The question asks to identify the state where the Gir forest, known for its dry deciduous characteristics, is located. This requires knowledge of the geographical distribution of major forests and wildlife sanctuaries in India.
Correct Option: B) Gujarat. The Gir Forest National Park and Wildlife Sanctuary, a significant dry deciduous forest and the only natural habitat for Asiatic Lions, is located in the state of Gujarat.
This problem involves work and time. We will use the concept that work done is equal to the rate of work multiplied by the time taken. We'll set up equations based on the given information about Sandra and Mayuri working together and separately, and then solve for Sandra's individual work rate.
Let the number of days Sandra takes to complete the work alone be \(S\) days, and Mayuri takes \(M\) days to complete the work alone.
Their individual daily work rates are \(\frac{1}{S}\) (for Sandra) and \(\frac{1}{M}\) (for Mayuri).
When they work together, their combined daily work rate is \[\frac{1}{S} + \frac{1}{M}\].
They complete the work together in 45 days. So, the total work is 1 unit. Therefore:
\[ \left(\frac{1}{S} + \frac{1}{M}\right) \times 45 = 1 \]\[ \frac{1}{S} + \frac{1}{M} = \frac{1}{45} \quad \text{(Equation 1)} \]In the second scenario, Mayuri works alone for a certain number of days to complete one-third of the work. Let this be \(D_M\) days. So, \[\frac{1}{M} \times D_M = \frac{1}{3}\].
Then, Sandra completes the remaining two-thirds of the work alone. Let this be \(D_S\) days. So, \[\frac{1}{S} \times D_S = \frac{2}{3}\].
The total time taken in this scenario is 104 days. So, \(D_M + D_S = 104\).
From steps 5 and 6, we can express \(D_M\) and \(D_S\) in terms of \(M\) and \(S\):
\[ D_M = \frac{M}{3} \]\[ D_S = \frac{2S}{3} \]Substitute these into the total time equation:
\[ \frac{M}{3} + \frac{2S}{3} = 104 \]\[ M + 2S = 312 \quad \text{(Equation 2)} \]From Equation 1, we can express \(M\) in terms of \(S\):
\[ \frac{1}{M} = \frac{1}{45} - \frac{1}{S} = \frac{S - 45}{45S} \]\[ M = \frac{45S}{S - 45} \]Substitute this expression for \(M\) into Equation 2:
\[ \frac{45S}{S - 45} + 2S = 312 \]Multiply by \((S - 45)\) to clear the denominator:
\[ 45S + 2S(S - 45) = 312(S - 45) \]\[ 45S + 2S^2 - 90S = 312S - 14040 \]\[ 2S^2 - 45S = 312S - 14040 \]\[ 2S^2 - 45S - 312S + 14040 = 0 \]\[ 2S^2 - 357S + 14040 = 0 \]Solve this quadratic equation for \(S\) using the quadratic formula \(S = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}\):
\[ S = \frac{357 \pm \sqrt{(-357)^2 - 4(2)(14040)}}{2(2)} \]\[ S = \frac{357 \pm \sqrt{127449 - 112320}}{4} \]\[ S = \frac{357 \pm \sqrt{15129}}{4} \]\[ S = \frac{357 \pm 123}{4} \]This gives two possible values for \(S\):
\[ S_1 = \frac{357 + 123}{4} = \frac{480}{4} = 120 \]\[ S_2 = \frac{357 - 123}{4} = \frac{234}{4} = 58.5 \]Now, we need to check which value of \(S\) satisfies the condition that Mayuri is faster than Sandra. This means \(M < S\).
If \(S = 120\):
\[ M = \frac{45 \times 120}{120 - 45} = \frac{5400}{75} = 72 \]In this case, \(M = 72\) and \(S = 120\). Since \(72 < 120\), Mayuri is faster than Sandra. This is a valid solution.If \(S = 58.5\):
\[ M = \frac{45 \times 58.5}{58.5 - 45} = \frac{2632.5}{13.5} = 195 \]In this case, \(M = 195\) and \(S = 58.5\). Since \(195 > 58.5\), Sandra would be faster than Mayuri, which contradicts the given condition. So, this solution is not valid.Therefore, Sandra alone will complete the work in 120 days.
Correct Option: D) 120
Write the sum of the place value of 5 in \( \frac{6}{8} \) and place value of 4 in \( \frac{6}{25} \)
\( \frac{8}{100} \)
\( \frac{99}{100} \)
\( \frac{9}{100} \)
\( \frac{88}{100} \)
To find the sum of the place values, we first need to convert the given fractions into decimal form. Then, identify the place value of the specified digit in each decimal number. Finally, sum these place values.
Convert the first fraction to decimal and find the place value of 5:
The first fraction is \( \frac{6}{8} \). Let's convert it to a decimal:
\[ \frac{6}{8} = \frac{3}{4} = 0.75 \]In the decimal \( 0.75 \), the digit 5 is in the hundredths place.
