Test Preparation on GATE CS Mock Tests-1

Which of the following statement(s) is/are correct?

1 is the remainder when 7^700 is divided by 100.

1 is the remainder when 7^26 is divided by 100.

2 is the remainder when 7^35 is divided by 13

1Only (1)
2Only (2)
3Only (1) and (3)
4All (1), (2), and (3)

(7^700) mod 100 = 7^(700 mod 100) = 7^0 = 1.
Last two digits of 7^1 are 07 Last two digits of 7^2 are 49 Last two digits of 7^3 are 43 Last two digits of 7^4 are 01. This cycle is 7, 9, 3, 1, 7, 9, … And, 26 mod 4 = 2. Therefore, 7^26 = 7^(4n+2) will end in 49. → 7^26 mod 100 = 7^2 mod 100 = 49.
(7^35) mod 13 = ((7^12)*(7^12)*(7^11)) mod 13 A^(P-1)/P (where A is any natural number, and P is any prime number which is not a factor of A) will give remainder 1. Therefore, (7^12) mod 13 = 1 So, → (1*1*(7^11)) mod 13 → (7^11) mod 13 → ((7)*(7^10)) mod 13 → ((7)*((7^2)^5)) mod 13 → ((7)*(49^5)) mod 13 → ((7)*((39+10)^5)) mod 13 → ((7)*(10^5)) mod 13 → ((7)*(100*100*10)) mod 13 → ((7)*(9*9*10)) mod 13 → 2

Therefore, only statements (1) and (3) are correct. Option (C) is true

I haven't worked as a mechanic before, ________ I've been fixing cars since I was a child.

1always
2yet
3no longer
4already

Always is an adverb of frequency, like never, often, frequently, and usually.Yet is a conjunction meaning nevertheless or however. Yet usually carries a sense of negation, so and yet means the same thing as but still. No longer means not now as formerly; not any more. We use already to show that something has happened sooner than it was expected to happen. Therefore, "yet" is most appropriate choice here. Option (B) is correct.

A dice is thrown. Let A be the event that the number obtained is greater than 5. Let B be the event that the number obtained is less than 5. Then P (AUB) is-

15/6
22/6
33/6
4None of these

Since, A{6}, and B{1, 2, 3, 4}. Therefore, A∩B = {∅}. So, P(A∪B) = P(A)+P(B)-P(A∩B) = 1/6 + 4/6 - 0 = 5/6 So, option (A) is correct.

____________ is usually used for something that was done in the past and still applies (multiple events).

1Had/has/have been
2Was/were
3Had/was/were
4All of the above

Had/has/have been is usually used for something that was done in the past and still applies (multiple events). Was/were usually applies to something done in the past that no longer applies (single event). So, option (A) is correct.

Ram is smarter than Mohan. Rakesh is smarter than Ramu and Mohini is smarter than Rakesh. Which of the following is a set(s) of additional information that can determine the smartest person?

(I) Mohini is smarter than Ram and Mohan is smarter than Rakesh.
(II) Mohan is smarter than Mohini.
(III) Ram is smarter than Mohini.

1Only (II)
2Only (III)
3Either (I) or (II)
4None of these

It is given that : Ram is smarter than Mohan, (i.e., Ram > Mohan). Rakesh is smarter than Ramu and Mohini is smarter than Rakesh (Mohni > Rakesh > Ramu). Our purpose is to add more possible set(s) of additional information that can determine smartest person. With the help of set (I), we can get Mohini as smartest person. With the help of set (II), we can get Ram as smartest person. But we can not conclude smartest person with set (III), because we have ambiguity (can be either Ram or Mohni). So, only set (I) or (II) can decide smartest person. Option (C) is correct.

The long, anxious, and frustrating wait by people outside banks and ATMs across the country over the last five days is an inevitable consequence of the decision to demonetize notes of Rs.500 and Rs.1,000. When 86 per cent of the value of notes in circulation turns suddenly invalid, as it did with Prime Minister Modi’s ‘surgical strike’ last week, a certain degree of disruption and pain is unavoidable. But the question is whether this chaos could have been anticipated and managed better than it has been. Replacement of the demonetized notes is a time-consuming exercise that requires planning of the highest order. The experience of the last few days shows that preparation was lacking and the transition could have been handled much better. Thankfully, the Centre has woken up to ease the pressure on the system by increasing withdrawal limits, allowing for petroleum outlets and hospitals to accept the old series of notes until November 24 and pushing more cash through post offices. Why do you think that the replacement of the demonetized notes is a time-consuming exercise?

1It takes more than 50 days to replace demonized notes.
2Demonetization is a ‘futile exercise’ to target black money and fake currency
3The government was lazy enough to issue the decision of demonetization before.
4Replacement process requires planning of the highest order and careful implementation.

According to the passage, the demonetization process requires careful thought process, well-chalked out implementation strategies and above all planning of the highest order from the policy makers as well as government. So, option (D) is most appropriate choice.

The long, anxious, and frustrating wait by people outside banks and ATMs across the country over the last five days is an inevitable consequence of the decision to demonetize notes of Rs.500 and Rs.1,000. When 86 per cent of the value of notes in circulation turns suddenly invalid, as it did with Prime Minister Modi’s ‘surgical strike’ last week, a certain degree of disruption and pain is unavoidable. But the question is whether this chaos could have been anticipated and managed better than it has been. Replacement of the demonetized notes is a time-consuming exercise that requires planning of the highest order. The experience of the last few days shows that preparation was lacking and the transition could have been handled much better. Thankfully, the Centre has woken up to ease the pressure on the system by increasing withdrawal limits, allowing for petroleum outlets and hospitals to accept the old series of notes until November 24 and pushing more cash through post offices. Which of the following option is false ?

1'Unconcerned’ is similar in meaning to the word ‘anxious’ as used in the passage.
2'Disorder' is similar in meaning to the word ‘chaos’ as used in the passage.
3'Hardship' is opposite in meaning to the word ‘ease’ as used in the passage.
4‘Shift’ is opposite in meaning to the word ‘transition’as used in the passage.

(A) ‘Unconcerned’ is opposite in meaning to the word ‘anxious’ as used in the passage. (B) ‘Disorder’ word implies that due to the demonetization, citizens all over the country were facing issues with the currency exchange. (C) ‘Hardship’ is the right choice. (D) ‘shift’ is the right choice. Only option (A) is false.


Right Ans	Wrong Ans	Not Attempted

Which of the following statement(s) is/are correct? 1 is the remainder when 7^700 is divided by 100. 1 is the remainder when 7^26 is divided by 100. 2 is the remainder when 7^35 is divided by 13

I haven't worked as a mechanic before, ________ I've been fixing cars since I was a child.

A dice is thrown. Let A be the event that the number obtained is greater than 5. Let B be the event that the number obtained is less than 5. Then P (AUB) is-

____________ is usually used for something that was done in the past and still applies (multiple events).

Check your progress:

Which of the following statement(s) is/are correct?

1 is the remainder when 7^700 is divided by 100.

1 is the remainder when 7^26 is divided by 100.

2 is the remainder when 7^35 is divided by 13