To evaluate the given expression, we must follow the order of operations, commonly remembered by the acronym PEMDAS/BODMAS. This stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
Thus, the value of the expression is \(5\).
B) 5 — The calculation following the order of operations (BODMAS/PEMDAS) correctly yields 5.
The problem asks us to identify symbols in a given series that are immediately preceded by a number and immediately followed by another number. We need to scan the series from left to right and apply this condition to each symbol.
3 & ^ 5 7 # 9 % 8 * 4 < 1 \( 2 @ * 6A) 5 — There are 5 symbols (#, %, *, <, $) that are immediately preceded by a number and immediately followed by another number in the given series.
The problem presents a series of letter groups, and we need to find the next group in the sequence. We will analyze the pattern for each letter's position (first, second, and third) across the groups based on their alphabetical order.
The pattern for the first letter is an increment of 2: \(8 + 2 = 10\), \(10 + 2 = 12\), \(12 + 2 = 14\). Following this pattern, the next first letter should be \(14 + 2 = 16\), which corresponds to 'P'.
The pattern for the second letter is also an increment of 2: \(6 + 2 = 8\), \(8 + 2 = 10\), \(10 + 2 = 12\). Following this pattern, the next second letter should be \(12 + 2 = 14\), which corresponds to 'N'.
The pattern for the third letter is an increment of 2: \(3 + 2 = 5\), \(5 + 2 = 7\), \(7 + 2 = 9\). Following this pattern, the next third letter should be \(9 + 2 = 11\), which corresponds to 'K'.
The next group in the series will be formed by combining the determined letters: P, N, K. So, the next group is PNK.
Correct Option: B) PNK
The question asks for the location where the Indigo Rebellion took place during 1859-1860. This requires knowledge of major peasant uprisings in colonial India and their geographical contexts.
B) Bengal is the correct answer. The Indigo Rebellion (Nil Bidroho) of 1859-1860 was a major peasant uprising against exploitative indigo planters, primarily concentrated in the Bengal Presidency.
The question asks about the application of Fleming's Left-Hand Rule. This rule is a fundamental principle in electromagnetism used to understand the interaction between magnetic fields and electric currents. We need to recall what each finger represents in this rule.
C) the direction of force on a current-carrying conductor. As explained above, Fleming's Left-Hand Rule specifically helps in determining the direction of the force (or motion) experienced by a current-carrying conductor when it is placed in a magnetic field.
The problem asks us to identify the letter-cluster that does not follow the same pattern as the others, based on English alphabetical order. We need to find the positional value of each letter in the alphabet and then look for a consistent mathematical relationship or sequence within each cluster.
C) ZWU — The differences between the positional values of consecutive letters are \(26 - 23 = 3\) and \(23 - 21 = 2\). This pattern \((3, 2)\) is different from the \((4, 3)\) pattern observed in the other options.
Tarun ranked 21st from the top and 12th from the bottom in his class. How many students are there in his class?
To find the total number of students in the class, we need to consider Tarun's rank from both the top and the bottom. When we add his rank from the top and his rank from the bottom, Tarun is counted twice. Therefore, to get the total number of students, we must subtract 1 from the sum of his ranks.
Using the formula:
\[ \text{Total students} = (\text{Rank from top}) + (\text{Rank from bottom}) - 1 \]Substitute the given values:
\[ \text{Total students} = 21 + 12 - 1 \] \[ \text{Total students} = 33 - 1 \] \[ \text{Total students} = 32 \]Alternatively, we can think of it as:
B) 32
This is a linear arrangement puzzle. We need to deduce the seating positions of seven people (W, X, Y, Z, E, F, G) in a row facing north based on the given clues. We will build the arrangement step-by-step, starting with the most restrictive clues.
Clue 1: Only two people sit to the right of Y.
Since there are 7 people, this means Y is at the 5th position from the left end.
_ _ _ _ Y _ _
Clue 2: W sits to the immediate left of Y.
Placing W to the immediate left of Y:
_ _ _ W Y _ _
Clue 3: Only two people sit between Y and F.
From Y's position (5th), two people sit between Y and F. This means F must be at the 2nd position from the left end (since there's no space to the right of Y for F to be further away).
_ F _ W Y _ _
Clue 4: Only two people sit between E and W.
