The question asks for the name of a specific book launched by Bhim Singh on August 11, 2024. This is a factual recall question related to current affairs or general knowledge. To answer this, one needs to be aware of recent book launches and their authors.
A) 75 Great Revolutionaries of India is the correct answer. Bhim Singh indeed launched a book with this title on August 11, 2024, which focuses on the lives of 75 Indian freedom fighters.
This problem involves setting up a system of linear equations based on the given information about the cost of pens and pencils. We will define variables for the original costs, form two equations, and then solve for the required expression.
Let the original cost of one pen be \(P\) and the original cost of one pencil be \(C\).
From the first statement, "The cost of 12 pens and 7 pencils is ₹233", we can form the first equation:
\[ 12P + 7C = 233 \quad \text{(Equation 1)} \]From the second statement, "If the cost of a pen decreases by ₹1.50 and the cost of a pencil increases by ₹1, then the cost of 2 pens and 3 pencils is ₹48".
The new cost of a pen is \(P - 1.50\).
The new cost of a pencil is \(C + 1\).
So, the second equation is:
\[ 2(P - 1.50) + 3(C + 1) = 48 \]Simplify Equation 2:
\[ 2P - 3 + 3C + 3 = 48 \]\[ 2P + 3C = 48 \quad \text{(Equation 2)} \]We need to find the original cost of 2 pens and 3 pencils, which is \(2P + 3C\).
Looking at Equation 2, we have already found the expression for the original cost of 2 pens and 3 pencils:
\[ 2P + 3C = 48 \]D) The original cost of 2 pens and 3 pencils is directly given by the simplified second equation, which is ₹48.
We need to calculate the initial income, expenditure, and savings. Then, we will calculate the new expenditure and savings based on the given percentage changes. Finally, we will find the new income and determine the percentage increase in income.
Establish initial relationship:
Let Swarna's savings be \(S\).
Her expenditure \(E\) is 125% more than her savings. This means:
Calculate initial income: Income \(I\) is the sum of expenditure and savings:
\[ I = E + S = 2.25S + S = 3.25S \]Calculate new expenditure: Expenditure decreases by 6%.
\[ E_{\text{new}} = E - 0.06E = 0.94E = 0.94 \times (2.25S) = 2.115S \]Calculate new savings: Savings increase by 26.5%.
\[ S_{\text{new}} = S + 0.265S = 1.265S \]Calculate new income: New income \(I_{\text{new}}\) is the sum of new expenditure and new savings:
\[ I_{\text{new}} = E_{\text{new}} + S_{\text{new}} = 2.115S + 1.265S = 3.38S \]Calculate the percentage increase in income: Percentage increase \( = \frac{I_{\text{new}} - I}{I} \times 100 \)
\[ \text{Percentage increase} = \frac{3.38S - 3.25S}{3.25S} \times 100 \] \[ = \frac{0.13S}{3.25S} \times 100 \] \[ = \frac{0.13}{3.25} \times 100 \] \[ = 0.04 \times 100 = 4\% \]Correct Option: D) 4%
This problem involves substituting given symbols with mathematical operators and then evaluating the expression according to the order of operations (BODMAS/PEMDAS).
(24 J 3) K 6 I (14 J 2) L 19 = ?Thus, the value of the expression is 21.
B) 21 is the correct answer, as calculated by substituting the operators and following the order of operations.
This problem involves calculating the original marked price of an item given its sale price and the discount percentage. We will use the formula relating sale price, marked price, and discount percentage.
The Sale Price is calculated by subtracting the discount amount from the Marked Price. The discount amount is a percentage of the Marked Price.
\[ SP = MP - (D\% \times MP) \]Alternatively, this can be written as:\[ SP = MP \times (1 - \frac{D}{100}) \]To find \(MP\), divide the Sale Price by 0.70:
\[ MP = \frac{12,460}{0.70} \]\[ MP = \frac{12,460}{\frac{70}{100}} \]\[ MP = \frac{12,460 \times 100}{70} \]\[ MP = \frac{1,246,000}{70} \]\[ MP = \frac{124,600}{7} \]\[ MP = 17,800 \]The marked price of the item is ₹17,800.
Correct Option: A) ₹17,800
The problem describes a situation where toxic waste is being mixed with dry waste by apartment complexes, leading to danger for waste processing personnel and the environment. We need to evaluate two proposed courses of action to determine which logically follow from the statement to address this issue.
C) Both I and II follow
Select the set, from the given options, in which the numbers are related in the same way as are the numbers of the following sets.
(NOTE: Operations should be performed on the whole numbers, without breaking down the numbers into their constituent digits. E.g. 13 – Operations on 13 such as adding to/subtracting from/multiplying with 13 can be performed. Breaking down 13 into 1 and 3 and then performing mathematical operations on 1 and 3 is not allowed.)
(2, 24, 6)
(4, 32, 2)
The problem asks us to identify a set of three numbers that follow the same relationship as the given sets: (2, 24, 6) and (4, 32, 2). We need to find a mathematical operation or pattern connecting the three numbers in each set.
