IIFT 5th Dec 2021 Slot 1

S =$$\frac{3}{7}+\frac{4}{7^2}+\frac{5}{7^3}+\frac{3}{7^4}+\frac{4}{7^5}+\frac{5}{7^6}+......$$
Now here S is a summation of 3 distinct infinite geometric series
And we know that sum of an infinite geometric progression = (a/1-r) where a is the first term and r is the common ratio .
Therefore we can say S will be : $$\frac{3}{\frac{7}{1-\frac{1}{7^3}}}+\ \frac{4}{\frac{7^2}{1-\frac{1}{7^3}}}+\frac{5}{\frac{7^3}{1-\frac{1}{7^3}}}$$
solving we get S = $$\frac{180}{7^3-1}=\frac{180}{342}$$

The board is as follows.

The required probability = $$\frac{\pi\left(5\right)^2-\pi\left(3\right)^2}{\pi\left(9\right)^2}=\frac{25-9}{81}=\frac{16}{81}$$

Hence, the answer is option D.

Let the total time taken by Samiksha be '5t'.

Total distance = t(20) + 2t(30)+2t(50) = 180t

Shreshta travelled distances 30t, 30t and 120t at 20 km/hr, 30 km/hr and 50 km/hr.

Time taken by Shreshta = $$\frac{30t}{20}+\frac{30t}{30}+\frac{120t}{50}$$ = 1.5t + t + 2.4t = 4.9t

Required % = $$\ \frac{\ 5t-4.9t}{5t}\times\ 100\ =\ 2\%$$

Answer is option B.

= $$\log\sin 40^\circ \log \sin 41^\circ..... \log \sin 90^\circ...... \log \sin 99^\circ \log \sin 100^\circ$$

= $$\log \sin 90^\circ$$

= log 1

= 0

Answer is option B.

Time taken by A alone to finish the work = 18*9 hrs

Time taken by B alone to finish the work = 22*9 hrs

Let the total work be LCM(18*9, 22*9) = 198*9 units

Work done by A in 1 hour = 11 units

Work done by B in 1 hour = 9 units

Let the number of hours B worked be 'x'

work done by A + work done by B = Total work done

(6)(11)+(13)(9)(11)+(3)(11) + x(9) = 198*9

x = 44 hours

Number of days B worked = 4 days 8 hours

Therefore, B stopped working on 30th Nov at 11 am.

Answer is option C.

The correct use of the phrases are "free rein", "put through a wringer" and "toe the line".

Hence, the answer is option C.

"Armistice" means a temporary suspension of hostilities or a truce. Thus, the antonym of "armistice" will be dispute or fight.

Among the options, C is the correct answer.

1. "tic" means a sudden twitch of a muscle, whereas "tick" is a small parasitic bug. For the given sentence, "tic" is the appropriate answer.

2. "peaked" means to reach the highest level, and "piqued" means to arouse. From the context of the given sentence, "piqued" is the correct option.

3. "augur" means bode, whereas "auger" is a device used to drill wood.

4. the correct phrase is "to throw off yoke"

Thus, the answer is option A.

Option A: Correct spellings are "Acquaintance" and "Exoneration".

Option B: Correct spellings are "Adolescence" and "Octennial"

Option C: Correct spellings are "Acquaintance" and "Ignominious"

Hence, the answer is option D.

"forbear" means to "restrain an impulse" or "refrain from an action".

Considering the meaning of "forbear", it is used incorrectly only in sentence D.

Hence, the answer is option A.