[Download PDF] IIFT 2018 Paper with Solutions

Instructions

Choose the appropriate answer for rephrasing the underlined portion of the sentence.

Question 91

Sky-Airlines recently announced aggressive cost-cutting measures ranging from a new airport check-in procedures that encourage passengers to use self-service kiosks and reductions in the size of its fleet.

Video Solution

Solution

Options A and D have errors in parallelism. Option B mentions 'from...and to' which is not correct. Option C is correct, considering all the aspects. The answer is option C.

Question 92

Although the square root of a negative number has no real value, it is not necessarily true that equations involving imaginary numbers like these are practically inapplicable.

Video Solution

Solution

The idea conveyed by the whole sentence is that while the square root of a negative number has no real value, equations involving such numbers may have practical applications. Due to the usage of "not necessarily," the answer we are looking for should be phrased as "such equations have no practical applications" and the double negation will give the sentence a positive essence.

The only answer that conveys the required sense is B.

Instructions

The sentences given in each question, when properly sequenced, form a coherent paragraph. Each sentence is labelled with a letter. Choose the most logical order of sentences from among the given choices to construct a coherent paragraph.

Question 93

A. But, clearly, the government still has the final say.
B. In the past few years, the Reserve Bank of India might have wrested considerable powers from the government when it comes to monetary policy.
C. The RBI's announcements on certain issues become effective only ,after the government notifies them.
D. Isn't it time the government vested the RBI with powers to sanction such changes, leaving their ratification later?

Video Solution

Solution

B is an opening statement in which it is suggested that that RBI has taken over several aspects of monetary policies from the government. A indicates that despite having certain powers, the final decision rests with the government. C elaborates A with an example. D poses a question for the reader to decide after reading all the above statements.

Hence the correct order is BACD.

Question 94

A. All levels of demand, whether individual, aggregate, local, national, or international are subject to change.
B. At the same time, science and technology add new dimensions to products, their uses and the methods used to market them.
C. Aggregate demand fluctuates with changes in the level of business activity, GNP and national income.
D. The demand of individuals tend to vary with changing needs and rising income.

Video Solution

Solution

Sentence A gives the basic premise of what is being discussed in the passage i.e. that all demands are subject to change. Thus, sentence A is apt as the opening sentence of the paragraph. D further discusses the individual demands and C discusses aggregate demand. DC discuss the demands chronologically and hence ADC is the mandatory pair. B is driving the paragraph on a tangential nuanced idea apart from demand. Thus ADCB is the right choice.

Instructions

For the following questions answer them individually

Question 95

A Business Group has 3 Companies X,Y,Z and a Trust P which is engaged in charitable activities. Each group company has to donate 5% of its own funds to the Trust, excluding the loan which the company has taken from other companies of the group. X has given a loan to Y which is equivalent to 10% of the funds of Y. After receiving the loan, Y has funds which are 2 times the funds of Z. If Z gave Rs. 10,000 as donation to the Trust P, how much is the approximate contribution of 'Y' to the Trust P ?

Video Solution

Solution

Z's funds = 10000 x 100/5 = 2 lakhs

Y has funds which are 2 times the funds of Z => 4 lakhs

X has given loan to Y which is equal to 10% of funds of Y

y's funds + 10% of Y's funds = 4 lakhs

Y's funds = 4/1.1 lakhs

Y's donation = 5/100 (4/1.1lakhs) = 18181.81

Question 96

A bucket contains 200cc of liquid. A solid ball is dropped in the bucket resulting in the rise of liquid level to 1.3 times of its original level. If the radius of the base of the bucket is 3 cm and the radius of the surface of the liquid level is 1 cm more than the radius of the base of the bucket before the ball is dropped. Find the volume of the solid metal ball.

Video Solution

Solution

Let height of liquid level before the ball was dropped be h

The radius of the surface of the liquid level then is 4cm

$$\frac{h}{3}\pi\ \left(4^2+3^2+4\cdot3\right)\ =200cc$$

=> h = $$\frac{600}{37\pi\ }$$

The liquid level raises by 0.3h as a result of the solid metal ball being dropped.

By similarity, the radius of the surface of the liquid level after metal ball is dropped is 4.3cm

Volume of he solid metal ball = $$\frac{1.3h}{3}\left(4^2+3^2+4.3\left(3\right)\right)\ -\ 200$$ = 83.82cc

Question 97

P.....Q
R.....S
T.....U
V.....W
Using 5 dots in each of the lines PQ, RS, TU and VW as the vertices, how many triangles can be drawn such that the base is on any one of the above lines?

