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Research Aptitude Test - 23

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Research Aptitude Test - 23
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  • Question 1
    2 / -0.5

    There are 25 points on a plane of which 7 are collinear. Now solve the following:

    Q. How many straight lines can be formed?

    Solution

    Total number of straights lines

    = 25 C2 - 7 C2 + 1 = 280

    25C2 selecting 2 points from total of 25 points
    7C2  selecting 2 points from total of 7 points [ subtracting them because they are collinear  

  • Question 2
    2 / -0.5

    There are 25 points on a plane of which 7 are collinear. Now solve the following:

    Q. How many triangles can be formed from these points?

    Solution

    Total triangle formed will be equal to 25 C3 - 7 C3 = 2265

  • Question 3
    2 / -0.5

    Three coins are tossed. Find the probability of no heads.

    Solution

    Sample space S = |HHH, HHT, HTH, HTT, THT, TTH, THH, TTT)

    Number of exhaustive cases = -8

    P (no heads) = P (ail tails) = 1/8 (∵ there is only favourable case TTT)

  • Question 4
    2 / -0.5

    What is the chance that a leap year, selected at random, will contain 53 Sunday?

    Solution

    We know that a leap year has 366 days and thus a leap year has 52 weeks and 2 days over.

    The two left over (successive days have the following likely cases:

    (i) Sunday and Monday

    (ii) Monday and Tuesday

    (iii) Tuesday and Wednesday

    (iv) Wednesday and Thursday

    (v) Thursday and Friday

    (vi) Friday and Saturday

    (vii) Saturday and Sunday

    ∴ Number of exhaustive cases ‘n’ = 7

    Out of these, the favourable cases are...(i) and (vii)

    ∴ Number of favourable cases ‘m’ = 2

    ∴ Probability of having 53 Sunday = 2/7

  • Question 5
    2 / -0.5

    In a simultaneous throw of two dice, find P (A or B) if A denotes the event 'a total of 11 and B denotes the event’ ‘an odd number on each die'.

    Solution

    A: Getting total of 11 B: Getting odd number one each die

    A = [(6, 5), (5, 6)]

    B = [(1, 1), (1, 3), (1, 5), (3, 1), (3, 3), (3, 5), (5, 1), (5, 3), (5, 5)]

    P(A) = 2/36, P(B) = 9/36 , P(A∩B) = 0

    ∴ Required probability

    = P(A) + P(B) - P(A∩B)

  • Question 6
    2 / -0.5

    Direction: Read the following in Information carefully and answer the question below it.

    A family consists of six members P, Q, R, X, Y and Z. Q is the son of R but R is not mother of Q. P and R are a married couple. Y is the brother of R. X is the daughter is the brother of P. Z is the brother of P.

    Who is the brother-in-law of R?

    Solution

    Y..R - P ..Z

    Q..X

  • Question 7
    2 / -0.5

    Direction: Read the following in Information carefully and answer the question below it.

    A family consists of six members P, Q, R, X, Y and Z. Q is the son of R but R is not mother of Q. P and R are a married couple. Y is the brother of R. X is the daughter is the brother of P. Z is the brother of P.

    How is Q related to X?

    Solution

     

    Explanation:


    • Q is the son of R, so Q is the child of R.

    • Since P and R are a married couple, X is the daughter of P and R.

    • Since Y is the brother of R, Y is also the brother of X.

    • Therefore, Q and X are siblings, making Q the brother of X.



    •  
    •  

     

  • Question 8
    2 / -0.5

    Direction: Read the following information carefully and answer the question below it

    P. Q. R. S. T. U and V are seven positive integers and (P x Q x R x S x T x U x V) is odd.

    Maximum how many of these integers can be odd?

    Solution

    All integer should be odd to get odd result.

  • Question 9
    2 / -0.5

    Direction: Read the following information carefully and answer the question below it

    P. Q. R. S. T. U and V are seven positive integers and (P x Q x R x S x T x U x V) is odd.

    Minimum how many of these integers can be even?

    Solution

    None of the Integer should be even

  • Question 10
    2 / -0.5

    Direction: A cuboid is divided into 192 identical cubelets This is done by making minimum no. ot cuts possible. All cuts are parallel to some of the face. But before doing so. The cube is painted with green color on one set of opposite faces. Blue on other set of opposite faces and red on their pair of annosit faces.

    What is the maximum number of cubelets possible which one colored with green colored only?

    Solution

    As we want maximize number of cubelets with green in color only cuboid has to painted with green color on set of opposite faces of 6 x 8. Hence no. of green colored only cubelets will (6 - 2) x (8 - 4) = 4 x 6 = 24, from face. There are two such faces hence maximum total no. of only green painted cubelets will be = 24 x 2 = 48

    Hence option (a)

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