The problem presents a number series with a missing term. We need to identify the pattern or rule governing the series to find the missing number. We will look for arithmetic or geometric progressions, or a combination of operations between consecutive terms.
The complete series is \(8, 12, 30, 105, 472.5\).
The missing number is \(12\).
D) 12 — The pattern identified is that each term is multiplied by a factor that increases by \(1\) for each subsequent step. The multipliers are \(1.5, 2.5, 3.5, 4.5\). Applying this, \(8 \times 1.5 = 12\).
The question asks to identify the state with the highest literacy rate in India according to the Census 2011. This requires knowledge of the literacy statistics from the Census 2011 report.
As per the Census 2011, Kerala recorded the highest literacy rate among all Indian states. Lakshadweep, a Union Territory, had a slightly higher literacy rate than Kerala, but the question specifically asks for a "state".
C) Kerala had the highest literacy rate among Indian states as per Census 2011, with a literacy rate of 94.0%. Lakshadweep, a Union Territory, had an even higher literacy rate of 91.85%, but Kerala is the highest among states.
To simplify the given expression, we must follow the order of operations, often remembered by the acronym BODMAS/PEMDAS. This means we perform operations in the following order: Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), and Addition and Subtraction (from left to right). We will work from the innermost brackets outwards.
First, evaluate the innermost parenthesis: \((11 - 12 \div 3)\).
According to BODMAS, division comes before subtraction:
\[ 12 \div 3 = 4 \]\[ 11 - 4 = 7 \]Substitute this value back into the expression:
\[ 245 - [135 - \{84 \div 4 \text{ of } 3 - 7\}] \]Next, evaluate the term \((4 \text{ of } 3)\) inside the curly braces. "Of" means multiplication.
\[ 4 \text{ of } 3 = 4 \times 3 = 12 \]Substitute this back into the expression:
\[ 245 - [135 - \{84 \div 12 - 7\}] \]Now, evaluate the expression inside the curly braces: \(\{84 \div 12 - 7\}\).
Division comes before subtraction:
\[ 84 \div 12 = 7 \]\[ 7 - 7 = 0 \]Substitute this value back into the expression:
\[ 245 - [135 - 0] \]Next, evaluate the expression inside the square brackets: \([135 - 0]\).
\[ 135 - 0 = 135 \]Finally, perform the last subtraction:
\[ 245 - 135 = 110 \]D) 110 is the correct answer, as derived from the step-by-step simplification of the expression following the BODMAS rule.
The question asks for the commencement year of the Dowry Prohibition Act. This is a factual question related to Indian legislation. To answer it correctly, one needs to recall the specific year this significant act was enacted.
Correct Option: B) The Dowry Prohibition Act was enacted and commenced in 1961. This Act made the practice of giving or taking dowry a punishable offense.
To determine which word comes in the middle when arranged alphabetically, we need to compare the words letter by letter from left to right, just like in a dictionary. We will list them in alphabetical order and then identify the middle word.
Correct Option: A) Dear — When the words are arranged in alphabetical order (as in a dictionary), 'Dear' is the third word, making it the middle word among the five given words.
The question asks for the total forest cover of India as per the India State of Forest Report (ISFR) 2019. This requires recalling specific data from the ISFR 2019 report, which is a factual question.
Correct Option: D) 21.67% of the total geographical area of the country
We need to find the principal amount (sum invested). We are given the time period, annual interest rate, and the difference in compound interest when calculated annually versus half-yearly. We will set up equations for the compound interest in both scenarios and then use the given difference to solve for the principal.
Define variables:
Calculate Compound Interest (CI) when compounded annually:
The formula for amount \(A\) compounded annually is \(A = P \left(1 + \frac{R}{100}\right)^T\).
So, the amount \(A_1\) after 2 years compounded annually is:
\[ A_1 = P \left(1 + \frac{10}{100}\right)^2 = P \left(1 + \frac{1}{10}\right)^2 = P \left(\frac{11}{10}\right)^2 = P \times \frac{121}{100} = 1.21P \]The Compound Interest \(CI_1\) is \(A_1 - P\):
\[ CI_1 = 1.21P - P = 0.21P \]Calculate Compound Interest (CI) when compounded half-yearly:
When compounded half-yearly, the rate becomes \(\frac{R}{2}\) and the time becomes \(2T\).
The amount \(A_2\) after 2 years compounded half-yearly is:
\[ A_2 = P \left(1 + \frac{5}{100}\right)^4 = P \left(1 + \frac{1}{20}\right)^4 = P \left(\frac{21}{20}\right)^4 \] \[ A_2 = P \times \frac{21 \times 21 \times 21 \times 21}{20 \times 20 \times 20 \times 20} = P \times \frac{194481}{160000} = 1.21550625P \]The Compound Interest \(CI_2\) is \(A_2 - P\):
\[ CI_2 = 1.21550625P - P = 0.21550625P \]Use the given difference in interest:
We are given that \(CI_2 - CI_1 = \text{₹}1,762\).
\[ 0.21550625P - 0.21P = 1762 \] \[ 0.00550625P = 1762 \] \[ P = \frac{1762}{0.00550625} \] \[ P = \frac{1762}{550625/100000000} = \frac{1762 \times 100000000}{550625} \]Let's simplify the calculation:
\[ P = \frac{1762}{0.00550625} \approx \frac{1762}{0.0055} \approx 320363.63 \]To get an exact value, we can perform the division:
\[ P = 320000 \]Correct Option: B) ₹3,20,000
The question asks to identify India's newest nuclear power plant among the given options. This requires knowledge of the operational timelines and recent developments in India's nuclear energy sector.
Correct Option: A) Kudankulam. The Kudankulam Nuclear Power Plant, particularly its Unit 2, which began commercial operation in April 2017, is the newest operational nuclear power plant in India among the given choices. While other plants have older units, Kudankulam's latest operational unit is the most recent.
Study the given pattern carefully and select the number from among the given options that can replace the question mark (?).
| 5 | 4 | 141 |
| 6 | 2 | 220 |
| 7 | 3 | ? |
The problem presents a pattern involving three numbers in each set: two input numbers and one output number. We need to identify the mathematical relationship between the first two numbers and the third number in the given sets and then apply the same logic to find the missing number.
D) 352 is the correct answer, derived from applying the pattern \(A^3 + B^2\) to the given numbers.