To find the missing number in a series, we need to identify the pattern or rule governing the sequence of numbers. This often involves looking at the differences between consecutive terms, or identifying a mathematical operation that transforms one term into the next.
Analyze the given series: The series is 3, 7, 13, 21, 31, ?
Calculate the differences between consecutive terms:
Identify the pattern in the differences: The differences are 4, 6, 8, 10. This is an arithmetic progression where each term increases by 2. The next difference in this sequence should be \(10 + 2 = 12\).
Apply the pattern to find the missing term: To find the next number in the original series, add the next difference (12) to the last known term (31).
\[ 31 + 12 = 43 \]Therefore, the missing number is 43.
C) 43 — The pattern of differences between consecutive terms is an arithmetic progression (4, 6, 8, 10, ...), where each difference increases by 2. The next difference is 12, so \(31 + 12 = 43\).
The question asks to identify the state with the second-highest number of Lok Sabha seats. This requires knowledge of the distribution of Lok Sabha seats among Indian states.
Maharashtra has 48 Lok Sabha seats, which is the second-highest number after Uttar Pradesh.
The problem is a coding-decoding question where a word is coded into another word based on a specific pattern. We need to identify the pattern used to transform "TABLE" into "RYZJC" and then apply the same pattern to decode "CHAIR".
Original word: T A B L E
Coded word: R Y Z J C
The pattern is consistently subtracting 2 from the alphabetical position of each letter. If the result goes below A, it wraps around from Z.
C H A I R becomes A F Y G P.
B) AFYGP is the correct code for CHAIR based on the identified pattern (each letter shifted two places backward in the alphabet).
The question asks to identify the odd pair out among the given options. This means we need to evaluate each pair and determine if the components listed are primary constituents of the substance mentioned. We are looking for a pair where the components are NOT the main constituents of the associated substance.
D) Magnesium & Silver : Stainless steel — This pair is the odd one out because stainless steel is an alloy primarily made of iron, chromium, and nickel, not magnesium and silver.
The question asks to identify the first product in India to receive a Geographical Indication (GI) tag. This requires knowledge of the history of GI tagging in India.
Correct Option: A) Darjeeling Tea was the first product in India to receive the Geographical Indication (GI) tag. It was registered in 2004-2005 under the Geographical Indications of Goods (Registration and Protection) Act, 1999.
The question asks for the freezing point of water in Fahrenheit. This is a fundamental concept in physics and general science, often tested in competitive exams. We need to recall the standard freezing point of water in different temperature scales.
The problem presents a series of letter groups. We need to identify the pattern in how these groups are formed and then apply that pattern to find the next group in the sequence.
Correct Option: D) GJMP
If the rate of interest is 8% per annum and Rs. 10,000 lent at the compound interest half yearly then calculate the equivalent simple rate of interest for the first year?
To find the equivalent simple rate of interest for the first year when interest is compounded half-yearly, we need to calculate the total interest earned in one year under compound interest and then express it as a simple interest rate. The principal amount is Rs. 10,000, the annual interest rate is 8%, and compounding occurs half-yearly.
Determine the compounding periods and rate per period:
Since the interest is compounded half-yearly, there are two compounding periods in a year.
The annual rate of interest is \(R = 8\%\).
The rate of interest per half-year period is \[r = \frac{R}{2} = \frac{8\%}{2} = 4\%\].
Calculate the amount after one year using compound interest:
The principal amount is \(P = \text{Rs. } 10,000\).
The number of compounding periods in one year is \(n = 2\).
The formula for the amount \(A\) after \(n\) periods with compound interest is:
\[ A = P \left(1 + \frac{r}{100}\right)^n \]\[ A = 10000 \left(1 + \frac{4}{100}\right)^2 \]\[ A = 10000 (1 + 0.04)^2 \]\[ A = 10000 (1.04)^2 \]\[ A = 10000 \times 1.0816 \]\[ A = \text{Rs. } 10,816 \]Calculate the compound interest earned in one year:
Compound Interest \((CI) = A - P\)
\[ CI = 10816 - 10000 \]\[ CI = \text{Rs. } 816 \]Calculate the equivalent simple rate of interest:
The simple interest formula is \(SI = \frac{P \times R_{eq} \times T}{100}\), where \(R_{eq}\) is the equivalent simple interest rate and \(T\) is the time in years.
For the first year, \(T = 1\) year.
We want to find \(R_{eq}\) such that \(CI = SI\).
\[ 816 = \frac{10000 \times R_{eq} \times 1}{100} \]\[ 816 = 100 \times R_{eq} \]\[ R_{eq} = \frac{816}{100} \]\[ R_{eq} = 8.16\% \]A) 8.16% is the equivalent simple rate of interest for the first year, as calculated.
The question asks about the type of software used to create a '.docx' file. This requires knowledge of common file extensions and their associated applications.
Correct Option: C) Word processor
Evaluate (\( \frac{35}{2} \))% of 800 gm — (\( \frac{45}{2} \))% of 400 gm
The problem requires us to calculate the difference between two percentage values of given quantities. We will first calculate each percentage value separately and then find their difference.
To find a percentage of a number, we convert the percentage to a decimal or fraction and multiply it by the number.
\[ \left( \frac{35}{2} \right) \% = \frac{\frac{35}{2}}{100} = \frac{35}{2 \times 100} = \frac{35}{200} \]\[ \text{So, } \left( \frac{35}{2} \right) \% \text{ of } 800 \text{ gm} = \frac{35}{200} \times 800 \text{ gm} \]\[ = 35 \times \frac{800}{200} \text{ gm} = 35 \times 4 \text{ gm} = 140 \text{ gm} \]Similarly, for the second term:
\[ \left( \frac{45}{2} \right) \% = \frac{\frac{45}{2}}{100} = \frac{45}{2 \times 100} = \frac{45}{200} \]\[ \text{So, } \left( \frac{45}{2} \right) \% \text{ of } 400 \text{ gm} = \frac{45}{200} \times 400 \text{ gm} \]\[ = 45 \times \frac{400}{200} \text{ gm} = 45 \times 2 \text{ gm} = 90 \text{ gm} \]The problem asks for the value of (\( \frac{35}{2} \))% of 800 gm — (\( \frac{45}{2} \))% of 400 gm.
\[ \text{Difference} = 140 \text{ gm} - 90 \text{ gm} = 50 \text{ gm} \]A) 50 gm — The calculated difference is 50 gm, which matches this option.