Explore topic-wise InterviewSolutions in Current Affairs.

This section includes 7 InterviewSolutions, each offering curated multiple-choice questions to sharpen your Current Affairs knowledge and support exam preparation. Choose a topic below to get started.

1.

“Oh dear! It looks as if it is going to rain again.” Mother was afraid that _______. A) it was raining again B) it was going to rain C) it is going to rain again D) it looked like rain again

Answer»

Correct option is B) it was going to rain

2.

Write a paragraph on any one of the following : (a) A Rainy Day (b) The Dipawali (c) A Cricket Match (d) My Best Friend 

Answer»

(a) Rainy Day 

 It was the month of July last year. One day it was very hot. Men and animals were very painting. Suddenly in the afternoon the sky became cloudy. Wind started to blow. It started raining heavily. Streets and markets were flooded with water. Little children came out and played in the rain. They splashed water over each other. The rain stopped after two hours. It became very cool and pleasant. The city gave a fresh look.

(b) The Dipawali 

Dipawali means 'festivals of light'. It is an important festival. It falls in the month of October or November. It comes twenty days after Dussehra. Sri Ram came back to Ayodhya on this day. This festival is celebrated in every village and town. People do painting in their houses and shops. They light their homes with candles and electric lights. They buy sweets and crackers. They distribute gifts among friends and relatives. Children enjoy fire-works at night. On this day people worship Goddess Laxmi. Everyone looks very happy at that day.

(c) A Cricket Match 

Last Sunday, a cricket match was played between our school and Gardanibagh High School. Each team played 20 overs. The match started at 10:00 A.M. We won the toss, we decided to bat first. The two boys played as opener. The first batsman made 30 runs and was out. Then next player came and he continued for 5 overs. Overall our team was out for 100 runs. Now it was the turn of Gardanibagh School. 40 runs in starting overs without losing any wicket. But after seventh over our team started to take their wickets. Lastly we won the match by 20 runs. It was really an interesting match. 

(d) My Best Friend 

 Among all my friends, I love Avinash the most. He is my classmate. We have been together since childhood. He lives next door to me and we study in the same school. For the most part of the day we remain together. We play and study together. We share our secrets to each other. He is a good and simple boy. I love his simplicity. He respects his elders. He is a very polite person. He is popular among his class-fellows. Everybody wants to be friendly with him. He always advises me to do right things. He is very good friend of mine. I take pride in having such a nice friend. 

3.

You are president of the Cultural Society of your school. You are planning to organise an annual programme. Write a notice for the school noticeboard inviting names of . students willing to participate.

Answer»

Cultural Society 

ST. PETER’S SCHOOL, COIMBATORE

9 Sept. 20XX

NOTICE 

Opportunity For Budding Artists 

Talented students are invited to submit their names for a musical evening to be held on 21st 

September 20XX in the school open air theatre from 6 p.m. onwards:

Items : (i) Light vocal music (solo) 

(ii) Group Song

(iii) Group Dance 

(iv) Bharatnatyam (Solo)

Contact the undersigned before 16th Sept. 20XX 

Sugandhi 

Secretary 

Cultural Society

4.

You are Vinay/ Vibha, student of class X of your school. You are the President of the cultural society of your school. You want to hold a meeting for the celebration of Independence Day. Write a notice for your school notice board informing students about meeting. 

Answer»

Bankipur High School 

NOTICE 

16th December, 2018

All the students are notified that a programme is going to be organised on the occasion of Independence Day on 15th August at our school campus. 

Desired students are invited to submit their name and class to the undersigned within two days. 

President 

 Vinay/ Vibha 

5.

Change the following sentences into indirect form of speech : (i) My mother said, "It may rain." (ii) The culprit said to the judge, "I am innocent." (iii) She said, "What a lovely garden it is" (iv) The old lady said to me, "May you get the reward" 

Answer»

(i) My mother said that it might rain. 

(ii) The culprit told the judge that he was innocent. 

(iii) She exclaimed with wonder that it was a very lovely garden. 

(iv) The old lady wished me that I might get the reward. 

6.

Transform the sentence as per direction in the bracket : (i) Can a deaf hear? (change into assertive sentence) (ii) Tulsidas is the most famous poet. (change into positive degree) (iii) He was too slow to win the race. (change into remove too) (iv) Why has he beaten you? (change into passive voice)

Answer»

(i) A deaf can not hear. 

(ii) No other poet is as famous as Tulsidas. 

