The question asks to identify the river associated with the Dhuandhar Falls. This requires knowledge of major waterfalls in India and the rivers they are located on.
Correct Option: C) The Dhuandhar Falls are formed by the Narmada River as it flows through the Marble Rocks gorge near Jabalpur in Madhya Pradesh. The falls are famous for the mist created by the plunging water, giving them their name.
We are given the initial ratio of two numbers and a new ratio formed after subtracting specific values from each number. We can set up algebraic equations based on these ratios and solve for the numbers.
Let the two numbers be \(3x\) and \(2x\), since their ratio is \(3:2\).
According to the problem, if 8 is subtracted from the first number and 6 from the second number, the new ratio becomes \(8:5\). We can write this as an equation:
\[ \frac{3x - 8}{2x - 6} = \frac{8}{5} \]Now, we cross-multiply to solve for \(x\):
\[ 5(3x - 8) = 8(2x - 6) \]\[ 15x - 40 = 16x - 48 \]Rearrange the terms to solve for \(x\):
\[ 16x - 15x = 48 - 40 \]\[ x = 8 \]Substitute the value of \(x\) back into our initial expressions for the numbers:
First number \( = 3x = 3 \times 8 = 24 \)
Second number \( = 2x = 2 \times 8 = 16 \)
Thus, the two numbers are 24 and 16.
B) 24, 16
A) 3, 2 — These are the ratio values, not the actual numbers. If we subtract 8 from 3 and 6 from 2, we get negative numbers, which won't form a positive ratio.
C) 40, 30 — If the numbers were 40 and 30, their initial ratio is \(40:30 = 4:3\), which does not match the given initial ratio of \(3:2\).
D) 32, 24 — If the numbers were 32 and 24, their initial ratio is \(32:24 = 4:3\), which does not match the given initial ratio of \(3:2\).
Which constitutional amendment, known as 'mini constitution', gave effect to the recommendations of Swaran Singh Committee?
41st constitutional amendment
44th constitutional amendment
42nd constitutional amendment
43rd constitutional amendment
The question asks to identify the constitutional amendment that is known as the 'mini constitution' and implemented the recommendations of the Swaran Singh Committee. This requires knowledge of significant constitutional amendments in India and their key provisions.
Correct Option: C) 42nd constitutional amendment
The 42nd Constitutional Amendment Act, 1976, is famously known as the 'Mini Constitution' because it introduced a large number of changes to the Indian Constitution. It was enacted during the Emergency and implemented the recommendations of the Swaran Singh Committee, which was set up to study the Constitution and suggest amendments.
The question asks about the index used to calculate dearness allowance (DA) for government employees in India, which compensates for price increases. We need to identify the specific price index that tracks inflation relevant to this group.
D) Consumer Price Index Number for Industrial Workers (CPI-IW) — The CPI-IW is specifically designed to measure inflation affecting industrial workers, and it is the index officially used by the Indian government to calculate dearness allowance for its employees and pensioners to compensate for the rise in the cost of living.
The question asks to identify whose teachings are compiled in the Vinaya Pitaka and Sutta Pitaka. This requires knowledge of the sacred texts of major Indian religions, particularly Buddhism and Jainism.
Correct Option: A) Gautam Buddha. The Vinaya Pitaka and Sutta Pitaka are two of the three main divisions of the Tripitaka, the sacred scripture of Buddhism, which contains the teachings and discourses of Gautam Buddha.
The question asks to identify the religious tradition with which the concept of Bodhisattva is associated. This requires knowledge of the core tenets and key figures/concepts within major Indian religions, particularly different schools of Buddhism.
C) Mahayana Buddhism — The concept of Bodhisattva is a cornerstone of Mahayana Buddhism. A Bodhisattva is an enlightened being who, out of immense compassion, chooses to delay their own entry into nirvana to assist all other sentient beings in achieving liberation from suffering (samsara). This ideal emphasizes universal salvation and altruism, distinguishing Mahayana from other Buddhist schools.
The problem requires us to solve for the variable 'x' in a given equation involving percentages. We will convert the percentages into decimal or fractional form and then use algebraic manipulation to isolate 'x'.
