The problem involves decoding a letter based on given coded words. We need to identify the common letters and their corresponding codes to deduce the code for 'F'.
Given the first code: 'PLOW' is coded as '7164'.
Given the second code: 'WOLF' is coded as '1564'.
Now, let's compare the codes for common letters:
This indicates that the coding is not a direct one-to-one mapping based on position. Instead, it's a scrambled or mixed mapping where each letter has a unique code, and the order of digits in the code might not directly correspond to the order of letters in the word.
Let's re-examine the given codes and identify common letters and their corresponding digits.
Observe the common letters in 'PLOW' and 'WOLF': 'W', 'O', 'L'.
Let's try to match them:
Let's list the letters and their potential codes based on both words:
By comparing the letters and digits, we can deduce the unique code for each letter:
Let's try to assign the codes by finding unique matches:
Let's list the letters and their possible codes from the given information:
Now, let's find the common letters and common digits:
This means that the letters W, O, L must correspond to the digits 1, 6, 4 in some order. The remaining letter in 'PLOW' is 'P', and its code must be '7'. The remaining letter in 'WOLF' is 'F', and its code must be '5'.
Let's verify this:
This is consistent. The letters W, O, L are mapped to the digits 1, 6, 4 (the specific mapping for each of these three letters is not uniquely determined, but it's not needed to find 'F').
Therefore, the code for 'F' is 5.
Correct Option: C) 5
This problem involves calculating the height of an image formed by a convex mirror, given the magnification and the height of the object. We will use the formula for magnification, which relates the height of the image to the height of the object.
Identify the given values:
Recall the formula for magnification (\(m\)):
\[ m = \frac{\text{Height of image} (h_i)}{\text{Height of object} (h_o)} \]Substitute the given values into the formula:
\[ 0.2 = \frac{h_i}{5 \text{ cm}} \]Solve for the height of the image (\(h_i\)):
\[ h_i = 0.2 \times 5 \text{ cm} \]\[ h_i = 1.0 \text{ cm} \]D) The height of the image is 1 cm. This matches our calculated value.
To find the total surface area of a cylinder, we need to sum the areas of its two circular bases and its curved surface. The formula for the total surface area of a cylinder is \(2\pi r(r+h)\), where \(r\) is the radius of the base and \(h\) is the height of the cylinder.
B) 266π cm² — This matches our calculated total surface area.
The problem requires us to transform the letters of the word "OPTICAL" based on specific rules: vowels move to the next letter in the alphabet, and consonants move to the previous letter. After applying these rules, we need to identify which letter is repeated in the newly formed group.
A) B is the correct option because the letter 'B' is repeated twice in the new group of letters (POSJBBK).
To evaluate the given expression, we must follow the order of operations, commonly remembered by the acronym PEMDAS/BODMAS. This rule dictates the sequence in which mathematical operations should be performed: Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), and Addition and Subtraction (from left to right).
The given expression is:
\[ 13 - 12 \div 4 \times 2 \]According to the order of operations (BODMAS/PEMDAS), Division and Multiplication have higher precedence than Subtraction. When both Division and Multiplication are present, we perform them from left to right.
First, perform the division:
\[ 12 \div 4 = 3 \]Substitute this result back into the expression:
\[ 13 - 3 \times 2 \]Next, perform the multiplication:
\[ 3 \times 2 = 6 \]Substitute this result back into the expression:
\[ 13 - 6 \]Finally, perform the subtraction:
\[ 13 - 6 = 7 \]Correct Option: C) 7
The equivalent resistance of the two resistors of resistance R ohm each connected in series is _______.
\( \frac{R}{2} \) ohm
3R ohm
2R ohm
\( \frac{2}{R} \) ohm
To find the equivalent resistance of resistors connected in series, we use a simple formula: the total resistance is the sum of individual resistances. This concept is fundamental in basic circuit analysis.
Therefore, the equivalent resistance of the two resistors connected in series is \(2R\) ohm.
C) 2R ohm — This is the correct result obtained by summing the individual resistances of the two resistors connected in series.
The question asks to identify the correct statement(s) regarding the function of an electromagnet. We need to recall the basic principle of how an electromagnet works and what energy conversions it involves.
Correct Option: B) Neither Statement I nor II
To evaluate the product \(297 \times 303\), we can use the algebraic identity \((a-b)(a+b) = a^2 - b^2\). This method simplifies the multiplication of numbers that are equidistant from a common reference number.
\(297 \times 303 = (300 - 3)(300 + 3)\)
\( = 300^2 - 3^2\)
\(300^2 = 300 \times 300 = 90000\)
\(3^2 = 3 \times 3 = 9\)
\(90000 - 9 = 89991\)
Thus, \(297 \times 303 = 89991\).
Correct Option: A) 89991
This is a linear seating arrangement puzzle. We need to deduce the positions of seven people (B, C, D, E, F, G, K) sitting in a straight line facing north based on the given clues. We will build the arrangement step-by-step and then answer the question about the number of people to the right of G.
Clue 1: Seven people, B, C, D, E, F, G and K are sitting in a straight line, facing north.
Let's represent the seven positions as _ _ _ _ _ _ _.
Clue 2: Only two people sit to the left of B.
This means B is in the 3rd position from the left.
Arrangement: _ _ B _ _ _ _
Clue 3: Only three people sit between B and K.
Since B is at position 3, K must be at position 7 (3 + 3 + 1 = 7).
Arrangement: _ _ B _ _ _ K
Clue 4: F sits second to the right of B.
B is at position 3, so F is at position 5 (3 + 2 = 5).
Arrangement: _ _ B _ F _ K
Clue 5: Only two people sit between F and C.
F is at position 5. If C is to the right of F, C would be at position 8, which is not possible as there are only 7 seats. So, C must be to the left of F. Counting two places to the left from F (position 5), C will be at position 2 (5 - 2 - 1 = 2).
Arrangement: _ C B _ F _ K
Clue 6: G sits some place to the right of E but at some place to the left of D.
The remaining people are D, E, G. The remaining seats are 1, 4, 6.
From the clue, the order must be E, G, D. This means E is at position 1, G is at position 4, and D is at position 6.
Final Arrangement: E C B G F D K
Answer the question: How many people sit to the right of G?
In the final arrangement E C B G F D K, G is at position 4. The people to the right of G are F, D, and K.
There are 3 people to the right of G.
B) Three
This problem involves calculating the combined work rate of two individuals and then determining the time required to complete a larger task. We will first find the individual work rates, then their combined work rate, and finally use this combined rate to find the total time needed to make 14 chairs.
Calculate Jaggu's work rate:
Jaggu can make 1 chair in 3 days. So, in 1 day, Jaggu makes:
Calculate Rabbu's work rate:
Rabbu can make 1 chair in 4 days. So, in 1 day, Rabbu makes:
Calculate their combined work rate:
When they work together, their work rates add up. In 1 day, they together make:
To add these fractions, find a common denominator, which is 12:
\[ \text{Combined work rate} = \frac{4}{12} + \frac{3}{12} = \frac{7}{12} \text{ chairs/day} \]Calculate the total time to make 14 chairs:
If they make \(\frac{7}{12}\) chairs per day, to find the number of days to make 14 chairs, we divide the total number of chairs by their combined work rate:
Correct Option: C) 24 days