Explore topic-wise InterviewSolutions in Current Affairs.

Let x be the width, then length = x + 2

x (x + 2) = 80

x² + 2x = 80

x² + 2x + 1 = 80 + 1

(x + 1)² = 81

x + 1 = 9 

x = 8 

length = 10 

width = 8

Let the numbers be x, x + 6 

Products : x (x+6) = 216

x² + 6x = 216

x² + 6x + 9 = 216 + 9 = 225

(x + 3)² = 225

x + 3 = 15

x = 15 – 3 = 12

Numbers : 12, 18

Smaller side = x

Perpendicular side = 2x – 1

Hypotenus = 2x + 1

x² + (2x – 1)² = (2x + 1)²

x² + 4x² – 4x + 1 = 4x² + 4x + 1

x² – 8x = 0

x (x – 8) = 0

x = 0 or x = 8

Side = 8 cm, 15 cm, 17 cm

Let x be the number

\(x+\frac{1}{x}=\frac{5}{2}\)

\(\frac{x^2+1}{x}=\frac{5}{2}\)

2x² + 2 = 5x

2x² - 5x + 2 = 0

If we take numbers as 6 + x, 6 – x

\(\frac{1}{6+x}+\frac{1}{6-x}=\frac{3}{8}\)

12 x 8 = 3 (36 - x²),

96 = 108 - 3x²

3x² = 12x² = 4,

x - 2 or -2

Numbers = 6 + 2 = 8, 6 - 2 = 4

Let number = x, then its reciprocal = 1/x

\(x+\frac{1}{x}=\frac{13}{6},(x^2+1)\times6=13x\)

6x² - 13x + 6 = 0

\(x=\frac{13\pm \sqrt{(-13)^2-4\times6\times6}}{2\times6}\)

= \(\frac{13\pm \sqrt{169-144}}{12}=\frac{13\pm \sqrt{25}}{12}\)

Number = \(\frac{3}{2}\) or \(\frac{2}{3}\)

2 + 4 + 6 + + 2n = 420

2(1 + 2 + 3 + ….+ n) = 420

\(2\times\frac{n(n+1)}{2}=420\)

n² + n - 420 = 0

Number = x, its reciprocal = 1/x then, x − \(\frac{1}{x}\) = k

\(x^2-kx-1=0,x=\frac{+k\,\pm \sqrt{k^2+\,4} }{2}\)

Since k being a positive number, k² + 4 also negative.

Let x be the number

x + √x = 6

x – 6 = √x

(x – 6)² =(–√x)²

x² – 12x + 36 = x

x² – 13 x + 36 = 0

Sum of first n natural numbers

= \(\frac{n(n+1)}{2}=465\)

n² + n = 930

\(n^2+n+\frac{1}{4}=930+\frac{1}{4}\)

\((n+\frac{1}{2}){^2}=\frac{3721}{4},n+\frac{1}{2}=\frac{61}{2}\)

n = 30

The sum of first 30 natural numbers = 465

\(\frac{n(n+1)}{2}=210\)

n² + n = 420

n² + n – 420 = 0

Let the side of the squares be x and y meters.

According to the condition,

x² + y² = 500

4x – 4y = 40

(x – y) = 10

y = x – 10

Substituting the value of y in, we get

x² + (x – 10)² – 500

2x² – 20x – 400 = 0

x² – 10x – 200 = 0

x = 20 or x = – 10

As the side cannot be negative, x = 20 

Hence, side of the first square, x = 20 m 

Side of the second square, y = 20 – 10 = 10 m

If the numbers are x, x + 1, x + 2, then

x² + ( x + 1)² + (x + 2)² = 110

x² + x² + 2x + 1 + x² + 4x + 4 = 110

3x² + 6x – 105 = 0

\(x=\frac{-6\pm\sqrt{6^2-4\times3\times-105}}{2\times3}\)

= \(\frac{-6\pm\sqrt{1296}}{6}=\frac{-6\pm36}{6}=5.7\)

Let the number be x

x + 1 = x²

x² - x - 1 = 0

\(x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{1\pm \sqrt{1+4}}{2}\) \(=\frac{1\pm \sqrt{5}}{2}\)

