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2251.

Both x and y vary directly with each other and when x = 20, y = 28. Which of the following is not a possible pair of corresponding values?1. 25 ∶ 35 2. 35 ∶ 253. 35 ∶ 494. 15 ∶ 21

Answer» Correct Answer - Option 2 : 35 ∶ 25

Given:

Both x and y vary directly with each other and when x = 20, y = 28.

Concept Used:

Concept of ratio and proportion

Calculation:

Both x and y vary directly with each other and when x = 20, y = 28

That means x and y are directly proportional

The ratio of x and y is x : y = 20 : 28

⇒ x : y = 5 : 7

Now from the given options get,

25 : 35 ⇒ 5 : 7

35 : 25 ⇒ 7 : 5

35 : 49 ⇒ 5 : 7

15 : 21 ⇒ 5 : 7

Except the 2nd option all are in similar form that means our required answer is the 2nd option i.e. 35 : 25

∴ 35 : 25 is not a possible pair of corresponding values.

2252.

Computers normally solve problem by breaking them down into a series of yes-or-no decisions represented by 1s and 0s. What is the name of the logic that allows computers to assign numerical values that fail somewhere between 0 and 1?(a) Human logic(b) Fuzzy logic(c) Boolean logic(d) Operational logic

Answer» The correct choice is (b) Fuzzy logic

Easy explanation: None.
2253.

Which cannot be represented by a set of attributes?(a) Program(b) Three-dimensional configuration of a protein molecule(c) Agents(d) None of the mentioned

Answer» Correct choice is (b) Three-dimensional configuration of a protein molecule

Best explanation: Because the configuration inherently refers to relationships between objects.
2254.

End Nodes are represented by __________(a) Disks(b) Squares(c) Circles(d) Triangles

Answer» The correct option is (d) Triangles

To explain I would say: None.
2255.

What can be represented by using histograms or empirical frequency distributions?(a) Words(b) Color(c) Texture(d) Both Color & Texture

Answer» The correct answer is (d) Both Color & Texture

To explain I would say: Color and texture can be represented by using histograms or empirical frequency distributions.
2256.

In a cumulative frequency polygon, the cumulative frequency of each class is plotted against: (a) Mid-point (b) Lower class boundary (c) Upper class boundary (d) Upper class limit

Answer»

(c) Upper class boundary 

2257.

Cumulative frequency polygon can be used for the calculation of: (a) Mean (b) Median (c) Mode (d) Geometric mean

Answer»

Correct option is (b) Median

2258.

In a continuous frequency distribution, the median of the data is 21. If each observation is increased by 5. then find the new median will be?

Answer»

Median = 21

Median is middle data(observation)

So, if each observation is increased by 5

new median = 21 + 5 = 26

2259.

If A = { 10,20,30,40,50,60,70} , B = { 50,60,70,80} and C = { 30,40,90} Verify that ((A∪ ) ∩ )) = (A∩ ) ∪ ( ∩ )

Answer»

Given A = {10, 20, 30, 40, 50, 60, 70}

B = {50, 60, 70, 80}

C = {30, 40, 90}

∴ A ∪ B  = {10, 20, 30, 40, 50, 60, 70, 80}

A ∩ C = {30, 40}

and B ∩ C = ϕ

Now, (A ∪ B) ∩ C = {30, 40}.

And (A ∩ C) ∪ (B ∩ C) = {30, 40} ∪ ϕ = {30, 40}

Therefore, (A ∩ B) ∪ C = (A ∩ C) ∪ (B ∩ C).

2260.

Tom’s father was a CRUEL man. A) honest B) kind C) funny D) serious E) light

Answer»

Correct option is B) kind

2261.

