This problem involves tracking movement and direction. We can solve it by visualizing Avadhesh's path on a coordinate plane or by drawing a simple diagram, keeping track of the distances covered in each direction. We need to find the final position relative to the starting point and then determine the distance and direction to return to the start.
B) 7 km towards the south. From Point M \((0,7)\), Avadhesh needs to travel 7 km in the negative Y-direction (south) to reach Point A \((0,0)\).
In a certain code language, ‘DIARY’ is written as ‘FLFXF’ and ‘READY’ is written as ‘THFJF’. How will ‘ERROR’ be written in that language?
The problem is a coding-decoding question. We need to identify the pattern or rule used to transform the given words into their coded forms. Once the rule is found, we apply it to the word "ERROR" to find its coded form.
The pattern for DIARY seems to be adding +2, +3, +5, +6, +7 to the letter positions.
The pattern is consistent: the letters are shifted by +2, +3, +5, +6, +7 respectively.
So, 'ERROR' will be coded as 'GUWUY'.
D) GUWUY is the correct code for 'ERROR' based on the identified pattern of adding +2, +3, +5, +6, +7 to the consecutive letters.
The problem involves decoding a pattern in a given code language. We need to identify the rule applied to transform the letters of the original words into their coded forms. Once the rule is found, we apply it to the word 'WHITE' to find its coded form.
The pattern for 'SHOUT' is a progressive addition of +3, +4, +5, +6, +7 to the alphabetical position of each letter.
The pattern holds true for 'TOTAL' as well.
C) ZLNZL is the correct code for 'WHITE' based on the identified pattern.
The question asks us to evaluate two statements regarding electrovalent compounds (also known as ionic compounds). We need to determine if each statement is true or false and then select the correct option.
B) Both the statements are true. As explained above, Statement-I correctly defines electrovalent compounds based on electron transfer from metal to non-metal, and Statement-II accurately describes their solubility characteristics (soluble in water, insoluble in non-polar solvents).
Which of the below two signs should be interchanged to make the following equation correct?
75 ÷ 8 × 6 + 24 − 6 = 31
The problem requires us to find which two mathematical signs, when interchanged in the given equation, will make the equation correct. We will test each option by interchanging the specified signs and then applying the BODMAS/PEMDAS rule to evaluate the expression.
The given equation is:
\[ 75 \div 8 \times 6 + 24 - 6 = 31 \]Interchange × and − in the original equation:
\[ 75 \div 8 - 6 + 24 \times 6 \]Since \(147.375 \neq 31\), Option A is incorrect.
Interchange − and + in the original equation:
\[ 75 \div 8 \times 6 - 24 + 6 \]Since \(38.25 \neq 31\), Option B is incorrect.
Interchange + and ÷ in the original equation:
\[ 75 + 8 \times 6 \div 24 - 6 \]Since \(71 \neq 31\), Option C is incorrect.
Interchange ÷ and − in the original equation:
\[ 75 - 8 \times 6 + 24 \div 6 \]Since \(31 = 31\), Option D is correct.
Correct Option: D) ÷ and −
If ‘+’ means ‘−’, ‘−’ means ‘×’, ‘×’ means ‘÷’, and ‘÷’ means ‘+’, what will come in place of the question mark (?) in the following equation?
18 × 3 − 5 ÷ 6 + 4 =?
This problem involves applying a set of given symbol transformations to a mathematical expression and then evaluating the modified expression using the order of operations (BODMAS/PEMDAS).
The value of the expression is \(32\).
Correct Option: A) 32
This problem involves arranging six participants based on their scores, given a set of comparative statements. We need to deduce the exact or relative order of scores to find the participant with the second-highest score. We will build a score hierarchy step-by-step using the given clues.
Clue 1: T scored more than Q.
This can be written as: \(T > Q\)
Clue 2: S scored more than Q.
This can be written as: \(S > Q\)
From clues 1 and 2, we know that both T and S scored more than Q. However, we don't yet know the relationship between T and S.
Clue 3: Q scored more than P.
This can be written as: \(Q > P\)
Combining with previous clues: \(T > Q > P\) and \(S > Q > P\)
Clue 4: P scored more than R.
