The question asks about the founder of the 'Slave Dynasty', also known as the Mamluk Dynasty, which was the first dynasty of the Delhi Sultanate. To answer this, one needs to recall the key figures associated with the establishment of this dynasty.
C) Qutb-ud-din Aibak — He was a Mamluk slave of Muhammad Ghori and became the first Sultan of Delhi, establishing the Slave Dynasty in 1206 AD.
The question asks for the underlying assumption that supports the claim "Pleasure is desirable." This is a philosophical question, often related to utilitarianism or hedonism, where the desirability of pleasure is linked to its universal appeal or pursuit. We need to identify the statement that acts as a foundational premise for pleasure to be considered desirable.
Correct Option: A) Everyone desires pleasure. This statement directly provides the foundational premise for the claim that pleasure is desirable. If everyone desires pleasure, then pleasure is, by definition, something that is desired, and thus desirable. This is a common argument in ethical theories like utilitarianism, where the greatest good is often equated with the greatest pleasure for the greatest number.
The question asks to identify the author of the famous philosophical work 'Republic'. This requires knowledge of prominent philosophers and their key literary contributions.
B) Plato. 'The Republic' (Greek: Politeia) is a Socratic dialogue written by Plato around 375 BC. It is one of the most influential works of philosophy and political theory, dealing with justice, the character of the just city-state, and the just man.
On the first day 84500 people visited a trade fair. On the 4th day number reduced to 16900. By what percentage people reduced on the 4th day?
To find the percentage reduction in the number of people, we first need to calculate the actual reduction in the number of people. Then, we divide this reduction by the initial number of people and multiply by 100 to express it as a percentage.
Initial number of people (on the first day) = \(84500\)
Final number of people (on the fourth day) = \(16900\)
Reduction = Initial number - Final number
\[ \text{Reduction} = 84500 - 16900 = 67600 \]Percentage reduction is calculated using the formula:
\[ \text{Percentage Reduction} = \left( \frac{\text{Reduction}}{\text{Initial Number}} \right) \times 100 \% \]\[ \text{Percentage Reduction} = \left( \frac{67600}{84500} \right) \times 100 \% \]\[ \text{Percentage Reduction} = 0.8 \times 100 \% \]\[ \text{Percentage Reduction} = 80 \% \]Thus, the number of people reduced by 80% on the 4th day.
A) 80% is the correct answer, as calculated above.
When two objects move in opposite directions from the same point, their relative speed is the sum of their individual speeds. We can use this relative speed to calculate the total distance between them after a given time.
Alternatively, we can calculate the distance covered by each person individually and then add them up:
Both methods yield the same result.
Correct Option: D) 83.75 km
To determine which number should be added to the given sum to make it a complete square, we first need to calculate the sum of the given numbers. Then, we find the nearest perfect square greater than this sum and determine the difference.
The given expression is \(1+3+7+9+11+13\).
\[ \text{Sum} = 1 + 3 + 7 + 9 + 11 + 13 \]\[ \text{Sum} = 4 + 7 + 9 + 11 + 13 \]\[ \text{Sum} = 11 + 9 + 11 + 13 \]\[ \text{Sum} = 20 + 11 + 13 \]\[ \text{Sum} = 31 + 13 \]\[ \text{Sum} = 44 \]We need to find a perfect square that is greater than 44.
So, the next complete square after 44 is 49.
To make 44 a complete square (49), we need to add the difference between 49 and 44.
\[ \text{Number to be added} = 49 - 44 \]\[ \text{Number to be added} = 5 \]Therefore, 5 should be added to the expression to make it a complete square.
Correct Option: B) 5
The question asks for the host city of the 2022 Commonwealth Games. This is a factual question related to current affairs and major international sporting events. Recalling the host city for this specific event is key to answering correctly.
Correct Option: C) Birmingham
The 2022 Commonwealth Games were indeed held in Birmingham, England, from 28 July to 8 August 2022. This was the third time England hosted the Commonwealth Games, after London in 1934 and Manchester in 2002.
The problem is a coding-decoding question. We need to identify the pattern used to convert "VIARAIL" to "XKCTCKN" and then apply the same pattern to "STRATEGY".
| Original Letter | Coded Letter | Position (A=1) | Difference |
|---|---|---|---|
| V | X | V=22, X=24 | +2 |
| I | K | I=9, K=11 | +2 |
| A | C | A=1, C=3 | +2 |
| R | T | R=18, T=20 | +2 |
| A | C | A=1, C=3 | +2 |
| I | K | I=9, K=11 | +2 |
| L | N | L=12, N=14 | +2 |
| Original Letter | Position (A=1) | Shifted Position | Coded Letter |
|---|---|---|---|
| S | 19 | 19 + 2 = 21 | U |
| T | 20 | 20 + 2 = 22 | V |
| R | 18 | 18 + 2 = 20 | T |
| A | 1 | 1 + 2 = 3 | C |
| T | 20 | 20 + 2 = 22 | V |
| E | 5 | 5 + 2 = 7 | G |
| G | 7 | 7 + 2 = 9 | I |
| Y | 25 | 25 + 2 = 27 (which is A, as Z=26) | A |
Correct Option: B) UVTCVGIA
To solve this problem, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS (Brackets/Parentheses, Orders/Exponents, Division and Multiplication (from left to right), Addition and Subtraction (from left to right)). We will evaluate each bracketed expression separately and then combine the results.
The given expression is:
\( (4 + 2 - 16 \div 4 + 3) + \{ (1 + 8 \times 7) \div 19 \} \times [ (3 + 5 - 4) + (17 - 9 \times 4) ] \)
So, the first part is \(5\).
So, the second part is \(3\).
So, the third part is \(-15\).
Substitute the calculated values back into the original expression:
\[ 5 + 3 \times (-15) \]Perform multiplication first:
\[ 3 \times (-15) = -45 \]Then perform addition:
\[ 5 + (-45) = 5 - 45 = -40 \]The problem asks for the value of a sum of four cosine terms. We can use trigonometric identities, specifically the sum-to-product formula for cosines, or properties of angles in different quadrants, to simplify the expression.
The given expression is:
\[ \cos 12^\circ + \cos 84^\circ + \cos 168^\circ + \cos 96^\circ \]We know that \(\cos (180^\circ - \theta) = -\cos \theta\) and \(\cos (90^\circ + \theta) = -\sin \theta\).
Let's rewrite \(\cos 168^\circ\) and \(\cos 96^\circ\):
Substitute these values back into the original sum:
\[ \cos 12^\circ + \cos 84^\circ + (-\cos 12^\circ) + (-\cos 84^\circ) \]Combine the terms:
\[ \cos 12^\circ + \cos 84^\circ - \cos 12^\circ - \cos 84^\circ \]The terms cancel each other out:
\[ (\cos 12^\circ - \cos 12^\circ) + (\cos 84^\circ - \cos 84^\circ) = 0 + 0 = 0 \]B) 0. The value of the expression is 0.