The question asks to identify the state where the Anthurium Festival is celebrated to promote farmers, flowers, and horticulture. This requires knowledge of specific cultural and agricultural festivals in different Indian states, particularly in the North-Eastern region.
Correct Option: A) The Anthurium Festival is an annual festival celebrated in Mizoram, typically in the month of September. It is organized by the Department of Tourism, Government of Mizoram, with the primary objective of promoting farmers, flowers (especially the Anthurium flower, which is suitable for the state's climate), and horticulture. It also aims to boost tourism and cultural exchange in the state.
Which of the following interchanges of numbers would make the given equation correct?
25 ÷ 5 × 2 + 25 – 11 = 24
The problem requires us to find which interchange of two numbers will make the given equation mathematically correct. We need to test each option by swapping the specified numbers in the original equation and then evaluating the left-hand side (LHS) to see if it equals the right-hand side (RHS), which is 24. We will follow the order of operations (BODMAS/PEMDAS).
The original equation is: \(25 \div 5 \times 2 + 25 - 11 = 24\)
Let's evaluate the original equation first to confirm it's incorrect:
Wait, the original equation is already correct! Let's re-read the question carefully. Ah, the question asks "Which of the following interchanges of numbers would make the given equation correct?" This implies the given equation is currently incorrect, and we need to make it correct. However, my calculation shows it's already correct. This is a common trick in competitive exams. If the original equation is already correct, then an interchange of numbers that maintains this correctness would be the answer. Let's assume the question implies that the equation *as written* is intended to be incorrect, and we need to find an interchange that *results* in it being correct. Or, perhaps my initial evaluation was wrong.
Let's re-evaluate the original equation carefully:
\[ 25 \div 5 \times 2 + 25 - 11 \]\[ 5 \times 2 + 25 - 11 \]\[ 10 + 25 - 11 \]\[ 35 - 11 \]\[ 24 \]The original equation is indeed correct: \(24 = 24\). This means we are looking for an interchange that, when applied to the original, *still results in 24*. This is unusual for such problems, which usually start with an incorrect equation. Let's proceed by checking the options, assuming we need to maintain the correctness.A) 11, 24
Interchange 11 and 24 in the original equation. The equation becomes:
\[ 25 \div 5 \times 2 + 25 - 24 = 11 \]Let's evaluate the LHS:\[ 25 \div 5 \times 2 + 25 - 24 \]\[ 5 \times 2 + 25 - 24 \]\[ 10 + 25 - 24 \]\[ 35 - 24 \]\[ 11 \]So, \(11 = 11\). This makes the equation correct. Therefore, option A is the correct answer.Interchange 2 and 5 in the original equation:
\[ 25 \div 2 \times 5 + 25 - 11 = 24 \]Evaluate the LHS:\[ 12.5 \times 5 + 25 - 11 \]\[ 62.5 + 25 - 11 \]\[ 87.5 - 11 \]\[ 76.5 \]Since \(76.5 \neq 24\), this option is incorrect.Interchange 5 and 25 in the original equation. There are two 25s. Let's assume the first 25 and the 5 are swapped.
\[ 5 \div 25 \times 2 + 25 - 11 = 24 \]Evaluate the LHS:\[ 0.2 \times 2 + 25 - 11 \]\[ 0.4 + 25 - 11 \]\[ 25.4 - 11 \]\[ 14.4 \]Since \(14.4 \neq 24\), this option is incorrect. If we swap the second 25 with 5, the equation becomes:\[ 25 \div 5 \times 2 + 5 - 11 = 24 \]Evaluate the LHS:\[ 5 \times 2 + 5 - 11 \]\[ 10 + 5 - 11 \]\[ 15 - 11 \]\[ 4 \]Since \(4 \neq 24\), this option is also incorrect.Interchange 24 and 25. The original equation has 25 twice. Let's assume we swap 24 (the RHS value) with the first 25 in the LHS.
\[ 24 \div 5 \times 2 + 25 - 11 = 25 \]Evaluate the LHS:\[ 4.8 \times 2 + 25 - 11 \]\[ 9.6 + 25 - 11 \]\[ 34.6 - 11 \]\[ 23.6 \]Since \(23.6 \neq 25\), this option is incorrect. If we swap 24 with the second 25, the equation becomes:\[ 25 \div 5 \times 2 + 24 - 11 = 25 \]Evaluate the LHS:\[ 5 \times 2 + 24 - 11 \]\[ 10 + 24 - 11 \]\[ 34 - 11 \]\[ 23 \]Since \(23 \neq 25\), this option is also incorrect.The question asks to identify which language was added to the list of official languages of India in 1967. This requires knowledge of the amendments made to the Eighth Schedule of the Indian Constitution.
Correct Option: D) Sindhi was added to the Eighth Schedule of the Indian Constitution in 1967 by the 21st Constitutional Amendment Act, increasing the number of official languages from 14 to 15.
The problem involves finding two numbers given their difference and the product of their LCM (Least Common Multiple) and HCF (Highest Common Factor). We will use the fundamental property that for any two positive integers, the product of the numbers is equal to the product of their LCM and HCF. Then we will use the given difference to find the numbers.
Let the two numbers be \(a\) and \(b\).