This can be written as: \(P > R\)
Combining with previous clues: \(T > Q > P > R\) and \(S > Q > P > R\)
Clue 5: T scored more than S.
This can be written as: \(T > S\)
Now we can combine all the relationships involving T, S, Q, P, and R: \(T > S > Q > P > R\)
Clue 6: R scored more than only one participant.
We have 6 participants: P, Q, R, S, T, U. So far, we have ordered 5 of them: \(T > S > Q > P > R\). This means R is the 5th highest scorer among these five. If R scored more than only one participant, it implies that R is the second lowest scorer overall. In our current sequence, R is greater than only one participant, which is U. Therefore, U must be the participant R scored more than. This places U at the very bottom of the scoring order.
So, the complete order is: \(T > S > Q > P > R > U\).
Identify the second highest scorer:
From the final order \(T > S > Q > P > R > U\), the highest scorer is T, and the second highest scorer is S.
To calculate the profit percentage, we first need to determine the total cost price (original purchase price plus repair costs) and the selling price. Then, we find the profit by subtracting the total cost price from the selling price. Finally, the profit percentage is calculated by dividing the profit by the total cost price and multiplying by 100.
The man bought the car for Rs 2,50,000 and spent Rs 30,000 on its repair. The total cost price is the sum of these two amounts.
\[ \text{Total CP} = \text{Purchase Price} + \text{Repair Cost} \]\[ \text{Total CP} = \text{Rs } 2,50,000 + \text{Rs } 30,000 \]\[ \text{Total CP} = \text{Rs } 2,80,000 \]The man sold the car for Rs 3,50,000.
\[ \text{SP} = \text{Rs } 3,50,000 \]Profit is the difference between the selling price and the total cost price.
\[ \text{Profit} = \text{SP} - \text{Total CP} \]\[ \text{Profit} = \text{Rs } 3,50,000 - \text{Rs } 2,80,000 \]\[ \text{Profit} = \text{Rs } 70,000 \]The profit percentage is calculated using the formula:
\[ \text{Profit Percentage} = \left( \frac{\text{Profit}}{\text{Total CP}} \right) \times 100 \% \]\[ \text{Profit Percentage} = \left( \frac{70,000}{2,80,000} \right) \times 100 \% \]\[ \text{Profit Percentage} = \left( \frac{7}{28} \right) \times 100 \% \]\[ \text{Profit Percentage} = \left( \frac{1}{4} \right) \times 100 \% \]\[ \text{Profit Percentage} = 25 \% \]Correct Option: D) 25 %
To find the fourth proportional of three given numbers, we set up a proportion where the ratio of the first two numbers is equal to the ratio of the third number to the unknown fourth number. This allows us to solve for the unknown value.
Let the three given numbers be \(a = 17\), \(b = 32\), and \(c = 51\).
Let the fourth proportional be \(x\).
According to the definition of proportion, the ratio of the first two numbers is equal to the ratio of the third and fourth numbers. So, we can write the proportion as:
\[ \frac{a}{b} = \frac{c}{x} \]Substitute the given values into the proportion:
\[ \frac{17}{32} = \frac{51}{x} \]To solve for \(x\), cross-multiply:
\[ 17 \times x = 32 \times 51 \]Now, isolate \(x\):
\[ x = \frac{32 \times 51}{17} \]Simplify the expression. Notice that 51 is a multiple of 17 (\(51 = 17 \times 3\)):
\[ x = \frac{32 \times (17 \times 3)}{17} \]Cancel out 17 from the numerator and the denominator:
\[ x = 32 \times 3 \]Calculate the final value of \(x\):
\[ x = 96 \]B) 96 is the correct fourth proportional.
We are given the ratio of the current ages of A and B. We are also given information about B's age after 7 years. We will use this information to find B's current age, then A's current age using the ratio, and finally A's age six years ago.
Determine B's current age:
We are told that after 7 years, B's age will be 52 years. Let B's current age be \(B_{\text{current}}\).
Determine A's current age:
The ratio of the ages of A and B is 5:9. Let A's current age be \(A_{\text{current}}\).
Determine A's age six years ago:
To find A's age six years ago, subtract 6 from A's current age.
Correct Option: A) 19 years