👆Ans. D
Explanation:

Here, first two positions are fixed for alphabets and the last two for numbers.

Let encrypted code be a1 a2 b1 b2. Where a1, a2 are English alphabets, and b1, b2 are numbers.

There are 26 English alphabets and we have to choose 2 distinct alphabets. First alphabet can be selected in 26 ways and second alphabet can be chosen in 25 ways.

Out of 9 digits (1 to 9), first digit can be selected in 9 ways and second digit can be selected in 8 ways. Thus, the number of possible distinct codes = 26 × 25 × 9 × 8 = 46800

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📌30 Nov 2023

Q1. Two trains A & B running in opposite directions take 5 minutes to cross each other. Their lengths are 2000 meters and 1600 meters respectively. Speeds of these trains are x & y kmph respectively. Which of the following relationship(s) between their speeds is/are true?

(a) 100x + 10y = 360

(b) 100x + 100y = 3600

(c) x + y = 43.2

(d) Both (b) & (c) are correct

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👆Ans. C
Explanation

Time taken by the two trains to cross each other = 5 minutes = 1/12 hrs.

Distance covered in crossing each other = 2000 + 1600 = 3600 meters = 3.6 km

Speeds of these trains are x & y kmph respectively.

Time taken to cross each other = distance/speed= 3.6/ (x+y) = 1/12

or (x+y) = 3.6 × 12

or (x+y) = 43.2 kmph

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Q2. Four-digit numbers are to be formed using the digits 5, 6, 7 and 8, and none of these four digits are to be repeated in any manner. Further, 5 is not to appear at the first place. Numbers 6 and 7 are not to immediately follow each other. 8 is not to appear at the last place, and number 5 is not to be immediately followed by 7. How many such numbers can be formed?

(a) 6

(b) 8

(c) 9

(d) 10

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👆Ans. A
Explanation:

According to question, four-digit numbers are to be formed. From the conditions given for the four positions (digits) of the number, we get:

➡️ 5 cannot come at the first place. So, 6, 7 and 8 can appear there.
➡️ 8 is not to appear at the last place. So, 5, 6 and 7 can appear there.
➡️ 6 and 7 are not to immediately follow each other, i.e. they cannot be together. So, 67 and 76 are not allowed.
➡️ 5 is not to be immediately followed by 7. So, 57 is not allowed.
➡️ List of possible numbers - 6875, 6587, 7586, 7856, 7865 and 8756.

Hence, six such numbers can be formed.

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Q3. Given 4 flags of different colours, how many different signals can be generated, if a signal requires the use of 2 flags one below the other?

(a) 6

(b) 8

(c) 12

(d) None of the above

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👆Ans. C
Explanation:

There will be as many signals as there are ways of filling in 2 vacant places in succession by the 4 flags of different colours.

It is mentioned that the signal requires the use of 2 flags one below the other.

The upper vacant place can be filled in 4 different ways by any one of the 4 flags. After this, the lower vacant place can be filled in 3 different ways by any one of the remaining 3 different flags.

Hence, by the multiplication principle, the required number of signals = 4 × 3 = 12.

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Q4. Ram’s salary is more than Shyam’s salary, but less than Mayank’s salary. On the other hand, Vijay’s salary is more than that of Ganesh. Mayank’s salary, however, is less than the salary of Ganesh. Whose salary is the lowest?

(a) Vijay

(b) Mayank

(c) Shyam

(d) Ram

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👆Ans. C
Explanation:

As per the question,

Ram’s salary is more than Shyam’s salary, but less than Mayank’s salary: Mayank > Ram > Shyam

Vijay’s salary is more than that of Ganesh: Vijay > Ganesh

However, Mayank’s salary is less than that of Ganesh, therefore overall order is: Vijay > Ganesh > Mayank > Ram > Shyam

Therefore, Shyam’s salary is the lowest.

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Q. A ship sails in still water at a speed of 40 km/hr. It enters a river wherein the flow of stream is 10 km/hr. The ship has to cover a distance of 120 km in the river. What is the percent increase/decrease in time taken to cover this distance upstream compared to that in still water?

(a) 25%

(b) 100/3%

(c) 400/3%

(d) 50%

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👆Ans. B
Explanation:

➡️ Speed of ship upstream = 40 – 10 = 30 kmph
➡️ Speed of ship in still water = 40 kmph
➡️ Time taken by the ship to reach its destination when it sails upstream = distance covered /upstream speed = 120/30 = 4 hours
➡️ Time taken by the ship to reach its destination, when it sails in still water = distance covered/speed of ship in still water = 120/40 = 3 hours
➡️ Extra time taken = 4 - 3 = 1 hour
➡️ Percentage of extra time the ship will take to reach its destination when it sails upstream than that in still water (i.e. Percent increase in time) = (1/3) × 100 = (100/3)%

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👆Ans. C
Explanation:

➡️ Number of Officers in ATS, n(A) = 20
➡️ Number of Officers in cyber security, n(C) = 14
➡️ Number of Officers in both ATS and cyber security = n(A ∩ C) = 8
➡️ So, Number of Officers only in ATS = 20 – 8 = 12
➡️ Number of Officers only in cyber security = 14 – 8 = 6
➡️ Hence, number of officers only in ATS or only in cyber security = 12 + 6 = 18

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Vedprakash and Sain Singh are preparing for Civil Services Examinations, and read The Hindu & Indian Express newspapers respectively. In the test in which they both appear, Vedprakash gets 30% questions from the newspaper he reads, and Sain gets 20% questions from the newspaper he reads. 10% of total questions are from both newspapers. If the test has 100 questions, how many questions in total have been covered by these two newspapers together?

(a) 10
(b) 40
(c) 50
(d) 55

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👆Ans. B
Explanation:

➡️ Total number of questions in the test = 100
➡️ Number of questions from The Hindu = H = 30% of 100 = 30
➡️ Number of questions from Indian Express = I = 20% of 100 = 20
➡️ Number of questions from both The Hindu and Indian Express = H ꓵ I = 10% of 100 = 10
➡️ (Here ꓵ denotes intersection)
➡️ Hence, total number of questions covered by these two newspapers together, H ꓴ I = H + I - (H ꓵ I) = 30 + 20 – 10 = 40

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