The problem requires us to first arrange the letters of the given word 'ACQUIRE' in alphabetical order. Then, we need to identify the fifth letter from the left end and the first letter from the right end in this new arrangement. Finally, we count the number of letters in the English alphabetical series that fall between these two identified letters.
A) 3. As determined in the step-by-step explanation, there are 3 letters (R, S, T) between 'Q' and 'U' in the English alphabetical series.
Find the mode of the given frequency distribution.
| Marks | Frequency |
| 51 | 3 |
| 29 | 4 |
| 85 | 6 |
| 40 | 7 |
The mode of a frequency distribution is the value that appears most frequently in the data set. To find the mode from a given frequency distribution table, we need to identify the item (or mark, in this case) that has the highest frequency.
Correct Option: D) 40 is the mark with the highest frequency (7), making it the mode.
The question asks to identify a combination reaction from the given options. A combination reaction is a type of chemical reaction in which two or more reactants combine to form a single product. The general form is \(A + B \rightarrow AB\).
A) \(2\text{H}_2(\text{g}) + \text{O}_2(\text{g}) \rightarrow 2\text{H}_2\text{O}(\text{l})\) is a combination reaction because two reactants (\(\text{H}_2\) and \(\text{O}_2\)) combine to form a single product (\(\text{H}_2\text{O}\)).
The question asks to identify the main waste products produced by plants. To answer this, we need to recall the primary metabolic processes in plants, namely photosynthesis and respiration, and their respective by-products.
A) COâ‚‚, Oâ‚‚ and water vapour - This option correctly lists all the major waste products released by plants: carbon dioxide (from respiration), oxygen (from photosynthesis), and water vapour (from transpiration).
The total amount payable at maturity on a certain sum invested at simple interest at 8% p.a. for 3\( \frac{1}{2} \) years exceeds the simple interest payable on the same sum at 10.5% p.a. for 12 years by ₹156. The sum (in ₹) is:
The problem involves simple interest calculations. We need to set up equations for the total amount payable (Principal + Simple Interest) for the first scenario and the simple interest for the second scenario. Then, use the given difference between these two values to find the principal sum.
The sum is ₹7,800.
A) 7,800 is the correct sum calculated based on the given conditions.
To find the least number that leaves a specific remainder when divided by several numbers, we first find the Least Common Multiple (LCM) of the divisors. Then, we add the common remainder to the LCM.
First, we find the prime factorization of each number:
To find the LCM, we take the highest power of each prime factor present in the numbers:
\[ \text{LCM}(12, 16, 18) = 2^4 \times 3^2 \]\[ \text{LCM}(12, 16, 18) = 16 \times 9 \]\[ \text{LCM}(12, 16, 18) = 144 \]The problem states that the number leaves a remainder of 5 in each case. So, the required number will be the LCM plus the remainder.
\[ \text{Required Number} = \text{LCM} + \text{Remainder} \]\[ \text{Required Number} = 144 + 5 \]\[ \text{Required Number} = 149 \]The number 149 satisfies all the conditions.
D) 149. This is the least number that leaves a remainder of 5 when divided by 12, 16, and 18.
The question asks to identify which of the given options is NOT one of the Purusharthas, the four aims of human life in Hinduism. To answer this, we need to recall the four traditional Purusharthas.
B) Sattva
Sattva is one of the three Gunas (qualities or tendencies) in Samkhya philosophy, which are Sattva, Rajas, and Tamas. These Gunas describe the fundamental qualities of nature (Prakriti) and influence the mind and consciousness. Sattva represents purity, goodness, knowledge, and harmony. While important in Hindu philosophy, it is a quality or a state of being, not one of the four Purusharthas (aims of life).
To find the loss percentage, we first need to calculate the total cost price of the items and the total selling price. The loss is the difference between the total cost price and the total selling price. The loss percentage is then calculated by dividing the loss by the total cost price and multiplying by 100.
The cost of the camera is ₹25,000.
The cost of the leather case is ₹2,750.
Total Cost Price \( = \text{Cost of Camera} + \text{Cost of Leather Case}\)
\[ \text{CP} = \text{₹}25,000 + \text{₹}2,750 = \text{₹}27,750 \]Arti sold both items for ₹26,085.
\[ \text{SP} = \text{₹}26,085 \]Since the selling price is less than the cost price, there is a loss.
Loss \( = \text{CP} - \text{SP}\)
\[ \text{Loss} = \text{₹}27,750 - \text{₹}26,085 = \text{₹}1,665 \]The formula for loss percentage is:
\[ \text{Loss Percentage} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100 \% \]\[ \text{Loss Percentage} = \left( \frac{\text{₹}1,665}{\text{₹}27,750} \right) \times 100 \% \]\[ \text{Loss Percentage} = 0.06 \times 100 \% = 6 \% \]B) 6% — The total cost price was ₹27,750 and the selling price was ₹26,085, resulting in a loss of ₹1,665. When calculated as a percentage of the cost price, the loss is 6%.
This problem involves setting up and solving a system of linear equations based on given age relationships at different points in time. We will define variables for their present ages and then translate the given conditions into equations.
Define variables for present ages:
Let Praveena's present age be \(P\) years.
Let her daughter's present age be \(D\) years.
Formulate the first equation based on the past condition:
"One year ago, Praveena was four times as old as her daughter."
One year ago, Praveena's age was \(P-1\).
One year ago, her daughter's age was \(D-1\).
So, we have the equation:
Formulate the second equation based on the future condition:
"Six years hence, Praveena's age will exceed twice her daughter's age by 7 years."
Six years hence, Praveena's age will be \(P+6\).
Six years hence, her daughter's age will be \(D+6\).
So, we have the equation:
Solve the system of equations:
We have two expressions for \(P\). Equate them:
Find Praveena's present age:
Substitute \(D=8\) into Equation 1 (or Equation 2):
Calculate the sum of their present ages:
Sum \(= P + D = 29 + 8 = 37\) years.
B) 37 years is the sum of their present ages.