(iii) He was so slow that he could not win the race. 

(iv) Why have you been beaten by him?

7.

Write a paragraph how you spent your last weekend.

Answer»

I went to Delhi during the last week end. My elder brother lives there. He took me round the city. We visited the Red Fort, Qutub Minar, Birla Mandir, and Zoo. We also went to India Gate. In evening we went to Cannaught Place. I saw there big shops of all kinds. Next day my brother took me to Palika Bazar. I had never seen such a big and beautiful bazar in my city. It was all underground. Next morning I came back to home. It was a well-spent weekend. I will always remember this weekend. 

8.

Transform the sentence as per direction in the bracket : (i) I am doubtful. (change into negative sentence)(ii) It is too cold to go out. (change into remove too) (iii) I am not better than you. (change into positive degree) (iv) Give me you book, please. (change into passive voice)  

Answer»

(i) I am not sure. 

(ii) It is so cold that no one can go out. 

(iii) You are as good as I. 

(iv) You are requested to give me your book. 

9.

Read,the following passage and answer the questions that follow :Man has altered many of the physical features of the earth with the tools of science. He has transformed woodlands and prairies into farmland. He has constructed lakes and dams to irrigate or to harness hydroelectric power. By cutting through mountain, he has almost modified the Very face of the earth.However his attemps to bring about change in the physical environment have not always been beneficial. Today pollution of the air and water endangers the health of our planet. The automobile exhausts and the smokes from the factories are affecting our health. Pollution from oil is killing marine life. The whole ecological balance of the sea is getting changed due to oil slick. Industrial and domestic wastes have choked several rivers. Conservationists strongly feel that if mankind and life were to survive on earth man must limit the growth of technology.1. What are the effects of pollution?2. How has man altered the earth?

Answer»

1.  Today pollution of the air and water endangers all the living createures on the planet Earth, including man. It also affecting our health. Leakage of oil killing the marine life. Industrial and domestic wastes have choked several rivers.

2. Man has altered many of the physical features of the earth with the tools of science. He has transformed woodlands and prairies into farmland. He has constructed lakes and dams to irrigate and harness hydroelectric power. By cutting through mountains, he has almost modified or altered the very face of the earth.

10.

The symbol “Û” refers to?(a) Amount(b) Rate of enthalpy(c) Molar flow rate(d) Specific internal energy

Answer» Right option is (d) Specific internal energy

The explanation is: The symbol “Û” refers to Specific internal energy in a close system in Enthalpy change in non-reactive processes whereas in an open- system symbol “Ĥ” refers to specific enthalpy.
11.

Write an essay on Role of an ideal Citizen.

Answer»

An ideal citizen is the one who is aware of his duties even as he exercises his rights. The constitution of India has assured us both rights and duties. But unfortunately, most of us enjoy our rights without fulfilling our duties. So, we can say that ideal citizen is the one who prioritises his duties over his rights. 

What are the duties to be upheld by an ideal citizen? First and foremost, an ideal citizen is the one who loves his country and who is proud of his country’. So he should promote secularism and bring people of different communities together in the true spirit of brotherhood.

The word ‘brother hood’ points out that in society all of us should get equal opportunities. So an ideal citizen would strive to ensure that there is social justice and people get equal benefit without a huge gap between the rich and the poor. An ideal citizen should exhibit the virtue of philanthropy and social consciousness.

In addition to these lofty ideals, an ideal citizen should also keep in mind practical values like saving the environment, preserving natural resources, keeping the surroundings clean and protecting public amenities. 

If each one of us does what is expected of an idal citizen, this world certainly be a better place to live in and we can experience the heaven on the earth.

12.

Write in your own words the summary of the poem ‘The song of India’

Answer»

He/She asked their mother that they can sing for her. They questioned their mother that what type of song they want to sing ? They explained that they want to sing about the Himalayas, their snow – bound peaks or the three great oceans such as Bay of Bengal, Arabian sea and the Indian ocean which wash her feet or the beautiful dawn with its golden touch of the nature.

For this the mother said in a calm voice. She wants the song of beggar, leper or any untrodden people. Or the crowd of the streets, impure or dirty places or any secluded places. The son / daughter (poet) ignores their mother’s request and again asked about the topic of the Song.

