Study the given diagram carefully and answer the question. The numbers in different sections indicate the number of persons.
How many rural females are there who are NOT employed?
To find the number of rural females who are not employed, we need to analyze the diagram and identify the relevant sections.
Correct Option: D) 6
The question asks for the full form of MGNREGA. This requires knowledge of common acronyms related to Indian government schemes, particularly those focused on rural employment and welfare.
D) Mahatma Gandhi National Rural Employment Guarantee Act
MGNREGA is the acronym for the Mahatma Gandhi National Rural Employment Guarantee Act, which is an Indian labour law and social security measure that aims to guarantee the 'right to work'. It was passed in 2005.
The question asks for the full form of "MICR" in the context of MICR code. This is a direct knowledge-based question related to banking and financial technology.
B) Magnetic Ink Character Recognition. This is the correct and universally accepted full form of MICR. It refers to the technology that uses special magnetic ink to print characters, which can then be read by a machine for automated processing, especially in banking for cheques.
The problem presents a series of number pairs where the relationship between the numbers in each pair needs to be identified. We need to find a consistent pattern that applies to the first two pairs (32:56 and 42:66) and then apply it to the third pair (52:?) to find the missing number.
Let the first number be \(A\) and the second number be \(B\).
We can observe that \(32 = 4 \times 8\). The next number \(56 = 7 \times 8\).
Another way to look at it is \(32 = 4^2 \times 2\). This doesn't seem to lead anywhere simple.
Let's consider the digits. \(32\). The digits are 3 and 2. Their sum is \(3+2=5\). Their product is \(3 \times 2 = 6\). This doesn't directly relate to 56.
Consider the number itself. \(32\). If we add its digits, \(3+2=5\). If we multiply its digits, \(3 \times 2 = 6\). This gives us 5 and 6, which form 56. Let's test this hypothesis.
Hypothesis: For a number \(XY\), the related number is \((X+Y)(X \times Y)\).
For 32: \(X=3, Y=2\).
Sum of digits: \(3+2=5\).
Product of digits: \(3 \times 2 = 6\).
Combining these gives 56. This matches the first pair.
Let's apply the hypothesis to the third pair (42 : 66).
For 42: \(X=4, Y=2\).
Sum of digits: \(4+2=6\).
Product of digits: \(4 \times 2 = 8\).
Combining these gives 68. However, the given second number is 66. So, this hypothesis is incorrect.
Let's re-evaluate the relationship for 32 : 56.
Consider the number \(A\). Let \(A = 10x + y\).
Another common pattern is based on squares or cubes, or multiplication factors.
If we take the digits of 32, which are 3 and 2.
Consider \((3+2) \times (3 \times 2) = 5 \times 6 = 30\). Not 56.
Let's try a different approach: Operations on the number itself.
For 32: \(32 \times 2 - 8 = 64 - 8 = 56\). This works for the first pair.
Hypothesis: For a number \(A\), the related number is \(2A - 8\).
For 42: \(2 \times 42 - 8 = 84 - 8 = 76\). However, the given number is 66. So, this hypothesis is also incorrect.
Let's look at the numbers again:
32 : 56
42 : 66
Difference: \(56 - 32 = 24\)
Difference: \(66 - 42 = 24\)
It appears the pattern is that the second number is obtained by adding 24 to the first number.
The pattern is: Second number = First number + 24.
For 52: \(52 + 24 = 76\).
C) 76 is the correct answer because applying the consistent pattern of adding 24 to the first number yields 76 for the third pair.
The question asks to identify the active ingredient in antacids from the given options. Antacids are substances that neutralize stomach acid (hydrochloric acid, HCl) to relieve heartburn, indigestion, or an upset stomach. Therefore, we need to look for a basic salt among the options.
Correct Option: A) NaHCO₃
Sodium bicarbonate (\(\text{NaHCO}_3\)), commonly known as baking soda, is a weak base. When ingested, it reacts with the excess hydrochloric acid (\(\text{HCl}\)) in the stomach to produce water, carbon dioxide, and sodium chloride. This neutralization reaction helps to reduce acidity and alleviate symptoms like heartburn. The reaction is:
\[ \text{NaHCO}_3 (\text{aq}) + \text{HCl} (\text{aq}) \rightarrow \text{NaCl} (\text{aq}) + \text{H}_2\text{O} (\text{l}) + \text{CO}_2 (\text{g}) \]The problem presents a series of numbers, and we need to find the next number in the sequence. We will analyze the differences between consecutive terms to identify a pattern.
