IIFT 2021 Slot 1 Question Paper (5th Dec)

S =$$\frac{3}{7}+\frac{4}{7^2}+\frac{5}{7^3}+\frac{3}{7^4}+\frac{4}{7^5}+\frac{5}{7^6}+......$$ 

S is a summation of 3 distinct infinite geometric series as we can see that the terms {1,4,7...}, {2,5,8...}, {3,6,9...} are forming 3 separate infinite GPs.
We know that the sum of an infinite geometric progression = $$\dfrac{a}{1\ -\ r}$$ where a is the first term and r is the common ratio.

Therefore we can say S will be : $$\dfrac{\frac{3}{7}}{1-\frac{1}{7^3}}+\ \dfrac{\frac{4}{7^2}}{1-\frac{1}{7^3}}+\dfrac{\frac{5}{7^3}}{1-\frac{1}{7^3}}$$

solving we get S = $$\dfrac{180}{7^3-1}=\dfrac{180}{342}$$

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

Answer is option B.

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

We know that $$sin 90^\circ$$ = 1. And $$\log 1 = 0$$

= $$\log\sin 40^\circ \log \sin 41^\circ..... 0...... \log \sin 99^\circ \log \sin 100^\circ$$

Anything multiplied by 0 is 0.

Hence, option B is the answer.

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.

"Free rein" (A) → Means giving full freedom. "Reign" is about ruling, which doesn’t fit.

"Vise" (D) → A tool that tightly grips something (used metaphorically for a squeezing feeling). "Vice" means a bad habit.

"Wringer" (E) → "Put through the wringer" means going through a tough time. "Ringer" means an impostor, which doesn't fit.

"Toe the line" (H) → Means to follow rules. "Tow the line" is incorrect because "tow" means pulling something.

Hence, the correct option 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" refers to a sudden, involuntary muscle twitch, while "tick" can refer to a small parasitic insect or a repetitive clicking sound. Since the sentence describes an involuntary twitch, "tic" is the correct answer.

2. "Peaked" means to reach the highest point, whereas "piqued" means to arouse or stimulate (such as interest or curiosity). Since the sentence refers to arousing interest, "piqued" is the correct choice.

3. "Augur" means to predict or foretell a future outcome (bode well or ill), while "auger" is a tool used for boring holes. Since the sentence refers to predicting something, "augur" is the correct word.

4.   The correct phrase is "throw off the yoke" (not just "throw off yoke"). "Yoke" symbolizes oppression or burden, whereas "yolk" refers to the yellow part of an egg. "Yoke" is the correct choice in this context.

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.