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

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**Question 6:**

A five digit number N has all digits different and contains digits 1,3,4,5, and 6 only. If N is the smallest possible number such that it is divisible by 11, then what is the tens place digit of N.

Topic: divisibility

[1] 1

[2] 3

[3] 4

[4] 5

**Answer: **Option: 2

**Question 7:**

If \(\alpha \) and \( - \alpha \) are the roots of the equation \(2{x^3} - 5{x^2} - 8x + n = 0\) . Find the value of n?

Topic: equations

**Answer: **20

**Question 8:**

The bases of a trapezoid have lengths 10 and 15. A segment parallel to the bases passes through the point of intersection of the diagonals and extends from one side to the other. Find the length of the segment

Topic: quadrilaterals

[1] 5

[2] \(\sqrt {150} \)

[3] \(\frac{{25}}{{\sqrt 2 }}\)

[4] 12

**Answer: **Option: 4

**Question 9:**

The value of a fraction represented in base n is \(0.\overline {111} \) while in base 2n it takes the simpler form 0.2n. What is n?

Topic: base system

**Answer: **5

**Question 10:**

If Gopal and Harish can complete a work together in 20 days, and Gopal alone can do the same work in 32 days. When both work together their efficiencies reduce by 20% compare to the efficiency when they would have worked alone. Find the number of days Harish alone takes to complete the same work.

Topic: work and time

**Answer: **32

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