**Note:**These Quant questions have been selected from

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**Question 16:**

Let \(N = 1! \times 2! \times 3! \times ..... \times 99! \times 100!\), and if \(\frac{N}{{p!}}\) is a perfect square for some positive integer \(p \le 100\), then find the value of p.

Topic: factorials

**Answer: **50

**Question 17:**

If \({x^2} + {y^2} = 1\) , find the maximum value of \({x^2} + 4xy - {y^2}\)

Topic: maxima minima

[1] \(1\)

[2] \(\sqrt 2 \)

[3] \(\sqrt 5 \)

[4] \(4\)

**Answer: **Option: 3

**Question 18:**

The compound interest on a certain amount for two years is Rs. 291.2 and the simple interest on the same amount is Rs. 280. If the rate of interest is same in both the cases, find the Principal amount

Topic: sici

[1] 1200

[2] 1400

[3] 1700

[4] 1750

**Answer: **Option: 4

**Question 19:**

In the diagram given below, the circle and the square have the same center O and equal areas. The circle has radius 1 and intersects one side of the square at P and Q. What is the length of PQ?

Topic: circles

[1] 1

[2] 3/2

[3] \(\sqrt {4 - \pi } \)

[4] \(\sqrt {\pi - 1} \)

**Answer: **Option: 3

**Question 20:**

What is the remainder when \({{x}^{276}}+12\) is divided by \({{x}^{2}}+x+1\) given that the remainder is a positive integer?

Topic: remainders

**Answer: **13

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Can you tell the name of the theorem that you said in the first quetion

stewarts theorem

Sir, for question no. 23:- we can do as x+y=2-z

=> cubing both sides:- x3+y3+z3=8-(2-z)(6z+3xy)

=>as given that x3+y3+z3=8, then (2-z)(6z+3xy)=0 => z=2(considering an integer value for easy output) ,now putting z value in every eqn given :- x+y=0

x2+y2=2

x3+y3=0

from the above three eqns we find that if one of x or y is +ve then another ll be -ve but both ll be of same magnitude i.e. (+-)1….thus x4+y4+z4=18

Set 1 Question 5.

I want to know the below logic would be wrong.

Distance is constant. If the Speed increases by 10km/hr, the time decreases by 4 hours.

So to decrease time by 2 hours, Speed can be increased by 5km/hr.

20 + 5= 25 kmph.

I understand something might be wrong with this logic but could someone help pinpoint that?