They continues then- talk asking about the song of rock – cut temples, Epics in stone or sacrifice of her children and her own children or the inspired persons, famous prophets or the great persons who made great tasks or any worthy pilgrims. Hearing the sons/ daughter’s words, mother get upset and angrily she asked to sing about millions of people who toiled and kept their life to great cause, the experienced old people or ignorant people or helpless children who were very meek and dwelt in dark places.

These words make the author that his heart beat increased and the words heard a sound of bell and make him to emotinal. This situation is like a great white birds flew in a pitiful manner. He/she become very nervous and asked about the topic of the poem.

Even though he was afraid to question her but believed in his work, again he requested her what type of songs she liked whether he can sing about the dams and lakes or any steel mills (factorices and Industries) or ship building yard like Vishakapattanam or any great technologies or any great recognised events or any atomic incidents etc.,

For this mother rejected and said you may sing on these topics but you can sing about the early and the important strikes, brave men and their goal, their achievements or any class wars and their consequences. The poet complained and in a humble condition he/she questioned that they could n’t sing for her whole heartedly and in a pure love ? He/she sang for her. That song was bathed in the stainless blue that means it is very touching and appear into nothingness.

13.

In the poem ‘I am the land’ the speaker is patient, yet assertive. Substantiate in your own words.

Answer»

In the first stanza she explains the man says he owned the earth she simply waits. Is it possible to own the earth because it is a planet and who gave the rights to own her ? But the earth will not dispute with the man, She would wait. The person shouted with rage then also the earth lie patiently.

He says that he bought her still she waits. The man would exploit her making muddy holes and the lights of the parking vehicles but she would stares these things. The farmer ploughs the land and grow the plants, trees crops, etc, The children would come and dance on the earth. 

Someone comes and sings, The soldiers come with guns and put the fence it makes the earth to suffocate. The earth felt it very bad though she is suffocated but she patiently waits. Though the mother earth suffers a lot, she can patiently tolerate and challenged the man that he cannot put a fence around the planet earth. 

Earth as a whole planet is very big’ and the man cannot put a fence and it is impossible for him. She can wait because she is the land (mother).

14.

Determine the density, specific gravity, and mass of the air in a room whose dimensions are 4m × 5m × 6m at 100 kPa and 25° C.(a) 1.16 kg/m^3, 0.00116, 140 kg(b) 1.17 kg/m^3, 0.00117, 140 kg(c) 1.15 kg/m^3, 0.00115, 140 kg(d) 1.14 kg/m^3, 0.00114, 140 kg

Answer» Correct choice is (b) 1.17 kg/m^3, 0.00117, 140 kg

To elaborate: At specified conditions, air can be treated as ideal gas.

The gas constant of air is R = 0.287 k Pa-m^3/Kg K

The density of the air is determined from the ideal-gas relation, P = ρ R T to be

ρ = P/RT = (100 kPa)/((0.287 k Pa-m^3/Kg K) (25+273.15)K) = 1.17 kg/ m^3

Then the specific gravity of the air becomes

SG = (ρ)/ρH2O = (1.17 kg/m^3)/(1000 kg/m^3) = 0.00117

Finally, the volume and mass of the air in the room are

V = (4m) (5m) (6m) = 120 m^3

m = ρV = (1.17 kg/m^3) (120 m^3) = 140 kg.
15.

What is the maximum number of electrons in the M-Shell ?1. 62. 83. 184. 32

Answer» Correct Answer - Option 3 : 18

  • Concept:
    • The distribution of electrons into different orbits of an atom was suggested by Bohr and Bury. The orbits or shells are represented by the letters K, L, M, N,… or the numbers, n = 1, 2, 3, 4.
    • The following rules are followed for writing the number of electrons in different energy levels or shells:
    • The maximum number of electrons present in a shell is given by the formula 2n2, where ‘n’ is the orbit number or energy level index. 
  • Calculation:
    • Given:
    • Shell given = M, orbit number = 3.
    • The maximum number of electrons present in a shell is given by the formula 2n2.
    • Therefore, 2 × 32 = 18
16.

Which one of the following elements’ isotopes is used in the treatment of cancer ?1. Iodine2. Sodium3. Cobalt4. Uranium

Answer» Correct Answer - Option 3 : Cobalt

The correct answer is Cobalt - 60. 

