The question asks for the full form of ESIC, an autonomous body under the Ministry of Labour and Employment, Government of India. This is a direct knowledge-based question requiring recall of the correct acronym expansion.
Correct Option: A) Employees' State Insurance Corporation
ESIC stands for Employees' State Insurance Corporation. It is a statutory corporate body established under the Employees' State Insurance Act, 1948, which works under the Ministry of Labour and Employment, Government of India. Its primary function is to provide social security and health insurance to Indian workers.
This is a syllogism problem. We will use Venn diagrams to represent the given statements and then evaluate each conclusion based on these diagrams. The key is to assume the statements are true, even if they contradict common knowledge.
From these, we can deduce:
B) Only conclusion II follows. As determined in the step-by-step analysis, only conclusion (II) "No grape is a pine" logically follows from the given statements.
If a = \(\left(\frac{3}{7}\right)^{2}\) ÷ \(\left(\frac{9}{7}\right)^{0}\), then find the value of a(-2).
\(\frac{2401}{81}\)
\(\frac{81}{2401}\)
\(\frac{343}{81}\)
\(\frac{81}{343}\)
The problem requires us to first calculate the value of 'a' using the given expression, which involves exponents and division. Once 'a' is found, we need to calculate \(a^{(-2)}\). We will use the properties of exponents, specifically that any non-zero number raised to the power of 0 is 1, and that \(x^{-n} = \frac{1}{x^n}\).
Evaluate the expression for 'a':
The given expression for 'a' is:
\[ a = \left(\frac{3}{7}\right)^{2} \div \left(\frac{9}{7}\right)^{0} \]Apply the exponent rule \(x^0 = 1\):
Any non-zero number raised to the power of 0 is 1. So, \(\left(\frac{9}{7}\right)^{0} = 1\).
Substitute this back into the expression for 'a':
\[ a = \left(\frac{3}{7}\right)^{2} \div 1 \]Simplify the division:
Dividing any number by 1 results in the number itself.
\[ a = \left(\frac{3}{7}\right)^{2} \]Calculate the square:
Square both the numerator and the denominator:
\[ a = \frac{3^2}{7^2} = \frac{9}{49} \]Calculate \(a^{(-2)}\):
Now we need to find the value of \(a^{(-2)}\). Substitute the value of 'a' we found:
\[ a^{(-2)} = \left(\frac{9}{49}\right)^{(-2)} \]Apply the negative exponent rule \(x^{-n} = \frac{1}{x^n}\) or \[\left(\frac{x}{y}\right)^{-n} = \left(\frac{y}{x}\right)^{n}\]:
Using the rule \[\left(\frac{x}{y}\right)^{-n} = \left(\frac{y}{x}\right)^{n}\], we get:
\[ \left(\frac{9}{49}\right)^{(-2)} = \left(\frac{49}{9}\right)^{2} \]Calculate the final square:
Square both the numerator and the denominator:
\[ \left(\frac{49}{9}\right)^{2} = \frac{49^2}{9^2} = \frac{2401}{81} \]Thus, the value of \(a^{(-2)}\) is \(\frac{2401}{81}\).
Correct Option: A) \(\frac{2401}{81}\) is the correct answer, as derived from the step-by-step calculation.
This problem can be solved by setting up a system of two linear equations with two variables, representing the ages of Bob and Will. We can then use methods like elimination or substitution to find the value of one of the variables, which in this case is Bob's age.
Let Bob's age be \(B\) years and Will's age be \(W\) years.
From the first statement, "The sum of 6 times Bob's age and 5 times Will's age is 43 years", we can form the first equation:
\[ 6B + 5W = 43 \quad \text{(Equation 1)} \]From the second statement, "the sum of 5 times Bob's age and 5 times Will's age is 40 years", we can form the second equation:
\[ 5B + 5W = 40 \quad \text{(Equation 2)} \]To find Bob's age (\(B\)), we can subtract Equation 2 from Equation 1. This will eliminate \(W\).
Subtract (Equation 2) from (Equation 1):
\[ (6B + 5W) - (5B + 5W) = 43 - 40 \]\[ 6B + 5W - 5B - 5W = 3 \]\[ (6B - 5B) + (5W - 5W) = 3 \]\[ B + 0 = 3 \]\[ B = 3 \]Thus, Bob's age is 3 years.
