Explore topic-wise InterviewSolutions in Current Affairs.

(a) The fox could not get out of the well because the well was deep.

(b) When the work was over, we went home.

(c) A library is a public place where we see a number of books kept for reading.

(d) As soon as the culprit was caught, he was taken to the police station.

(e) While the boys were stealing mangoes, the owner of the grove came in.

(f) Artificially flavoured juices are hazardous to health and they lead to kidney problems.

(g) Adit as well as Ranjan have been promoted.

(h) After Caesar was declared the emperor, the conspirators killed him.

(a) With reference to your advertisement in a local newspaper, I am applying for the post of a salesman.

(b) The assignment will be completed in a few weeks.

(c) Ravi was appreciated by his teachers.

(d) We feel sorry for our mistakes.

(e) The boy studied well in spite of many obstacles.

(f) Our nation is famous for its glorious culture.

(g) We are proud of our children.

(h) My brother will return home in the evening.

(a) because 

(b) so 

(c) As 

(d) Though, and 

(e) how

(f) therefore 

(g) so 

(h) Although 

(i) Unless 

(j) As soon as 

(k) and 

(l) neither, nor 

(m) consequently 

(n) for

(a) instead of 

(b) in spite of 

(c) on behalf of 

(d) on the whole 

(e) in favour of 

(J) On account of 

(g) According to 

(h) In case of

Correct option is A) so that

Correct option is B) since

Correct option is C) in that

Correct option is B) to

Correct option is D) in

Correct option is B) out

Correct option is B) about

Correct option is A) into

Correct option is C) up

Correct option is A) to

Correct option is D) Certainly / Very good

Correct option is C) since

Correct option is A) of

Correct option is E) try out

Correct option is D) shy

Given:

A filling pipe can fill a pot in 40 minutes and wastage pipe can empty the filled pot in 60 minutes

Concept:

If a tap can fill a tank in x hours, then the tank filled by the tap in 1 hour = 1/x of the total tank.

Calculation:

Part of the pot filled in 1 minutes by both the taps

= \(\frac{1}{{40}} - \frac{1}{{60}}{\rm{}} = {\rm{}}\frac{{3 - 2}}{{120}}{\rm{}} = {\rm{}}\frac{1}{{120}}\)

∴ Empty pot can be filled in 120 minutes.

Given:

Two pipes A and B can fill a container in 12 and 15 minutes respectively

Concept:

If a tap can fill a tank in x hours, then the tank filled by the tap in 1 hour = 1/x of the total tank.

Calculation:

Part of the container filled in 3 minutes by pipes A and B

⇒ \(3{\rm{}}\left( {\frac{1}{{12}}{\rm{}} + {\rm{}}\frac{1}{{15}}} \right)\)

⇒ \(3{\rm{}}\left( {\frac{{5{\rm{\;}} + {\rm{\;}}4}}{{60}}} \right){\rm{}} = {\rm{}}\frac{{3 \;\times\; 9}}{{60}}{\rm{}} = {\rm{}}\frac{9}{{20}}\)

Remaining part = \(1 - \frac{9}{{20}}{\rm{}} = {\rm{}}\frac{{11}}{{20}}\)

Time taken by B = \(\frac{{11}}{{20}} \times 15{\rm{}} = {\rm{}}\frac{{33}}{4}{\rm{}} = {\rm{}}8\frac{1}{4}\) minutes

∴ The required time is \(8\frac{1}{4}\)minutes.

Concept Used:

The concept of proportion states that

a ∶ b ∶∶  c ∶ x

Where a, b and c are the first three numbers of the proportion,

and the fourth proportion is x 

⇒ a/b = c/x 

x = (b × c)/a

Calculation:

Let the fourth proportional be  x

0.14 ∶ 0.21 ∶∶ 13 ∶ x

0.14/0.21 = 13/x

x = 13 × 0.21/0.14

x = 19.5

∴ The fourth proportional is 19.5

Given:

Tap X can fill a pot in 6 hours and tap Y can fill it in 8 hours

Concept:

If a tap can fill a tank in x hours, then the tank filled by the tap in 1 hour = 1/x of the total tank.

Calculation:

Part of the pot filled in 2 hours by tap X and Y

⇒ \(2{\rm{}}\left( {\frac{1}{6}{\rm{}} + {\rm{}}\frac{1}{8}} \right){\rm{}} = {\rm{}}2{\rm{}}\left( {\frac{{4{\rm{\;}} + {\rm{\;}}3}}{{24}}} \right){\rm{}} = {\rm{}}\frac{7}{{12}}\)

Remaining part = \(1 - \frac{7}{{12}}{\rm{}} = {\rm{}}\frac{5}{{12}}\)

Time taken by tap Y in filling \(\frac{5}{{12}}\) part

⇒ \(\frac{5}{{12}} \times 8{\rm{}} = {\rm{}}\frac{{10}}{3}{\rm{}} = {\rm{}}3\frac{1}{3}\) hours

∴ The required time is \(3\frac{1}{3}\) hours.

