CAT 2023 Question Paper (Available): Download CAT Question Paper with Solutions PDF

1.

If \(x\) and \(y\) are positive real numbers such that \(log_x(x^2+12)=4\) and \(3\;log_yx=1\),then \(x+y\) equals

• 11
• 20
• 10
• 68

2.

The number of integer solutions of equation \(2|x|(x^2+1)=5x^2\) is

3.

In a company, 20% of the employees work in the manufacturing department. If the total salary obtained by all the manufacturing employees is one-sixth of the total salary obtained by all the employees in the company, then the ratio of the average salary obtained by the manufacturing employees to the average salary obtained by the non-manufacturing employees is

• 6 : 5
• 4 : 5
• 5 : 4
• 5 : 6

4.

A merchant purchases a cloth at a rate of Rs. 100 per meter and receives 5 cm length of cloth free for every 100 cm length of cloth purchased by him. He sells the same cloth at a rate of Rs.110 per meter but cheats his customers by giving 95 cm length of cloth for every 100 cm length of cloth purchased by the customers. If the merchant provides a 5% discount, the resulting profit earned by him is

• 9.7%
• 16%
• 4.2%
• 15.5%

5.

Let \(\alpha\) and \(\beta\) be the two distinct roots of the equation of 2x²-6x+k=0, such that (\(\alpha+\beta\)) and \(\alpha\beta\) are the distinct roots of the equation x²+px+p=0, then, the value of 8(k-p) ?