A teacher collects and reads the work of the class, then plans and adjusts the next lesson to meet student needs. He/She is doing1. Assessment of learning2. Assessment as learning3. Assessment for learning4. Assessment at learning

Answer» Correct Answer - Option 3 : Assessment for learning

Assessment is educational evaluation, the systematic way of collecting information and reading the work of class which is used to guide and improve student's performance in terms of learning and development. There are several methods that teachers use to evaluate the learning progress and skills of students or the need for any academic assistance. It actually determines whether or not the goals of education are met.

Summative Assessment (Assessment of Learning):

  • It is also known as Assessment OF Learning is to evaluate student learning by comparing it against some standard or level.
  • The main objective is to rank, grade, classify and compare students periodically that indicate their level of performance.
  • It is considered a Formal method of Assessment as it is conducted at a specific time.
  • Example: Mid-term Exams, unit tests, final projects, semester exams, etc.

Formative Assessment (Assessment for Learning) :

  • It is also known as Assessment for Learning, used to evaluate student learning progress and achievement.
  • The goal is to collect detailed information like strengths, weaknesses, knowledge, skills, etc., and then plan the next lesson in a way to improve the performance of the students.
  • It helps teachers to identify problem-facing areas, to understand and learning needs for achieving academic growth. 
  • It is considered an Informal Method of assessment as it can be conducted at any time or during teaching also.
  • Example: Discussions, Class tests, homework, assignments, debate, plays, etc.

Assessment as Learning

  • When learners are asked to assess their performance on their own, they use various assessment techniques and strategies to assess themselves.
  • This practice helps learners to identify their knowledge gaps, adopt appropriate learning strategy and use assessment as a tool for new learning.
  • It encourages students to take responsibility for their own learning.
  • It requires students to ask questions about their learning.
  • It involves teachers and students creating learning goals to encourage growth and development.
  • It provides ways for students to use formal and informal feedback and self-assessment to help them understand the next steps in learning.
  • It encourages peer assessment, self-assessment, and reflection

So, If a teacher collects and reads the work of the class, then plans and adjusts the next lesson to meet student needs. He/She is doing Assessment for Learning (Formative Assessment).

2262.

I’m afraid the lift is out of ______ so well have to walk up the stairs. A) function B) movement C) order D) practice E) running

Answer»

Correct option is C) order

2263.

I knew that she ___ Miss Betsy, because I remembered how my mother ___ her. A) was / had described B) is / described C) would be / had described D) had been / described E) has been / describes

Answer»

Correct option is A) was / had described

2264.

If you know one FOREIGN language it will be easier for you to learn the second one. A) local B) modern C) popular D) old E) native

Answer»

Correct option is E) native

2265.

he was afraid to walk FARTHER as she knew her life was in danger. A) mother B) out near C) near D) nearer E) away

Answer»

Correct option is D) nearer

2266.

Which student is near the teacher? Malcolm is ________ . A) much near B) very nearer C) the nearest D) the next

Answer»

Correct option is C) the nearest

2267.

What value will come in place of question mark in the following equation? (i) 0.006 +? = 0.6 (ii) ? + 0.025 = 80

Answer»

(i) Let 0.006 / x = 0.6, Then, x = (0.006 / 0.6) = (0.006*10) / (0.6*10) = 0.06/6 = 0.01 

(ii) Let x / 0.025 = 80, Then, x = 80 * 0.025 = 2

2268.

Find the equation of the straight lien of inclination 135° with x–axis and an intercept – 3 on the y–axis.

Answer»

Inclination is 135° => Slope = tan 135° = –1

Equation of the line having slope –1 and y-intercept –3 is y = (–1)(x – 3)

=> x + y + 3 = 0.

2269.

Find the area of the triangle formed by the coordinate axes and the line 2x – 4y – 7 = 0.

Answer»

Area of the triangle formed =(-7)2/2|2(-4)|=49/16 sq.unit

2270.

