To solve this problem, we need to follow the order of operations, often remembered by the acronym PEMDAS/BODMAS. This stands for Parentheses/Brackets, Exponents/Orders, Multiplication and Division (from left to right), Addition and Subtraction (from left to right).
Thus, the final value of the expression is 98.
C) 98 is the correct answer, obtained by correctly applying the order of operations (BODMAS/PEMDAS).
In a certain code language, ‘BOUTS’ is written as ‘54%8#’ and ‘ULTRA’ is written as ‘%38@9’. How will ‘BLARE’ be written in that language?
The problem is a coding-decoding question. We need to identify the pattern or mapping between letters and symbols/numbers from the given coded words and then apply that mapping to decode the new word.
Given: 'BOUTS' is coded as '54%8#'.
Given: 'ULTRA' is coded as '%38@9'.
By comparing both coded words, we can establish a consistent mapping for the common letters and new letters:
We need to find the code for 'BLARE'. Using the established mapping:
So, 'BLARE' would be coded as '539@2'.
D) 539@2. This matches our derived code for 'BLARE' based on the established letter-to-symbol/number mapping.
To find who scored the third highest marks, we need to establish the relative order of marks obtained by each person based on the given statements. We will use inequalities to represent the relationships and then combine them to form a complete sequence from highest to lowest marks.
Therefore, Abhishek scored the third highest marks.
Correct Option: C) Abhishek
To find the missing number in the series, we need to identify the pattern or relationship between consecutive terms. This often involves looking at the differences between numbers, or differences of differences (second-order differences).
\(1, 9, 22, 32, 47, ?, 76, 90, 109\)
The first-order differences are: \(8, 13, 10, 15, x, y, 14, 19\)
The second-order differences are: \(5, -3, 5, \text{?, ?}, 5\)
It appears there's a repeating pattern in the second-order differences: \(5, -3, 5\). If this pattern continues, the missing second-order differences should be \(-3\) and \(5\).
The next second-order difference should be \(-3\). Let's check: \(14 - y = 14 - 17 = -3\). This matches the pattern.
We found \(x = 12\), which is the difference between the missing number and \(47\).
So, Missing Number \(= 47 + x = 47 + 12 = 59\)
The difference between \(76\) and the missing number should be \(y = 17\).
\(76 - 59 = 17\). This also matches.
B) 59 — The series follows a pattern where the second-order differences alternate between \(5\) and \(-3\). By applying this pattern, the missing number is found to be \(59\).
This problem involves calculating the current flowing through an electric fan given its power and the voltage of the source. We can use the fundamental formula relating power, voltage, and current in an electrical circuit.
The relationship between power, voltage, and current is given by:
\[ P = V \times I \]To find the current, we can rearrange the formula as:
\[ I = \frac{P}{V} \]Substitute \(P = 10 \text{ W}\) and \(V = 20 \text{ V}\) into the rearranged formula:
\[ I = \frac{10 \text{ W}}{20 \text{ V}} \]Thus, the current flowing through the fan is 0.5 amp.
Correct Option: B) 0.5 amp
A, B, C, D, E and F live on six different floors of the same building. The lowermost floor in the building is numbered 1, the floor above it is numbered 2 and so on till the topmost floor is numbered 6. A lives on floor number 5. Only two people live between A and C. Neither D nor B lives on the topmost floor. E lives immediately below C. B does not live on an even-numbered floor. Who lives on floor number 3?
This is a logical reasoning problem involving arrangement. We need to deduce the living arrangements of six people (A, B, C, D, E, F) on six different floors based on the given clues. We will systematically place each person on their respective floor by using the clues and eliminating possibilities.
Floors: There are 6 floors, numbered 1 to 6 from bottom to top.
| Floor No. | Person |
|---|---|
| 6 | |
| 5 | |
| 4 | |
| 3 | |
| 2 | |
| 1 |
Clue 1: A lives on floor number 5.
| Floor No. | Person |
|---|---|
| 6 | |
| 5 | A |
| 4 | |
| 3 | |
| 2 | |
| 1 |
Clue 2: Only two people live between A and C.
Since A is on floor 5, and there are two people between A and C, C must be on floor 2 (Floors 4 and 3 are between A and C).
| Floor No. | Person |
|---|---|
| 6 | |
| 5 | A |
| 4 | |
| 3 | |
| 2 | C |
| 1 |
Clue 3: E lives immediately below C.
Since C is on floor 2, E must be on floor 1.
| Floor No. | Person |
|---|---|
| 6 | |
| 5 | A |
| 4 | |
| 3 | |
| 2 | C |
| 1 | E |
Clue 4: B does not live on an even-numbered floor.
Even-numbered floors are 2, 4, 6. Odd-numbered floors are 1, 3, 5.
From the current arrangement:
| Floor No. | Person |
|---|---|
| 6 | |
| 5 | A |
| 4 | |
| 3 | B |
| 2 | C |
| 1 | E |
Clue 5: Neither D nor B lives on the topmost floor (floor 6).
We already placed B on floor 3. This clue confirms B is not on floor 6. Also, D is not on floor 6. The only remaining empty floors are 4 and 6. Since D cannot be on floor 6, D must be on floor 4.
| Floor No. | Person |
|---|---|
| 6 | |
| 5 | A |
| 4 | D |
| 3 | B |
| 2 | C |
| 1 | E |
Final Placement: The only person left is F, and the only floor left is 6. So, F lives on floor 6.
| Floor No. | Person |
|---|---|
| 6 | F |
| 5 | A |
| 4 | D |
| 3 | B |
| 2 | C |
| 1 | E |
The question asks: Who lives on floor number 3?
From our final arrangement, B lives on floor number 3.