B) (6, 108, 3)
Here, \(A=6\), \(B=108\), \(C=3\).
Using the pattern \(B = A^2 \times C\):
\(A^2 \times C = 6^2 \times 3 = 36 \times 3 = 108\).
This matches the middle number \(B=108\). Therefore, option B follows the same relationship.
The question asks about the number of members in the steering committee of the GlobE Network, specifically mentioning India's recent election to it. This is a factual question related to current affairs and international organizations.
B) 15 — The steering committee of the GlobE Network, to which India was elected, comprises 15 member countries. This was a significant development announced by the CBI, highlighting India's growing role in combating transnational financial crime.
To solve this problem, we need to test each option by interchanging the given numbers in the equation and then evaluating the expression using the order of operations (BODMAS/PEMDAS). The goal is to find the interchange that makes the equation true, i.e., the left-hand side equals 62.
The given equation is:
\((27 + 15) \times 2 - (95 \div 5) + 25 \times 4 - 135 = 62\)
Let's evaluate the original equation first to see if it's already correct or how far it is from 62:
Original Equation:
\[ (27 + 15) \times 2 - (95 \div 5) + 25 \times 4 - 135 \\ = (42) \times 2 - (19) + 100 - 135 \\ = 84 - 19 + 100 - 135 \\ = 65 + 100 - 135 \\ = 165 - 135 \\ = 30 \]Since \(30 \neq 62\), the original equation is incorrect.
The equation becomes:
\[ (27 + 15) \times 4 - (95 \div 5) + 25 \times 2 - 135 \\ = (42) \times 4 - (19) + 50 - 135 \\ = 168 - 19 + 50 - 135 \\ = 149 + 50 - 135 \\ = 199 - 135 \\ = 64 \]Since \(64 \neq 62\), Option A is incorrect.
The equation becomes:
\[ (25 + 15) \times 2 - (95 \div 5) + 27 \times 4 - 135 \\ = (40) \times 2 - (19) + 108 - 135 \\ = 80 - 19 + 108 - 135 \\ = 61 + 108 - 135 \\ = 169 - 135 \\ = 34 \]Since \(34 \neq 62\), Option B is incorrect.
The equation becomes:
\[ (27 + 15) \times 2 - (135 \div 5) + 25 \times 4 - 95 \\ = (42) \times 2 - (27) + 100 - 95 \\ = 84 - 27 + 100 - 95 \\ = 57 + 100 - 95 \\ = 157 - 95 \\ = 62 \]Since \(62 = 62\), Option C is correct.
The equation becomes:
\[ (27 + 5) \times 2 - (95 \div 15) + 25 \times 4 - 135 \]Here, \(95 \div 15\) does not result in an integer, which is often a hint that this might not be the correct interchange in such problems, unless the final answer is expected to be non-integer. Let's proceed:
\[ = (32) \times 2 - \left(\frac{95}{15}\right) + 100 - 135 \\ = 64 - \left(\frac{19}{3}\right) + 100 - 135 \\ = 164 - 135 - \frac{19}{3} \\ = 29 - \frac{19}{3} \\ = \frac{87 - 19}{3} \\ = \frac{68}{3} \]Since \(\frac{68}{3} \neq 62\), Option D is incorrect.
Correct Option: C) Interchanging 95 and 135 makes the equation correct.
This problem can be solved by visualizing the situation as a right-angled triangle. The horizontal distance between the mud buildings forms one leg, and the difference in their heights forms the other leg. The distance between their tops will be the hypotenuse of this right-angled triangle. We will use the Pythagorean theorem to find the length of the hypotenuse.
The vertical distance between the tops of the buildings will be the absolute difference between their heights.
\[ \text{Difference in height} = |H_S - H_R| = |15 \text{ cm} - 8 \text{ cm}| = 7 \text{ cm} \]Imagine a horizontal line drawn from the top of the shorter building (Ramesh's) to a point directly above the base of the taller building (Suresh's). This line segment will have a length equal to the distance between the bases of the buildings, which is 24 cm. The vertical distance from this point to the top of the taller building is the difference in their heights, which is 7 cm.
These two lengths (24 cm and 7 cm) form the two perpendicular sides (legs) of a right-angled triangle. The distance between the tops of the mud buildings is the hypotenuse of this triangle.
Let \(a\) and \(b\) be the lengths of the two legs, and \(c\) be the length of the hypotenuse. The Pythagorean theorem states:
\[ a^2 + b^2 = c^2 \]Here, \(a = 24 \text{ cm}\) (horizontal distance) and \(b = 7 \text{ cm}\) (vertical difference in height).
\[ (24)^2 + (7)^2 = c^2 \]\[ 576 + 49 = c^2 \]\[ 625 = c^2 \]\[ c = \sqrt{625} \]\[ c = 25 \text{ cm} \]C) 25 cm is the correct answer. The distance between the tops of the mud buildings is 25 cm, calculated using the Pythagorean theorem.