The equation of common tangent of the curve `x^(2) + 4y^(2) = 8` and `y^(2) =4x` areA. x-2y + 4 = 0 , x + 2y + 4 = 0B. 2x-y + 4 = 0 , 2x + y + 4 = 0C. 2x-y +2 = 0 , 2x + y + 2 = 0D. None of these

Answer» Correct Answer - A
Ellipse `(x^(2))/(8) + (y^(2))/(2) = 1 `
Equation of tangent y = mx `pm sqrt(8m^(2) +2) ……(1)`
and parabola `y^(2) = 4x`
Equation fo tangent `implies y = mx +(1)/(m) " " …..(2)`
for common tangent
`pm sqrt(8m^(2) + 2) = (1)/(m)`
`implies 8m^(2) + 2 = (1)/(m^(2))`
`implies 8m^(4) + 2m^(2) - 1 = 0`
`implies (4m^(2) - 1) (2m^(2) + 1) = 0 implies m = pm(1)/(2)`
`therefore Eq^(n)` of common tangent
`y = pm (1)/(2) x pm 2 `
`implies x - 2y + 4 = 0` and x + 2y + 4 = 0
2271.

What value will replace the question mark in the following equations ? (i) 5172.49 + 378.352 + ? = 9318.678(ii) ? – 7328.96 + 5169.38

Answer»

(i) Let 5172.49 + 378.352 + x = 9318.678 

Then , x = 9318.678 – (5172.49 + 378.352) = 9318.678 – 5550.842 = 3767.836 

(ii) Let x – 7328.96 = 5169.38. 

Then, x = 5169.38 + 7328.96 = 12498.34.

2272.

Find the products: (i) 6.3204 * 100 (ii) 0.069 * 10000

Answer»

(i) 6.3204 * 1000 = 632.04 

(ii) 0.069 * 10000 = 0.0690 * 10000 = 690

2273.

Solve the problem:\(3 \frac{4}{5} + 2 \frac{3}{10} + 1 \frac{1}{15}\)

Answer»

First convert each mixed fraction into improper fraction.

We get,

\(\Rightarrow 3 \frac{4}{5} = \frac{19}{5}\)

\(\Rightarrow 2 \frac{3}{10} = \frac{23}{10}\)

\(\Rightarrow 1 \frac{1}{15} = \frac{16}{15}\)

Then,

\(\frac{19}{5} + \frac{23}{10} + \frac{16}{15}\)

LCM of 5,10,15 = 30

Now,let us change each of the given fraction into an equivalent fraction having 30 as the denominator

\(\Rightarrow \frac{19}{5} \times \frac{6}{6} = \frac{114}{30}\)

\(\Rightarrow \frac{23}{10} \times \frac{3}{3} = \frac{69}{30}\)

\(\Rightarrow \frac{16}{15} \times \frac{2}{2} = \frac{32}{30}\)

Now,

\(= \frac{114}{30} + \frac{69}{30} + \frac{32}{30}\)
\(= \frac{114+69+32}{30}\)
\(=\frac{215}{30}\)
\(= 7 \frac{1}{5}\)
2274.

Observations of data are x/5,x,x/4,x/2,and X/3then X>0 if median of data is 8 then find x

Answer» 24 is the answear
2275.

You are Sunil Kumar Sharma. Write a letter to the editor of the Indian Express about democracy with special reference to India.

Answer»

68 Basant Vihar Jaipur
9 March 2020
The Editor
Indian Express
New Delhi

Sub: Democracy

Sir,

Through the columns of your esteemed newspaper, I would like to highlight ‘Democracy’. Democracy has been accepted to be the best governing system in international thinkers on global level. It is a government of the people, for the people and by the people. People can make the government of their own choice.

India is the biggest democracy in the world. The election system of India has been praised by most of the countries. People are directly or indirectly involved in every election to form a government. There is no place for autocracy in democracy.

Thus, democracy is the best way to be governed for mankind. All countries should seek possibility for it.

Thanking you

Yours truly

Sunil Kumar Sharma

2276.

Write a letter to the Principal of your college requesting him/her to issue Transfer Certificate, the reason being the transfer of your father.

Answer»

Shankar C.S.

