To find the gain percent, we need to determine the profit and the cost price. We are given a relationship between the profit and the selling price of a certain quantity of cloth. We can assume a unit selling price to simplify calculations.
Let the selling price of 1 m of cloth be \( \text{Re. } 1 \).
According to the problem, the selling price of 33 m of cloth is:
\[ \text{SP}_{33\text{m}} = 33 \times \text{Re. } 1 = \text{Re. } 33 \]The profit is equal to the selling price of 11 m of cloth. So, the profit is:
\[ \text{Profit} = \text{SP}_{11\text{m}} = 11 \times \text{Re. } 1 = \text{Re. } 11 \]We know that Profit = Selling Price - Cost Price. Therefore, Cost Price = Selling Price - Profit.
The cost price of 33 m of cloth is:
\[ \text{CP}_{33\text{m}} = \text{SP}_{33\text{m}} - \text{Profit} = \text{Re. } 33 - \text{Re. } 11 = \text{Re. } 22 \]Now, we can calculate the gain percent using the formula:
\[ \text{Gain Percent} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100 \]Substitute the values:
\[ \text{Gain Percent} = \left( \frac{11}{22} \right) \times 100 \]\[ \text{Gain Percent} = \left( \frac{1}{2} \right) \times 100 \]\[ \text{Gain Percent} = 50\% \]Correct Option: B) 50% gain
The question asks to identify a specific health scheme launched by the Government of India in April 2005, focusing on accessible, affordable, and reliable primary healthcare for the poor and vulnerable. We need to recall the major government health and social welfare schemes and their launch dates and objectives.
Correct Option: C) NRHM
The question asks to identify the chemist who established atomic number as a more fundamental property than atomic mass, leading to the modification of Mendeleev's Periodic Law. We need to recall the contributions of prominent chemists to the development of the periodic table.
D) Henry Moseley — Henry Moseley's X-ray diffraction experiments provided the experimental evidence that atomic number, not atomic mass, is the fundamental property governing the chemical properties of elements. This led to the modification of Mendeleev's Periodic Law and the development of the Modern Periodic Table.
This question tests the understanding of different types of numbers, specifically focusing on the definition of a terminating decimal and its classification within the number system. We need to recall the definitions of integers, whole numbers, rational numbers, and natural numbers.
Correct Option: C) a rational number
The question asks to identify the Indian classical dance form traditionally associated with Lord Brahma revealing it to Sage Bharata, who then codified it in the 'Natya Shastra'. This requires knowledge of the origins and historical texts related to various Indian classical dance forms.
C) Bharatanatyam — Bharatanatyam is the classical dance form whose theoretical foundations are traced back to the ancient Sanskrit text 'Natya Shastra' by Bharata Muni. According to Hindu mythology, Lord Brahma revealed this art form to Bharata, who then documented it.
To find the ratio of the volumes of two cylinders, we need to use the formula for the volume of a cylinder, which is \(V = \pi r^2 h\). We are given the ratios of their radii and heights. We will set up the volumes for both cylinders and then find their ratio.
Let the radii of the two cylinders be \(r_1\) and \(r_2\), and their heights be \(h_1\) and \(h_2\).
According to the problem, the ratio of their radii is 2 : 3. So, we can write:
\[ \frac{r_1}{r_2} = \frac{2}{3} \]The ratio of their heights is 5 : 3. So, we can write:
\[ \frac{h_1}{h_2} = \frac{5}{3} \]The formula for the volume of a cylinder is \(V = \pi r^2 h\). Let \(V_1\) be the volume of the first cylinder and \(V_2\) be the volume of the second cylinder.
The volume of the first cylinder is \(V_1 = \pi r_1^2 h_1\).
The volume of the second cylinder is \(V_2 = \pi r_2^2 h_2\).
Now, we need to find the ratio of their volumes, \(\frac{V_1}{V_2}\):
\[ \frac{V_1}{V_2} = \frac{\pi r_1^2 h_1}{\pi r_2^2 h_2} \]Cancel out \(\pi\) from the numerator and denominator:
\[ \frac{V_1}{V_2} = \frac{r_1^2 h_1}{r_2^2 h_2} \]Rearrange the terms to group the ratios of radii and heights:
\[ \frac{V_1}{V_2} = \left(\frac{r_1}{r_2}\right)^2 \times \left(\frac{h_1}{h_2}\right) \]Substitute the given ratios into the equation:
\[ \frac{V_1}{V_2} = \left(\frac{2}{3}\right)^2 \times \left(\frac{5}{3}\right) \]Calculate the square of the ratio of radii:
\[ \left(\frac{2}{3}\right)^2 = \frac{2^2}{3^2} = \frac{4}{9} \]Now, multiply the results:
\[ \frac{V_1}{V_2} = \frac{4}{9} \times \frac{5}{3} \]\[ \frac{V_1}{V_2} = \frac{4 \times 5}{9 \times 3} \]\[ \frac{V_1}{V_2} = \frac{20}{27} \]So, the ratio of their volumes is 20 : 27.
C) 20 : 27 is the correct ratio of the volumes of the two cylinders.
Find the value of (\(\sqrt{1.69}\) + \(\sqrt{0.49}\)) × \(\sqrt{400}\) :
To solve this problem, we need to evaluate the square roots of the given decimal numbers and the integer, then perform the addition and multiplication operations in the correct order.
D) The final calculated value is 40.
The problem asks us to simplify the expression \(1 - \sin 35^{\circ} \cos 55^{\circ}\). We will use trigonometric identities, specifically the complementary angle identity, to convert one of the terms so that we can apply the Pythagorean identity.
Recall the complementary angle identity: \( \cos (90^{\circ} - \theta) = \sin \theta \) or \( \sin (90^{\circ} - \theta) = \cos \theta \).
We have \( \cos 55^{\circ} \). We can write \( 55^{\circ} \) as \( 90^{\circ} - 35^{\circ} \).
Apply the complementary angle identity: \( \cos 55^{\circ} = \cos (90^{\circ} - 35^{\circ}) = \sin 35^{\circ} \).
Substitute this back into the original expression:
\[ 1 - \sin 35^{\circ} \cos 55^{\circ} = 1 - \sin 35^{\circ} (\sin 35^{\circ}) \]
\[ = 1 - \sin^2 35^{\circ} \]
Recall the Pythagorean identity: \( \sin^2 \theta + \cos^2 \theta = 1 \). From this, we can derive \( 1 - \sin^2 \theta = \cos^2 \theta \).
Apply the Pythagorean identity to the expression:
\[ 1 - \sin^2 35^{\circ} = \cos^2 35^{\circ} \]
Thus, the value of the given expression is \( \cos^2 35^{\circ} \).
Correct Option: C) \( \cos ^{2} 35^{\circ} \)
The question asks to identify the full form and purpose of MPLADS. This requires knowledge of government schemes and acronyms relevant to Indian governance.
Correct Option: A) A scheme launched by the government of India which enables Members of Parliament to do development work in their constituencies
The decimal expansion of \( \frac{31}{2.5} \) will terminate after:
two decimal places
one decimal place
more than three decimal places
three decimal places
To determine when a decimal expansion terminates, we first simplify the given fraction. Then, we convert the fraction into a decimal by performing the division. The number of decimal places after which the expansion terminates can be directly observed from the result.
B) The decimal expansion of \( \frac{31}{2.5} \) is \( 12.4 \), which terminates after one decimal place.