CAT 2019 | Quantitative Aptitude || Super Quiz 7 || 2019-20

Suppose that both the roots of the equation x² +ax + 2018 = 0 are positive integers. The number of possible values of a is _____.

The number of 3-digit numbers xyz such that we can construct an isosceles triangle (excluding the equilateral triangle) with sides x, y and z is

Let abcdefghij be a 10-digit number, where all the digits are distinct . 'a' obviously, is a non-zero numeral. Further, a > b > c, a + b + c = 9, d > e > f > g are consecutive odd numbers and h > i > jare consecutive even numbers. Then b is

Two sides of a triangle are of length 5 cm and 4 cm. Then the maximum possible area (in cm²) of the triangle is:

x, y, z are all prime numbers such that x + y +z = 30. How many such triplets (x, y, z) exist?

If all the roots of the equation x⁴ – 8x³ + px² + qx + 16 = 0 are natural numbers, then the value of 2p + q is

Using only the digits 9, 3, 2, how many 6-digit numbers can be formed which are divisible by 2 as well as 3?

Let N be the product of five distinct integers taken from the set of first 100 natural numbers. What can be the largest integer x, such hat 2^x divides N.

Consider 5 players P₁, P₂, P₃, P₄ and P₅. A team consists of 2 players and thus there are 10 distinct teams. Two teams play a match exactly once if there is no common player, else they do NOT play. For example, team {P₄, P₅} can play with team {P₂, P₃}, but cannot play with team {P₃, P₄}. The total number of possible matches is

The number of solution of the equation 6x+15y = 8, where x and y are both integers is

In how many ways can 25 identical chocolates be distributed among 6 children so that each child gets at least 2 chocolates and exactly two children get at least 3 chocolates each?

The last digit of 120! + 17¹²⁰ is