Veerashaiva PU.

College Bailan

19 January 2019

The Principal

Veerashaiva P.U. College

Sallan

Dear Sir

Sub: Issue of TC

I am a student of the I year RU.C. ‘C’ section and I write to you with a request for a Transfer Certificate. My father has been transferred to Hassan and we will be relocating to Hassan. The TC could be sent to the following address: Narayana College, Central Market Road. Hassan. I was fortunate to be a student of Veerashaiva P.U. College for a year I carry happy memories of the college.

Thank you.

Yours faithfully,

Shankar C.S.

2277.

Suppose you are Sumana/Sunil living at Civil Lines, Agra. Write a letter to your friend describing about your new school. You may use the following points :(i) The building, classroom etc.(ii) The Principal, the staff, the students.(iii) Other facilities of computer, games etc.

Answer»

21 Civil Lines
Agra
2 July 2020

My dear Seema/Suresh,

I am well and good here and I hope you to be the same there.

Now I have taken admission to Maharani/Maharaja school in Jaipur. The following features make it one of the best schools of the City.

The school building is of double storey. It is in E-shape. The classrooms are spacious, airy, well-ventilated, well furnished, airconditioned and computerized.

The Principal is the prominent educationist. She/He is a friend, philosopher and guide to every student. The staff is highly professional. Teachers here use modem technology in teaching. The students of this school are well-behaved. They focus their attention on all round development. ,

It has other facilities of computer, games, debates, cultural programmes etc. Thus, it’s an outstanding school.
Please convey my best regards to your parents.

With deep love.

Warmly yours
Sumana/Sunil

2278.

To the Principal of your school, requesting him/her to provide you with a bonafide certificate, enabling you to join a computer course.

Answer»

Ms. ABC 

IX Std. 

XYZ School 

Bengaluru 

14 July 2019

The Principal 

XYZ School 

Bengaluru

Respected Sir, 

Subject: Bonafide Certificate 

I am a student of IX Standard and I write this letter to make a request to you. I want to join a computer course at Cryonics Computers. One of the criteria of admission is that I submit a bonafide certificate from my school. I request you to issue me one.

I thank you sincerely. 

Yours faithfully 

ABC

2279.

Write a letter to your friend describing the annual day celebrations in your school.

Answer»

23, B. H. Road 

Chikkamagaluru 

18 October 2019

Dear Krithi, 

How have you been? Sorry for not writing earlier. I was busy with my Annual Day celebrations.

We take a lot of trouble over our Annual Day celebrations. This time too we had a grand celebration. Can you guess who our chief guest was? You will probably be amused to know that we had comedian Kapil Sharma as our chief guest. He regaled the audience with his witty remarks. The speech had a good message too for the students. The entertainment programme was too good. We had a dance drama on the theme of light as this year is the International Year of Light.

I’m glad to inform you that I received five prizes, three in academics and two in extra-curricular. They gave us cash prizes and I’m richer by Rs. 1000!

What news from your side? When is your Annual Day? Will you be doing anything special? Do write to me about all the details. Bye for now.

Yours, 

Anitha

2280.

Write a letter to your friend inviting her to attend your birthday party.

Answer»

27, 4th cross 

Basaveshwara Extension

Belagavi 

7 June 2019

Dear Kavitha, 

It’s such a long time since we have corresponded with each other. I suppose both of us were caught up in our world of assignments and tests. I think we must take some time off to catch up with each other.

On the 18th of this month, I’ll be celebrating my birthday at Ocean Pearl with a few of my friends and relatives. As it’s my 15th birthday, my parents want to make it very special for me.

As you are a special friend, I invite you to be with us. The party starts at 6 p.m. and will end at 9 p.m. with dinner. I promise you that it will be fun. My sister has kept a number of party games ready. You can be a lucky winner too. I’ll be very happy if you can make it with your family. Please inform Mom and Dad that I’ll be disappointed if they don’t make it.