  • Cobalt - 60 radioisotopes are used in the treatment of blood cancer [leukemia].
  • Cobalt - 60:
    • Cobalt-60 (60Co) is an artificial radioactive isotope of cobalt with a half-life of 5.2713 years.
    • It is generated artificially in nuclear reactors.
    • Intentional industrial production depends on neutron activation of bulk samples of the monoisotopic and mononuclidic cobalt isotope 59 Co.
    • Measurable quantities are also generated as a by-product of typical nuclear power plant operation and may be detected externally when leaks occur.
    • In the hindmost case (in the absence of added cobalt) the incidental generator 60Co is largely the result of multiple stages of neutron activation of iron isotopes in the reactor's steel structures via the creation of its 59 Co precursor.
    • The easiest case of the latter would result from the activation of 58Fe.
    • 60Co pass off beta decay to the stable isotope nickel-60 (60Ni).
    • The activated nickel nucleus emits two gamma rays with energies of 1.17 and 1.33 MeV.
17.

Chlorine occurs in nature in two isotopic forms of masses 35 u and 37 u in the ratio of 3 ∶ 1 respectively. What is the average atomic mass of the Chlorine atom ?1. 36.1 u2. 35.5 u3. 36.5 u4. 35.1 u

Answer» Correct Answer - Option 2 : 35.5 u

  • Explanation:
    • The average atomic mass is the weighted average of the atomic masses of the naturally occurring isotopes of an element.
    • To find the average atomic mass of an atom, we take into account all of the isotopes that exist and the percentage of each type.
    • Average atomic mass = (Mass of isotope × Relative abundance).
    • The isotopes of chlorine, found in nature are in the ratio 3 : 1.
  • Calculation:
    • Given:
    • Isotopic forms of masses 35 u and 37 u
    • The average atomic mass of chlorine 

\(M=(35 \times \frac{75}{100})+(37 \times \frac{25}{100})\)

\(M=\frac{105}{4}+\frac{37}{4}\)

\(M=\frac{142}{4}\)

M = 35.5 u 

The average atomic mass of chlorine is equal to 35.5 u.​

18.

A concave mirror of focal length `f` produces a real image `n` times the size of the object. What is the distance of the object from the mirror?A. `(n-1)f`B. `(n+1)f`C. `(n+1)f//n`D. `(n-1)g//n`

Answer» Correct Answer - C
`(C) - n = (-f)/(-f-u)` (u coodinate)
`|u|=((n+1)f)/(n)`.
19.

The distance of the point `(3,0,5)` from the line `x-2y+2z-4=0=x+3z-11` is

Answer» Correct Answer - 3
Equation of line `(x+10)/(-6)=(y-0)/(-1)=(z-7)/(2)=lamda` (let)
Now `6(6lamda+13)+lamda+2(2lamda+2)=0`
`implieslamda=-2`
Distance `=sqrt(1+4+4)=3`
20.

If `veca, vecb, vecc` are non coplanar vectors such that `vecbxxvecc=veca, vecaxxvecb=vecc aned veccxxveca=vecb` then (A) `|veca|+|vecb|+|vecc|=3` (B) `|vecb|=1` (C) `|veca|=1` (D) none of these

Answer» Correct Answer - 3
All vertors will be mutuallly perpendicular and their magnitude are equal to 1.
21.

`((cos15^(@)-sin15^(@)+1)/(cos15^(@)+sin15^(@)+1))((1+sin15^(@))/(cos15^(@)))`A. `2-sqrt(3)`B. 1C. `2+sqrt(3)`D. None of these

Answer» Correct Answer - A
22.

If `a_1x^2 + b_1 x + c_1 = 0` and `a_2x^2 + b_2 x + c_2 = 0 ` has a common root, then the common root isA. `alpha = (c_(1)a_(2) - c_(2)a_(1))/(a_(1)b_(2)-a_(2)b_(1)) = (b_(1)c_(2)-b_(2)c_(1))/(c_(1)a_(2)-c_(2)a_(1))`B. `alpha = (c_(1)a_(2) - c_(2)a_(1))/(a_(1)b_(2)-a_(2)b_(1)) = (b_(1)c_(2)-b_(2)c_(1))/(c_(1)a_(2)-c_(2)a_(1))`C. the condition for one common root is `(c_(1)a_(2)+c_(2)a_(1))^(2)=(a_(1)b_(2)-a_(2)b_(1))(b_(1)c_(2)-b_(2)c_(1))`D. The condition for one common root is `(a_(1)b_(2)-b_(1)a_(2))^(2) = (c_(1)a_(2) - a_(1)c_(2)) (b_(1)c_(2) - b_(2)c_(1))`

Answer» Correct Answer - A
23.

