This problem can be solved using the principles of set theory, specifically involving percentages and the concept of inclusion-exclusion. We are given percentages of students who passed in individual subjects and failed in both, and the absolute number of students who passed in both. We need to find the total number of students.
First, let's denote the events:
We are given:
If 15% students failed in both subjects, it means 15% of students are neither in \(P\) nor in \(C\). Therefore, the percentage of students who passed in at least one subject is \(100\% - 15\% = 85\%\).
So, \(P(P \cup C) = 85\%\).
We use the formula for the union of two sets:
\[ P(P \cup C) = P(P) + P(C) - P(P \cap C) \]Substitute the known values into the formula:
\[ 85\% = 80\% + 70\% - P(P \cap C) \]Calculate the percentage of students who passed in both subjects, \(P(P \cap C)\):
\[ 85\% = 150\% - P(P \cap C) \]\[ P(P \cap C) = 150\% - 85\% \]\[ P(P \cap C) = 65\% \]We are given that 325 students passed in both subjects. This number corresponds to the 65% we just calculated.
Let \(T\) be the total number of students. Then:
\[ 65\% \text{ of } T = 325 \]\[ 0.65 \times T = 325 \]Solve for \(T\):
\[ T = \frac{325}{0.65} \]\[ T = \frac{325}{\frac{65}{100}} \]\[ T = \frac{325 \times 100}{65} \]\[ T = \frac{32500}{65} \]\[ T = 500 \]Therefore, the total number of students who appeared in the examination is 500.
Correct Option: C) 500
The question asks to identify the first Indian Governor of the Reserve Bank of India (RBI). This requires knowledge of the history of RBI governors.
C) CD Deshmukh — C.D. Deshmukh was the first Indian Governor of the Reserve Bank of India, serving from 1943 to 1949. He played a crucial role in the post-independence financial administration of India.
The question asks to identify the state where India's longest single-lane steel cable suspension bridge was inaugurated over the Siang river. This is a factual question related to current affairs or general knowledge about infrastructure projects in India.
A) Arunachal Pradesh — India's longest (300 m) single-lane steel cable suspension bridge, known as the Byorung Bridge or Siang bridge, was inaugurated over the Siang river in Arunachal Pradesh in December 2018. This bridge was constructed by the Border Roads Organisation (BRO).
The question asks about a specific collaboration between the World Bank and a commercial bank for secondary bond trading using blockchain technology. This requires knowledge of recent financial technology developments and partnerships involving international financial institutions.
Correct Option: A) The World Bank partnered with the Commonwealth Bank of Australia to enable secondary bond trading recorded on Blockchain. This initiative was part of the World Bank's efforts to explore the potential of distributed ledger technology (DLT) in capital markets, specifically with its "bond-i" (blockchain operated new debt instrument) issuance.
To find the area of the four walls of a room, we need to calculate the lateral surface area of the cuboid formed by the room's dimensions. The area of the four walls is given by the formula: \(2 \times (\text{length} + \text{breadth}) \times \text{height}\).
The area of the four walls of a room (lateral surface area of a cuboid) is given by:
\[ \text{Area} = 2 \times (L + B) \times H \]Thus, the area of the four walls of the room is 2100 m².
Correct Option: C) 2100 m²
The question asks to identify the Force Commander of the UN Mission in South Sudan (UNMISS) appointed in 2019. This is a factual question related to international appointments and current affairs, specifically concerning India's contribution to UN peacekeeping missions.
D) Shailesh Tinaikar was appointed as the Force Commander of the UN Mission in South Sudan (UNMISS) in May 2019. He is an Indian Army officer.
To determine the digit 'x' that makes the number 93248x6 divisible by 11, we use the divisibility rule for 11. This rule states that a number is divisible by 11 if the alternating sum of its digits (starting from the rightmost digit) is either 0 or a multiple of 11.
Write down the given number: \(93248x6\).
Apply the divisibility rule for 11. We sum the digits at odd places (from the right) and subtract the sum of the digits at even places (from the right).
