Quant Boosters - Gaurav Sharma - Set 6


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Number of Questions - 30
    Solved ? - Not yet
    Topic - Quant Mixed Bag
    Source - Genius Tutorial Preparation Forum


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q1) Max no of intersection of diagonals of polygon of side 8 is

    [OA : 70]


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q2) Find x,y all positive integers such that x^y + y^x + x^y * y^x = 5329


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q3) If x^2 + y^2 = 10x + 6y - 17, find minimum value of 2x + 7y


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q4) How many 4 digit numbers consist of max. only 2 distinct digits?

    [OA : 576]


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q5) Two person A and B start moving towards each other from point P and Q respectively which are 1400 km apart. Speed of A is 50 km/hr and that of B is 20km/hr. How far is A from Q when he meets B for 22nd time?


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    For 1st meeting they need to travel 1400 km and for rest 21 round they will cover 2800 km
    So total 2800 x 21 + 1400= 60200km
    A will travel 5/7 x 60200= 43000 km
    For 42000 km he needs 30 rounds
    In the last round he will cover 1000km from P
    So he is at 1400-1000= 400km from Q


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q6) A die is rolled three times, the probability of getting a larger number than the previous number is
    (a) 1/54
    (b) 5/54
    (c) 5/108
    (d) 13/108


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q7) A mixture contains alcohol and water in the ratio 4 : 3. If 7 litres of water is added to the mixture, the ratio of alcohol and water becomes 3 : 4. The quantity of alcohol in the mixture is
    (a) 10 litres
    (b) 12 litres
    (c) 32 litres
    (d) 48 litres


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q8) The points (0, 8/3), (1, 3) and (82, 30)
    (a) form an obtuse angled triangle.
    (b) form an acute angled triangle.
    (c) form a right angled triangle.
    (d) lie on a straight line.


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Slope of AB = slope of BC
    So striaght line


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q9) Sum of digits of a 5-digit number is 41.The probability that such a number is divisible by 11 is k/ 35 where k =


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    The 5-digit combination whose sum = 41 are
    ● 99995 : No. of arrangements = 5
    ● 99986 : No. of arrangements = 20
    ● 99977 : No. of arrangements = 10
    ● 99887 : No. of arrangements = 30
    ● 98888 : No. of arrangements = 5
    Total = 70

    Now, for a number (abcde) to be divisible by 11, we should have (a + c + e) – (b + d) = 11
    and (a + c + e) + (b + d) = 41
    So, a + c + e = 26, b + d = 15
    Thus (a, c, e) = (9, 9, 8 ) and (b, d) = (7, 8 ) or (6, 9)
    Hence total 12 cases

    Probability = 12/70 = 6/35
    k = 6


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q10) There is a frog who could climb either 1 stair or 3 stairs in one shot. In how many ways he could reach at 10th stair ?


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Fibonacci with a gap of 1 : 1, 1, 2, 3, 4, 6, 9, 13, 19, 28

    Answer : 28

    Method 2 :
    1 step in 1 way
    2 steps in 1 way
    3 steps in 2 ways
    4 steps in 3 ways
    5 steps in 4 ways
    6 steps in 6 ways
    7 steps in 9 ways
    8 steps in 13 ways
    9 steps in 19 ways
    10 steps in 28 ways
    So 28 should be the answer

    Method 3 :

    x + 3y = 10
    (1 , 3 ) -> 4
    (4 , 2 ) -> 6!/4!2! = 15
    (7 , 1) -> 8!/7! = 8
    (10 , 0) -> 1
    TOTAL = 15 + 4 + 8 + 1 = 28


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q11) If an integer n is to be chosen at random from the integers 1 to 96, inclusive, what is the probability that n(n + 1)(n + 2) will be divisible by 8?

    [OA : 5/8]


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q12) If March 1, 2006 was a Wednesday, which day was it on March 1, 2002?


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q13) N is a natural number of at least 5 digits and its leftmost digit is 6. When this 6 is removed from N, the number thus obtained is found to be 1/25 times of N. What is the sum of the digits of N?


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q14) Number of terms in the expansion of (a + b + c)^10
    a) 11
    b) 21
    c) 55
    d) 66


  • Director, Genius Tutorials, Karnal ( Haryana ) & Delhi | MSc (Mathematics)


    Q15) The product of all the factors of a number is equal to the tenth power of the number. N cannot be exactly divisible by which of the following?
    a. 90
    b.200
    c. 210
    d. 126


 

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