The question asks to identify the set of materials that are the best insulators. An insulator is a material that resists the flow of electric current. This means it has a very high electrical resistivity. We need to evaluate each option based on the electrical conductivity properties of the materials listed.
D) Plastics, ebonite, paper, cotton, Bakelite, dry air, rubber. This set exclusively contains materials that are excellent electrical insulators. They are used to prevent the flow of electricity in wires, electrical components, and protective gear.
To find the selling price when there is a loss, we first calculate the amount of loss based on the given percentage and the cost price. Then, we subtract this loss amount from the cost price to get the selling price.
Therefore, the selling price of the table is Rs 720.
Correct Option: A) Rs 720
Solve the following Equation: \(\frac{1+2}{\left\{1+\frac{2}{\left(1+\frac{1}{3}\right)}\right\}}\)=?
\( \frac{9}{4} \)
\( \frac{21}{5} \)
\( \frac{6}{5} \)
\( \frac{21}{4} \)
To solve this complex fraction, we will simplify it step-by-step, starting from the innermost part of the denominator and working our way outwards. This method ensures that each calculation is manageable and reduces the chance of errors.
First, simplify the innermost expression in the denominator: \(\left(1+\frac{1}{3}\right)\).
\[ 1 + \frac{1}{3} = \frac{3}{3} + \frac{1}{3} = \frac{3+1}{3} = \frac{4}{3} \]Substitute this value back into the next part of the denominator: \[\left\{1+\frac{2}{\left(\frac{4}{3}\right)}\right\}\].
\[ 1 + \frac{2}{\frac{4}{3}} \]Simplify the fraction \[\frac{2}{\frac{4}{3}}\]. Dividing by a fraction is equivalent to multiplying by its reciprocal.
\[ \frac{2}{\frac{4}{3}} = 2 \times \frac{3}{4} = \frac{6}{4} = \frac{3}{2} \]Substitute this simplified value back into the denominator:
\[ 1 + \frac{3}{2} \]Calculate this sum:
\[ 1 + \frac{3}{2} = \frac{2}{2} + \frac{3}{2} = \frac{2+3}{2} = \frac{5}{2} \]Now, substitute this entire simplified denominator back into the original equation. The numerator is \(1+2 = 3\).
\[ \frac{1+2}{\left\{1+\frac{2}{\left(1+\frac{1}{3}\right)}\right\}} = \frac{3}{\frac{5}{2}} \]Finally, simplify the main fraction. Again, dividing by a fraction is multiplying by its reciprocal.
\[ \frac{3}{\frac{5}{2}} = 3 \times \frac{2}{5} = \frac{6}{5} \]Correct Option: C) \( \frac{6}{5} \)
Identify the equation of the line with slope = -4 and y-intercept = 2.
2x + \( \frac{y}{2} \) = 1
2x + \( \frac{y}{3} \) = 1
2x + y = 1
2x + \( \frac{y}{4} \) = 1
The problem asks us to find the equation of a line given its slope and y-intercept. We can use the slope-intercept form of a linear equation, \(y = mx + c\), where \(m\) is the slope and \(c\) is the y-intercept. Then, we will rearrange the equation to match the format of the given options.
Correct Option: A) \(2x + \frac{y}{2} = 1\)
The question asks about the constitutional provision regarding who administers the Oath of Office to the President of India. This is a direct question from the Indian Constitution, specifically Article 60.
Correct Option: C) The Chief Justice of India
Article 60 of the Indian Constitution clearly mandates that the Chief Justice of India (CJI) administers the Oath of Office to the President. In the absence of the CJI, the senior-most Judge of the Supreme Court available performs this duty.
This question tests logical reasoning, specifically the ability to distinguish between certainty and possibility. We are given two statements and asked to evaluate a conclusion based on them. The key is to understand that while nitrogen is a gas, not all gases are nitrogen.
C) Probably True or False — This option correctly reflects the situation. The chamber *might* contain nitrogen gas (making the conclusion true), or it might contain some other gas (making the conclusion false). Without more information, we cannot be certain either way, so it is a matter of probability or possibility.
To solve this problem, we need to follow the order of operations, often remembered by the acronym BODMAS/PEMDAS (Brackets/Parentheses, Orders/Exponents, Division/Multiplication, Addition/Subtraction). We will evaluate the expression inside the parentheses first, performing division and multiplication before addition and subtraction, and finally divide the result by 2.
