Half-life of a radioisotope is 4 × 108 years. If there are 103 radioactive nuclei in a sample today, the number of such nuclei in the sample 4 × 109 years ago were

Half-life of a radioisotope is 4 × 108 years. If there are 103 radioactive nuclei in a sample today, the number of such nuclei in the sample 4 × 109 years ago were

Which of the following statements are true?
1. All radioactive elements decay exponentially with time.
2. Half-life time of radioactive elements is the time required for one-half of the radioactive atoms to disintegrate.
3. Age of the earth can be determined by radioactive dating.
4. Half-life time of a radioactive element is fifty percent of its average life period.
Select the correct answer:

A

1 and 3

B

1, 3 and 4

C

1, 2 and 3

D

2 and 3

Which of the following statements about ‘fission’ is correct ? 1. It is related with the creation of new individuals by means of cell division in unicellular organism. 2. It is related with the transformation of heavier nuclei into smaller nuclei. 3. It is related with the creation of a heavier nuclei by means of combining two higher nuclei. Select the correct answer using the code given below :

A

1 only

B

3 only

C

1 and 2 only

D

1 and 3 only

Nuclear wastes is waste that contains radioactive material. Radioactive material is normally a by product of nuclear power generation. Radioactive waste is regulated by government agencies in order to protect human health and the environment. Radioactivity naturally decays over time, so radioactive waste has to be isolated and confined in appropriate disposal facilities for a sufficient period until it no longer poses a threat. Which of the following statements can be inferred from the paragraph?

A

Radioactive material is very expensive.

B

Since radioactive material decays over time, it is not hazardous.

C

Radioactive material is extremely hazardous to humans.

D

Disposal of radioactive material, is extremely difficult.

The critical reasoning question is based on a short argument, a set of statements, or a plan of action. For each question, select the best answer of the choices given. Radioactive pollution is highly dangerous and has become a very important topic to be concerned about in today's scenario. Radioactive pollution is caused when radioactive byproducts of a nuclear reaction is dumped in the environment. This is contaminating the eco-system causing air, water and soil pollution. It can lead to cancer in humans when it comes in contact with the body. Given below are few options, select which isn't one of the effects of this on the humans.

A

Low levels of exposure can cause mild skin irritation.

B

If human body comes in contact with these it causes nausea, vomiting, diarrhea.

C

When radioactive waste is introduced in water bodies it affects the entire aquatic food web.

D

Radioactive rays can cause damage to DNA molecules.

E

If parents are exposed to such radiations, their child could have severe birth defects.

Jack’s age 7 years ago is equal to Ricky’s present age. The sum of Jack’s age 10 years from now and Ricky’s age 5 years ago is 94 years. What was Jill’s age 12 years ago if Jill is 6 years younger to Ricky?

A

23 years

B

24 years

C

33 years

D

30 years

Selena closed her account in an investment option scheme by withdrawing Rs. 10,000. One year ago, she had withdrawn Rs. 6000. Two years ago, she had withdrawn Rs. 5000. Three years ago, she had not withdrawn any amount. How much money had she deposited (approx.) at the time of opening the account four years ago, given the annual simple interest was 10%?

A

Rs. 15,600

B

Rs. 16,500

C

Rs. 17,600

D

Rs. 14,800

A person closes his account in an investment scheme by withdrawing Rs. 10000. One year ago, he had withdrawn Rs. 6000. Two years ago he had withdrawn Rs. 5000. Three years ago he had not withdrawn any money. How much money had he deposited approximately at the time of opening the account 4 years ago, if the annual rate of compound interest is 10%

A

Rs. 15470

B

Rs. 16680

C

Rs. 14250

D

Rs. 15200

Today is Alka's birthday. 3 years from today she will be twice as old as she was 12 years ago. How old is Alka today ?

A

23 years

B

24 years

C

26 years

D

27 years

Each question below is followed by two statements I and II. You have to determine whether the data given in the statements are sufficient for answering the question. You should use the data and your knowledge of Mathematics to choose the best possible answer. 11 Aman is how many years younger than Jadhav? I. Six years back Lokesh was as old as Aman is now. The ratio of age of Lokesh three ago and age of Jadhav 2 years ago was 7 ∶ 11. II. Jadhav is 3 years younger than Ranjit. The ratio of the age of Lokesh 2 years ago and the present age of Ranjit is 3 ∶ 5.

A

If the data in statement I alone is sufficient to answer the question, while the data in statement II alone are not sufficient to answer the question.

B

If the data in statement II alone is sufficient to answer the question, while the data in statement I alone are not sufficient to answer the question.

C

If the data either in statement I alone or in statement II alone is sufficient to answer the question.

D

If the data even in both the statements I and II together are not sufficient to answer the question.

E

If the data in both statements I and II together are needed to answer the question.

8 years ago the average age of a family with 7 members was 34 years. 4 years ago, a male member of the family got married. Now, the present average age of the family is 7 years more than the average age of the family 8 years ago. What was the age of the new female member of the family at the time of her marriage?

A

29 years

B

30 years

C

31 years

D

32 years

Half-life of a radioisotope is 4 × 10⁸ years. If there are 10³ radioactive nuclei in a sample today, the number of such nuclei in the sample 4 × 10⁹ years ago were

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