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Research Aptitude Test - 7

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Research Aptitude Test - 7
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Weekly Quiz Competition
  • Question 1
    2 / -0.5

    A system consists of N particles, interacting with each other (for example, protein molecules). Which one of the following statements is FALSE?

    Solution

    The number of vibrational degrees of freedom depends on the total degrees of freedom for the system minus the translational and rotational degrees of freedom. For a system of N particles, there are 3N total degrees of freedom. Therefore, the number of vibrational degrees of freedom is 3N - (3 translational + 3 rotational) = 3N - 6, which is not always equal to 3.

  • Question 2
    2 / -0.5

    Three pipes A, B and C can fill a tank in 6 hrs. After working at it together for 2 hrs C is closed and A and B can fill the remaining part in 7 hrs. The total number of hrs taken by C alone to fill the tank is

    Solution

    Say Pipe A can do a piece of work in 1 hr

    Say Pipe B can do b piece of work in 1 hr

    Say Pipe C can do c piece of work in 1 hr.

    So, (a+b+c)6 = 1 ----------1st Condition (a+b+c)2 + (a+b)7 = 1 ------------- 2(1/6) + (a+b)7 = 1

    So, a+b = 2/21 ............. Eqn l

    So, c = 1/6-2/21 = 1/14

    Now C can do 1/14 piece of work Hence, 1 piece of work can be done by C in 14 days.

  • Question 3
    2 / -0.5

    If (√3)5x 92= 3αx 3√3, then α equals:

    Solution

    (√3)5 x 92 = 3α x 3√3

  • Question 4
    2 / -0.5

    If x, y, z are real numbers, then the value of: is

    Solution

     

  • Question 5
    2 / -0.5

    Solution

    Given Exp.

    = x(b-c)(b+c-a) x(c-a)(c+a-b) x(a-2)(a+b-c)

    = x0 .x0 = 1

  • Question 6
    2 / -0.5

    If 2x+4- 2 x+2= 3, then x is equal to:

    Solution

    2x+4 -2x+2 =3

    ⇒2x+2 (22 - 1) = 3

    ⇒ 2x+2 = 1 = 2.

    ∴ x + 2 = 0 or x = -2.

  • Question 7
    2 / -0.5

    The sum of the first 16 terms of an AP whose first term and third are 5 and 15 respectively is

    Solution

    a = 5, a + 2d = 15

    So d = 5

    now sum of 16 term will be 16/2[10 + 15 x 5] = 680

  • Question 8
    2 / -0.5

    A boy agrees to work at the rate of one rupee on the first day, two rupees on the second day, four rupees on the third day and so on. How much will the boy get if he starts working on the 1st of February and finishes on the 20thof February?

    Solution

    This sequence is in GP 1,2,4, 8, …. Now sum of first 20 term will be

  • Question 9
    2 / -0.5

    The seventh term of a GP is 8 times the fourth term, but will it be the first term when its fifth term is 48?

    Solution

    It is given that

    ar6 = 8 ar3

    R3 = 8, r = 2

    Now ar4 = 48

    A x 24 = 48, a = 3

  • Question 10
    2 / -0.5

    The sum of three numbers on a GP is 14, and the sum of their squares is 84. Find the largest number,

    Solution

    a, ar, ar2

    Now a + ar +ar2 = 14 …(i)

    Also, a2 + a2 r2 + a2 r4 = 84 …(ii)

    only suitable combination is 2 , 4 , 8

    So the largest term is 8.

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