If a 1 x = b 1 y = c 1 z and a , b , c are in G.P., then which of the following are true? Options: A . &nbspx,y,z will be in A.P. B . &nbspx,y,z will be in G.P. C . &nbspx,y,z will be in H.P. D . &nbspNone of the above

Answer: Option A : A Let a 1 x = b 1 y = c 1 z = k . ⇒ a = k x , b = k y , c = k z . Since a , b , c are in G.P., b 2 = a c . ∴ k 2 y = k x . k z = k x + z ∴ 2 y = x + z ⇒ x , y , z are in A.P.

If a1x=b1y=c1z and a,b,c are in G.P., then which of the following are true?

Question

a^{\frac{1}{x}} = b^{\frac{1}{y}} = c^{\frac{1}{z}}

and

a, b, c

are in G.P., then which of the following are true?

Options:

A . x,y,z will be in A.P.

B . x,y,z will be in G.P.

C . x,y,z will be in H.P.

D . None of the above

Answer: Option A
:
A
Let

a^{\frac{1}{x}} = b^{\frac{1}{y}} = c^{\frac{1}{z}} = k .

\Rightarrow a = k^{x}, b = k^{y}, c = k^{z} .

Since

a, b, c

are in G.P.,

b^{2} = a c .

∴ k^{2 y} = k^{x} . k^{z} = k^{x + z}

∴ 2 y = x + z

\Rightarrow x, y, z

are in A.P.

Was this answer helpful ?

Next Question

Submit Solution

More Questions on This Topic :

Question 1. The number which should be added to the number added to the numbers 2, 14, 62 so that the resulting numbers may be in G.....so that the resulting numbers may be in G.P. is

Question 2. If a, b, c, d are in H.P., then ab + bc + cd is equal to....

Question 3. Sum of first n terms in the following series cot−13 + cot−17 + cot−113 + cot....cot−17 + cot−113 + cot−121 + .........n terms.is given by

Question 4. If sixth term of a H.P. is 161 and its tenth term is 1105, then first term of that H.P. is....

Question 5. The sum of infinite terms of the following series 1 + 45 + 752 + 1053 + ...........∞ ....the following series 1 + 45 + 752 + 1053 + ...........∞ will be

Question 6. Harikiran purchased a house in Rs. 15000 and paid Rs. 5000 at once. Rest money he promised to pay in annual instalment o....interest. How much money is to be paid by him

Question 7. The sum of the first n terms is 12 + 34 + 78 + 1516 + .......... is....

Question 8. If the aritmetic, geometric and harmonic menas between two positive real numbers be A, G and H, then....

Question 9. If p, q, r are in A.P. and are positive, the roots of the quadratic equation p x2 + qx + r = 0 are all real for ___.....

Question 10. If m≠n and the sequences p,a,b,q and p,m,n,q each are in AP, then b−an−m is ___.....

Chapter 1 - GLOBAL STEEL SCENARIO & INDIAN STEEL INDUSTRY Part 1 : (13-04-2024) INDUSTRY AND COMPANY AWARENESS (ICA)

Direction Sense Test Part 1 Reasoning (Hindi)

Chapter 1 - RMHP / OHP / OB & BP Part 1 : (14-02-2024) GPOE

Cube & Cuboid Part 1 Reasoning (Hindi)

Data Interpretation (DI) Basic Concept Reasoning (Hindi)

Counting Figures Part 1 Counting Of Straight Lines Reasoning (Hindi)

Sail E0 free webinar Webinars

Real Numbers Part 7 Class 10 Maths

Real Numbers Part 1 Class 10 Maths

Polynomials Part 1 Class 10 Maths

Pie Chart - Test Paper 1 Data Interpretation Reasoning & DI

Tabulation - Test Paper 2 Data Interpretation Reasoning & DI

Test Paper 1 Direction Sense Test Reasoning & DI

ICA , RDIC,GFM Free Modal Test Paper - Non - Technical Branch Old Syllabus 2022 - SAIL Junior Officer E0

GFM Combined 1 Free Revision Test SAIL JO E-0

Submit Solution

More Questions on This Topic :

Latest Videos

Latest Test Papers