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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

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?