CAT 2021 Slot 2

Instructions

For the following questions answer them individually

Question 51

Suppose one of the roots of the equation $$ax^{2}-bx+c=0$$ is $$2+\sqrt{3}$$, Where a,b and c are rational numbers and $$a\neq0$$. If $$b=c^{3}$$ then $$\mid a\mid$$ equals.

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Question 52

From a container filled with milk, 9 litres of milk are drawn and replaced with water. Next, from the same container, 9 litres are drawn and again replaced with water. If the volumes of milk and water in the container are now in the ratio of 16 : 9, then the capacity of the container, in litres, is

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Question 53

If a rhombus has area 12 sq cm and side length 5 cm, then the length, in cm, of its longer diagonal is

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Question 54

If $$\log_{2}[3+\log_{3} \left\{4+\log_{4}(x-1) \right\}]-2=0$$ then 4x equals

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Question 55

The sides AB and CD of a trapezium ABCD are parallel, with AB being the smaller side. P is the midpoint of CD and ABPD is a parallelogram. If the difference between the areas of the parallelogram ABPD and the triangle BPC is 10 sq cm, then the area, in sq cm, of the trapezium ABCD is

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Question 56

For all real values of x, the range of the function $$f(x)=\frac{x^{2}+2x+4}{2x^{2}+4x+9}$$ is:

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Question 57

For a sequence of real numbers $$x_{1},x_{2},...x_{n}$$, If $$x_{1}-x_{2}+x_{3}-....+(-1)^{n+1}x_{n}=n^{2}+2n$$ for all natural numbers n, then the sum $$x_{49}+x_{50}$$ equals

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Question 58

For a real number x the condition $$\mid3x-20\mid+\mid3x-40\mid=20$$ necessarily holds if

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Question 59

Anil can paint a house in 60 days while Bimal can paint it in 84 days. Anil starts painting and after 10 days, Bimal and Charu join him. Together, they complete the painting in 14 more days. If they are paid a total of ₹ 21000 for the job, then the share of Charu, in INR, proportionate to the work done by him, is

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Question 60

A box has 450 balls, each either white or black, there being as many metallic white balls as metallic black balls. If 40% of the white balls and 50% of the black balls are metallic, then the number of non-metallic balls in the box is

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