Question:
If p, 1 and q are in AP and p and 2 q are in GP, then which of the following statements is/are correct? I. p, 4, q are in HP . II. 11 4 1 pq ,, are in AP . Select the answer using the code given below:
If p, 1 and q are in AP and p and 2 q are in GP, then which of the following statements is/are correct? I. p, 4, q are in HP . II. 11 4 1 pq ,, are in AP . Select the answer using the code given below:
Options:
- a) I only
- b) II only
- c) Both I and II
- d) Neither I nor II
- a) I only
- b) II only
- c) Both I and II
- d) Neither I nor II
correct answer : c)
Explanation:
\ p, 1 and q are A.P .
Þ p + q = 2 …. (i)
p, 2 and q are G.P Þ pq = 4 …(ii)
Now,
2pq
pq+
= 8
2
= 4
\ pq
pq
+
2
=
1
4
\ 11
4
1
pq, and
are in A.P .
\ p, 4 and q are in H.P .
Both statements are correct.
\ p, 1 and q are A.P .
Þ p + q = 2 …. (i)
p, 2 and q are G.P Þ pq = 4 …(ii)
Now,
2pq
pq+
= 8
2
= 4
\ pq
pq
+
2
=
1
4
\ 11
4
1
pq, and
are in A.P .
\ p, 4 and q are in H.P .
Both statements are correct.