B) 3 years is the correct answer. By setting up and solving the system of linear equations, we found Bob's age to be 3 years.
The radius of the base of a right circular closed cylinder is 3.5 cm and its total surface area is 269.5 cm². What is the ratio of its height to its diameter? (Take π = \( \frac{22}{7} \))
The problem asks for the ratio of the height to the diameter of a right circular closed cylinder, given its base radius and total surface area. We will use the formula for the total surface area of a cylinder, substitute the given values, and solve for the height. Then, we will calculate the diameter and find the required ratio.
The total surface area of a closed cylinder is given by the sum of the areas of the two circular bases and the curved surface area.
\[ \text{TSA} = 2\pi r^2 + 2\pi rh \]\[ \text{TSA} = 2\pi r (r + h) \]We are given \(\text{TSA} = 269.5\) and \(r = 3.5\). We need to find \(h\).
\[ 269.5 = 2 \times \frac{22}{7} \times 3.5 (3.5 + h) \]First, calculate \(2 \times \frac{22}{7} \times 3.5\):
\[ 2 \times \frac{22}{7} \times 3.5 = 2 \times \frac{22}{7} \times \frac{7}{2} = 22 \]The diameter \(d\) is twice the radius \(r\).
\[ d = 2r \]\[ d = 2 \times 3.5 \]\[ d = 7 \text{ cm} \]The required ratio is \(\frac{h}{d}\).
\[ \frac{h}{d} = \frac{8.75}{7} \]To simplify, we can multiply the numerator and denominator by 100 to remove the decimal:
\[ \frac{8.75}{7} = \frac{875}{700} \]\[ \frac{875}{700} = \frac{175 \times 5}{175 \times 4} = \frac{5}{4} \]The ratio of height to diameter is \(5:4\).
C) 5 : 4
This question tests the understanding of how a fuse works as a safety device in an electrical circuit. Fuses are designed to protect electrical appliances and wiring from damage due to overcurrents. Their operation relies on a specific physical property of the material used.
C) melts — When a huge current flows through the fuse, the heat generated (\(H = I^2 R t\)) causes its temperature to rise until it reaches its melting point. The fuse wire then melts, breaking the circuit and protecting the appliance.
This is a work and time problem. We need to find the individual work rate of a man and a woman. We can set up a system of linear equations based on the given information and solve for the work done by one man and one woman in one day. Once we have the work rate of one woman, we can calculate the total days required for one woman to complete the entire work.
Let \(M\) be the amount of work one man can do in one day, and \(W\) be the amount of work one woman can do in one day.
From the first statement: "6 men and 10 women complete a work in 10 days."
The total work done by 6 men and 10 women in one day is \(\frac{1}{10}\) of the total work.
\[ 6M + 10W = \frac{1}{10} \quad \text{(Equation 1)} \]From the second statement: "5 men and 4 women complete the same work in 14 days."
The total work done by 5 men and 4 women in one day is \(\frac{1}{14}\) of the total work.
\[ 5M + 4W = \frac{1}{14} \quad \text{(Equation 2)} \]Now we have a system of two linear equations:
Equation 1: \(6M + 10W = \frac{1}{10}\)
Equation 2: \(5M + 4W = \frac{1}{14}\)
To solve for \(M\) and \(W\), we can use the elimination method. Multiply Equation 1 by 5 and Equation 2 by 6 to make the coefficients of \(M\) equal:
Multiply Equation 1 by 5:
\[ 5 \times (6M + 10W) = 5 \times \frac{1}{10} \]\[ 30M + 50W = \frac{5}{10} \]\[ 30M + 50W = \frac{1}{2} \quad \text{(Equation 3)} \]Multiply Equation 2 by 6:
\[ 6 \times (5M + 4W) = 6 \times \frac{1}{14} \]\[ 30M + 24W = \frac{6}{14} \]\[ 30M + 24W = \frac{3}{7} \quad \text{(Equation 4)} \]Subtract Equation 4 from Equation 3:
\[ (30M + 50W) - (30M + 24W) = \frac{1}{2} - \frac{3}{7} \]\[ 26W = \frac{7 - 6}{14} \]\[ 26W = \frac{1}{14} \]Solve for \(W\):
\[ W = \frac{1}{14 \times 26} \]\[ W = \frac{1}{364} \]This means one woman can complete \(\frac{1}{364}\) of the work in one day.
