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All questions of Harmonic Progressions for SSC CGL Exam
Three numbers 5, p and 10 are in Harmonic progression if p = ?- a)10/3
- b)20/3
- c)3/10
- d)3/20
Correct answer is option 'B'. Can you explain this answer?
Three numbers 5, p and 10 are in Harmonic progression if p = ?
a)
10/3
b)
20/3
c)
3/10
d)
3/20
 | G.K Academy answered |
Concept:
Three numbers x, y, and z are in H.P if and only if y 
Calculation:
Calculation:
Given: Three numbers 5, p and 10 are in Harmonic progression
Now, According to the concept used
Now, According to the concept used
If 1/4, 1/x, 1/10 are in HP, then what is the value of x?- a)5
- b)6
- c)7
- d)8
Correct answer is option 'C'. Can you explain this answer?
If 1/4, 1/x, 1/10 are in HP, then what is the value of x?
a)
5
b)
6
c)
7
d)
8
 | Pranab Goyal answered |
Given:
1/4, 1/x, 1/10 are in Harmonic Progression (HP)
To find:
The value of x
Solution:
Harmonic Progression (HP):
In a Harmonic Progression (HP), the reciprocals of the terms are in Arithmetic Progression (AP).
Given terms:
1/4, 1/x, 1/10
Reciprocals of the given terms:
4/1, x/1, 10/1
As per the concept of HP:
2 * (1/x) = (1/4) + (1/10)
Solving the equation:
2/x = (10 + 4) / 40
2/x = 14 / 40
x = 40 / 14
x = 20 / 7
x = 7
Therefore, the value of x is 7.
Hence, the correct answer is option C) 7.
1/4, 1/x, 1/10 are in Harmonic Progression (HP)
To find:
The value of x
Solution:
Harmonic Progression (HP):
In a Harmonic Progression (HP), the reciprocals of the terms are in Arithmetic Progression (AP).
Given terms:
1/4, 1/x, 1/10
Reciprocals of the given terms:
4/1, x/1, 10/1
As per the concept of HP:
2 * (1/x) = (1/4) + (1/10)
Solving the equation:
2/x = (10 + 4) / 40
2/x = 14 / 40
x = 40 / 14
x = 20 / 7
x = 7
Therefore, the value of x is 7.
Hence, the correct answer is option C) 7.
If a, b, c are in geometric progression, then logax x, logbx x and logcx x are in- a)Arithmetic progression
- b)Geometric progression
- c)Harmonic progression
- d)Arithmetico-geometric progression
Correct answer is option 'C'. Can you explain this answer?
If a, b, c are in geometric progression, then logax x, logbx x and logcx x are in
a)
Arithmetic progression
b)
Geometric progression
c)
Harmonic progression
d)
Arithmetico-geometric progression
 | Iq Funda answered |
Concept:
If a, b, c are in geometric progression then b2 = ac
If b - a = c - b, than a, b, c are in AP.
If 1/a, 1/b, 1/c are in AP than a, b, c are in HP.
Calculation:
If a, b, c are in geometric progression then b2 = ac
So, by multiplying both side by x2 and taking log on both side to the base x
How many two digit numbers are divisible by 7?- a)13
- b)15
- c)11
- d)None of these
Correct answer is option 'A'. Can you explain this answer?
How many two digit numbers are divisible by 7?
a)
13
b)
15
c)
11
d)
None of these
| | G.K Academy answered |
CONCEPT:
Let us suppose a be the first term and d be the common difference of an AP. Then the nth term of an AP is given by:an = a + (n - 1) × d.
Note: If l is the last term of a sequence, then l = an = a + (n - 1) × d.
CALCULATION:
Here we have to find two digit numbers which are divisible by 7.
i.e 14, 21,............,98 is an AP sequence with first term a = 14, common difference d = 7 and the last term l = 98.
As we know that, if l is the last term of a sequence, then l = an = a + (n - 1) × d
⇒ 98 = 14 + (n - 1) × 7
⇒ 84 = 7(n - 1)
⇒ 12 = n - 1
⇒ n = 13
are in HP, then which of the following is/are correct?1. a, b, c are in AP2. (b + c)2, (c + a)2, (a + b)2 are in GP. Select the correct answer using the code given below.- a)1 only
- b)2 only
- c)Both 1 and 2
- d)Neither 1 nor 2
Correct answer is option 'A'. Can you explain this answer?
are in HP, then which of the following is/are correct?1. a, b, c are in AP
2. (b + c)2, (c + a)2, (a + b)2 are in GP. Select the correct answer using the code given below.
a)
1 only
b)
2 only
c)
Both 1 and 2
d)
Neither 1 nor 2
 | EduRev SSC CGL answered |
Concept:
- If a, b and c are three terms in GP then b2 = ab and vice-versa
- If three terms a, b, c are in HP, then
and vice-versa - When three quantities are in AP, the middle one is called as the arithmetic mean of the other two.
- If a, b and c are three terms in AP then
- and vice-versa
- If a, b and c are in A.P then 1/a, 1/b, 1/c are in H.P and vice-versa
Calculation:
(b + c), (c + a) and (a + b) are in A.P
⇒ 2(c + a) = b + c + a + b
⇒ 2c + 2a = 2b + a + c -----(i)
⇒ 2c + 2a - 2b - a - c = 0
⇒ 2b = c + a
So, a, b, c are in AP
Now, Let (b + c)2, (c + a)2, (a + b)2 are in GP
(c + a)2 = √[(b + c).(a + b)]2
⇒ c2 + a2 + 2ac = (b + c).(a + b)
⇒ c2 + a2 + 2ac = ab + b2 + ac + bc
⇒ c2 + a2 - b2 + ac - ab - bc = 0
From here we are unable to check the relation between a, b and c
So, Our assumption was wrong
So, (b + c)2, (c + a)2, (a + b)2 are not in GP.
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