**1**. What is the value of the following integral?

- (
**A**) (*π*/4) log2022 - (
**B**) (*π*/2) log2022 - (
**C**) *π *log2022 - (
**D**) (1/2) log2022 - (
**E**) None of these

**2**. Using only the digits 2, 3 and 9, how many six digit numbers can be formed which are divisible by 6?

- (
**A**) 41 - (
**B**) 80 - (
**C**) 81 - (
**D**) 161 - (
**E**) None of these

**3**. For a real number *x*, let [*x*] denote the greatest integer less than or equal to *x*. The number of real solutions of the equation |2*x* − [*x*]| = 4 is

- (
**A**) 1 - (
**B**) 2 - (
**C**) 3 - (
**D**) 4 - (
**E**) None of these

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Problem #2) Solution :

B D=x cm;;

C o s

Or (A B ^2+ B D ^2-A D ^2)/(2 * A B* B D)=(A C ^2+C D ^2-A D ^2)/(2* A C * C D);

Or ( 1 7^2 +x ^2 -1 5 ^2/(2* 17 * x)=(1 7^2 + 4 ^2-1 5 ^2)/(2 * 17* 4);

Or (64+ x^2)/x= (80)/4=20;

Or 64+ x^2=20 *x; or x=4 or 16 ;

Admissible value of x=16B D= x cm=16 cm

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Thank you sir for another solution

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Please explain this answer.

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Solution of problem1.

First we will measure 3 conis each side.

Case1 – if balance is eqall we will measure two out of 3 coins putting one on each side, thus we will get the heavier one.

Case 2 – if one side is heavier them we will take 2 coins of the heavier side and measure by putting one each side, thus we can find the heavier one.

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Solution of problem1.

First we will measure 3 conis each side.

Case1 – if balance is eqall we will measure two out of 3 coins putting one on each side, thus we will get the heavier one.

Case 2 – if one side is heavier them we will take 2 coins of the heavier side and measure by putting one each side, thus we can find the heavier one.

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Thank you so much Sir

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Question 1 solution :

(c)

As 10 houses have less than 6rooms, they are to be excluded.

Given,

4 houses have more than 8 rooms .

Therefore, number of houses having either less than 6 or greater than 8 rooms = 10 + 4 = 14.

The remaining houses, that is 11 houses fulfill the above mentioned criteria.

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