CAT 2017 Slot 1 Question Paper

Instructions

For the following questions answer them individually

CAT 2017 Slot 1 - Question 91


The number of solutions $$(x, y, z)$$ to the equation $$x - y - z = 25$$, where x, y, and z are positive integers such that $$x\leq40,y\leq12$$, and $$z\leq12$$ is

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CAT 2017 Slot 1 - Question 92


For how many integers n, will the inequality $$(n - 5) (n - 10) - 3(n - 2)\leq0$$ be satisfied?

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CAT 2017 Slot 1 - Question 93


If $$f_{1}(x)=x^{2}+11x+n$$ and $$f_{2}(x)=x$$, then the largest positive integer n for which the equation $$f_{1}(x)=f_{2}(x)$$ has two distinct real roots is

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CAT 2017 Slot 1 - Question 94


If $$a, b, c,$$ and $$d$$ are integers such that $$a+b+c+d=30$$ then the minimum possible value of $$(a - b)^{2} + (a - c)^{2} + (a - d)^{2}$$  is

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CAT 2017 Slot 1 - Question 95


Let AB, CD, EF, GH, and JK be five diameters of a circle with center at 0. In how many ways can three points be chosen out of A, B, C, D, E, F, G, H, J, K, and O so as to form a triangle?

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CAT 2017 Slot 1 - Question 96


The shortest distance of the point $$(\frac{1}{2},1)$$ from the curve y = I x -1I + I x + 1I is

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CAT 2017 Slot 1 - Question 97


If the square of the 7th term of an arithmetic progression with positive common difference equals the product of the 3rd and 17th terms, then the ratio of the first term to the common difference is

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CAT 2017 Slot 1 - Question 98


In how many ways can 7 identical erasers be distributed among 4 kids in such a way that each kid gets at least one eraser but nobody gets more than 3 erasers?

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CAT 2017 Slot 1 - Question 99


$$f(x) = \frac{5x+2}{3x-5}$$ and $$g(x) = x^2 - 2x - 1$$, then the value of $$g(f(f(3)))$$ is

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CAT 2017 Slot 1 - Question 100


Let $$a_1$$, $$a_2$$,.............,  $$a_{3n}$$ be an arithmetic progression with $$a_1$$ = 3 and $$a_{2}$$ = 7. If $$a_1$$+ $$a_{2}$$ +...+ $$a_{3n}$$= 1830, then what is the smallest positive integer m such that m($$a_1$$+ $$a_{2}$$ +...+ $$a_n$$) > 1830?

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