`tan^(-1)(sinx)=sin^(-1)(tanx)` holds true forA. `"x" epsilonR`B. `2npi-(pi)/2lexle2npi+(pi)/2("n" epsilonz)`C. `"x" epsilon{0,z^(+)}`D. `"x" epsilonnpi("n" epsilonz)`

Answer» Correct Answer - D
`tan^(-1)(sinx)=sin^(-1)(tanx)`
`impliestan^(-1)(sinx)=tan^(-1)((tanx)/(sqrt(1-tan^(2)x)))`
`impliessinx=(tanx)/(sqrt(1-tan^(2)x))`
`implies sinx=0` or `cos^(2)x(1-tan^(2)x)x=1`
`impliessinx=0` or `cos2x=1`
`impliesx=npi`
24.

If `f(x)=((1-tanx)/(1+sinx))^(cosec x)` is to be made continuous at `x=0,` then `f(0)` must be equal toA. `e^(2)`B. `e`C. `(I)/(e)`D. `(I)/(e^(2))`

Answer» Correct Answer - D
If f (x) is continuous at x=0,`
then underset(xrarr0)lim f (x) -f(0)`
`impliesf (0) =underset(xrarr0)lim f (x) = e^(underset(srarr0)lim((-tanx-sin x)/((1-sin x).sin x)))`
`= e^(underset(xrarr0)(lim)).((1+cos x))/((1-sin x),cos x)=e^(-2)`
25.

If `(tan^(-1)x)^(3)+(tan^(-1)y)^(3)=1-3tan^(-1)x.tan^(-1)y`. Then which of the following may be trueA. `(x+y)/(tan1)=-2`B. `(tan^(-1)x)/(1-tan^(-1)y)=2`C. `(x+y)/(tan1)=2`D. `(x+y)/(cot1)=1`

Answer» Correct Answer - A
`a^(3)+b^(3)+c^(3)=3abc`
`impliesa+b+c=0` or `a=b=c`
`impliestan^(-1)x+tan^(-1)y=1` or `tan^(-1)x=tan^(-1)y=-1`
`impliesx=y=-tan1` or `(x+y)/(1-xy)=tan1`
`(x+y)/(tan1)=-2`
26.

If `a(p+q)^2+2b p q+c=0a b da(p+r)^2+2b p r+c=0(a!=0)`, then`q r=p^2`b. `q r=p^2+c/a`c. `q r=p^2`d. none of theseA. `qr = p^(2) + (c)/(a)`B. `qr = p^(2)`C. `(q + r)/(a + b) = -(2p)/(a)`D. `(q + r)/(a + b) = -(p)/(a)`

Answer» Correct Answer - A::C
`q` and `r` are the roots of the equation
`a(p + x)^(2) + 2bpx + c = 0`
`ax^(2) + 2(a + b)px + ap^(2) + c = 0`
`rArr` Product of roots is `qr = (ap^(2) + c)/(a) rArr qr = p^(2) + (c)/(a)`
Sum of roots is `q + r = -(2p(a + b))/(a)`
27.

Eccentricity of ellipse `2(x-y+1)^(2)+3(x+y+2)^(2)=5` isA. `1/(sqrt(2))`B. `1/(sqrt(3))`C. `1/2`D. `2/3`

Answer» Correct Answer - B
`1/2=1/2(1-e^(2))`
`e^(2)=1- 2/3`
`e=1/(sqrt(3))`
28.

If `lim_(nrarroo) (n*2^(n))/(n(3x-4)^(n)+n*2^(n+1)+2^(n))=1/2` where `n in NN` then the number of integers in the range of `x` isA. `0`B. `2`C. `3`D. `1`

Answer» Correct Answer - D
`lim_(nrarroo) 1/(((3x-4)/2)^(n)+2+1/n)=1/2`
`implies-1lt(3x-4)/2lt1implies-2lt3x-4lt2`
`2lt3xlt6=2/3ltxlt2`
Only one integer `x=1`
29.

If `lim_(nrarroo) (n.2^(n))/(n(3x-4)^(n)+n.2^(n+1)+2^(n))=1/2` where `"n" epsilonN` then the number of integers in the range of `x` isA. `0`B. `2`C. `3`D. `1`

Answer» Correct Answer - D
`lim_(nrarroo) 1/(((3x-4)/2)^(n)+2+1/n)=1/2`
`implies-1lt(3x-4)/2lt1implies-2lt3x-4lt2`
`2lt3xlt6=2/3ltxlt2`
Only one integer `x=1`
30.

