NDA 2016 Paper 2 | Sequence And Series Question 14 | Mathematics

If $${x^{\ln \left( {{y \over z}} \right)}}.{y^{\ln {{(xz)}^2}}}.{z^{\ln \left( {{x \over y}} \right)}} = {y^{4\,\ln \,y}}$$ for any x > 1, y > 1 and z > 1, then which one of the following is correct?

$$\ln y$$ is the GM of $$\ln x$$, $$\ln x$$, $$\ln x$$ and $$\ln z$$

$$\ln y$$ is the AM of $$\ln x$$, $$\ln x$$, $$\ln x$$ and $$\ln z$$

$$\ln y$$ is the HM of $$\ln x$$, $$\ln x$$, $$\ln x$$ and $$\ln z$$

$$\ln y$$ is the AM of $$\ln x$$, $$\ln x$$, $$\ln z$$ and $$\ln z$$

NDA 2016 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

Read the following information carefully and answer the questions given below.

Given that $${\log _x}y,\,{\log _z}x,\,{\log _y}z$$ are in GP, xyz = 64 and x³, y³ and z³ are in AP.

Which one of the following is correct?

x, y and z are

in AP only

in GP only

in both AP and GP

Neither in AP nor in GP

NDA 2016 Paper 1

MCQ (Single Correct Answer)

+2.5

-0.83

Read the following information carefully and answer the questions given below.

Given that $${\log _x}y,\,{\log _z}x,\,{\log _y}z$$ are in GP, xyz = 64 and x³, y³ and z³ are in AP.

Which one of the following is correct?

xy, yz and zx are

in AP only

in GP only

in both AP and GP

Neither in AP nor in GP

NDA 2017 Paper 2

MCQ (Single Correct Answer)

+2.5

-0.83

The value of the product $${6^{{1 \over 2}}} \times {6^{{1 \over 4}}} \times {6^{{1 \over 8}}} \times {6^{{1 \over {16}}}} \times ....$$ up to infinite terms is

216

512

PREVIOUS NEXT

NDA Subjects

English

Reading Comprehension Synonyms Antonyms Cloze Rearranging Sentences in a Paragraph Idioms and Phrases Word Classes Sentence Completion Improvement of Sentence

General Science

Physics Chemistry Biology

General Studies

History Geography Polity Economy General Knowledge