To find the ratio of the volumes of a cylinder and a cone under the given conditions, we need to recall the formulas for the volumes of a cylinder and a cone. Then, we will substitute the given conditions (same base and same height) into these formulas and simplify the ratio.
Recall the formula for the volume of a cylinder:
The volume of a cylinder (\(V_c\)) with base radius \(r\) and height \(h\) is given by:
\[ V_c = \pi r^2 h \]Recall the formula for the volume of a cone:
The volume of a cone (\(V_k\)) with base radius \(r\) and height \(h\) is given by:
\[ V_k = \frac{1}{3} \pi r^2 h \]Apply the given conditions:
The problem states that the base of the cylinder is the same as that of the cone, which means they have the same radius \(r\). It also states that the height of the cylinder is the same as that of the cone, meaning they have the same height \(h\).
Calculate the ratio of their volumes:
We need to find the ratio of the volume of the cylinder to the volume of the cone, i.e., \(V_c : V_k\).
\[ \frac{V_c}{V_k} = \frac{\pi r^2 h}{\frac{1}{3} \pi r^2 h } \]Simplify the ratio:
Cancel out the common terms \(\pi r^2 h\) from the numerator and the denominator:
\[ \frac{V_c}{V_k} = \frac{1}{\frac{1}{3}} \]\[ \frac{V_c}{V_k} = 3 \]Therefore, the ratio \(V_c : V_k\) is \(3 : 1\).D) 3 : 1 — The calculation shows that the ratio of the volume of the cylinder to the volume of the cone is \(3:1\).
To calculate the approximate percentage profit, we first need to find the profit per calculator. Profit is the difference between the selling price and the cost price. Once we have the profit, we can calculate the percentage profit by dividing the profit by the cost price and multiplying by 100.
Profit = Selling Price (SP) - Cost Price (CP)
\[ \text{Profit} = \text{₹}580 - \text{₹}550 = \text{₹}30 \]Percentage Profit is calculated using the formula:
\[ \text{Percentage Profit} = \left( \frac{\text{Profit}}{\text{Cost Price}} \right) \times 100\% \]\[ \text{Percentage Profit} = \left( \frac{30}{550} \right) \times 100\% \]\[ \text{Percentage Profit} = \left( \frac{3}{55} \right) \times 100\% \]\[ \text{Percentage Profit} = 0.054545... \times 100\% \]\[ \text{Percentage Profit} \approx 5.45\% \]Correct Option: D) 5.45%
To find the number of integers divisible by 3 or 4, we use the Principle of Inclusion-Exclusion. This principle states that for two sets A and B, the number of elements in their union is given by \(|A \cup B| = |A| + |B| - |A \cap B|\). In this case, A represents numbers divisible by 3, and B represents numbers divisible by 4. We need to find the number of integers from 1 to 100 that are divisible by 3, by 4, and by both (i.e., by their least common multiple).
Numbers divisible by 3:
To find the count of numbers divisible by 3 within the first 100 positive integers, we divide 100 by 3 and take the floor (integer part).
\[ N_3 = \left\lfloor \frac{100}{3} \right\rfloor = 33 \]Numbers divisible by 4:
Similarly, for numbers divisible by 4:
\[ N_4 = \left\lfloor \frac{100}{4} \right\rfloor = 25 \]Numbers divisible by both 3 and 4:
Numbers divisible by both 3 and 4 are divisible by their least common multiple (LCM). The LCM of 3 and 4 is 12.
So, we find the count of numbers divisible by 12 within the first 100 positive integers:
\[ N_{3 \cap 4} = \left\lfloor \frac{100}{12} \right\rfloor = 8 \]Apply the Principle of Inclusion-Exclusion:
The number of integers divisible by 3 or 4 is given by:
\[ N_{3 \cup 4} = N_3 + N_4 - N_{3 \cap 4} \]\[ N_{3 \cup 4} = 33 + 25 - 8 \]\[ N_{3 \cup 4} = 58 - 8 \]\[ N_{3 \cup 4} = 50 \]D) 50 — This is the correct count obtained by applying the Principle of Inclusion-Exclusion.
The question asks to identify which of the given countries is NOT a member of the South Asian Association for Regional Cooperation (SAARC). To answer this, one needs to know the member countries of SAARC.
Correct Option: C) Malaysia is not a member of SAARC. Malaysia is a Southeast Asian country and a member of ASEAN (Association of Southeast Asian Nations), not SAARC. SAARC focuses on regional cooperation among South Asian countries.
The question asks about the purpose of the Sharda Act, passed in 1929 during British rule. To answer this, one needs to recall the social reform legislations enacted during that period and their specific objectives.
D) Child marriage — The Sharda Act (Child Marriage Restraint Act, 1929) was specifically enacted to prevent child marriage by setting minimum age limits for marriage.
The question asks to identify the scientist known as the father of binomial nomenclature. This requires knowledge of key figures in biology and their contributions to classification.
Correct Option: D) Carolus Linnaeus is credited with formalizing and popularizing the system of binomial nomenclature, which is still used today for naming all species of living things.
The question asks to identify the country with the largest mica deposits in the world from the given options. This requires knowledge of global mineral resources and their distribution.
A) India — India is renowned for having the largest deposits of mica globally, particularly high-quality muscovite mica.
This question tests knowledge of current affairs, specifically the Union Cabinet ministers in India as of a particular date (October 2020). To answer correctly, one needs to recall who held the portfolio of Road Transport and Highways at that time.
Correct Option: D) Nitin Jairam Gadkari
The question asks for the year in which the National Human Rights Commission (NHRC) was launched in India. This is a factual question related to Indian polity and governance. We need to recall the establishment date of the NHRC.
Correct Option: C) 1993
The question asks to identify the court poet of King Harshavardhana. This requires knowledge of prominent historical figures and their associated patrons during ancient Indian history, specifically the Pushyabhuti dynasty.
Correct Option: D) Banabhatta was the court poet of King Harshavardhana. His work "Harshacharita" is a biographical account of the king.