XAT 2017

The 1st handi of sabji is brought from home. This can be served for 12 customers. Two plates of puri's are made in 10 mins. 

Now in 30 min, the number of puri-sabji that can be served = 6

After 30 min, the sabji needs to be heated which taken 10 mins.

Hence, in the remaining 20 min 4 plates of puri-sabji can be served.

Hence, in total in the first hour 10 plates of puri-sabji can be served.

Hence, option C is the correct answer.

Since he already has one handi of sabji, he will invest the first 30 minutes of starting time in making puris in the oven.

As 1 oven cooks 2 plates of puris in 15 minutes, in the first 30 minutes, he will be able to prepare 8 plates of puris.

Total plates of Puri = 11*2

Now, profit = 15 × 22 = 330 - 50 (Transport cost) = 280

Thus, the correct answer is B.

Since the efficiency of Aman in making both Sabji and Puri is better than that of Shyam, Shyam should use his proficiencies in both parts.

For the first 20 minutes, Aman will make sabji and Shyam will make puri in the next 10 min. Then they can make puris in the ovens simultaneously and hence, can work on both the parts.

Thus, the correct answer is D.

Humility is the quality of not being proud of being perfect as you are aware of your limitations. Therefore, among the options, the option that focuses on awareness of the self with respect to limitations should be in the consideration for the correct answer. However, the focus on awareness of self is not neceesarily linked Improvement" or "overcoming' the limitations. Moreover, the culture of humility should not be confused with the performance measurement or rewards and compensation. Among the options, Option D focuses on making one aware of one self without any link with rewards or performance and hence, Option D is the right answer.

The Principal did need not mention the anonymous mail. Hence option A is eliminated. She can directly address the concerns of the students without referring to the mail. Option C and D tantamount to accepting that the syllabi are outdated. It is necessary to address the concerns of the students; hence option E is also eliminated. Option B is correct as it assures the students about the efforts being made from the management side.

The given series is (-100)+ (-95)+ (-90)+....+110 + 115 + 120. 
We can observe that -100 will cancel out 100, -95 will cancel out 95 and so on. Therefore, the only terms that will be remaining are 105, 110, 115 and 120.
Sum of the series = 105 + 110 + 115 + 120 = 450.
Therefore, option D is the right answer.

Let us assume the volume of the tank to be 60 litres. 
A can fill or empty 60/4 = 15 litres in a minute.
B can fill or empty 60/10 = 6 litres in a minute.
C can fill or empty 60/12 = 5 litres in a minute.
D can fill or empty 60/20 = 3 litres in a minute. 

We have to find the combination for which the tank will be half-full in 30 minutes (i.e., completely filled in 1 hour).
Therefore, the combination must result in a net input of 60/60 = 1 litre per minute.

Let us evaluate the options.
Option B:
Pipe A drained and pipes B, C and D filled

The net result will be -15 + 6 + 5 + 3 = -1 litre/minute. We can eliminate option B. 

Option C:
Pipes A and D drained and pipes B and C filled

The net result will be -15-3+6+5 = -7 litres/minute. We can eliminate option C as well. 

Option D:
Pipes A and D filled and pipes B and C drained
The net result will be 15+3-6-5 = 7 litres/minute. We can eliminate option D as well.

Option A:
Pipe A filled and pipes B, C and D drained

The net result will be 15-6-5-3 = 1 litre/minute. 
Therefore, option A is the right answer. 

Patel bought 20 shirts. He would have gotten every fourth shirt at Rs. 100. He would have paid the marked price for 15 shirts and would have gotten 5 shirts at Rs. 100 each. 

Let the marked price of one shirt be 'x'.
15x + 5*100 = 20000
15x = 19500
x = 19500/15 = Rs. 1300.
The marked price of a shirt is Rs. 1300. Therefore, option B is the right answer. 

Let us draw the diagram using the given conditions.

AB = 24 cm and P is the mid-point of AB. Therefore, AP=PB=12 cm. 
MN is perpendicular to AB and passes through P. 
PM < PN. Therefore, M should be closer to A and B than N.
MN and AB are 2 perpendicular chords intersecting at P. 
Therefore, according to the intersecting chords theorem, AP*PB = PM*PN
12*12=8*PN
=> PN = 18 cm.
Therefore, option B is the right answer. 

$$4(x - 2)^{2} + 4(y - 3)^{2} - 2(x - 3)^{2}$$
$$y$$ is an independent variable. The value of $$y$$ is unaffected by the value of $$x$$. Therefore, the least value that the expression $$4(y-3)^2$$ can take is $$0$$ (at $$y=3$$).

Let us expand the remaining terms. 
$$4(x-2)^2-2(x-3)^2$$=4*$$(x^2-4x+4)-2*(x^2-6x+9)$$
$$=2x^2-4x-2$$
=$$2(x^2-2x-1)$$
=$$2(x^2-2x+1-2)$$
=$$2((x-1)^2-2)$$
The least value that the expression $$(x-1)^2$$ can take is $$0$$ (at $$x$$ = $$1$$)
Therefore, the least value that the expression $$2((x-1)^2-2$$ can take is $$2*(0-2)=2*(-2) = -4$$
Therefore, option B is the right answer.