So, the place value of 5 in \( 0.75 \) is \[5 \times \frac{1}{100} = \frac{5}{100}\].
Convert the second fraction to decimal and find the place value of 4:
The second fraction is \( \frac{6}{25} \). Let's convert it to a decimal:
\[ \frac{6}{25} = \frac{6 \times 4}{25 \times 4} = \frac{24}{100} = 0.24 \]In the decimal \( 0.24 \), the digit 4 is in the hundredths place.
So, the place value of 4 in \( 0.24 \) is \[4 \times \frac{1}{100} = \frac{4}{100}\].
Calculate the sum of the place values:
Now, we need to find the sum of the two place values we found:
\[ \text{Sum} = \frac{5}{100} + \frac{4}{100} \] \[ \text{Sum} = \frac{5 + 4}{100} \] \[ \text{Sum} = \frac{9}{100} \]C) \( \frac{9}{100} \)
The question asks to identify the field in which 'Ilayaraja' is known for his contributions. This requires general knowledge about prominent personalities and their respective fields of work.
Correct Option: D) Music — Ilayaraja is a legendary Indian music composer, singer, and conductor, primarily known for his work in the South Indian film industry. He has composed over 7,000 songs, scored for more than 1,400 films, and performed in over 20,000 concerts, making him one of the most prolific composers in the world. His contributions to music are immense and widely recognized.
30% of sales of a food retail chain is from dairy products and the rest is from fresh produce. If the chain has sales of about Rs. 50,000 in a month then what is the sale amount from dairy products?
The problem asks us to calculate the sales amount from dairy products given the total sales and the percentage of sales from dairy products. We need to find 30% of the total sales amount.
Sales from dairy products \( = 30\% \text{ of Rs. } 50,000 \)
This can be written as:
\[ \text{Sales from dairy products} = \frac{30}{100} \times 50,000 \]Now, perform the multiplication:
\[ \text{Sales from dairy products} = 30 \times 500 \] \[ \text{Sales from dairy products} = 15,000 \]So, the sale amount from dairy products is Rs. 15,000.
Correct Option: A) Rs. 15,000
One mole of any substance contains 6.023 × 1023 particles. If 3.0115 × 1023 molecules of CO2 are present, then the number of moles of CO2 is:
The problem asks us to calculate the number of moles of CO\(_2\) given the number of molecules of CO\(_2\) and Avogadro's number. We will use the relationship between the number of moles, the number of particles, and Avogadro's number.
A) 0.5 — The calculation shows that \(3.0115 \times 10^{23}\) molecules of CO\(_2\) correspond to 0.5 moles.
This problem involves determining the final direction relative to the starting point after a series of movements. We can visualize the movements on a coordinate plane or by drawing a simple diagram to track the changes in direction.
Correct Option: A) Southeast
If we denote the initial position as \((0,0)\):
The point \((0.5, -3)\) is in the Southeast quadrant relative to \((0,0)\).
The question asks to identify the winner of the 2016 World Chess Championship. This requires knowledge of major chess tournaments and their outcomes.
Correct Option: B) Magnus Carlsen
To find the required profit percentage on the TV, we need to calculate the total loss incurred from selling the radios. Since the overall loss should be zero, the profit from selling the TV must exactly compensate for this loss. We will first determine the cost price of a radio, then the total loss, and finally the selling price and profit percentage for the TV.
Let the cost price of one radio be \( \text{₹}100 \). This makes percentage calculations easier.
The shopkeeper sold radios at a 20% loss.
\[ \text{Loss per radio} = 20\% \text{ of } \text{₹}100 = \frac{20}{100} \times 100 = \text{₹}20 \]There are 6 radios sold.
\[ \text{Total loss from radios} = 6 \times \text{₹}20 = \text{₹}120 \]The cost price of the TV is 3 times that of each radio.
\[ \text{CP of TV} = 3 \times \text{CP of one radio} = 3 \times \text{₹}100 = \text{₹}300 \]For an overall zero loss, the profit from the TV must be equal to the total loss from the radios.
\[ \text{Profit on TV} = \text{Total loss from radios} = \text{₹}120 \]Profit percentage is calculated with respect to the cost price of the TV.
\[ \text{Profit percentage on TV} = \left( \frac{\text{Profit on TV}}{\text{CP of TV}} \right) \times 100\% \] \[ \text{Profit percentage on TV} = \left( \frac{120}{300} \right) \times 100\% \] \[ \text{Profit percentage on TV} = \frac{12}{30} \times 100\% = \frac{2}{5} \times 100\% = 40\% \]Correct Option: A) 40%
This question asks us to evaluate the strength of two arguments concerning the statement: "There should be a power cut to save electricity." We need to determine which argument provides a strong and logical reason for or against the statement, considering practical implications.
D) Only argument 2 is strong. Argument 2 correctly points out the severe negative impact of power cuts on institutions requiring continuous electricity, making it a strong counter-argument against the statement. While power cuts do save electricity, the method itself is highly disruptive and undesirable, especially for critical sectors.