One last word – please don’t get any gifts. Your presence will be my biggest present.

Hope you won’t disappoint me. I’ll be grateful if you could drop a line confirming your presence by the 16th.

Love and best wishes.

Yours, 

Suma

2281.

Write a letter to your friend inviting her to attend your birthday party

Answer»

27, 4th cross 

Basaveshwara Extension 

Belagavi 

7 April 2020

Dear Kavitha, 

It’s such a long time since we have corresponded with each other. I suppose both of us were caught up in our world of assignments and tests. I think we must take some time off to catch up with each other.

On the 18th of this month, I’ll be celebrating my birthday at Ocean Pearl with a few of my friends and relatives. As it’s my 15th birthday, my parents want to make it very special for me.

As you are a special friend, I invite you to be with us. The party starts at 6 p.m. and will end at 9 p.m. with dinner. I promise you that it will be fun. My sister has kept a number of party games ready. You can be a lucky winner too. I’ll be very happy if you can make it with your family. Please inform Mom and Dad that I’ll be disappointed if they don’t make it.

One last word – please don’t get any gifts. Your presence will be my biggest present.

Hope you won’t disappoint me. I’ll be grateful if you could drop a line confirming your presence by the 16th.

Love and best wishes.

Yours, 

Suma

2282.

Sometimes a lot of guests ___ to his birthday party. A) had invited B) was invited C) were inviting D) are invited E) is inviting

Answer»

Correct option is D) are invited

2283.

(Radha’s sister has met with an accident In Hubit. Radha was on a tour and Is in Davanagere. She is on her way to the bus station to go to Hub (She enquras the way to the bus station with a stranger.) Radha: ......... Could you please tell me the way to the bus station?Stronger: You .......... and turn left.Radha: Is there a bus to Hubli now. My sister has met with an accident. I need to reach there urgently.Stronger: Oh! ........... A bus leaves for Hubil in 10 minutes. bu better hurry up.Radha: .............  bye.

Answer»
  • Radha: Excuse me. Could you please tell me the way to the bus station?
  • Stranger: Go straight and turn left.
  • Radha: Is there a bus to Hubli now? My sister has met with an accident. I need to reach there urgently.
  • Stranger: Oh! That’s an emergency then. A bus leaves for Hubli in 10 minutes. You better hurry up. 
  • Radha: Thank you very much for the information. You have been kind, bye.
2284.

Leela is Radha’s younger sister. Leela is 4 years younger than Radha. Write Leela’s age with respect to Radha’s age. Take Radha’s age to be x years.

Answer»

Let Radha’s age be x years
Leele’s age = Radha’s age −4
=(x−4) years.

2285.

What do you do differently from other people

Answer»
  • I believe in being open minded i.e words learn something new everyday. Knowledge is power.
  • Have a positive atittude.
  • Influence people positively because that is Leadership.
  • Be creative, analyze situations, turn issues & risks into opportunities, and ownership
  • Lead by example.
  • Learn from your mistakes and others.
2286.

The Complement Of Supplement of 160° is x+50° then x is =

Answer»

Supplement of 160º is 20º (160º + 20º = 180º , the sums is 180º then it is supplement)

Complement of supplement of 160º

= Complement of 20º

= 70º ( 20º + 70º = 90º , angle sum is 90º then it is complement)

x + 50º = 70º

x = 20º

2287.

One ticket is drawn at random from a bag containing 20 tickets numbered 1 to 20. Find the probability that it is a multiple of 2 or 5,

Answer»

Since the bag has 20 tickets, total number of cases n = 20 

Let A: getting a multiple of 2 

B: getting a multiple of 5 

Event A has 10 favourable outcomes 

A = {2, 4, 6, 8, 10, 12, 14, 16, 18, 20} 

∴ P(A) = \(\frac{10}{20} =\frac{1}{2}\)

Event B has four favourable outcomes 

B = {5, 10, 15, 20) 

∴ P(B) = \(\frac{4}{20}\)

A ∩ B = {10,20] 

∴ P(A ∩ B) = \(\frac{2}{20}\)

∴ P(multiple of 2 or 5 ) = P(A ∪ B) =P(A) + P(B) – P(A ∩ B)

\(\frac{10}{20} + \frac{4}{20} - \frac{2}{20} = \frac{12}{20} = \frac{3}{5}\)

2288.

