APPoliceSIMains2019ArithmeticandReasoning Related Question Answers
52. The value of $$\frac{1}{1^2.3^2} + \frac{2}{3^2.5^2} + \frac{3}{5^2.7^2} + \frac{4}{7^2.9^2} + ...... + \frac{15}{29^2.31^2}$$ is
53. If $$x = \frac{3 + \sqrt{6}}{5\sqrt{3} - 2\sqrt{12} - \sqrt{32} + \sqrt{50}}$$, then $$\frac{x^4 - 1}{x^4 + 1}$$ =
54. Each mango costs Rs.5 and each orange costs Rs.7. If a person spends Rs.38 on these two varieties of fruits, then the sum of the number of mangos and oranges purchased by that person is
55. If $$x = \frac{1}{\sqrt{13} - 3}, y = \frac{1}{\sqrt{7} - \sqrt{3}}, z = \frac{1}{\sqrt{2}(\sqrt{3} - 1)}$$, then
56. The smallest of the differences between the perfect sqares lying on either side of the least positive integer that is divisible by 3, 4, 5, 6, 8 is
57. If $$x = \sqrt{2} + \sqrt[3]{5}$$ and $$y$$ is such that $$xy$$ is rational, then a value of $$y$$ is
58. If the mean proportional of $$b, c$$ and the $$4^{th}$$ proportional of $$a, b, c$$ are both equal to 8, then $$abc$$ =
60. If $$x = 1 + \frac{1}{2^2} + \frac{1}{2^3} + ....\infty$$ and $$y = x + \frac{1}{2} + \frac{x}{9} + \frac{1}{18} + \frac{x}{81} + \frac{1}{162} + ....\infty$$, then
61. The number of ordered pairs (x,y) of positive integers satisfying the inequality 5x + 3y $$\leq$$ 15 is
62. In a class, the number of boys who can swim is one more than the number of girls who can swim. The number of girls who cannot swim is one more than the number of boys that cannot swim. The difference between number of boys who can swim and number of girls who cannot swim is two. Then which of the following is true?
63. A book costs Rs.35 and a pen costs Rs.20. A person has purchased less number of books than the number of pens by spending maximum amount out of Rs. 350, that he has. The amount left unspent (in rupees) is
64. Which one of the following point does not lie in the region bounded by x + y < 5, 2x - 4y >1 and x < y is
65. If A gives Rs.30 to B, then B will have twice the money left with A. If B gives Rs.10 to A, then A will have thrice as much money as is left with B. Then the amount A has initially (in rupees) is
69. In 12 hours, how many times the hours and minutes hands of a clock will coincide with- each other?
70. At what time between 3 O'clock and 4 O'clock will the hands of a clock lie on a straight line but do not coincide?
71. A clock is set right at 8AM on 1.1.2018. The clock gains 15min in 24hours. The time on the clock when the actual time is 10 AM on 4.1.2018, is (nearly)
72. A well of 4m diameter and 35m deep is dugout and the excavated soil is transported in a rectangular parallelopiped shaped truck with dimensions $$5m\times2m\times0.5m$$. To avoid over during transportation only 80% of its capacity is filled. If the loose soil occupies 20% more space while filling into the truck, then the number of trips required to transport the soil completely away from the place of digging is
73. If the volumes of a sphere and a cube are in the ratio $$9\pi$$ : 2, then the ratio of the radius of the sphere to the edge of the cube is
74. The dimensions of a rectangular plot is $$40m\times20m$$. A path is formed across the plot along the length and breadth with a uniform width of 2 meters. If the cot of forming, the path is Rs. 500 per sq.meter, the cost of laying that path (in Rs.) is
75. A person packs sweets boxes of dimensions $$15cm\times15cm\times15cm$$ in a basket of size $$120cm\times120cm\times120cm$$. If he now wants to carry the maximum number of cubical boxes having the maximum integer dimensions but less than the dimensions of the earlier boxes without leaving any space unused, the number of such boxes he can carry is
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