Contrapostive of the statement "If two numbers are not equal, then their squares are not equal" isA. If the squares of two numbers are not equal, then the numbers are not equal.B. If the squares of two numbers are equal, then the numbers are equal.C. If the squares of two numbers are not equal, then the numbers are equal.D. If the squares of two numbers are equal, then the numbers are not equal.

Answer» Correct Answer - B
We know that, contrapositive of `p to q " is " ~q to ~p`
Therefore, the contrapositive of the given statement is "If the squares of two numbers are equal, then the numbers are equal".
31.

If `q` is false and `(p^^q)`harr r` is also true then which of the following are tautology (A) `(pvvr)-gt(p^^r)` (B) `(pvvr)` (C) `(p^^r)-gt(pvvr)` (D) `p^^r`A. `p vee r`B. `(p wedge r) to (p vee r)`C. `(p vee r) to (p wedge r)`D. `p wedge r`

Answer» Correct Answer - B
Given, `(p wedge q) harr r ` is true. This is possible under two cases
Case I When both `p wedge q and r` are true , which is not possible because q is false.
Case II When both `(p wedge q)` and r are false.
`rArr P -= T or F, q-= F, r-=F`
In this case,
(a) `p vee r ` is T or F
(b) `(p wedge r) to (p vee r) " is " F to (T or F)`, which always result in T.
(c) `(p vee r) to (p wedge r) " is "(T or F) to F,` which may be T or F.
(d) `p wedge r ` is F.
32.

Find the area bounded by the curves `y=6x-x^2a n dy=x^2-2xdot`A. 18B. 19C. 20D. 21

Answer» Correct Answer - A::B::C::D
`A=int_(0)^(4){(6x-x^(2))-(x^(2)-2x)}dx`
`A=int_(0)^(4)(8x-2x^(2))dx`
`A=[4x^(2)-(2)/(3)x^(3)]_(0)^(4)=64-(128)/(3)=(64)/(3)` sq. units
33.

The outcome of each of 30 items was observed , 10 items gave an outcome `(1)/(2)-d` each, 10 items gave outcome `(1)/(2)` each and the remaining 10 items gave outcome `(1)/(2) +d` each. If the variance of this outcome data is `(4)/(3)`, then |d| equalsA. `(2)/(3)`B. `(sqrt(5))/(2)`C. `sqrt(2)`D. 2

Answer» Correct Answer - C
`sigma^(2)=(Sigmax^(2))/(n)-mu^(2)`
`=(10((1)/(2)-d)^(2)+10xx(1)/(4)+10((1)/(2)+d)^(2))/(30)`
`-((10((1)/(2)-d)+10xx(1)/(2)+10((1)/(2)+d))/(30))^(2)" "[because mu=(Sigma x_(i))/(n)]`
`=(20((1)/(4)+d^(2))+5//2)/(30)-((1)/(4))`
`=((15)/(2)+20d^(2))/(30)-(1)/(4)=(1)/(4)+(2d^(2))/(3)-(1)/(4)=(2)/(3)d^(2)`
` therefore (2)/(3) d^(2)=(4)/(3) rArr d^(2)=2 rArr |d|=sqrt(2)`
34.

The mean of five observations is 5 and their variance is 9.20. If three of the given five observations are 1,3 and 8, then a ratio of other two observations isA. `4:9`B. `6:7`C. `10:3`D. `5:8`

Answer» Correct Answer - A
Let 1, 3, 8, x and y be the five observations.
Then, mean `bar(x)=(Sigma x_(i))/(n)`
`rArr bar(x) =(1+3+8+x+y)/(5)=5 " " `(given)
`rArr x+y=25-12=13`
`rArr x+y=13 " ...(i)" `
and variance `=sigma^(2)=(Sigma(x_(i)-bar(x))^(2))/(n)`
`=([(1-5)^(2)+(3-5)^(2)+(8-5)^(2)+(x-5)^(2)+(y-5)^(2)])/(5)=9.2` (given)
`rArr 16+4+9+(x^(2)-10x+25)+(y^(2)-10y+25)=46`
`rArr x^(2)+y^(2)-10(x+y)=46-79`
`rArr x^(2)+y^(2)-10xx13= -33 " "[ because x+y=13]`
`rArr x^(2)+y^(2)=97 " ...(ii) " `
Let `(y)/(x)=t`
`rArr y=xt`
Putting y = xt in Eq. (i), we get
`x(1+t)=13`
`rArr x^(2)(1+t)^(2)=169 " ...(iii)" `
Putting y = xt in Eq. (ii), we get
`x^(2)(1+t^(2))=97 " ...(iv)" `
Dividing Eq. (iii) by Eq. (iv), we get
`(x^(2)(1+t)^(2))/(x^(2)(1+t^(2)))=(169)/(97)`
`rArr97(t^(2)+2t+1)=169(1+t^(2))`
`rArr (169-97)t^(2)-194t+(169-97)=0`
`rArr 36t^(2)-97t+36=0`
`rArr (4t-9)(9t-4)=0`
`rArr t=(9)/(4)`
`or t=(4)/(9)`
35.

