CAT Question Bank (Quant) - Gaurav Sharma - Set 2


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


    Q9) If P Q R are three points on a circle, What is the maximum area of the triangle formed by them where radius of circle is 'a' units?


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


    Q10) Find the no of positive divisor of N^2 such that the positive divisor are less than N and do not divide N completely. where N = 2^17 * 3^9 * 5^3.


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


    Q11) The highest power of 2 in 10! + 11! + 12! + 13! + ...+ 1000! is
    (a) 8
    (b) 9
    (c) 10
    (d) 11


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


    Q12) Two points are chosen randomly on the circumference of a circle. What is the probability that the distance between the 2 points is at least 'r', the radius of the circle?


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


    Q13) How many 10-digit positive integers with distinct digits are multiples of 11111?
    a) 1234
    b) 2345
    c) 3456
    d) 4567
    e) None of these


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


    Q14) For how many natural numbers less than 10^5 the sum of their digits equal to 10?


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


    Q15) f is a real function such that f(x + y) = f(xy) for all real values of x and y. If f(– 5) = 5, then the value of f(– 25) + f(25) is
    a. 5
    b. 10
    c. 0
    d. 25


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


    Q16)
    0_1508301921266_9a636174-b649-4844-ba31-93fd3594fca5-22308983_10214478437945914_3216051023347361318_n.jpg


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


    Q17)
    0_1508301992867_2c62f61a-892e-4b58-8bdf-b984470e1f54-22289966_10214431914382854_6690758586319973395_o.jpg


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


    Q18) The sum of 2 five digit numbers AMC10 and AMC12 is 123422. What is A + M + C ?
    a) 10
    b) 11
    c) 12
    d) 13
    e) 14


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


    Q19) A positive integer n has exactly 4 positive divisors that are perfect fifth powers, exactly 6 positive divisors that are perfect cubes, and exactly 12 positive divisors that are perfect squares. Find the least possible number of possible integers that are divisors of n


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


    Q20) Find the remainder when 1 × 2 + 2 × 3 + 3 × 4 + … + 98 × 99 + 99 ×100 is divided by 101.


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


    Q21) What are the last two digits of (86789)^41?


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


    Q22) All the divisors of 360, including 1 and the number itself, are summed up. The sum is 1170. What is the sum of the reciprocals of all the divisors of 360?
    a. 3.25
    b. 2.75
    c. 2.5
    d. 1.75


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


    Q23) Last 2 digits of the number (299)^33


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


    Q24) Find the remainder when 1^39 + 2^39 + 3^39 + 4^39 + ... + 12^39 is divided by 39.
    a. 0
    b. 1
    c. 12
    d. 38


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


    Q25) Last digit of the LCM of(3^2003-1) and (3^2003+1) :
    a. 8
    b. 2
    c. 4
    d. 6


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


    Q26) What is the remainder when x + x^9 + x^25 + x^49 + x^81 is divided by (x^3 - x)?


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


    Q27) A number when divided by 8 leaves remainder 3 and quotient Q. The number when divided by 5 leaves remainder 2 and quotient Q + 8. What is the number?


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


    Q28)
    0_1508302403840_d77de21e-484e-44f6-b045-1eef4f0369b8-22049821_10214402373244344_7158731637781032774_n.jpg


 

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