Therefore, to complete the entire work (which is 1 unit of work), one woman will take 364 days.
A) 364 is the correct answer. One woman completes \(\frac{1}{364}\) of the work in one day, so she will take 364 days to complete the entire work.
The question asks about the year when the provision for parents or guardians to provide educational opportunities for children aged six to fourteen became part of the right to education legislation. This refers to a specific amendment to the Indian Constitution and the subsequent act.
Therefore, the legislation that incorporated this duty was passed in 2009.
Correct Option: A) 2009
Refer to the following letter, number, symbol series and answer the question.
(Left) 9 C W 7 S K T @ B 1 6 L C S 8 & J F 2 % U D 7 P 5 * 4 V Z ? A (Right)
If all the elements that are on the prime number position in the above series are to be dropped, then which of the following elements will be 18th from the left end?
The problem asks us to identify the 18th element from the left end of a given series after dropping all elements that are at prime number positions. First, we need to list the original series and identify the positions of its elements. Then, we identify prime number positions and remove the elements at those positions. Finally, we count to find the 18th element in the modified series.
Original Series and Positions:
Let's write down the given series with their corresponding positions:
| Position | Element | Position | Element | Position | Element | Position | Element |
|---|---|---|---|---|---|---|---|
| 1 | 9 | 11 | B | 21 | 8 | 31 | P |
| 2 | C | 12 | 1 | 22 | & | 32 | 5 |
| 3 | W | 13 | 6 | 23 | J | 33 | * |
| 4 | 7 | 14 | L | 24 | F | 34 | 4 |
| 5 | S | 15 | C | 25 | 2 | 35 | V |
| 6 | K | 16 | S | 26 | % | 36 | Z |
| 7 | T | 17 | 8 | 27 | U | 37 | ? |
| 8 | @ | 18 | & | 28 | D | 38 | A |
| 9 | B | 19 | J | 29 | 7 | ||
| 10 | 1 | 20 | F | 30 | P |
Identify Prime Number Positions:
Prime numbers are natural numbers greater than 1 that have no positive divisors other than 1 and themselves. The prime numbers up to 38 are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37.
Elements to be Dropped:
We drop the elements at these prime positions:
Construct the New Series:
Let's write down the series after dropping these elements and then count the elements to find the 18th one.
Original Series (with positions):
1(9) 2(C) 3(W) 4(7) 5(S) 6(K) 7(T) 8(@) 9(B) 10(1) 11(B) 12(1) 13(6) 14(L) 15(C) 16(S) 17(8) 18(&) 19(J) 20(F) 21(2) 22(%) 23(U) 24(D) 25(7) 26(P) 27(5) 28(*) 29(4) 30(V) 31(Z) 32(?) 33(A)
Wait, the original series provided in the question is: 9 C W 7 S K T @ B 1 6 L C S 8 & J F 2 % U D 7 P 5 * 4 V Z ? A. Let's re-list the elements and their positions carefully.
1: 9, 2: C, 3: W, 4: 7, 5: S, 6: K, 7: T, 8: @, 9: B, 10: 1, 11: 6, 12: L, 13: C, 14: S, 15: 8, 16: &, 17: J, 18: F, 19: 2, 20: %, 21: U, 22: D, 23: 7, 24: P, 25: 5, 26: *, 27: 4, 28: V, 29: Z, 30: ?, 31: A
The prime number positions are: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31.
Elements to be dropped:
Let's list the remaining elements and count them:
Original series: 9 C W 7 S K T @ B 1 6 L C S 8 & J F 2 % U D 7 P 5 * 4 V Z ? A
Elements after dropping (elements at prime positions are marked with strikethrough for clarity):
9 C W 7 S K T @ B 1 6 L C S 8 & J F 2 % U D 7 P 5 * 4 V Z ? A
Let's list the elements of the new series and their new positions:
Counting from the left end of this new series, the 18th element is '4'.
C) 4
The problem asks us to identify the number of odd digits in a given series that satisfy two conditions: they must be immediately preceded by an odd digit and immediately followed by an even digit. We need to scan the series and check each odd digit against these conditions.
B) Two. There are exactly two such odd digits in the series that are immediately preceded by an odd digit and immediately followed by an even digit.