The equation is:
\[ 20\% \text{ of } 75 = 225 - x\% \text{ of } 420 \]Recall that \(P\%\) can be written as \(\frac{P}{100}\). So, the equation becomes:
\[ \frac{20}{100} \times 75 = 225 - \frac{x}{100} \times 420 \]Calculate the left side of the equation:
\[ \frac{20}{100} \times 75 = \frac{1}{5} \times 75 = 15 \]Simplify the term with 'x' on the right side:
\[ \frac{x}{100} \times 420 = \frac{420x}{100} = \frac{42x}{10} = 4.2x \]Substitute these simplified values back into the equation:
\[ 15 = 225 - 4.2x \]Move the term \(4.2x\) to the left side and \(15\) to the right side of the equation:
\[ 4.2x = 225 - 15 \]\[ 4.2x = 210 \]Divide both sides by \(4.2\):
\[ x = \frac{210}{4.2} \]To simplify the division, multiply the numerator and denominator by 10 to remove the decimal:
\[ x = \frac{2100}{42} \]Perform the division:
\[ x = 50 \]Correct Option: A) 50
This problem involves setting up and solving a system of linear equations based on the given age conditions. We will define variables for the present ages of Kirti and Kunal and then translate the two given statements about their ages into two separate equations. Finally, we will solve these equations simultaneously to find their present ages.
Define variables:
Let Kirti's present age be \(K\) years.
Let Kunal's present age be \(U\) years.
Formulate the first equation:
"Six years from now, Kirti's age will be twice the age of her brother Kunal."
Kirti's age six years from now: \(K + 6\)
Kunal's age six years from now: \(U + 6\)
According to the statement:
Formulate the second equation:
"4 years ago she was four times as old as Kunal was then."
Kirti's age four years ago: \(K - 4\)
Kunal's age four years ago: \(U - 4\)
According to the statement:
Solve the system of equations:
We have two expressions for \(K\). We can set them equal to each other:
Solve for \(U\):
Subtract \(2U\) from both sides:
State the answer:
Kunal's present age is 9 years.
Correct Option: A) 9 years
What is the difference between \( \frac{3}{5} \) of 200 and \( \frac{1}{2} \) of 300?
To find the difference, we need to calculate the value of each fraction of the given numbers separately and then subtract the smaller value from the larger one.
To simplify, divide 200 by 5:
\[ \text{First value} = 3 \times \frac{200}{5} = 3 \times 40 = 120 \]To simplify, divide 300 by 2:
\[ \text{Second value} = 1 \times \frac{300}{2} = 1 \times 150 = 150 \]D) 30. The difference between \( \frac{3}{5} \) of 200 (which is 120) and \( \frac{1}{2} \) of 300 (which is 150) is \( 150 - 120 = 30 \).
By which number should 2 \( \frac{1}{5} \) be multiplied to get 5 \( \frac{2}{5} \)?
2 \( \frac{5}{11} \)
\( \frac{11}{27} \)
3
3 \( \frac{1}{5} \)
To find the number by which \(2 \frac{1}{5}\) should be multiplied to get \(5 \frac{2}{5}\), we can set up an algebraic equation. Let the unknown number be \(x\). We will convert the mixed fractions into improper fractions, set up the equation, and then solve for \(x\).
First, convert \(2 \frac{1}{5}\) to an improper fraction:
\[ 2 \frac{1}{5} = \frac{(2 \times 5) + 1}{5} = \frac{10 + 1}{5} = \frac{11}{5} \]Next, convert \(5 \frac{2}{5}\) to an improper fraction:
\[ 5 \frac{2}{5} = \frac{(5 \times 5) + 2}{5} = \frac{25 + 2}{5} = \frac{27}{5} \]Let the unknown number be \(x\). According to the problem statement, when \(2 \frac{1}{5}\) is multiplied by \(x\), the result is \(5 \frac{2}{5}\). So, we can write the equation as:
\[ \frac{11}{5} \times x = \frac{27}{5} \]To find \(x\), we need to isolate it. Divide both sides of the equation by \( \frac{11}{5} \):
\[ x = \frac{27}{5} \div \frac{11}{5} \]Dividing by a fraction is the same as multiplying by its reciprocal:
\[ x = \frac{27}{5} \times \frac{5}{11} \]Now, multiply the fractions:
\[ x = \frac{27 \times 5}{5 \times 11} \]Cancel out the common factor of 5:
\[ x = \frac{27}{11} \]To compare with the options, convert \( \frac{27}{11} \) back to a mixed fraction:
Divide 27 by 11:
\[ 27 \div 11 = 2 \text{ with a remainder of } 5 \]So, the mixed fraction is:
\[ x = 2 \frac{5}{11} \]A) 2 \( \frac{5}{11} \) is the correct answer, as calculated in the steps above.