Correct Option: C) B
Suppose Raghu has kept an object in front of a concave mirror of focal length (f) at various distances (u) and he has measured the corresponding image distances (v). From such an experiment, Raghu is able to plot a graph of u against 1/magnification, i.e. u vs. 1/m. (Take magnification m = v/u.) Which of the following options is true?
It is a straight line with slope +f, and x intercept +1 and y intercept –f
It is a straight line with slope –1/f, and x intercept +1 and y intercept –f
It is a straight line with slope 1/f, and x intercept –1 and y intercept +f
It is a straight line with slope +f, and x intercept –1 and y intercept +f
To determine the characteristics of the graph of u vs. 1/m, we need to establish a relationship between u, m, and f using the mirror formula and the magnification formula. Then, we will rearrange this relationship into the form of a straight line equation, \(y = Ax + B\), where \(y = u\) and \(x = 1/m\), to identify the slope, x-intercept, and y-intercept.
The mirror formula for a concave mirror is given by:
\[ \frac{1}{f} = \frac{1}{v} + \frac{1}{u} \]Where \(f\) is the focal length, \(v\) is the image distance, and \(u\) is the object distance. For a concave mirror, \(f\) is taken as negative in sign convention, but in competitive exams, often the magnitude is used unless specified. Let's assume \(f\) is the magnitude here, and we will use the standard sign convention for \(u\) and \(v\).
The magnification \(m\) for a mirror is given by:
\[ m = -\frac{v}{u} \]The question states to take magnification \(m = v/u\). This implies that the question is asking for the magnitude of magnification or is using a convention where the negative sign is absorbed or ignored for the purpose of the graph. Let's proceed with \(m = v/u\), as given.
From this, we can write \(v = mu\).
Substitute \(v = mu\) into the mirror formula:
\[ \frac{1}{f} = \frac{1}{mu} + \frac{1}{u} \]Combine the terms on the right side:
\[ \frac{1}{f} = \frac{1 + m}{mu} \]Rearrange to solve for \(u\):
\[ u = f \frac{1 + m}{m} \] \[ u = f \left( \frac{1}{m} + \frac{m}{m} \right) \] \[ u = f \left( \frac{1}{m} + 1 \right) \] \[ u = f \left( \frac{1}{m} \right) + f \]The equation is in the form \(y = Ax + B\), where \(y = u\) and \(x = 1/m\).
Comparing \(u = f \left( \frac{1}{m} \right) + f\) with \(y = Ax + B\):
The x-intercept occurs when \(y = u = 0\).
\[ 0 = f \left( \frac{1}{m} \right) + f \] \[ -f = f \left( \frac{1}{m} \right) \]Assuming \(f \neq 0\), we can divide by \(f\):
\[ -1 = \frac{1}{m} \]So, the x-intercept (value of \(1/m\)) is \(-1\).
Correct Option: D) It is a straight line with slope +f, and x intercept –1 and y intercept +f
Based on our derivation, the slope is \(+f\), the x-intercept is \(-1\), and the y-intercept is \(+f\). This matches option D.
This is incorrect because the x-intercept is \(-1\), not \(+1\), and the y-intercept is \(+f\), not \(-f\).
This is incorrect because the slope is \(+f\), not \(-1/f\), and the intercepts are also incorrect.
This is incorrect because the slope is \(+f\), not \(1/f\).
The question asks about the authority responsible for transferring a State Governor from one state to another. This falls under the constitutional provisions related to the appointment and tenure of Governors in India.
B) President — The President of India is the appointing authority for the Governor and also holds the power to remove or transfer a Governor from one state to another. This is a discretionary power exercised by the President.
The question asks to identify the chemical suitable for removing a stain from a shirt. This implies finding a substance that can effectively clean or dissolve common stains without damaging the fabric. We need to evaluate the properties of each given chemical.
A) Sodium carbonate – Sodium carbonate, commonly known as washing soda, is a basic salt that is effective in removing various stains, especially greasy or acidic ones. It acts as a water softener and helps in emulsifying oils and fats, making it a suitable choice for laundry and stain removal without being overly harsh on fabrics.
The problem asks us to find the principal sum given the difference between compound interest (CI) and simple interest (SI) for a certain period and rate. We will use the formulas for CI and SI and their difference to solve for the principal.
The formula for simple interest is:
\[ \text{SI} = \frac{P \times R \times T}{100} \]Substituting \(R = 8\) and \(T = 4\):
\[ \text{SI} = \frac{P \times 8 \times 4}{100} = \frac{32P}{100} = 0.32P \]The formula for the amount (\(A\)) after compound interest is:
\[ A = P \left(1 + \frac{R}{100}\right)^T \]Compound Interest (\(\text{CI}\)) is then \(A - P\):
\[ \text{CI} = P \left(1 + \frac{R}{100}\right)^T - P \]Substituting \(R = 8\) and \(T = 4\):
\[ \text{CI} = P \left(1 + \frac{8}{100}\right)^4 - P \]\[ \text{CI} = P \left(1 + 0.08\right)^4 - P \]\[ \text{CI} = P (1.08)^4 - P \]Calculate \((1.08)^4\):
\[ (1.08)^2 = 1.1664 \]\[ (1.08)^4 = (1.1664)^2 = 1.36048896 \]So,
\[ \text{CI} = P (1.36048896) - P \]\[ \text{CI} = P (1.36048896 - 1) \]\[ \text{CI} = 0.36048896 P \]We are given that \(\text{CI} - \text{SI} = 20\).
\[ 0.36048896 P - 0.32 P = 20 \]\[ (0.36048896 - 0.32) P = 20 \]\[ 0.04048896 P = 20 \]Rounding \(493.9639\) to two decimal places gives \(493.96\).
Correct Option: C) The calculated principal sum is approximately Rs 493.96, which matches option C.