**1**. When a certain natural number is multiplied by 7, the product obtained consists only of fives. What is the least value of such a natural number?

- (
**A**) 78465 - (
**B**) 79365 - (
**C**) 755 - (
**D**) 7965 - (
**E**) None of these

**2**. In the given figure, *PQ* = *QR* = *RS* = *ST* = *TU* = *UV* = *VP*. The value of ∠*SPT* is

- (
**A**) 30° - (
**B**) 26° - (
**C**) 20° - (
**D**) 15° - (
**E**) None of these

**3**. Let **R** be the set of real numbers. A continuous function *f* : **R** → **R** satisfies *f*(1) = 1, *f*(2) = 4, *f*(3) = 9 and *f*(4) = 16. Suppose *f* is a polynomial, then which of the following are possible values of its degree?

- (
**A**) 5 - (
**B**) 3 - (
**C**) 4 - (
**D**) 2 - (
**E**) None of these

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Problem #2) Solution :

B D=x cm;;

C o s

Or (A B ^2+ B D ^2-A D ^2)/(2 * A B* B D)=(A C ^2+C D ^2-A D ^2)/(2* A C * C D);

Or ( 1 7^2 +x ^2 -1 5 ^2/(2* 17 * x)=(1 7^2 + 4 ^2-1 5 ^2)/(2 * 17* 4);

Or (64+ x^2)/x= (80)/4=20;

Or 64+ x^2=20 *x; or x=4 or 16 ;

Admissible value of x=16B D= x cm=16 cm

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Thank you sir for another solution

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Please explain this answer.

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Solution of problem1.

First we will measure 3 conis each side.

Case1 – if balance is eqall we will measure two out of 3 coins putting one on each side, thus we will get the heavier one.

Case 2 – if one side is heavier them we will take 2 coins of the heavier side and measure by putting one each side, thus we can find the heavier one.

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Solution of problem1.

First we will measure 3 conis each side.

Case1 – if balance is eqall we will measure two out of 3 coins putting one on each side, thus we will get the heavier one.

Case 2 – if one side is heavier them we will take 2 coins of the heavier side and measure by putting one each side, thus we can find the heavier one.

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Thank you so much Sir

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Question 1 solution :

(c)

As 10 houses have less than 6rooms, they are to be excluded.

Given,

4 houses have more than 8 rooms .

Therefore, number of houses having either less than 6 or greater than 8 rooms = 10 + 4 = 14.

The remaining houses, that is 11 houses fulfill the above mentioned criteria.

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