First, calculate \(7 \times 23\).
\[ 7 \times 23 = 161 \]Next, calculate \(247 \div 13\).
\[ 247 \div 13 = 19 \]The expression inside the parentheses becomes:
\[ -45 + 161 - 19 - 11 \]First, \(-45 + 161\):
\[ -45 + 161 = 116 \]Next, \(116 - 19\):
\[ 116 - 19 = 97 \]Finally, \(97 - 11\):
\[ 97 - 11 = 86 \]The entire expression is \((86) \div 2\).
\[ 86 \div 2 = 43 \]Thus, the value of the given expression is 43.
D) 43 — The step-by-step calculation following the BODMAS/PEMDAS rule correctly yields 43.
Solve the following Equation:
\(\frac{3^2-8^2}{(3+8)^2}\) =?
\( \frac{5}{11} \)
\( \frac{-3}{11} \)
\( \frac{3}{11} \)
\( \frac{-5}{11} \)
To solve the given expression, we will first evaluate the numerator and the denominator separately. The numerator involves the difference of squares, which can be simplified using the identity \(a^2 - b^2 = (a-b)(a+b)\). The denominator involves squaring a sum. After simplifying both parts, we will perform the division.
The numerator is \(3^2 - 8^2\).
We can calculate the squares directly:
\[ 3^2 = 9 \]\[ 8^2 = 64 \]\[ 3^2 - 8^2 = 9 - 64 = -55 \]Using the identity \(a^2 - b^2 = (a-b)(a+b)\) where \(a=3\) and \(b=8\):
\[ 3^2 - 8^2 = (3-8)(3+8) \]\[ 3^2 - 8^2 = (-5)(11) \]\[ 3^2 - 8^2 = -55 \]The denominator is \((3+8)^2\).
First, perform the addition inside the parenthesis:
\[ 3+8 = 11 \]\[ (3+8)^2 = (11)^2 \]\[ (11)^2 = 121 \]Now, substitute the simplified numerator and denominator back into the original expression:
\[ \frac{3^2-8^2}{(3+8)^2} = \frac{-55}{121} \]Both -55 and 121 are divisible by 11.
\[ \frac{-55}{121} = \frac{-55 \div 11}{121 \div 11} = \frac{-5}{11} \]D) \( \frac{-5}{11} \) is the correct answer, as derived from the step-by-step calculation.
The Indian Government launched which scheme that aims to reduce expenditure by patients on treatment of cancer and cardiovascular diseases to make health care affordable for the needy?
AYUSH (Assuring Your Ultimate Security and Health)
PADMA (Proper and Due Medical Assistance)
AMRIT (Affordable Medicine and Reliable Implants for Treatment)
MAARC (Medical Assistance At Reduced Cost)
The question asks to identify the Indian Government scheme aimed at reducing patient expenditure on cancer and cardiovascular disease treatments to make healthcare affordable. This requires knowledge of specific government health initiatives.
C) AMRIT (Affordable Medicine and Reliable Implants for Treatment)
The AMRIT scheme was launched by the Ministry of Health & Family Welfare, Government of India, to make cancer and cardiovascular disease drugs, surgical implants, and other consumables available at affordable prices. Under this scheme, retail pharmacies are opened at various hospitals (like AIIMS) to sell medicines and implants at significantly discounted rates (up to 50-60% less than market price), thereby reducing the financial burden on patients suffering from these critical illnesses.
This problem involves calculating work rates of pipes. We will determine the individual work rates of the pipes and then use these rates to find the remaining work and the time taken by pipe C alone.
Determine the combined work rate of A, B, and C:
Pipes A, B, and C together can fill the tank in 4 hours. So, their combined work rate is:
Determine the combined work rate of A and B:
Pipes A and B together can fill the tank in 9 hours. So, their combined work rate is:
Determine the work rate of C alone:
The work rate of C is the difference between the combined work rate of (A+B+C) and (A+B):
Calculate the work done by A, B, and C in the first 3 hours:
All three pipes are opened simultaneously for 3 hours. The work done is:
Calculate the remaining work:
The total tank capacity is 1 unit. The remaining work is:
Calculate the time C alone will take to fill the remaining tank:
After 3 hours, pipes A and B are closed, and C alone continues to fill the remaining portion. Time taken by C is:
Therefore, C alone will require 1.8 hours to fill the remaining tank.
B) 1.8