The question asks to identify the option where the listed city is NOT the capital of its corresponding country. This requires knowledge of world capitals.
Correct Option: B) Sydney, Australia — Sydney is a prominent city in Australia, but the capital of Australia is Canberra.
The question asks to identify the English writer who received the Jnanpith Award in 2018. This requires knowledge of the Jnanpith Award recipients, specifically for the year 2018, and their primary language of writing.
Correct Option: D) Amitav Ghosh
The question asks to identify the first person to walk on the Moon. This is a historical fact related to space exploration, specifically the Apollo 11 mission. We need to recall the names of the astronauts involved in this historic event.
Correct Option: C) Neil Armstrong was the first human to walk on the Moon on July 20, 1969, during the Apollo 11 mission.
To simplify the given expression, we need to follow the order of operations, commonly known as BODMAS/PEMDAS. This acronym stands for Brackets (Parentheses), Orders (Exponents), Division and Multiplication (from left to right), and Addition and Subtraction (from left to right).
The given expression is:
\[ 105 \div 5 \times 3 + 39 - 46 \]According to BODMAS, we first perform Division and Multiplication from left to right. The first operation from the left is division:
\[ 105 \div 5 = 21 \]Substitute this value back into the expression:
\[ 21 \times 3 + 39 - 46 \]Next, perform the multiplication:
\[ 21 \times 3 = 63 \]Substitute this value back into the expression:
\[ 63 + 39 - 46 \]Now, perform Addition and Subtraction from left to right. First, perform the addition:
\[ 63 + 39 = 102 \]Substitute this value back into the expression:
\[ 102 - 46 \]Finally, perform the subtraction:
\[ 102 - 46 = 56 \]Correct Option: B) 56
To find the percentage loss, we need to determine the cost price (CP) and selling price (SP) of the same quantity of rice. The problem states a relationship between the cost price of one quantity and the selling price of another. We can use this relationship to find the CP and SP per unit quantity or for a common quantity, and then calculate the loss percentage.
Let the cost price of 1 g of rice be \(CP_g\) and the selling price of 1 g of rice be \(SP_g\).
According to the problem statement, the cost price of 120 g of rice is the same as the selling price of 150 g of rice.
This can be written as an equation:
\[ 120 \times CP_g = 150 \times SP_g \]
Now, we can find the ratio of \(CP_g\) to \(SP_g\):
\[ \frac{CP_g}{SP_g} = \frac{150}{120} = \frac{5}{4} \]
From the ratio, we can infer that if \(CP_g = 5k\), then \(SP_g = 4k\) for some constant \(k\). Since \(CP_g > SP_g\), there is a loss.
The loss is calculated as \(CP_g - SP_g\):
\[ \text{Loss} = 5k - 4k = k \]
The percentage loss is calculated using the formula:
\[ \text{Percentage Loss} = \left( \frac{\text{Loss}}{\text{CP}} \right) \times 100\% \]
\[ \text{Percentage Loss} = \left( \frac{k}{5k} \right) \times 100\% \]
\[ \text{Percentage Loss} = \left( \frac{1}{5} \right) \times 100\% \]
\[ \text{Percentage Loss} = 20\% \]
B) The percentage loss is 20%.
A) 12.5% loss: This would be the case if the loss was \((1/8) \times 100\%\), which is not what we calculated.
C) 15% loss: This would be the case if the loss was \((3/20) \times 100\%\), which is not derived from the given quantities.
D) 25% loss: This would occur if the loss was \((1/4) \times 100\%\). This might be incorrectly calculated if one divides the loss by the selling price instead of the cost price, or if the ratio was inverted.
The question asks about the essential role of the press in a democratic system. To answer this, we need to understand the fundamental principles of a free press in a democracy.
Correct Option: C) be free and impartial. This statement accurately describes the ideal and essential role of the press in a democracy. A free press ensures that information flows without censorship, and an impartial press ensures that this information is presented without bias, allowing citizens to make informed decisions and hold their government accountable.
To find the ratio of \(a\) to \(d\), we need to establish a common link between the given ratios. Both ratios involve \(b\). We can express \(a\) and \(d\) in terms of \(b\) and then find their ratio.