Concept:

• Sum of the first n Natural Numbers \(\rm 1+2+3+4+....+n =\sum n = \frac{n(n+1)}{2}\)
• Sum of the Square of the first n Natural Numbers \(\rm 1^2+2^2+3^2+4^2+....+ n^2=\sum n^2 = \frac{n(n+1)(2n+1)}{6}\)
• Sum of the Cubes of the first n Natural Numbers \(\rm 1^3+2^3+3^3+4^3+....+ n^3=\sum n^3 = \frac{[n(n+1)]^2}{4}\)

Calculation:

Here, we have to find the sum of the series (1 × 0 × 2) + (2 × 1 × 3) + (3 × 2 × 4) + (4 × 3 × 5) +....up to n terms.

nth term of the series = T_n = n ⋅ (n - 1) ⋅ (n + 1) = n3 - n 

Sum of series = \(\rm S_n = \sum T_n= \sum (n^3-n)=\sum n^3-\sum n\)

As we know that, \(\rm 1+2+3+4+....+n =\sum n = \frac{n(n+1)}{2}\)  and \(\rm 1^3+2^3+3^3+4^3+....+ n^3=\sum n^3 = \frac{[n(n+1)]^2}{4}\)

\(\Rightarrow \rm S_n =\left ( { \frac{n(n+1)}{2}} \right )^2-\frac{n(n+1)}{2}\)

\(\rm \Rightarrow S_n =\left ( { \frac{n(n+1)}{2}} \right )\left ( \frac{n(n+1)}{2}-1 \right )\)

\(\Rightarrow \rm S_n =\left ( { \frac{n(n+1)}{2}} \right )\left ( \frac{(n-1)(n+2)}{2} \right )\)

\(\Rightarrow \rm S_n =\left ( { \frac{n(n+1)(n-1)(n+2)}{4}} \right )\)

\(\Rightarrow \rm S_n = { \frac{n(n^2-1)(n+2)}{4}} \)

Hence, option 1 is the correct answer.

Given:

The first tap can fill it in 4 hours and the second tap can empty it in 16 hours

Concept:

If a tap can fill a tank in x hours, then the tank filled by the tap in 1 hour = 1/x of the total tank.

Calculation:

Part of the pot filled by both the taps in 1 hours = \(\frac{1}{4} - \frac{1}{{16}}\)

⇒ \(\frac{{4 - 1}}{{16}}{\rm{}} = {\rm{}}\frac{3}{{16}}\)

Time = (16/3) hours = \(5\frac{1}{3}\) hours

∴ The required time is \(5\frac{1}{3}\) hours.

Given:

A pipe can fill a pot in 8 hours and another tap can empty it in 16 hours

Concept:

If a tap can fill a tank in x hours, then the tank filled by the tap in 1 hour = 1/x of the total tank.

Calculation:

Part of the pot filled in 1 hours = 1/8

Part of the pot emptied in 1 hours = 1/16

When both the pipe are opened simultaneously,

Part of pot filled in 1 hours

⇒ (1/8) – (1/16)

⇒ (2 – 1)/16

⇒ 1/16

∴ The pot will be filled in 16 hours.

Given:

A pot can be filled by pipe X in 2 hours and pipe Y in 6 hours.

Pipe X was opened at 10 A.M.

Pipe Y is opened at 11 A.M.

Concept:

If a tap can fill a tank in x hours, then the tank filled by the tap in 1 hour = 1/x of the total tank.

Calculation:

Part of the pot filled in 1 hours by pipe X = \(\frac{1}{2}\)

Part of the pot filled by both pipes in 1 hour

⇒ \(\frac{1}{2}{\rm{}} + {\rm{}}\frac{1}{6}{\rm{}} = {\rm{}}\frac{{3{\rm{\;}} + {\rm{\;}}1}}{6}{\rm{}} = {\rm{}}\frac{2}{3}\)

Time taken to fill \(\frac{2}{3}\) part = 60 minutes

Time taken to fill \(\frac{1}{2}\) part

⇒ \(\frac{{60\; \times \;3}}{2} \times \frac{1}{2}{\rm{\;}}\)= 45 minutes

∴ The pot will be filled at 11:45 A.M.

Correct option is A) if the train had come on time

Correct option is A) she had lost the key of her room

Correct option is A) his

Correct option is A) never has

Correct option is B) she was

Correct option is A) got / had happened

Correct option is C) will / see

Correct option is C) do you have

1. a. The Ganga water is used for irrigation, transportation and fishing.

2. b.  Effluents from industries, urban waste from cities and metals discharged from tanneries are the major pollutants that make the river Ganga very dirty.

3. a. Reduction of pollution and revival of the river Ganga are the two purposes that will be served by the programme named "Namami Gange"

4. d. Most people in India consider the Ganga as mother and goddess.

5. b. Ganga the third largest river in the world.

6. d. Ash produced in small dark flecks by the burning of powdered coal or other materials are carried into the air.

7. c. The irony here is that in spite of being the most worshipped river, it is also the dirtiest one.

8. b. Ganga is the fifth most polluted river in the world.

9. b. "Namami Gange" means to worship Ganga river.

10. c. The Gangetic plain formed by the river Ganga is one of the most fertile lands on earth.

Correct option is C) wake up / will be shining

Correct option is C) lives

Correct option is D) woke up / was shining

Correct option is A) warm enough

Correct option is C) in

Correct option is A) was studying / tried

Correct option is E) congratulate

Correct option is A) any more

Correct option is C) no longer

Correct option is A) when

Correct option is B) ago

Correct option is B) for

The correct option is (d) 10 cm

Given, AR = 4 cm and, AR = AQ = 4 (Tangents from the same point are equal)

CQ = AC − AQ = 11 − 4 = 7 cm

CQ = CP = 7 cm (Tangents from the same point are equal)

BR = BP = 3 cm (Tangents from the same point are equal)

Now, BC = CP + BP

BC = 7 + 3 = 10 cm