X REAL NO & POWER & ACID BASE :ASSIGNMENT 6

X  REAL NO & POWER & ACID BASE :ASSIGNMENT 6

1.       [1]Why  13/120  is a non–terminating  rational number

2.       [1]Explain why 7 × 11 × 17 + 34 and is a composite numbers.                                         

3.       [1]Show that 12 ⁿ cannot end with the digit 0  for any natural number n.  

4.       [2]Use Euclid’s division algorithm to find the HCF of :  867 and 255

5.       [2]Find the LCM and HCF of the following pair of integers and verify that LCM × HCF = product of the two numbers. 510 and 92

6.       [3]Ramu, a book seller has  370 books of Maths and 130 books of English. He wants these to stack in such a fashion that each stack has sae number of books and they take least area of cupboard. What is the number of books can be places in each stack for this purpose

7.       [3]An army contingent of  356 members is to march behind an army band of 32 members in a parade. The two groups are to march in the same number of columns. What is the maximum number of columns in which they can march?    

8.        [1]Consider the 6ⁿ , where n is a natural number. Verify whether there is any value of n for which 6ⁿ can be divided by 7.

9.       [2]Find the LCM and HCF of the following integers by applying the prime factorization method.   27, 21 and 32

10.    [3]Four ribbons measuring 14 m, 18 m, 22 m and 26 m respectively are to be cut into least number of pieces of equal length. What is the length of each piece?          

11.    [3]Find the largest positive integers that will divide 398,436 and 542 leaving remainders 7,11 and 15 respectively.

12.    [4]Use Euclid’s division lemma to show that the cube of any +tive integer is of the form 9m, 9m + 1 or 9m – 1.

13.    [2]Prove that the following numbers are irrational :

(i) √3      (ii) 6+√2            (iv) 7√5  (v) 2– 3√11       (viii) √ 6

14.    [2]Use Euclid's division algorithm to show that any positive odd integer is of the form

4q + 1 or 4q + 3, where q  is some integer              

15.    [1]Name three mineral acids and Organic acids. Are these weak or strong ?

16.    [2]What are indicators? Name 2 natural and 2 synthetic indicators. How do these changes colours when acrted with acidic or basic substances? Mention.

17.    [2]Can hydrogen ion exist independantely? If not in what form does it exist?

18.    [1]Why does an aqueous solution of an acid conduct electricity?

19.    [2]Why a substance is acidic or basic in nature? What happens to these when these are dissolved in water ?

20.    [1]Why does dry HCl gas does not change the colour of a dry blue litmus paper?

21.    [2]Illustrate an activity to show that only substances that can disassociate its hydrogen ion can conduct electricity and not all .

22.    [2]An electric heater is rated 2kW, 220 V . If a fuse is to be connected to it; should it be 5A or 15 A. Find.

23.    [3] A bulb is rated as 220 V, 200 W. What is its resistance? Four such bulbs burn for 5 hours. What is the electrical energy consumed in kilowatt-hour?