CAT 2019 Slot 2 Question Paper

Instructions

For the following questions answer them individually

CAT 2019 Slot 2 - Question 71


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

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CAT 2019 Slot 2 - Question 72


Let $$a_1, a_2, ...$$ be integers such that
$$a_1 - a_2 + a_3 - a_4 + .... + (-1)^{n - 1} a_n = n,$$ for all $$n \geq 1.$$
Then $$a_{51} + a_{52} + .... + a_{1023}$$ equals

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CAT 2019 Slot 2 - Question 73


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

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CAT 2019 Slot 2 - Question 74


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

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CAT 2019 Slot 2 - Question 75


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

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CAT 2019 Slot 2 - Question 76


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

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CAT 2019 Slot 2 - Question 77


Let ABC be a right-angled triangle with hypotenuse BC of length 20 cm. If AP is perpendicular on BC, then the maximum possible length of AP, in cm, is

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CAT 2019 Slot 2 - Question 78


If x is a real number, then $$\sqrt{\log_{e}{\frac{4x - x^2}{3}}}$$ is a real number if and only if

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CAT 2019 Slot 2 - Question 79


If $$5^x - 3^y = 13438$$ and $$5^{x - 1} + 3^{y + 1} = 9686$$, then x + y equals

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CAT 2019 Slot 2 - Question 80


The strength of a salt solution is p% if 100 ml of the solution contains p grams of salt. Each of three vessels A, B, C contains 500 ml of salt solution of strengths 10%, 22%, and 32%, respectively. Now, 100 ml of the solution in vessel A is transferred to vessel B. Then, 100 ml of the solution in vessel B is transferred to vessel C. Finally, 100 ml of the solution in vessel C is transferred to vessel A. The strength, in percentage, of the resulting solution in vessel A is

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