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

7 comments

  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

    Liked by 1 person

    1. 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.

      Liked by 1 person

  2. 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.

    Liked by 1 person

  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.

    Liked by 2 people

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