Therefore, the number that replaces the question mark is 33.
Correct Option: B) 33
There is a 20% discount on a dozen pairs of identical shoes marked at a combined price of Rs 7,200. How many such pairs of shoes can be bought for Rs 1,440?
To solve this problem, we first need to determine the discounted price of one dozen (12 pairs) of shoes. Then, we can find the price of a single pair of shoes after the discount. Finally, we will divide the given amount (Rs 1,440) by the discounted price of one pair to find out how many pairs can be bought.
Calculate the discounted price of a dozen pairs of shoes:
The marked price of a dozen pairs is Rs 7,200.
The discount is 20%.
\[ \text{Discount amount} = 20\% \text{ of } 7,200 = \frac{20}{100} \times 7,200 = 0.20 \times 7,200 = \text{Rs } 1,440 \]The selling price (discounted price) of a dozen pairs is:
\[ \text{Selling Price} = \text{Marked Price} - \text{Discount Amount} = 7,200 - 1,440 = \text{Rs } 5,760 \]Alternatively, the selling price is \(100\% - 20\% = 80\%\) of the marked price:
\[ \text{Selling Price} = 0.80 \times 7,200 = \text{Rs } 5,760 \]Calculate the discounted price of one pair of shoes:
Since a dozen means 12 pairs, the price of one pair is:
\[ \text{Price of one pair} = \frac{\text{Selling Price of 12 pairs}}{12} = \frac{5,760}{12} = \text{Rs } 480 \]Calculate how many pairs can be bought for Rs 1,440:
The amount available is Rs 1,440.
The price of one pair is Rs 480.
\[ \text{Number of pairs} = \frac{\text{Total amount available}}{\text{Price of one pair}} = \frac{1,440}{480} = 3 \]Therefore, 3 pairs of shoes can be bought for Rs 1,440.
Correct Option: D) 3
To find the height of a triangle when its area and base are given, we use the standard formula for the area of a triangle: Area \( = \frac{1}{2} \times \text{base} \times \text{height} \). We can rearrange this formula to solve for the height.
Recall the formula for the area of a triangle:
\[ \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \]Identify the given values:
Substitute the given values into the formula:
\[ 85 = \frac{1}{2} \times 5 \times \text{height} \]Simplify the equation:
\[ 85 = \frac{5}{2} \times \text{height} \]Solve for the height:
To isolate 'height', multiply both sides of the equation by \( \frac{2}{5} \):
\[ \text{height} = 85 \times \frac{2}{5} \] \[ \text{height} = \frac{170}{5} \] \[ \text{height} = 34 \text{ cm} \]B) 34 cm is the correct answer because, by applying the area formula for a triangle and substituting the given area and base, we calculate the height to be 34 cm.
The question asks to identify the NRI (Non-Resident Indian) who was posthumously awarded the Padma Shri in the field of Science and Engineering in 2022. This requires knowledge of the Padma Awards recipients for the year 2022, specifically those honored posthumously in the mentioned category.
A) Sanjay Rajaram — Dr. Sanjay Rajaram was an eminent Indian-born Mexican agricultural scientist who was awarded the World Food Prize in 2014 for his work in developing disease-resistant wheat varieties. He passed away in 2021 and was posthumously honored with the Padma Shri in 2022 in the field of Science and Engineering.
This problem involves calculating a day of the week based on a given reference day and a number of days in the future. The key concept here is that the days of the week repeat in a cycle of 7. We need to determine the current day first and then use modular arithmetic to find the day after a certain number of days.
The problem states that "yesterday was Monday".
If yesterday was Monday, then today must be Tuesday.
We need to find the day of the week after 89 days starting from Tuesday.
The days of the week repeat every 7 days. So, we need to find the remainder when 89 is divided by 7.
\[ 89 \div 7 \]\[ 89 = (12 \times 7) + 5 \]The remainder is 5. This means that after 12 full cycles of 7 days, there will be 5 additional days.
Starting from Tuesday, we count 5 days forward:
Therefore, 89 days from today (Tuesday) will be Sunday.
Correct Option: A) Sunday