The question asks to identify a communication protocol from the given options. We need to recall common communication protocols used in computer networks and the internet.
A) HTTP — HTTP (Hypertext Transfer Protocol) is a well-known and widely used communication protocol that forms the basis of data exchange on the World Wide Web.
The problem involves comparing Compound Interest (CI) and Simple Interest (SI) for a given principal amount, time period, and final amount under CI. First, we need to find the rate of interest using the CI formula. Once the rate is known, we can calculate the SI for the same principal and time. Finally, the difference between the CI paid and the SI calculated will give the amount saved.
Calculate the Rate of Interest (R) using Compound Interest:
Given:
The formula for Compound Interest is: \[ A = P \left(1 + \frac{R}{100}\right)^n \] Substitute the given values: \[ 12544 = 10000 \left(1 + \frac{R}{100}\right)^2 \] \[ \frac{12544}{10000} = \left(1 + \frac{R}{100}\right)^2 \] \[ 1.2544 = \left(1 + \frac{R}{100}\right)^2 \] Take the square root of both sides: \[ \sqrt{1.2544} = 1 + \frac{R}{100} \] \[ 1.12 = 1 + \frac{R}{100} \] \[ 0.12 = \frac{R}{100} \] \[ R = 0.12 \times 100 \] \[ R = 12\% \] The rate of interest is 12% per annum.
Calculate the Simple Interest (SI) for the same principal, time, and rate:
Given:
The formula for Simple Interest is: \[ SI = \frac{P \times R \times T}{100} \] Substitute the values: \[ SI = \frac{10000 \times 12 \times 2}{100} \] \[ SI = 100 \times 12 \times 2 \] \[ SI = 2400 \] The Simple Interest would be ₹2,400.
Calculate the amount saved:
The amount paid under Compound Interest (CI) is the total interest paid, which is \(A - P = 12544 - 10000 = \text{₹}2544\).
If Zaved had borrowed the amount on Simple Interest, he would have paid ₹2,400 as interest.
The saving would be the difference between the Compound Interest paid and the Simple Interest: \[ \text{Saving} = \text{CI} - \text{SI} \] \[ \text{Saving} = 2544 - 2400 \] \[ \text{Saving} = 144 \] He would have saved ₹144.
A) ₹144 is the correct amount saved by borrowing on simple interest instead of compound interest.
To solve this problem, we need to identify numbers within the given range (3 to 60) that satisfy two conditions: they must be odd, and they must be exactly divisible by 5. We will list all numbers divisible by 5 in the range and then filter them to keep only the odd ones.
Identify numbers divisible by 5 in the range 3 to 60:
Numbers exactly divisible by 5 end in either 0 or 5. Listing them from 3 to 60:
\(5, 10, 15, 20, 25, 30, 35, 40, 45, 50, 55, 60\)
Filter for odd numbers:
An odd number is an integer that is not divisible by 2. This means its last digit cannot be 0, 2, 4, 6, or 8. From the list above, we select only the numbers ending in 5 (since numbers ending in 0 are even):
The odd numbers that are exactly divisible by 5 in the given range are:
\(5, 15, 25, 35, 45, 55\)
Count the identified numbers:
Counting these numbers, we find there are 6 such numbers.
D) 6. There are 6 numbers between 3 and 60 (inclusive) that are odd and exactly divisible by 5: 5, 15, 25, 35, 45, and 55.
The question asks to identify the shape most similar to a rectangle and a square. We need to compare the properties of a rectangle and a square with the properties of the given options.
Correct Option: A) Rhombus. A rhombus is a quadrilateral with all four sides equal. A square is a special type of rhombus where all angles are 90 degrees. Since a square is also a type of rectangle, a rhombus shares significant geometric properties with both. All three are quadrilaterals.
The question asks about the component in Earth's atmosphere that shields it from the Sun's harmful ultraviolet (UV) radiation. This is a fundamental concept in atmospheric science and environmental studies.