Express \(a\) in terms of \(b\) from the first ratio:
Given \(a : b = 3 : 4\), this can be written as:
\[ \frac{a}{b} = \frac{3}{4} \]From this, we can express \(a\) as:
\[ a = \frac{3}{4}b \quad \text{(Equation 1)} \]Express \(d\) in terms of \(b\) from the second ratio:
Given \(d : b = 4 : 3\), this can be written as:
\[ \frac{d}{b} = \frac{4}{3} \]From this, we can express \(d\) as:
\[ d = \frac{4}{3}b \quad \text{(Equation 2)} \]Find the ratio of \(a\) to \(d\):
Now, we need to find \(a : d\), which is \(\frac{a}{d}\). Substitute the expressions for \(a\) and \(d\) from Equation 1 and Equation 2:
\[ \frac{a}{d} = \frac{\frac{3}{4}b}{\frac{4}{3}b} \]Cancel out \(b\) from the numerator and denominator (assuming \(b \neq 0\)):
\[ \frac{a}{d} = \frac{3/4}{4/3} \]To simplify the complex fraction, multiply the numerator by the reciprocal of the denominator:
\[ \frac{a}{d} = \frac{3}{4} \times \frac{3}{4} \] \[ \frac{a}{d} = \frac{3 \times 3}{4 \times 4} \] \[ \frac{a}{d} = \frac{9}{16} \]So, the ratio \(a : d\) is \(9 : 16\).
Correct Option: B) 9 : 16
To find the largest four-digit number divisible by 12, 15, and 18, we first need to find the Least Common Multiple (LCM) of these three numbers. Any number divisible by 12, 15, and 18 must also be divisible by their LCM. Once we have the LCM, we find the largest four-digit number and divide it by the LCM. The remainder will help us find the required number.
The LCM is found by taking the highest power of all prime factors present in the numbers.
\[ \text{LCM}(12, 15, 18) = 2^2 \times 3^2 \times 5 = 4 \times 9 \times 5 = 180 \]The largest four-digit number is 9999.
Divide 9999 by 180 to find the remainder.
\[ 9999 \div 180 \]\[ 9999 = 180 \times 55 + 99 \]Here, the quotient is 55 and the remainder is 99.To find the largest four-digit number exactly divisible by 180, subtract the remainder from 9999.
\[ 9999 - 99 = 9900 \]9900 is divisible by 180, and thus by 12, 15, and 18. It is also the largest four-digit number with this property.
D) 9900 is the largest four-digit number divisible by 12, 15, and 18.
This question asks us to identify the odd one out from a set of four letter-clusters. This typically involves finding a pattern or rule that applies to three of the clusters, while one cluster does not follow that rule. We will assign numerical positions to each letter in the alphabet (A=1, B=2, ..., Z=26) and then look for a mathematical relationship between the positions of the letters within each cluster.
B) X S P is the odd one out because the difference between consecutive letter positions is not consistently -4, unlike the other options.
To find the ratio of the surface areas of two spheres given the ratio of their radii, we need to recall the formula for the surface area of a sphere. The surface area of a sphere is directly proportional to the square of its radius.
Let the radii of the two spheres be \(r_1\) and \(r_2\).
The given ratio of their radii is \(r_1 : r_2 = 2 : 3\). This can be written as:
\[ \frac{r_1}{r_2} = \frac{2}{3} \]The formula for the surface area of a sphere is \(A = 4 \pi r^2\), where \(r\) is the radius.
Let the surface areas of the two spheres be \(A_1\) and \(A_2\).
Using the formula, we have:
\[ A_1 = 4 \pi r_1^2 \]\[ A_2 = 4 \pi r_2^2 \]Now, we need to find the ratio of their surface areas, \(A_1 : A_2\):
\[ \frac{A_1}{A_2} = \frac{4 \pi r_1^2}{4 \pi r_2^2} \]Cancel out the common terms \(4 \pi\):
\[ \frac{A_1}{A_2} = \frac{r_1^2}{r_2^2} \]This can be written as:
\[ \frac{A_1}{A_2} = \left(\frac{r_1}{r_2}\right)^2 \]Substitute the given ratio of radii \[\frac{r_1}{r_2} = \frac{2}{3}\] into the equation:
\[ \frac{A_1}{A_2} = \left(\frac{2}{3}\right)^2 \]\[ \frac{A_1}{A_2} = \frac{2^2}{3^2} \]\[ \frac{A_1}{A_2} = \frac{4}{9} \]Therefore, the ratio of their surface areas is \(4 : 9\).
Correct Option: A) The ratio of the surface areas is \(4 : 9\), which is obtained by squaring the ratio of the radii.