Numbers \(\frac{1+\sqrt{5}}{2},\frac{1-\sqrt{5}}{2}.\)

(x - 4) (x - 6) = 0

x² - 10x + 24 = 0

The correct equation = x² - 10x - 24 = 0

a = 1, b = 10, c = 24

b² - 4ac = (-10)² - 4 x 1 x 24 = 196

\(x=\frac{-b\pm \sqrt{b^2-4ac}}{2a}=\frac{10\pm14}{2}\)

x = 12, -2

The correct answer is 12, -2

AC x CB = CD²

AC = x

x(x-15) = 10²

x² - 15x = 100

\(x^2-15x+\frac{225}{4}=100+\frac{225}{4}\)

\((x-\frac{15}{2})^2=\frac{625}{4},x-\frac{15}{2}=\frac{25}{2}\)

\(x=\frac{25}{2}+\frac{15}{2},\)

∴ AB = 20 + 5 = 25 cm

Sum of the numbers = 4

If, First number = x

Then second number = 4 – x

x(4 - x) = 2

-x² + 4x = 2

x² - 4x = -2

(x - 2)² = -2 + 4

(x - 2)² = 2

x - 2 = \(\pm\)√2

x - 2 = √2, x - 2 - √2

x = 2 + √2, x = 2 - √2

The numbers are 2 + √2, 2 - √2

If there is one solution, the discriminant = 0

b² - 4ac = 0

(-5)² - 4 x 4 x k = 0

25 - 16k = 0

16k = 25

\(K=\frac{25}{16}=1\frac{9}{16}\)

Let the number be x

x(x+2) = 168

x² + 2x = I68

x² + 2x + 1 = I68 + 1

(x+1)² = 169

x + 1 = ± 13

x + 1 = 13

x + 1= – 13

x = 13 – 1 = 12

x = -13 – 1 = – 14

The number is 12 and 14 or – 12 and – 14

a. Let the number be x, then second number is x + 8

x(x + 8) = 105

x² + 8x = 105

The number to be added to get a perfect square is 16

b. x² + 8x + 16 = 121

(x + 4)² = 121 ;

x + 4 = 11 or -11

x = 7 or -15

number 7, 15 or -15, -7

Let x be the side of square

(x + 4)² = 256

x² + 8 x - 240 = 0

\(x=\frac{-8\,\pm\, \sqrt{64\,+\,960}}{2}=\frac{-8 \,\pm\,32}{2}\) = 12, -20

x will not -20 

The side of the first square = 12 cm

Let the length of each side of the original square be x, then

(x - 2)² = 49

x - 2 = \(\pm\) 7

x - 2 = 7

x - 2 = -7

x = 7 + 2 = 9

x = -7 + 2 = -5

The length of each side of the original square = 9 cm

(a) Cholera: 

cause-Vibrio cholera

Concept: dehydration is the most common manifestation of cholera

Prevention: Sanitation measure and vaccination

(b) Salmonellosis: 

cause- Salmonella typhi 

Concept: mainly it affects the intestine and liberates toxins into blood circulation. 

Prevention: Sanitation measure and vaccination.

Let 2500 is the square of the n^th term of the arithmetic sequence 2, 5, 8, ……

x_n = dn + (f - d)

= 3n + (2 - 3) = 3n - 1

(3n - 1)² = 2500

3n - 1 = 50

3n = 51

n = 17

It is the 17^th term.

Let the two consecutive even numbers be x,

x + 2

x, x + 2 

x(x + 2) + 1 = 289 

x² + 2x = 288 

x² + 2x – 288 = 0 

x² + 2x = 288 

(x+1)² = 288 + 1 

(x+1)² = 289 

x + 1 = ± 17 

x = 16, – 18 

The numbers are 16, 18

Foods to include:

1. Plenty of fluids like juices, soups, 1. High fibre foods like whole grain coconut water, electrolyte, barley cereals and their products e.g. whole water, soups. wheat flour, whole wheat bread, oats

2. Milk and milk based beverages. and cracked wheat, whole pulses and 

3. Bland, well cooked, well mashed, pulses with husk. sieved, soft, semisolid foods.

Foods to avoid:

1. High fibre foods like whole grain coconut water, electrolyte, barley cereals and their products e.g. whole water, soups. wheat flour, whole wheat bread, oats 

2. Milk and milk based beverages. and cracked wheat, whole pulses and 

3. Bland, well cooked, well mashed, pulses with husk. sieved, soft, semisolid foods like 

4. Low fibre foods such as refined

He may be at home but I don't know.

