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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.

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

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