W is at the 4th position. Counting two places from W, E can be at the 1st position (left of W) or the 7th position (right of W). Since F is at the 2nd position, E cannot be at the 1st position. Thus, E must be at the 7th position.
_ F _ W Y _ E
Clue 5: Z sits to the immediate right of X.
The remaining empty spots are 1st, 3rd, and 6th. The only consecutive spots available for X and Z (where Z is to the immediate right of X) are the 1st and 3rd positions. However, if X is at 1st, Z cannot be at 3rd as there is a gap. So X and Z must occupy the 1st and 3rd positions. This means X is at 1st and Z is at 3rd.
X F Z W Y _ E
Final Arrangement:
The only person left is G, and the only empty spot is the 6th position. So, G sits at the 6th position.
X F Z W Y G E
Answer the question: Who sits at the third position from the left end of the row?
Looking at the final arrangement, the person at the third position from the left is Z.
D) G — Wait, let's recheck the final arrangement. The question asks for the third position from the left. In the arrangement X F Z W Y G E, the third person is Z. Let me re-evaluate the steps. Ah, I made a mistake in step 5. Let's correct it.
Re-evaluation of Step 5:
Remaining empty spots after step 4: 1st, 3rd, and 6th.
_ F _ W Y _ E
Clue 5: Z sits to the immediate right of X.
This means X and Z must be adjacent. The only adjacent empty spots are not available in the current configuration of empty spots (1st, 3rd, 6th). Let's re-examine Clue 3 and 4.
Re-evaluation from start:
Clue 1: Only two people sit to the right of Y.
_ _ _ _ Y _ _ (Y is 5th from left)
Clue 2: W sits to the immediate left of Y.
_ _ _ W Y _ _ (W is 4th from left)
Clue 3: Only two people sit between Y and F.
From Y (5th position), two people sit between Y and F. This means F must be at the 2nd position (5 - 2 - 1 = 2). If F were to the right of Y, there wouldn't be enough space.
_ F _ W Y _ _
Clue 4: Only two people sit between E and W.
W is at the 4th position. If E is to the left of W, E would be at 1st position (4 - 2 - 1 = 1). If E is to the right of W, E would be at 7th position (4 + 2 + 1 = 7).
Case 1: E is at 1st position.
E F _ W Y _ _
Case 2: E is at 7th position.
_ F _ W Y _ E
Clue 5: Z sits to the immediate right of X.
Let's check Case 1: E F _ W Y _ _
Empty spots: 3rd and 6th. There are no two adjacent empty spots for X and Z. So Case 1 is not possible.
Let's check Case 2: _ F _ W Y _ E
Empty spots: 1st, 3rd, and 6th. The only adjacent spots are not directly visible. Let's list them: (1,3,6). No adjacent spots. This means my interpretation of "Z sits to the immediate right of X" must be applied to the remaining available slots.
Let's reconsider the entire setup with the most restrictive clues first.
1. Y is 5th: P1 P2 P3 P4 Y P6 P7
2. W is immediate left of Y: P1 P2 P3 W Y P6 P7
3. Two people between Y and F. Y is 5th. F must be 2nd (5-2-1=2).
P1 F P3 W Y P6 P7
4. Two people between E and W. W is 4th. If E is to the left of W, E is 1st (4-2-1=1). If E is to the right of W, E is 7th (4+2+1=7).
If E is 1st: E F P3 W Y P6 P7. Remaining empty: P3, P6. No adjacent spots for X and Z.
If E is 7th: P1 F P3 W Y P6 E. Remaining empty: P1, P3, P6.
Now apply "Z sits to the immediate right of X\
The question asks to identify the Rashtrakuta king who defeated Dharmapala, the Pala king of Bengal. This requires knowledge of the Tripartite Struggle for control over Kannauj, a significant historical conflict involving the Palas, Pratiharas, and Rashtrakutas.
D) Dhruva Dharavarsha — Dhruva Dharavarsha was the Rashtrakuta king who defeated Dharmapala, the Pala king of Bengal, during the Tripartite Struggle for Kannauj.
The question asks to identify a UNESCO World Heritage Site in Maharashtra that is a cave complex known for its paintings and sculptures. We need to evaluate each option based on its location, characteristics, and UNESCO status.
D) Ajanta Caves are a UNESCO World Heritage Site in Maharashtra, famous for their stunning paintings and sculptures, primarily Buddhist art.