1. Understanding the audience 

2. Choosing the right data and visualisations 

3. Drawing attention to key information 

4. Developing a narrative 

5. Engaging your audience

Model High School 

NOTICE

22nd December, 2018

As part of social service our school has decided to clean the area around our school. All the students who wish to participate in this campaign should give their name to the undersigned. Whole hearted participation of student will ensure the success of this programme. 

Head Girl / Boy 

Shreya / Sanjit 

Govt. High School 

Lakshmana Nagar 

17 January 2018

Dear Daddy, 

As the exam dates are fast approaching, I know that you are worried about my studies. Please don’t worry. I put in two hours of study every morning and three hours in the evening.

Two tests have already been conducted and I am glad to inform you that in these preparatory exams I have scored above 85% in all the subjects. Teachers are satisfied with my performance although they have warned me about careless mistakes. They have also given me some tips about time management.

I have set a time table for myself and hope to complete revision well in time. I have the confidence of doing well in the final exams. Please convey my love to mummy. How is my little sister? Nothing more to pen now.

Yours affectionately 

Aruna

Yoga is an ancient art that connects the mind and body. It is an exercise that we perform by balancing the elements of our bodies. In addition, it helps us meditate and relax. Moreover, yoga helps us keep control of our bodies as well as mind.

(a) Summer Vacation 

 Holidays bring great joy and relief. We have to work hard when our school session is on. So, we get tired. We wait for the holidays eagerly. We make plans for spending the holidays. A long vacation gives us freedom from the boredom of our daily life. It brings a welcome change in our dull life. We can spend the vacation as we wish. During the vacation we are free from the monotony of our school life. So, we look forward to the vacation impatiently. Recently I have enjoyed the summer vacation.

(b) Secret of Work 

 Many are the blessings of work. All the humanity has achieved during the course of generations was a result of hard work. Man owes all his greatness to hard work. It is but the very 'secret of work'. Man is human because he is capable of hard work, while the animal is not. All human civilization and culture is the result of hard work. Our agriculture, industries, art, science, literature, architecture etc. have all been achieved through hard work. Indeed 'work is worship'. But it is also important that a part from our own work, we must also find out sometime to work for the well being of other persons of the society. 

(c) The Ganga The 

Ganga is considered the most holy river in our country. The Ganga rises in the Himalayas. Many famous cities are situated on its bank such as—Patna, Varanasi, Allahabad, Kanpur etc. Most of them have become the places of pilgrimage. Its water is pure and clean. Many rivers from north to south join the Ganga. The Hindus believe that a dip in the Ganga washes all sins. People take the dead bodies to its banks for cremation. The plains of Ganga is very fertile. But now a days Ganga is being polluted. The Ganga is very useful for our country. It also balances the level of water under earth. People worships it and call it 'Maa Ganga'.

(d) Importance of Labour 

 We say "labour never goes invain." There is no substitute for hard work. Without labour one cannot be successful. The person who do hard work has achieved success. There is a proverb 'Work is Worship'. We should work honestly and with a will. Hard work will bear fruit and change this world into a paradise. We must put in hard work. It is always rewarded. 

b) Active listening

Mr. Mahesh is telling a story to all his students. He made it an interesting activity by involving all the students. Active listening skill being developed by the teacher in students.

10, Kingston Gardens 

Bangalore 

12 October 2017

The Headmaster 

Mahatma Gandhi Govt. 

High School Bangalore.

Dear Sir, 

As l am the Cultural Secretary, I hope to be remembered by you. I am Anil of Standard X and i request you to issue me a character certificate. I am applying for membership in Gliders’ Club and I am asked to submit a character certificate signed by the Headmaster.

I have been studying in this school for the past six years. I have always been among the top ten in my examination scores. I have actively participated in school and inter-school competitions and have also won many prizes. On this merit, I have been chosen as the Cultural Secretary this year, i hope the information that I have furnished is enough for your perusal.

