I am writing Mock test and want to share my approach to the questions and wish if you can also share your method of solving the questions, it will be of great help to all of us.

I am writing Mock test and want to share my approach to the questions and wish if you can also share your method of solving the questions, it will be of great help to all of us.

1. How many natural numbers between 1 and 500 are not divisible by 7 and leave a remainder of 3when divided by 4?

(a) 125 (b) 107 (c) 106 (d) 124

2.

Two horses are tethered at the midpoints of two adjacent sides of a square field. Each of them is tied with a rope that does not allow it to go beyond the centre of the field for grazing. If the length of a side of the field is 8 m, what is the ratio of the areas of grazed to non-grazed regions?(a)pi+4/8-pi (b)pi-2/6+pi (c)pi+2/6-pi (d)8-pi/pi+4.

3. There are 10 points in a plane, of which 4 are collinear. How many quadrilaterals can be formed using any 4 of these points as vertices?(a) 185 (b) 190 (c) 195 (d) 2004.

4. Find the number of odd factors of 36036.(a) 72 (b) 46 (c) 24 (d) 365.

5. Let f(x) = – x^2 + 35, g(x) = | x + 5 | + | x – 5 | and h(x) = min {f(x), g(x)}. What is the number of integer values of x for which h(x) is equal to 10?(a) 9 (b) 10 (c) 11 (d) 12

Solution for Q 1.

All the numbers which leave a remainder of 3 when divided by 4 will be of the form 4n + 3, where n is a whole number.

For n = 0, 1, 2, 3, …, 124, we have 1

Therefore, the number of values of n in given range= 124 – 0 + 1 = 125.

Now observe that, 4n + 3 is divisible by 7 if and only if n = 7k + 1, where k is a whole number.

For k = 0, 1, 2, 3, …, 17, we have 1

Therefore, the number of values of k in the given range = 17 – 0 + 1 = 18

Hence, the required number of elements = 125 – 18= 107.

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