(i) Which of the following is not possible. (a) sin x = \(\frac{1}{2}\)(b) cos x = \(\frac{2}{3}\)(c) cosec x = \(\frac{1}{3}\)(d) tan x = 8(ii) Find the value of sin 15°.(iii) Hence write the value of cos 75°

Answer»

(i) (c) cosec x = \(\frac{1}{3}\)

(ii) sin 15° = sin(45° – 30°)

= sin45°cos30°- cos45°sin30°

\(\frac{1}{\sqrt 2} \times \frac{\sqrt 3}{2} - \frac{1}{2} \times \frac{1}{2} \) = \(\frac{\sqrt 3 - 1}{2 \sqrt 2}\)

(iii) sin 15° = sin(90° – 75°) = cos 75°

36.

If A = 15°, verify that 4 sin 2a. Cos 4a sin 6a = 1

Answer» If A = 15°
then
L.H.S = 4 sin2a. Cos4a sin6a
= 4 sin(2x15°). Cos(4x15°). sin(6x15°)
= 4 sin30°. Cos60°. sin 90°
= 4 X 1/2 X 1/2 x 1
= 1 = R.H.S
37.

The angles of elevation of the top of a tower the base and the top of a building are 60° and 30°. 3x + 5y ≤ 15, 5x + 2y ≤ 10 and x ≥ 0, y ≥ 0.

Answer»

Let AB = Building & CD is the tower. 

From the rt angled ∆ ACD 

We have tan 60 = \(\frac{h}{x}\)

√3 = \(\frac{h}{x}\) ⇒ x = √3(h -20) 

From 1 and 2 wet √3(h – 20) = \(\frac{h}{\sqrt 3}\) 

⇒ 3(h – 20) = h 

⇒ 3h – 60 = h 

⇒ 3h – 60 = h 

⇒ 2h = 60 

⇒ h = 30 mts 

∴ Height of the tower = 30 mts

38.

Find n if nC8 = nC7

Answer»

nC8 = nC7nC8 = nC7 ⇒ 8 = n – 7 ⇒ n = 15

39.

Solve : `1/(a+b+x)=1/a+1/b+1/x[ x ne 0, -(a+b)]`

Answer» `x=-a, x = -b`
40.

The external diameter of a gold - sphere is 12 cm and it is made of a gold - plate of thichness 1 cm. If the weight of 1 cc gold be `19*5` gm and the price of 1 gm gold is ₹ 1280, then find the total price of the gold - sphere.

Answer» Correct Answer - ₹ 9518080
41.

The price of a diamond is ₹ 2000. The diamond is broken into two pieses of equal weights. If the price of a diamond varies as the square of its weight, then find the amount of loss for the breakage.

Answer» Correct Answer - ₹ 1000
42.

If `x=3+2sqrt2`, then find the value of `(sqrtx -""1/sqrtx)`

Answer» `pi/12 "and "15^@`
43.

Which quantities will remain the same if a dielectric slab is inserted between the plates of an isolated charged capacitor?A.  The PD between the platesB.  Electric field in the capacitorC.  The charge on the capacitorD.  Energy stored in the capacitor

Answer»

D.  Energy stored in the capacitor

44.

Assertion: A dielectric slabis inserted between plates of an isolated charged capacitor which remain same. Reason Charge on an isolated system is conserved.

Answer» Correct Answer - A
Charge of plates remains same as there is no transfer of charge.
45.

