cat 2019 Complete Paper Solution | Slot 2

For the following questions answer them individually

The average of 30 integers is 5. Among these 30 integers, there are exactly 20 which do not exceed 5. What is the highest possible value of the average of these 20 integers?

Amal invests Rs 12000 at 8% interest, compounded annually, and Rs 10000 at 6% interest, compounded semi-annually, both investments being for one year. Bimal invests his money at 7.5% simple interest for one year. If Amal and Bimal get the same amount of interest, then the amount, in Rupees, invested by Bimal is

What is the largest positive integer n such that $n2+7n+12n2−n−12\frac{n^2 + 7n + 12}{n^2 - n - 12}$ is also a positive integer?

How many pairs (m, n) of positive integers satisfy the equation $m2+105=n2m^2 + 105 = n^2$?

Two ants A and B start from a point P on a circle at the same time, with A moving clock-wise and B moving anti-clockwise. They meet for the first time at 10:00 am when A has covered 60% of the track. If A returns to P at 10:12 am, then B returns to P at

Let $a1,a2,...a_1, a_2, ...$ be integers such that
$a1−a2+a3−a4+....+(−1)n−1an=n,a_1 - a_2 + a_3 - a_4 + .... + (-1)^{n - 1} a_n = n,$ for all $n≥1.n \geq 1.$
Then $a51+a52+....+a1023a_{51} + a_{52} + .... + a_{1023}$ equals

Two circles, each of radius 4 cm, touch externally. Each of these two circles is touched externally by a third circle. If these three circles have a common tangent, then the radius of the third circle, in cm, is

Let A be a real number. Then the roots of the equation $x2−4x−log2A=0x^2 - 4x - log_{2}{A} = 0$ are real and distinct if and only if

The quadratic equation $x2+bx+c=0x^2 + bx + c = 0$ has two roots 4a and 3a, where a is an integer. Which of the following is a possible value of $b2+cb^2 + c$?

The base of a regular pyramid is a square and each of the other four sides is an equilateral triangle, length of each side being 20 cm. The vertical height of the pyramid, in cm, is