[Mission 2022] Insta–DART (Daily Aptitude and Reasoning Test) 20 August 2021

Time limit: 0

Quiz-summary

0 of 5 questions completed

Questions:

1

2

3

4

5

Information

Considering the alarming importance of CSAT in UPSC CSE Prelims exam and with enormous requests we received recently, InsightsIAS has started Daily CSAT Test to ensure students practice CSAT Questions on a daily basis. Regular Practice would help one overcome the fear of CSAT too. We are naming this initiative as Insta– DART – Daily Aptitude and Reasoning Test. We hope you will be able to use DART to hit bull’s eye in CSAT paper and comfortably score 100+ even in the most difficult question paper that UPSC can give you in CSP-2021. Your peace of mind after every step of this exam is very important for us.

Looking forward to your enthusiastic participation (both in sending us questions and solving them on daily basis on this portal).

Wish you all the best ! 🙂

You have already completed the quiz before. Hence you can not start it again.

Quiz is loading...

You must sign in or sign up to start the quiz.

You have to finish following quiz, to start this quiz:

Results

0 of 5 questions answered correctly

Your time:

Time has elapsed

You have reached 0 of 0 points, (0)

Categories

Not categorized0%

1

2

3

4

5

Answered

Review

Question 1 of 5

1. Question

The HCF of two natural numbers m and n is 24 and their product is 552. How many sets of values of m and n are possible?

Correct

Sol.(d)

Given HCF of two natural numbers m and n = 24

and their product, m × n = 552

LCM of two natural numbers = Product of m and n / HCF of m and n = 552/24 = 23

Here, no set of m and n is possible satisfying the given conditions.

Incorrect

Sol.(d)

Given HCF of two natural numbers m and n = 24

and their product, m × n = 552

LCM of two natural numbers = Product of m and n / HCF of m and n = 552/24 = 23

Here, no set of m and n is possible satisfying the given conditions.

Question 2 of 5

2. Question

What is the highest common factor of 2x^{3} + x^{2} – x – 2 and 3x^{3 }– 2x^{2} + x – 2 ?

Correct

Sol.(a)

Let f(x) = 2x^{3} + x^{2} – x – 2 = (x – 1)(2x^{2} + 3x + 2)

and g(x)= 3x^{3 }– 2x^{2} + x – 2 = (x -1)(3x^{2} + x + 2)

Hence, the highest common factor of f(x) and g(x) is (x – 1).

Incorrect

Sol.(a)

Let f(x) = 2x^{3} + x^{2} – x – 2 = (x – 1)(2x^{2} + 3x + 2)

and g(x)= 3x^{3 }– 2x^{2} + x – 2 = (x -1)(3x^{2} + x + 2)

Hence, the highest common factor of f(x) and g(x) is (x – 1).

Question 3 of 5

3. Question

For any integer n, what is HCF (22n + 7,33n + 10) equal to?

Correct

Sol.(b)

HCF of (22n + 7, 33n + 10) is always 1.

Illustration: For n = 1, HCF (29, 43) = 1

For n = 2, HCF (51, 76) = 1

For n= 3, HCF (73, 109) = 1

Incorrect

Sol.(b)

HCF of (22n + 7, 33n + 10) is always 1.

Illustration: For n = 1, HCF (29, 43) = 1

For n = 2, HCF (51, 76) = 1

For n= 3, HCF (73, 109) = 1

Question 4 of 5

4. Question

In a fire range, 4 shooters are firing at the respective targets. The first, the second, the third and fourth shooters hit the target once in every 5 s, 6 s, 7s and 8 s, respectively. If all of them hit their target at 9 : 00 am, when will they hit their target together again?

Correct

Sol.(c)

Time after which they will hit the target again together

= LCM (5, 6, 7 and 8)

= 5 × 3 × 7 × 2 × 4

= 840 s

They will hit target together = 840/60 = 14 min.

So, they will hit together again at 9:14 am.

Incorrect

Sol.(c)

Time after which they will hit the target again together

= LCM (5, 6, 7 and 8)

= 5 × 3 × 7 × 2 × 4

= 840 s

They will hit target together = 840/60 = 14 min.

So, they will hit together again at 9:14 am.

Question 5 of 5

5. Question

What is the HCF of 8(x^{5} – x^{3 }+ x) and 28 (x^{6} + 1) ?