What will come in the place of the question mark (?) in the following equation, if '+' and '−' are interchanged and '×' and '÷' are interchanged?
43 ÷ 13 − 648 × 8 + 52 =?
The problem requires us to evaluate a given mathematical expression after interchanging certain operators. We need to replace '+' with '−', '−' with '+', '×' with '÷', and '÷' with '×'. After making these substitutions, we will apply the BODMAS/PEMDAS rule to solve the new expression.
\[ 43 \div 13 - 648 \times 8 + 52 = ? \]
Substitute these into the original expression:
\[ 43 \times 13 + 648 \div 8 - 52 = ? \]
BODMAS stands for Brackets, Orders (powers/roots), Division, Multiplication, Addition, Subtraction.
First, perform multiplication and division from left to right.
\[ 43 \times 13 = 559 \]
\[ 648 \div 8 = 81 \]
Now substitute these values back into the expression:
\[ 559 + 81 - 52 = ? \]
Next, perform addition and subtraction from left to right.
\[ 559 + 81 = 640 \]
\[ 640 - 52 = 588 \]
Correct Option: A) 588
The question asks to identify the larger body of water to which the Palk Strait is an inlet. This requires knowledge of the geographical location of the Palk Strait and its connection to surrounding major water bodies.
A) Bay of Bengal โ The Palk Strait connects the Palk Bay to the Bay of Bengal, making it an inlet of the Bay of Bengal.
The question asks to identify the country that will assume the BRICS presidency in January 2025. This requires knowledge of the BRICS rotational presidency system.
Correct Option: C) Brazil is scheduled to assume the BRICS presidency in January 2025, following Russia's presidency in 2024.
To find the volume of a hemispherical cap, we use the formula for the volume of a hemisphere, which is half the volume of a sphere. The formula for the volume of a sphere is \( \frac{4}{3}\pi r^3 \), so for a hemisphere, it is \( \frac{2}{3}\pi r^3 \). We are given the radius, and we need to calculate the volume and round it to two decimal places.
Radius of the hemispherical cap, \( r = 33.6 \text{ cm} \).
The volume \( V \) of a hemisphere is given by:
\[ V = \frac{2}{3}\pi r^3 \]Rounding \( 25288.704 \) to two decimal places gives \( 25288.70 \).
So, \( V = 25288.70\pi \text{ cm}^3 \).
Correct Option: C) 25,288.70ฯ
The problem requires us to modify a given number based on specific rules for its odd and even digits. Then, we need to identify the second digit from the left and the second digit from the right in the new number and calculate their sum.
The sum of the digits which are second from the left and second from the right in the new number is 10.
Correct Option: C) 10
The question asks about the primary function of setting a Page Break in MS Excel 365. We need to identify which printing aspect is directly controlled by this feature.
Correct Option: C) Where the worksheet splits across printed pages โ Setting a Page Break in MS Excel 365 gives you explicit control over where one printed page ends and the next begins, allowing you to customize how your data is distributed across physical sheets of paper.
A group of numbers and symbols is coded using letter codes as per the codes given below and the conditions that follow. Study the given codes and conditions and answer the question that follows.
Note: If none of the conditions apply, then codes for the respective number/symbol are to be followed directly as given in the table.
| Letter | Z | T | E | P | A | U | X |
| Code | 8 | $ | @ | 9 | 2 | % | 6 |
Conditions:
1. If the 1st letter is a vowel and the last letter is a consonant, their codes are to be interchanged.
2. If the 2nd letter is a vowel and the last letter is a consonant, both are to be coded as 'W'.
3. If the 3rd and 4th letters are consonants, both are to be coded as the code for the 3rd letter.
4. If the 1st and 2nd letters are vowels, then both are to be coded as 'Q'.
What will be the code for the following group?
AUTEA
The problem requires us to code a given group of letters based on a provided table of letter-to-code mappings and a set of conditions. We need to apply the conditions in the given order and only use the direct mapping if no conditions apply.
A) Q Q \( @ 2 โ This matches the code derived after applying Condition 4.
The problem is a coding-decoding question where letters are assigned numerical values based on their alphabetical position. We need to identify the pattern used to convert the given words into numbers and then apply the same pattern to the target word.
D) 61 is the correct code for 'YDOM' based on the identified pattern.
This problem requires us to substitute the given symbols with their corresponding mathematical operators and then evaluate each expression following the order of operations (BODMAS/PEMDAS) to find which one results in 94.
The given symbol-operator mappings are:
We will evaluate each option:
C) 48 W 8 Z 56 Y 24 X 6
Since the result is 94, option C is the correct answer.
A) 48 Y 8 X 56 W 24 Z 6
B) 48 Z 8 W 56 X 24 Y 6
D) 48 X 8 Y 56 Z 24 W 6
To solve this problem, we need to apply the given rules to each digit of the original number. First, identify whether each digit is even or odd. Then, perform the specified addition or subtraction. Finally, from the new number formed, identify the highest and lowest digits and calculate their sum.
Original Number: The given number is 8629475.
Apply the rules to each digit:
For even digits, add 1.
For odd digits, subtract 1.
Let's process each digit:
8 (even) \(\rightarrow 8 + 1 = 9\)
6 (even) \(\rightarrow 6 + 1 = 7\)
2 (even) \(\rightarrow 2 + 1 = 3\)
9 (odd) \(\rightarrow 9 - 1 = 8\)
4 (even) \(\rightarrow 4 + 1 = 5\)
7 (odd) \(\rightarrow 7 - 1 = 6\)
5 (odd) \(\rightarrow 5 - 1 = 4\)
Form the new number: The new number formed by these modified digits is 9738564.
Identify the highest and lowest digits in the new number:
The digits in the new number are 9, 7, 3, 8, 5, 6, 4.
The highest digit is 9.
The lowest digit is 3.
Calculate the sum of the highest and lowest digits:
Sum \( = \text{Highest digit} + \text{Lowest digit} \)
Sum \( = 9 + 3 \)
Sum \( = 12 \)
C) 12 is the correct sum of the highest and lowest digits in the new number.
A) 6 โ This would be the result if the lowest digit was 2 and the highest was 4, or similar incorrect calculation. It does not match the derived highest and lowest digits.
B) 16 โ This would be the result if the highest digit was 9 and the lowest was 7, or if the highest was 8 and the lowest was 8, or similar incorrect calculation. It does not match the derived highest and lowest digits.
D) 14 โ This would be the result if the highest digit was 9 and the lowest was 5, or if the highest was 8 and the lowest was 6, or similar incorrect calculation. It does not match the derived highest and lowest digits.