provide good roads for us. I hope you will act on our plea as soon as possible and help us. 

Thanking you Sir,

                                                                                                                          Yours faithfully

                                                                                                                                     ABC 

Enel : Our area people’s signature letter.

Moon words has one syllable.

(B) rain and his family

(C) to invite Pandit Ravishankar to her house.

Many people are suffering from poverty.

“The prime minister Mr Modi is Well known to everyone.

Wide

narrow

 Lunch  box .

Fast  Train.

Quick  glance

1. with;

2. the; 

3. the; 

4. a; 

5. of; 

6. The; 

7. to.

Ago has one syllables .

1. about; 

2. an;

3. The;

4. ;

5. to;

6. a.

The correct answer is Swami Keshawanand.

• Swami Kesavanand, the famous social reformer of Rajasthan, had his childhood name as 'Birama'. 
  • He was awarded 'Sahitya Vachaspati' for his contribution to the promotion and popularization of Hindi in 1942.

• Swami Keshavanand (1883 - 1972) was a freedom fighter and social reformer of India.
  • He contributed significantly in eradicating social evils like child marriage, female oppression, curtain practice, exploitation, and intoxication.

• Hanuman Singh Budania was a resident of Dudwa Khara, a village in Churu district of Rajasthan.
• He participated in the independence movement of India.
• Govind Giri was a great social reformer and contributed significantly to the revival of Bhil society.
• Dayanand Saraswati was the founder of Arya Samaj, and his childhood name was 'Moolshankar'.

1. an;

2. on;

3. an;

4. the;

5. ;

6. on.

1. in; 

2. a; 

3. through; 

4. the; 

5. in; 

6. an; 

7. for;

8. a; 

9.the; 

10. of.

1. The; 

2. of; 

3. by;

4. in;

5. to;

6. an; 

7. about; 

8. in;

9. in;

10. the.

The correct answer is 1912.

• In the North Atlantic Ocean, RMS Titanic sank in the early morning hours of 15 April 1912. 
• It resulted in the deaths of more than 1,500 people.
• Titanic had an estimated 2224 people on board when she struck an iceberg on 14 April 1912.
• The book "The Sinking of the Titanic" and "The Discovery of the Titanic" etc are also written on this event.

• RMS Titanic was a passenger liner operated by the White Star Line - a British company.
• RMS Titanic was the largest ship afloat at the time she entered into the service.
• It was the second of three Olympic-class ocean liners.

The airplane was flown to Bengaluru by the pilot. In the second sentence, the object has been shifted to the place of subject. It remains passive and allows the work to be done by the noun.