# CAT 2017 Shift-2

Instructions

For the following questions answer them individually

Question 81

Let ABCDEF be a regular hexagon with each side of length 1 cm. The area (in sq cm) of a square with AC as one side is

Question 82

The base of a vertical pillar with uniform cross section is a trapezium whose parallel sides are of lengths 10 cm and 20 cm while the other two sides are of equal length. The perpendicular distance between the parallel sides of the trapezium is 12 cm. If the height of the pillar is 20 cm, then the total area, in sq cm, of all six surfaces of the pillar is

Question 83

The points (2, 5) and (6, 3) are two end points of a diagonal of a rectangle. If the other diagonal has the equation y =3x+c,then c is

Question 84

ABCD is a quadrilateral inscribed in a circle with centre O such that O lies inside the quadrilateral. If $$\angle COD = 120$$ degrees and $$\angle BAC = 30$$ degrees, then the value of $$\angle BCD$$ (in degrees) is

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Question 85

If three sides of a rectangular park have a total length 400 ft, then the area of the park is maximum when the length (in ft) of its longer side is

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Question 86

Let P be an interior point of a right-angled isosceles triangle ABC with hypotenuse AB. If the perpendicular distance of P from each of AB,BC,and CA is $$4(\sqrt{2}-1)$$ cm,then the area, in sq cm, of the triangle ABC is

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Question 87

If the product of three consecutive positive integers is 15600 then the sum of the squares of these integers is

Question 88

If x is a real number such that $$\log_{3}5= \log_{5}(2 + x)$$, then which of the following is true?

Question 89

Let $$f(x) = x^{2}$$ and $$g(x) = 2^{x}$$, for all real x. Then the value of f[f(g(x)) + g(f(x))] at x = 1 is

Question 90

The minimum possible value of the sum of the squares of the roots of the equation $$x^2+(a+3)x-(a+5)=0$$ is

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