Video Solution

Solution

The base on any one of the lines can be formed in $$5_{C_2}=10\ ways$$

To form a triangle, the base has to be joined to any of the 15 points on the other lines

Number of triangles that can be drawn when the base is on any of the lines = 10 *15 =150

and number of triangles that can be drawn totally = 150*4 = 600

Question 98

In the triangle PQR, S is the midpoint of QR. X is any point on PR. T is the point on QR such that PT || SX. If the area of triangle PQR is 5.8 sq. cm. then the area of triangle RTX is

Video Solution

Solution

S is the midpoint of QR. So, area of PSR = $$\frac{1}{2}\left(Area\ of\ PQR\right)\ =\ \frac{5.8}{2}=2.9$$

PT||XS

So area of XSP = area of XST ( same height and same base)

Adding area of XSR on both sides, we have area of PSR = Area of RTX

=> area of PSR = Area of RTX = 2.9 sq.cm

Question 99

Given $$P(x,y) = x^2+ xy + y^2; Q(x,y) = x^2- xy + y^2.$$ Find the value of $$P(7, Q(9,4))$$

Video Solution

Solution

Q(x,y) = x^2- xy + y^2.$$

Q(9,4) = $$9^2-4\cdot9+4^2=81+16-36=61$$

P(7,61) = $$7^2+7\cdot61+61^2=\ 49+427+3721=4197$$

Question 100

In the given figure, PA=QB and PRQ is the arc of the circle, centre of which is O such that angle POQ = 90°. If AB= 25$$\sqrt{2}$$cm and the perpendicular distance of AB from centre O is 30cm. Find the area of the shaded region?

Video Solution

Solution

PA = QB and A=B = $$90^{\circ\ }$$

=> PQBA is a rectangle.

Area of the shaded region = (Area of PQBA - Area of the segment PRQ)

$$PQ=AB=25\sqrt{\ 5}$$

$$PO=QO=\frac{PQ}{\sqrt{\ 2}}=25$$ = radius of the circle.

The perpendicular from O to PQ is $$\frac{25}{\sqrt{\ 2}}$$

Distance from the foot of the perpendicular to AB = $$30-\frac{25}{\sqrt{\ 2}}$$

Area of PQBA = $$\left(30-\frac{25}{\sqrt{\ 2}}\right)\left(25\sqrt{\ 2}\right)=750\sqrt{\ 2}-625$$

Area of segment PRQ = Area of sector OPRQ - Area of triangle OPQ = $$\frac{90}{360}\pi\ 25^2-\frac{1}{2}25^2$$

Area of shaded region = $$\left(750\sqrt{\ 2}-625\right)-\left(\frac{90}{360}\pi\ 25^2-\frac{1}{2}25^2\right)$$

= option C

CAT Content

IIFT 2018

Sky-Airlines recently announced aggressive cost-cutting measures ranging from a new airport check-in procedures that encourage passengers to use self-service kiosks and reductions in the size of its fleet.

Although the square root of a negative number has no real value, it is not necessarily true that equations involving imaginary numbers like these are practically inapplicable.

P.....Q
R.....S
T.....U
V.....W
Using 5 dots in each of the lines PQ, RS, TU and VW as the vertices, how many triangles can be drawn such that the base is on any one of the above lines?

In the triangle PQR, S is the midpoint of QR. X is any point on PR. T is the point on QR such that PT || SX. If the area of triangle PQR is 5.8 sq. cm. then the area of triangle RTX is

Given $$P(x,y) = x^2+ xy + y^2; Q(x,y) = x^2- xy + y^2.$$ Find the value of $$P(7, Q(9,4))$$

In the given figure, PA=QB and PRQ is the arc of the circle, centre of which is O such that angle POQ = 90°. If AB= 25$$\sqrt{2}$$cm and the perpendicular distance of AB from centre O is 30cm. Find the area of the shaded region?

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CAT Content

IIFT 2018

Sky-Airlines recently announced aggressive cost-cutting measures ranging from a new airport check-in procedures that encourage passengers to use self-service kiosks and reductions in the size of its fleet.

Although the square root of a negative number has no real value, it is not necessarily true that equations involving imaginary numbers like these are practically inapplicable.

P.....Q R.....S T.....U V.....WUsing 5 dots in each of the lines PQ, RS, TU and VW as the vertices, how many triangles can be drawn such that the base is on any one of the above lines?

In the triangle PQR, S is the midpoint of QR. X is any point on PR. T is the point on QR such that PT || SX. If the area of triangle PQR is 5.8 sq. cm. then the area of triangle RTX is

Given $$P(x,y) = x^2+ xy + y^2; Q(x,y) = x^2- xy + y^2.$$ Find the value of $$P(7, Q(9,4))$$

In the given figure, PA=QB and PRQ is the arc of the circle, centre of which is O such that angle POQ = 90°. If AB= 25$$\sqrt{2}$$cm and the perpendicular distance of AB from centre O is 30cm. Find the area of the shaded region?

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P.....Q
R.....S
T.....U
V.....W
Using 5 dots in each of the lines PQ, RS, TU and VW as the vertices, how many triangles can be drawn such that the base is on any one of the above lines?