Edition 22

1. What is the value of the following integral?

$\int_{1/2022}^{2022} \frac{\tan^{-1}x}{x}dx$

• (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 |2x − [x]| = 4 is

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

1. 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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1. Rajan kumar says:

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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2. Rajan kumar says:

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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3. 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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