The question asks about the type of mirror dentists use to see enlarged images of teeth. This requires understanding the image formation properties of different types of mirrors, specifically their ability to produce magnified images.
B) Concave mirror — Concave mirrors are converging mirrors. When an object (like a tooth) is placed very close to a concave mirror (between its pole and principal focus), it forms a virtual, erect, and magnified image behind the mirror. This magnified view helps dentists examine teeth in detail.
The question asks to identify the two countries that possessed anti-satellite (ASAT) weapon systems before China became the third country to do so in 2010. This requires knowledge of the history and development of ASAT capabilities among major global powers.
D) The USA and Russia — Both the USA and Russia (as the successor to the Soviet Union) had developed and demonstrated anti-satellite weapon capabilities well before China's 2007 test, making them the first two countries to possess such systems.
To evaluate the given expression, we need to perform the operations in the correct order, following the rules of arithmetic (BODMAS/PEMDAS). First, we convert the decimals to fractions to simplify the division, then perform multiplication.
\(0.25 \div 0.0025 \times 0.025 \times 25\)
It's often easier to work with fractions when dealing with division of decimals.
Substitute these into the expression:
\[ \frac{25}{100} \div \frac{25}{10000} \times \frac{25}{1000} \times 25 \]Dividing by a fraction is the same as multiplying by its reciprocal.
\[ \frac{25}{100} \times \frac{10000}{25} \times \frac{25}{1000} \times 25 \]Cancel out common terms.
\[ \frac{\cancel{25}}{100} \times \frac{10000}{\cancel{25}} \times \frac{25}{1000} \times 25 \]\[ = \frac{10000}{100} \times \frac{25}{1000} \times 25 \]\[ = 100 \times \frac{25}{1000} \times 25 \]Multiply the terms from left to right.
\[ = 100 \times \frac{25}{1000} \times 25 \]\[ = \frac{100 \times 25}{1000} \times 25 \]\[ = \frac{2500}{1000} \times 25 \]\[ = 2.5 \times 25 \]B) 62.5 — The step-by-step calculation shows that the value of the expression is 62.5.
This problem involves compound interest. A key property of compound interest is that if an amount multiplies by a certain factor in a given period, it will multiply by the same factor again in the next identical period. We can use the compound interest formula or a simpler pattern-based approach for this type of question.
Let the principal amount be \(P\). After 5 years, the amount doubles, meaning it becomes \(2P\).
We want to find the time it takes for the amount to become 16 times the principal, i.e., \(16P\).
We can express 16 as a power of 2:
\[ 16 = 2^4 \]Since the amount doubles every 5 years, we can track its growth:
Alternatively, using the formula for compound interest, \(A = P(1+R/100)^T\):
Given that the amount doubles in 5 years:
\[ 2P = P \left(1 + \frac{R}{100}\right)^5 \] \[ 2 = \left(1 + \frac{R}{100}\right)^5 \quad \ldots(1) \]We want to find the time \(T'\) when the amount becomes 16 times the principal:
\[ 16P = P \left(1 + \frac{R}{100}\right)^{T'} \] \[ 16 = \left(1 + \frac{R}{100}\right)^{T'} \quad \ldots(2) \]Substitute equation (1) into equation (2):
\[ 2^4 = \left(1 + \frac{R}{100}\right)^{T'} \] \[ \left(\left(1 + \frac{R}{100}\right)^5\right)^4 = \left(1 + \frac{R}{100}\right)^{T'} \] \[ \left(1 + \frac{R}{100}\right)^{5 \times 4} = \left(1 + \frac{R}{100}\right)^{T'} \] \[ \left(1 + \frac{R}{100}\right)^{20} = \left(1 + \frac{R}{100}\right)^{T'} \]Comparing the exponents, we get:
\[ T' = 20 \text{ years} \]Correct Option: D) 20
The question asks for the phenomenon responsible for the blue color of the sky. This is a common observation explained by the interaction of sunlight with Earth's atmosphere. We need to identify the correct optical phenomenon among the given options.
B) scattering of light — Specifically, Rayleigh scattering is responsible for the blue color of the sky. The tiny particles in the atmosphere scatter shorter wavelengths (blue and violet) more efficiently than longer wavelengths (red and orange).
We are given the total population of a town and how it changes after a percentage increase in male and female populations. We need to find the initial female population. We can set up a system of two linear equations based on the given information and solve for the number of males and females.
The present female population is 6,000.
C) 6000 is the correct answer, as calculated above.
The question asks about the patron of the Third Buddhist Council. To answer this, recall the major Buddhist Councils and the rulers associated with them.
C) Ashoka — Emperor Ashoka (268 to 232 BCE) of the Mauryan dynasty was a devout Buddhist and played a crucial role in the propagation of Buddhism. He convened the Third Buddhist Council in Pataliputra (modern-day Patna) around 250 BCE to purify the Sangha and compile the Buddhist scriptures (Tripitaka).
Read the given statement and conclusions carefully and decide which of the conclusions logically follow(s) from the statement.
Statement:
Music is very good for peace of mind.
Conclusions:
I. Arijit Singh has a good voice.
II. Kishor Kumar was a famous singer.
Neither of the conclusions follows.
Only conclusion II follows.
Only conclusion I follows.
Both conclusions follow.
This is a statement and conclusion type of question. The goal is to determine which conclusions logically follow from the given statement. We must assume the statement to be absolutely true and not use any outside knowledge. The conclusions must be directly inferable from the statement.
Correct Option: A) Neither of the conclusions follows.
To find the quotient of 0.5 divided by 0.71, we need to perform the division and then round the result to three decimal places. The division can be simplified by converting the decimals into fractions or by moving the decimal points to make the divisor a whole number.
The given expression is \(0.5 \div 0.71\).
\[ \frac{0.5}{0.71} \]To make the denominator a whole number, multiply both the numerator and the denominator by 100 (since 0.71 has two decimal places).
\[ \frac{0.5 \times 100}{0.71 \times 100} = \frac{50}{71} \]Now, divide 50 by 71.
We need to find the result correct to three decimal places, so we will carry out the division to at least four decimal places.
\[ 50 \div 71 \]\[ 50.0000 \div 71 \]So, the result is approximately \(0.7042...\)
To round to three decimal places, we look at the fourth decimal place. If it is 5 or greater, we round up the third decimal place. If it is less than 5, we keep the third decimal place as it is.
The fourth decimal place is 2, which is less than 5.
Therefore, we round \(0.7042\) to \(0.704\).
Correct Option: C) 0.704
This problem involves calculating the future population based on a fixed annual percentage increase. This is a compound growth problem, similar to compound interest. We can use the formula for compound growth to find the population after three years.
The formula for population after \(n\) years is given by:
\[ P_n = P_0 \left(1 + \frac{r}{100}\right)^n \]C) 18,522 — After calculating the compound growth for three years, the population will be 18,522.