We are given that the product of their LCM and HCF is 48. The fundamental property of numbers states that for any two positive integers \(a\) and \(b\):
\[ a \times b = \text{LCM}(a, b) \times \text{HCF}(a, b) \]Using the given information, we have:
\[ a \times b = 48 \]We are also given that the two numbers differ by 13. Without loss of generality, let's assume \(a > b\). So,
\[ a - b = 13 \]Now we have a system of two equations with two variables:
From equation (ii), we can express \(a\) in terms of \(b\):
\[ a = 13 + b \]Substitute this expression for \(a\) into equation (i):
\[ (13 + b) \times b = 48 \]Expand the equation:
\[ 13b + b^2 = 48 \]Rearrange it into a standard quadratic equation form:
\[ b^2 + 13b - 48 = 0 \]Solve the quadratic equation for \(b\). We can factor the quadratic equation. We need two numbers that multiply to -48 and add up to 13. These numbers are 16 and -3.
\[ (b + 16)(b - 3) = 0 \]This gives two possible values for \(b\): \(b = -16\) or \(b = 3\).
Since numbers are usually considered positive in such problems (especially for LCM/HCF context, though HCF/LCM can be extended to negative integers, the common interpretation implies positive integers), we take \(b = 3\).
Now, substitute \(b = 3\) back into the equation \(a = 13 + b\):
\[ a = 13 + 3 \]\[ a = 16 \]So, the two numbers are 16 and 3.
Let's verify these numbers: Their product is \(16 \times 3 = 48\), which matches the given product of LCM and HCF. Their difference is \(16 - 3 = 13\), which also matches the given information.
Correct Option: A) 3 and 16
This problem involves calculating the combined work rate of two individuals working on alternate days to complete a bulk order. We need to determine the number of gowns each person stitches per day, then calculate the number of gowns stitched in a 2-day cycle, and finally find out how many such cycles are needed to complete the order, accounting for any remaining work.
They work on alternate days, starting with Rani.
Total gowns to stitch = 52.
Number of full 2-day cycles = \[\frac{\text{Total gowns}}{\text{Gowns per cycle}} = \frac{52}{5} = 10 \text{ cycles with a remainder of } 2 \text{ gowns}\].
After 20 days, 50 gowns are stitched. It's the end of Padma's turn (Day 2 of the 10th cycle).
Total days = \(20 \text{ days (for 50 gowns)} + 1 \text{ day (for remaining 2 gowns)}\) = 21 days.
Correct Option: C) 21 days
The sum of the ages of Sneha and Kishore is 26 years. If 3 years ago, Kishore was \( \frac{3}{2} \) times as old as Sneha, then the present age of Sneha is:
This problem involves setting up a system of two linear equations based on the given information about the ages of Sneha and Kishore. We will define variables for their present ages, form equations from the sum of their ages and their ages 3 years ago, and then solve these equations simultaneously to find Sneha's present age.
Let Sneha's present age be \(S\) years.
Let Kishore's present age be \(K\) years.
The sum of their present ages is 26 years.
\[ S + K = 26 \quad \text{(Equation 1)} \]Sneha's age 3 years ago was \(S - 3\) years.
Kishore's age 3 years ago was \(K - 3\) years.
3 years ago, Kishore was \( \frac{3}{2} \) times as old as Sneha.
\[ K - 3 = \frac{3}{2} (S - 3) \quad \text{(Equation 2)} \]Multiply both sides by 2 to eliminate the fraction:
\[ 2(K - 3) = 3(S - 3) \]\[ 2K - 6 = 3S - 9 \]\[ 2K = 3S - 9 + 6 \]\[ 2K = 3S - 3 \quad \text{(Equation 3)} \]From Equation 1, we can express \(K\) in terms of \(S\):
\[ K = 26 - S \]Add \(2S\) to both sides:
\[ 52 = 3S + 2S - 3 \]\[ 52 = 5S - 3 \]Add 3 to both sides:
\[ 52 + 3 = 5S \]\[ 55 = 5S \]Divide by 5:
\[ S = \frac{55}{5} \]\[ S = 11 \]So, Sneha's present age is 11 years.
D) 11 years is the correct answer, as calculated by solving the system of equations.
The problem presents a series of number pairs, and we need to find the relationship between the numbers in each pair. Once the pattern is identified, we apply it to the last number to find the missing value.
C) 157 is the correct answer, as it follows the pattern \(n^2 - 12\) derived from the given pairs.
The question asks about the implementing ministry for the 'Revised Pradhan Mantri Jan Vikas Karyakram' (PMJVK). This requires knowledge of government schemes and their nodal ministries.
Correct Option: D) Ministry of Minority Affairs
The problem asks us to calculate a percentage of a given number. We need to find 18% of 200. To do this, we convert the percentage to a decimal or a fraction and then multiply it by the number.
A) 36 is the correct answer because 18% of 200 is 36.
If the manufacturer gains 12%, the wholesale dealer gains 15% and the retailer gains 20%, then find the cost of production of a table, the retail price of which is ₹15,456
This problem involves a chain of transactions where each party (manufacturer, wholesale dealer, retailer) adds a percentage gain to their cost. We are given the final retail price and need to work backward to find the initial cost of production. We will use the concept of successive percentage increases.
B) 10,000 — The cost of production is ₹10,000, which, after successive gains of 12%, 15%, and 20%, results in a retail price of ₹15,456.