B) Ozone — The ozone layer, located primarily in the stratosphere, is composed of ozone molecules (\(O_3\)). These molecules are highly effective at absorbing harmful ultraviolet (UV) radiation from the Sun, preventing most of it from reaching the Earth's surface. This absorption is crucial for the survival of life on Earth.
The question asks about the recipient of the International Gandhi Peace Prize for the year 2018. This requires knowledge of current affairs and awards.
Correct Option: B) Yohei Sasakawa
The sum of the zeros of the polynomial
\( 5x^{2} + (5p - 1)x - (2p + 5) \) is the same as one fourth of their product. Find the value of p.
We are given a quadratic polynomial and a relationship between the sum and product of its zeros. We will use Vieta's formulas to express the sum and product of the zeros in terms of the coefficients of the polynomial. Then, we will substitute these expressions into the given relationship to form an equation and solve for the unknown variable \(p\).
C) \( \frac{1}{2} \) is the correct value of \(p\) obtained from the calculations.
A box contains 6 white, 2 black and 3 red balls. If a ball is drawn at random, what is the probability that it will not be white?
\( \frac{5}{6} \)
\( \frac{6}{5} \)
\( \frac{5}{11} \)
\( \frac{6}{11} \)
To find the probability that a randomly drawn ball will not be white, we first need to determine the total number of balls and the number of balls that are not white. The probability is then calculated as the ratio of favorable outcomes (not white balls) to the total possible outcomes (total balls).
Balls that are not white include black balls and red balls.
\[ \text{Number of non-white balls} = \text{Number of black balls} + \text{Number of red balls} = 2 + 3 = 5 \]The probability is given by the formula:
\[ P(\text{Event}) = \frac{\text{Number of favorable outcomes}}{\text{Total number of possible outcomes}} \]In this case, the event is drawing a ball that is not white.
\[ P(\text{not white}) = \frac{\text{Number of non-white balls}}{\text{Total number of balls}} = \frac{5}{11} \]Correct Option: C) \( \frac{5}{11} \)
This problem involves concepts of speed, distance, and time, specifically in the context of boats and streams. We are given the speed of the boat in still water, the distance traveled downstream, and the time taken. We need to find the speed of the stream. The key is to understand that downstream speed is the sum of the boat's speed in still water and the stream's speed.
The given time is 1 hour 45 minutes. We need to convert 45 minutes into hours.
\[ 45 \text{ min} = \frac{45}{60} \text{ h} = \frac{3}{4} \text{ h} = 0.75 \text{ h} \]Therefore, the total time is:\[ \text{Time} = 1 \text{ h} + 0.75 \text{ h} = 1.75 \text{ h} \]The formula for speed is \(\text{Speed} = \frac{\text{Distance}}{\text{Time}}\). We are given the distance traveled downstream as 28 km and the time taken as 1.75 h.
\[ \text{Downstream Speed} = \frac{28 \text{ km}}{1.75 \text{ h}} \]\[ \text{Downstream Speed} = 16 \text{ km/h} \]Let \(V_b\) be the speed of the boat in still water and \(V_s\) be the speed of the stream.
The downstream speed is given by:
\[ \text{Downstream Speed} = V_b + V_s \]We are given \(V_b = 14 \text{ km/h}\) and we calculated the Downstream Speed as \(16 \text{ km/h}\).Substitute these values into the equation:
\[ 16 \text{ km/h} = 14 \text{ km/h} + V_s \]\[ V_s = 16 \text{ km/h} - 14 \text{ km/h} \]\[ V_s = 2 \text{ km/h} \]The speed of the stream is 2 km/h.
Correct Option: D) 2 km/h
The question asks to identify the Governor-General of India during the Sepoy Mutiny (also known as the Indian Rebellion of 1857). This requires knowledge of key historical figures and their tenures during significant events in British Indian history.
Correct Option: C) Lord Canning