The Bombay stock exchange(BSE) sensex/index is given by S = log x and NSE index by $N = (l o g x)^{2}$ where x > 1. Find the number of times the two indices cross each other.

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Cannot be determined

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A
1

In simple words, we have to find the values for which N = S

$(l o g x)^{2} - l o g x = 0$

$l o g x * (l o g x - 1) = 0$

Since log $x \neq 0$ as x > 1

Therefore, log $x = 1 \Rightarrow x = 10$

Hence there is only one time when the two indices cross each other.

Suggest Corrections

Similar questions

Let f(x) = x + sin x. The area bounded by $y = f^{- 1} (x), y = x, x ϵ [0, π]$ is

Consider the following statements:

Which of the statements given above is/are correct?

1 only
1 and 3
2 and 3
None of these

NSE Indices
$\begin{matrix} Index & Current & Previous & % Change S & P CNX Nifty & 3641.1 & 3770.55 & - 3.43 % CNX Nifty Junior & 6458.55 & 6634.85 & - 2.66 % CNX IT & 5100.5 & 5314.05 & - 4.02 % Bank Nifty & 5039.05 & 5251.55 & - 4.05 % CNX 100 & 3519.35 & 3640.35 & - 3.32 % \end{matrix}$

World Markets
$\begin{matrix} Index & Current & Previous & % Change NYSE Cornposite & 8926.88 & 9120.93 & - 2.13 % NASDAQ Composite & 2350.57 & 2402.29 & - 2.15 % DOW Jones IA & 12076 & 12318.6 & - 1.97 % S & P 500 & 1377.95 & 1406.6 & - 2.04 % Nikkei 225 & 16676.9 & 17178.8 & - 2.92 % \end{matrix}$

The above figures are taken from the website of National Stock Exchange of India. They illustrate the movement of NSE stock indices as well as world stock indices on the date indicated.

What do you mean by a stock index? How is it calculated?

Which of the following is the Index of Bombay Stock Exchange?

NSE Indices	Word Markets
Index	Current	Prev.	% CHG	Index	Current	Prev.	% Change
S&P CNX Nifty	3641.1	3770.55	-3.43%	NYSE Composite	8926.88	9120.93	-2.13%
CNX Nifty Junior	6458.55	6634.85	-2.66%	NASDAQ Composite	2350.57	2402.29	-2.15%
CNX IT	5100.5	5314.05	-4.02%	DOW Jones I. A.	12076	12318.6	-1.97%
Bank Nifty	5039.05	5251.55	-4.05%	S & P 500	1377.95	1406.6	-2.04%
CNX 100	3519.35	3540.35	-3.32%	Nikkei 225	16676.9	17178.8	-2.92%
More

The above figures are taken from the website of national stock exchange of India. They illustrate the movement of NSE stock indices as well as world stock indices on the date indicated.

Questions

1. What do you mean by a stock index? How is it calculated?

2. What conclusions can you draw from the various movements of NSE stock indices?

3. What factors affect the movement of stock indices? Elaborate on the nature of these factors.

4. What relationship do you see between the movement of indices in world markets and NSE indices?

5. Give details of all the indices mentioned above. You can find information on the web or business magazines.

Join BYJU'S Learning Program

The Bombay stock exchange(BSE) sensex/index is given by S = log x and NSE index by N=(logx)2 where x > 1. Find the number of times the two indices cross each other.

The correct option is A 1 In simple words, we have to find the values for which N = S (logx)2−logx=0 log x∗(logx−1)=0 Since log x≠0 as x > 1 Therefore, log x=1⇒x=10 Hence there is only one time when the two indices cross each other.

The Bombay stock exchange(BSE) sensex/index is given by S = log x and NSE index by $N = (l o g x)^{2}$ where x > 1. Find the number of times the two indices cross each other.

The correct option is A
1

In simple words, we have to find the values for which N = S

$(l o g x)^{2} - l o g x = 0$

$l o g x * (l o g x - 1) = 0$

Since log $x \neq 0$ as x > 1

Therefore, log $x = 1 \Rightarrow x = 10$

Hence there is only one time when the two indices cross each other.