Odd places (1st, 3rd, 5th, 7th from right): \(6, 8, 2, 9\)
Even places (2nd, 4th, 6th from right): \(x, 4, 3\)
Calculate the sum of digits at odd places:
\[ S_{\text{odd}} = 6 + 8 + 2 + 9 = 25 \]Calculate the sum of digits at even places:
\[ S_{\text{even}} = x + 4 + 3 = x + 7 \]Find the difference between these two sums:
\[ \text{Difference} = S_{\text{odd}} - S_{\text{even}} = 25 - (x + 7) = 25 - x - 7 = 18 - x \]For the number to be divisible by 11, this difference must be either 0 or a multiple of 11. Since 'x' is a single digit (0-9), the value of \(18 - x\) must be within a certain range.
If \(x=0\), \(18 - x = 18\).
If \(x=9\), \(18 - x = 9\).
So, \(18 - x\) can be 0 or 11.
Set the difference equal to 0 or 11 and solve for x:
Case 1: \(18 - x = 0\)
\[ x = 18 \]This is not possible as 'x' must be a single digit (0-9).
Case 2: \(18 - x = 11\)
\[ x = 18 - 11 \] \[ x = 7 \]Since \(x=7\) is a single digit, it is the correct value.
Correct Option: D) 7
If \(x=7\), the number becomes 9324876. The alternating sum of digits is \((6+8+2+9) - (7+4+3) = 25 - 14 = 11\), which is a multiple of 11. Therefore, the number is divisible by 11.
A) 5 — If \(x=5\), the difference is \(18 - 5 = 13\), which is not a multiple of 11.
B) 8 — If \(x=8\), the difference is \(18 - 8 = 10\), which is not a multiple of 11.
C) 2 — If \(x=2\), the difference is \(18 - 2 = 16\), which is not a multiple of 11.
The question asks to identify the winner of the Rabindranath Tagore Literary Prize for 2019. This requires knowledge of current affairs and literary awards.
Correct Option: C) Rana Dasgupta won the Rabindranath Tagore Literary Prize 2019 for his novel Solo.
This problem involves setting up an algebraic equation based on the given information. We need to find the number of boys in the group, given the total number of apples and the distribution rule.
Correct Option: A) 20
This is a coding-decoding question. We need to identify the pattern used to code "PUNJAB" as "OSKKCE" and then apply the same pattern to code "PRAYAG".
Let's write down the letters of "PUNJAB" and their corresponding coded letters "OSKKCE" along with their alphabetical positions (A=1, B=2, ..., Z=26).
| Original Letter | Position | Coded Letter | Position | Difference |
|---|---|---|---|---|
| P | 16 | O | 15 | \(15 - 16 = -1\) |
| U | 21 | S | 19 | \(19 - 21 = -2\) |
| N | 14 | K | 11 | \(11 - 14 = -3\) |
| J | 10 | K | 11 | \(11 - 10 = +1\) |
| A | 1 | C | 3 | \(3 - 1 = +2\) |
| B | 2 | E | 5 | \(5 - 2 = +3\) |
The pattern for the difference in alphabetical positions is: \(-1, -2, -3, +1, +2, +3\).
Now, let's apply this pattern to each letter of "PRAYAG".
| Original Letter | Position | Pattern | New Position | Coded Letter |
|---|---|---|---|---|
| P | 16 | \(-1\) | \(16 - 1 = 15\) | O |
| R | 18 | \(-2\) | \(18 - 2 = 16\) | P |
| A | 1 | \(-3\) | \(1 - 3 = -2\) (or \(26 - 2 = 24\)) | X |
| Y | 25 | \(+1\) | \(25 + 1 = 26\) | Z |
| A | 1 | \(+2\) | \(1 + 2 = 3\) | C |
| G | 7 | \(+3\) | \(7 + 3 = 10\) | J |
For 'A' (position 1) with a \(-3\) shift: \(1 - 3 = -2\). When going backward past 'A', we wrap around from 'Z'. So, 'A' \(\rightarrow\) 'Z' (1 step back), 'Z' \(\rightarrow\) 'Y' (2 steps back), 'Y' \(\rightarrow\) 'X' (3 steps back). Thus, 'A' becomes 'X'.
Combining the coded letters, we get "OPXZCJ".
D) OPXZCJ is the correct code for PRAYAG based on the identified pattern.