I thank you for all the opportunity given and I once again request you to issue me a character certificate.

Yours faithfully 

Anil

The right upper quadrant (RUQ) includes the pancreas, right kidney, gallbladder, liver, and intestines.

Correct option: a) E-mail

To 

The Headmaster 

Government School 

Patna

Sub. :- Application for school leaving certificate.

R/Sir, 

With due respect, I beg to state that I am a student of class-X of your school. My father has been transferred to Shimla because he has a transferable job. He has therefore report to duty within three days. All the members of our family are leaving for Shimla tomorrow. I, too, have to leave with them. I, will do my further studies there. 

I have paid all the dues. Kindly issue me a School Leaving Certificate. I shall be thankful to you for this act of kindness. 

Yours obediently 

Ravi Raj 

Class-X/A

Correct answer is b) CTRL+Z 

544, Gandhi Road, 

New Delhi – 110023

25th November, 2012

My dear Papa, 

I received your letter yesterday and I was very glad to read it. Papa, you will be glad to know that I am quite well here and hope the same for you.

I am working hard now-a-days. My studies are going fairly well. I am sure that I will get very good marks in the examination.

After the examination I have planned to join a short – term course of English conversation for one and half months. This course will be fruitful to me. I assure you that I will leave no stone unturned to make it up. I will work hard to learn it well. I have also bought a few books of English suggested by my English teacher. I will do at my best.

Rest is o.k.. 

I wish you to convey my regards to mother and love to Sonu.

Yours Affectionate Son

Vivek Kumar

Correct answer is c) Email 

31 Veer Hostel Tonk Road Jaipur
21 April 2020

My dear Mother,

I’m well and good here and hope you to be the same.

In this letter, I’m describing an act of bravery of your son. Last Sunday, the weather was pleasant. I and my classmates decided to go for a picnic. We packed eatables and other essentials. We implored our science teacher. He became ready. We went on bicycles. He carried us on a riverside. We enjoyed singing, dancing and boating. A classmate didn’t’ know how to swim. Suddenly he fell down into the river. We saw him sinking and shouting for help. I saved the drowning classmate. I was happy. I was rewarded by his parents and the institution.

With regards

You loving son

Avinash

16 December, 2018 

Patna 

Respected father, 

The prize distribution function of our school was held last Monday. The Chief Minister presided over the function. 

You will be glad to know that I have won the first prize by standing first in the house examinations. (There were many prize-winners, but I was the first to be called for getting the prize. I went to the stage and shook hands with the President. The students gave loud cheers. The President gave me the prize. There was a loud applause again. After this I came back to my seat. My friends congratulated me again and again. I wish papa you would be here that day.

(i) Education is a device for helping a man to grow his full stature and makes him able to realize his own nature both mentally and spiritually. 

(ii) The man who received the right kind of education, find the world larger and more exciting. 

(iii) The qualities of intelligence and good taste are developed in man by education. 

(iv) 'Attributed'. 

To The Headmaster, 

 ABC High School, 

 Patna 

Sub. :- Application to arrange extra classes for class-X. 

R/Sir, 

I am the student of class-Xth. On the behalf of the class, I have to make one request. In the beginning of the year, we had no regular teacher of Mathematics. Only temporary arrangements were made. So, our classes suffered a lot. 

Sir, we have not done many important chapters. So, we request you to arrange extra class for maths and science also. We shall be thankful to you for this kindness. 

 Thanking you. 

Yours obediently 

 Animesh 

a. Population details of five villages

b. Suripadu

c. ii) Alkapur

d. iii) Veerukonda and Rambedu

e. i) The number of males and females in Rambedu is almost equal.

(i) Park provides a place to relax and play sports as well as a refuge from the often harsh environment of a city. So, parks are an important place for the people who live in cities. 

(ii) Plants absorb carbondioxide—a key pollutant and emit oxygen which human being needs to breath. Parks also make cities cool. These are two benefits that park provides us. 

(iii) Cities are warmer because of excessive use of building materials than the surrounding rural areas. 

(iv) The Building Materials such as metal, concrete, asphalt etc. absorb much more of the sun's heat and release it much more quickly than organic surfaces like trees and grass.