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

**1000+**CAT Quant Practice Problems with video solutions of Bodhee Prep’s Online CAT Quant Course

**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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