Bissoy.com
Doctors Medicines MCQs Q&A

If p > q >1 and 0 < a < 1 then which of the following is correct option?

If p > q >1 and 0 < a < 1 then which of the following is correct option? Correct Answer log<sub>a</sub>(p – a) &lt; log<sub>a</sub>(q – a)

Explanation:

For a log function with base a as 0 < a < 1, the graph of the function can be drawn as bellow

[ alt="F16 Yerra 25-6-2021 Swati D2" src="//storage.googleapis.com/tb-img/production/21/06/F16_Yerra_25-6-2021_Swati_D2.png" style="width: 250px; height: 195px;">

The above graph is valid for,

x > 0 and 0 < a < 1

Since the function y = logax is a decreasing function for base a ∈ (0, 1). So, while operating loga on a given inequality, the sign of the inequality will change.

Calculation:

Given:

p > q > 1

⇒ (p – 1) > (q – 1) > 0

Operating log function on both sides,

⇒ loga(p -1) < loga(q - 1)

⇒ Option 3 is correct.

Related Questions

Match List I with List II List I List II Hedging Concepts Description A. European option I. Option contract exercised on any date up to maturity B. Option premium II. When the immediate exercise of an option yields positive value to its holder C. In-money option III. Option contract exercised only on the maturity date D. American option IV. It is paid by the buyer of the options upfront to the option seller Choose the correct answer from the options given below:
A man has deposited his money in a bank under two separate options for 8 years. First option gives an interest rate of 8% for first 2 years and 11% for the rest of the time the money is kept in the bank. The second option is a fixed deposit that cannot be withdrawn before 8 years and gives an interest of 10% throughout the entire term. If interest on the deposit under option 1 is less than Second option by 15,400 at the time the term of second option ends and the total money is 80000. What is the amount of money deposited in each option? (Assume all interests are simple.)
The following two statements relate to financial derivatives. Choose the correct answer for statements being correct or incorrect.
Statement I When an option is allowed to be exercised only on the maturity date, it is called an American option.
Statement II If the option holder does not lose or gain whether he exercise his option or buys or sells the asset form the market, the option is said to be at-the-money.
Which of the following statements are correct?
1. A put option is said to bein the money or favourable for the option holder when the strike price is higher than the spot price.
2. A put option is said to be out of money when the strike price is lower than the market price.
3. Fir an option writer the maximum gain is the amount of premium received by the put option holder.
Two boysM and N start from the same point. M walks 5 km south, then turns to his left and walks 6 km, then turns to his right and walks 5 km, and then again turns to his right and walks 6 km. At the same time, N walks 5 km north, then turns to his left and walks 6 km, then turns to his left and walks 10 km, and then again turns to his left and walks 3 km and then turns to his right and walks 5 km.What is the position of N with respect to M?
Which of the following are the important features of option contracts?
1. Buyers of option have limited liability.
2. Options have high degree of risk to option writers.
3. Options are exercisable only by buyers of option.
4. Buyers of option have all rights which are available to equity shareholders of the concerned companies.
Choose the correct code for the following statements being correct or incorrect. Statement I: An option which gives its holder the privilege of selling to other party a fixed amount of some stock at a stated price on or before a predetermined date is known as call option. Statement II : In an option, the holder has the privilege of purchasing from other party a fixed amount of some stock at a stated price on or before a predetermined date is known as put option. 
A call center company had to arrange transportation for its employees. They asked for quotes from different provider agencies and the following are the options they got: A. This option allows having uniform rate for day and night trips. This would cost you Rs.1000 per trip. B. This option has differential fare for day and night trips. Day trips would cost 700 per trip and night trips would be charged 1200 per trip. C. This option charges depending on the total distance covered in a trip. It charges Rs.800 per trip if trip distance is more than 50 KM and Rs.1100 if trip distance is less than 50 KM. If the company has 3 night trips and all less than 50 KM and 3 day trips less than 50 KM, which would be the best option?
Garima starts walking towards the south from point R. He walks for 5m to reach Point S then turns right and walks for 2m to reach point T from there he turns left and walks for 3m to reach Point Z. He then turns right from point Z and walks for 6m to reach point Y and then turns right and walks for 3m to reach point X. He then turns right from point X and walks for 4m to reach point W and then turns left and walks for 5m to reach point V and then turns left and walks for 4m till point U and stops. What is the shortest distance between point V and point R?
From point P, Vikas walks towards the west for 2m, he then turns left and walks for 3m and then turns left and walks for 5m. He then turns left and walks for 4m and then turns left and walks for 2m. He then turns right and walks for 2m and then turns right and walks for 3m till point Q. What is the shortest distance between point P and point Q?