A ball is thrown vertically up with a certain velocity. It attains a height of `40 m` and comes back to the thrower. Then the : `(g = 10 m//s^(2))`.A. total distance covered by it is `40 m`B. total displacement covered by it is `80 cm`C. total displacement is zeroD. the average velocity for round trip is non zero.

Answer» Correct Answer - C
Displacement `=0` (initial position = final position)
average velocity `=0` (Total displacement `=0`).
2289.

The tires of aircraft are not made of ordinary rubber ( which is an insulater ) but of sphecial rubber is slightly conducting. Why ?

Answer»

Ordinary rubber is an insulator. But the special rubber tyres of aircrafts are made slightly conducting. This is because during landing or takeoff, the tyres of aircrafts get charged due to friction between tyres and fround. In case, the tyres are slightly conducting, the charges developed on the tyres will not stay on them and find its way to earth.

2290.

A bullet of mass 0.02 kg strikes a metal plate of thickness 10 cm with a velocity of 400 m/s and emerge from it with a velocity of 250 m/s. Find the average resistance force offered by the plate to the motion of bullet.

Answer»

We know that,

v2 = u2 + 2as

a = \(\cfrac{v^2-u^2}{2s}\)

a = \(\cfrac{(250)^2-(400)^2}{2\times0.1}\)

a = \(\cfrac{62500-160000}{2\times0.1}\)

a = \(\cfrac{-97500}{0.2}\)

a = -487500 m/s2

F = ma 

F = 0.02 x - 487500

F = -9750 N

2291.

What is rigid body

Answer»

A rigid body is an idealization of a body that does not deform or change shape. Formally it is defined as a collection of particles with the property that the distance between particles remains unchanged during the course of motions of the body.

2292.

The diagram shows the arrangement of three small uniformally charged spheres, `A,B` and `C`. The arrow indicate the direction of the electrostatic forces acting between the spheres (for example, the left arrow on sphere `A` indicates the electronstatic force on sphere `A` due to sphere `B`). At least two of the spheres are positively charged. Which sphere, if any, could be negatively charged? A. sphere AB. sphere BC. sphere CD. no sphere

Answer» Correct Answer - A
It can be seen from the diagram that only the sphere B and C repel. Hence they both must e of same type. According to the fact that at least two spheres are positively charged, therefore both spheres should be positively charged. Since attraction occurs for two remaining pairs it can be concluded that the sphere A is negatively charged.
2293.

The electrostatic field due to a point charge depends on the distance r as `1/r^2`. Indicate which of the following quantities shows same dependence on r.A. intensity of light from a point sourceB. electrostatic potential due to a point chargeC. electrostatic potential at a distance r from the center of a charged metallic sphere, given rltradius of the sphereD. none of these

Answer» Correct Answer - A
a. `I prop 1/(r^2), V prop 1/r, V prop r^0` for metallic sphere, at inside, at inside point.
2294.

Arrange the following groups in order of increasing `+I` effect: `CH_(3)^(-)," "(CH_(3))_(2)CH^(-)," "(CH_(3))_(3)C^(-)`

Answer» Atoms or groups which release electrons towards a carbon atom are said to have a `+I` effect. Methyl group releases electrons towards carbon, i.e., it has `+I` effect. `+I` effect increases as the number of methyl groups increases. Thus, the order is
`underset("(lowest)")(CH_(3)^(-))lt(CH_(3))_(2)CH^(-)lt underset("(highest)")((CH_(3))_(3)C^(-))`
2295.