Two geometrically identical homogeneous balls are manufactured of different materials. Their densities ball-`1` and ball-`2` are `800 kg//m^(3)` and `200 kg//m^(3)` respectively. Both balls are dropped from very high tower. Assume that the air resistance is proportional to the square of velocity. Determine the ratio of the maximum velocities of the ball -`1` to ball-`2`.A. `2`B. `3`C. `4`D. `6`

Answer» The ball will achieve its velocity when its acceleration is zero. So,
`m_(1)g=bv_(1_(max))^(2)`
`m_(2)g=bv_(2_(max))^(2)`
`((v_(1_(max)))/(v_(2_(max))))^(2)=(m_(1))/(m_(2))=(rho_(1))/(rho_(2))=4rArr(v_(1_(max)))/(v_(2_(max)))=2`
46.

Consider the binary operation * on Q defined by m * n = 1 + 12n + mn ∀ m, n ∈ Q, then 2 * 3 equals(A) 31 (B) 6 (C) 43 (D) None of these

Answer»

Correct option:

(C) 43 

47.

A ring of diameter 1m is rotating with an angular momentum of 10 Joule-sec. The necessary tangential force required to increase its angular momentum by 50 % in 1 sec will be (in newtons)A. 10B. 5C. 15D. 20

Answer» Correct Answer - A
`tau = (dL)/(dt) rArr F. r = (dL)/(dt) rArr F = 10`
48.

For which value of p,(2, 2) is a solution of the equation 3x + 4y – 2p = 0 ?(A) 3 (B) 5 (C) 7 (D) 9

Answer»

The correct option is (C)7

Explanation.

Given equation 3x + 4y – 2P = 0 

If (2 , 2) is a solution of this equation then it staisfy this equation. 

3(2) + 4 (2) – 2P = 0 

2P = 14 

P = 7

49.

∫(sec2x tan x)/(sec2x + tan2 x) dx is equal to(A) log (sec2x + tan2x) (B) log (sec2 – tan2x) + c(C) 1/4 log(sec2x + tan2x) + c(D) 1/4 log(sec2x - tan2x) + c

Answer»

(C) 1/4 log(sec2x + tan2x) + c

50.

Learn Arithmetic Progression Formula Maths Class 10 for better understanding.

Answer»

Arithmetic Progression Formula

Arithmetic progression is defined as the series of numbers having the difference between two consecutive term is constant every time. (A.P) is also known as Arithmetic Sequence. It’s series is obtained by adding or subtracting the finite number to its successive term. A.P generally deals as a part of mathematics which involves series in defining the position of the given number, addition or subtraction of numbers in series and much more. Formula are listed here.

Let us take an example

2, 4, 6, 8, 10.......... is a series of number which is in A.P.

We can say that this series is in A.P because the difference in each consecutive term is fixed i.e. 2. If 2 is being added to each successive term gives the next term.

Every series in A.P is in Infinite series so is said Infinite A.P and the finite part of Infinite A.P series is called Finite Arithmetic Progression.

The Sum of Finite A.P is known to be Arithmetic Series.

Terms Related to A.P:

  1. a – First term in A.P
  2. d – Common difference
  3. n – Number of Terms in A.P
  4. an – nth term of A.P
  5. Sn – Sum of n terms of A.P

Formula for nth Term of A.P:

an = a + (n – 1)d

For Example:

  1. If 2, 4, 6, 8, .... are in A.P then find its 20th term from left.

Solution:

Given,

a = 2, d = (4 – 2) = 2, n = 20

an = a + (n – 1)d

an = 2 + (20 – 1)x 2 = 40

Thus, 40 is the 20th term of given A.P.

Formula for Sum of n Terms of an A.P:

Sn = \(\frac{n}{2}\){2a + (n-1)d}

Also,

 Sn = \(\frac{n}{2}\)(first term + last term)

For Example:

  1. If 4, 8, 12, 16, ...... are in A.P then Find the sum of its first 20 terms.

Solution:

Given,

a = 4, d = 4, n = 20

Sn = \(\frac{n}{2}\){2a + (n-1)d}

Sn = \(\frac{20}{2}\){2x4 + (20 - 1)x4}

Thus, Sn = 840

  1. If 8, 10, 12, 14, ....... , 42 are the terms of an A.P than Find the sum of terms.

Solution:

a = 8, d = 2, n = ?

an = 42

First let’s find n

an = a + (n – 1)d

42 = 8 + (n – 10)x2

n = 27

Now, Sn = \(\frac{n}{2}\)(first term + last term)

Sn = \(\frac{27}{2}\)(8 + 42)

Sn = 675