EXERCISE 17.1
QUESTION 1
Evaluate the following :
(i)
Sol :
(ii)
Sol :
(iii)
Sol :
(iv)
Sol :
(v)
Sol :
= 31
QUESTION 2
If find the value of n
Sol :
Given :
QUESTION 3
If find
Sol :
Now,
= 66
QUESTION 4
If find
Sol :
We have,
Now
= 23
QUESTION 5
If find x
Sol :
QUESTION 6
If find x
Sol :
QUESTION 7
If find r
Sol :
QUESTION 8
If find r
Sol :
And
QUESTION 9
If find r
Sol :
We have,
QUESTION 10
If find n
Sol :
We have
QUESTION 11
If , find r
Sol :
We have
QUESTION 12
If and
are in A.P. then find n
Sol :
Since and
are in AP.
[ if a ,b ,c are in A.P then 2b=a+c ]
and 14
QUESTION 13
If find n
Sol :
Given :
or,
Now,
But this is not possible
QUESTION 14
If find
Sol :
Now ,
QUESTION 15
If then find the value of
Sol :
multiplying with 3 to numerator and denominator to make 4 :
QUESTION 16
Prove that the product of 2n consecutive negative integers is divisible by
Sol :
Let 2n negative integers be
Then, product
This is divisible by
[Alternate method]
Product
Hence
This is divisible by
QUESTION 17
For all positive integers n , show that
Sol :
LHS
RHS
QUESTION 18
Prove that:
Sol :
Hence , proved
QUESTION 19
Evaluate
Sol :
= 42504
QUESTION 20
Let r and n be positive integers such that . Then prove the following
(i)
Sol :
LHS
(ii)
Sol :
(iii)
Sol :
(iv)
Sol :
= R H S