Choose correct option for EMW(A) Electric & magnetic field are perpendicular to propagation of wave(B) Electric & magnetic field are parallel to propagation of wave(C) Energy is equally divided in electric and magnetic field(D) Energy divided in electric and magnitude field is different(1) A & B(2) A & C(3) B & C(4) C & D

Answer»

Correct option is (2) A & C

2296.

Activity of a ratio active sample is 64 x 10-4 dps and half life is 5 days. After how many days its activity becomes 5 x 10-5 dps.(1) 30 days(2) 25 days(3) 35 days(4) 40 days

Answer»

Correct option is (3) 35 days

\(A = \frac{A_0}{2^n}\)

\(2^n = \frac{A_0}A =\frac{64\times10^{-4}}{5 \times 10^{-5}} = 128 = 2^7\)

n = 7

7 half lifes

7 x 5 = 35 days

2297.

The laws of vibration of a string can be verified using a sonometer. If only one string is available on the sonometer, along with tuning forks of several different frequencies, which of the following laws can be verified? (a) Law of length only (b) Law of tension only (c) Law of length and law of tension (d) Law of length, law of tension and law of mass

Answer»

Correct Answer is: (c) Law of length and law of tension

Verification of the law of mass requires several strings with different masses per unit length.

2298.

The half life for radioactive decay of `.^(14)C` is 5730 years. An archaeological artifact containing wood had only `80%` of the `.^(14)C` found in a living tree. Estimat the age of the sample.

Answer» Correct Answer - 1845 years
`(N)/(N_(0))=80% or 0.80`
`t_(1//2)=5730 years`
`k=(0.693)/(t_(1//2))=(0.693)/(5730years)=1.21xx10^(-4)year^(-1)`
`k=(2.303)/(t)log``(N_(0))/(N)`
`1.21xx10^(-4)=(2.303)/(t)log``(1)/(0.8)`
`T=(2.303)/(1.21XX10^(4))log1.25`
`=(2.303)/(1.21xx10^(-4))log1.25`
`=(2.303)/(1.21xx10^(-4))xx0.0969=1845years`
Alternatively
Use direct relation,
`(t_(80%))/(t_(1//2))=(log(100)/(80))/(0.3)`
`t_(80%)=(5730years xx log0.8)/(0.3)~~1845years.`
2299.

The fossil bone has a `.^(14)C` : `.^(12)C` ratio, which is `[(1)/(16)]` of that in a living animal bone. If the half -life of `.^(14)C` is `5730` years, then the age of the fossil bone is :A. `11460` yearsB. `17190 `yearsC. `22920` yearsD. `45840` years

Answer» Correct Answer - c
After `n` half-lives (i.e., at `t=nT`) the number of nuclides left undecayed
`N=N_(0)((1)/(2))^(n)`
Given, `(N)/(N_(0))=(1)/(16)implies(1)/(16)=((1)/(2))^(n)`
or `((1)/(2))^(4)=((1)/(2))^(n)`
Equating the powers, we obtain
`n=4` i.e., `(t)/(T)=4`
or `t= 4T`
or `t=4xx5730= 22920 years`
`( because T= 5730 years)`
2300.

If specific ehat capacity of a substance in solid and liquid state is proportional to temperature of the substance, then if heat is supplied to the solid intially at `-20^(@)C` (having melting `0^(@)C`) at contant rate. Then the temperature dependence of solid with time will be best represented by:A. B. C. D.

Answer» As `dQ=msdT`
`(dQ)/(dt)=ms(dT)/(dt)`
From question `SpropT`
or `S=K_(1)T.(K_(1)` being propertionality constant)
Also, `(dtheta)/(dt)="constant"=K_(2)("say")impliesms(dT)/(dt)=K_(2)impliesm(K_(1)T)(dT)/(dt)=K_(2)`
`implies(m(K_(1))/(K_(2)))(T^(2))/(2)=timpliesT-propsqrt(t)`