Which of the following groups of hydrocarbons follows the general formula of CnH2n?
The question asks to identify the group of hydrocarbons that follows the general formula \( \text{C}_n\text{H}_{2n} \). This requires knowledge of the general formulas for different types of hydrocarbons: alkanes, alkenes, alkynes, and alkyl groups.
Correct Option: D) Alkene — Alkenes are hydrocarbons characterized by the presence of at least one carbon-carbon double bond. Their general formula is \( \text{C}_n\text{H}_{2n} \). For example, ethene (\(n=2\)) is \( \text{C}_2\text{H}_{2 \times 2} = \text{C}_2\text{H}_4 \), and propene (\(n=3\)) is \( \text{C}_3\text{H}_{2 \times 3} = \text{C}_3\text{H}_6 \).
Study the given letter, number, symbol series and answer the question that follows:
7 T % N 9 * M S 3 U = L 8 Y @ G & 3 E > 5 & R 3 ! K # 7 % H = Y 6
Find out the total number of letters that are immediately followed by a number and immediately preceded by a symbol.
The problem asks us to identify letters in a given series that satisfy two conditions simultaneously: they must be immediately preceded by a symbol AND immediately followed by a number. We need to scan the series and count how many such letters exist.
7 T %
(No)T % N
(No)% N 9
Here, '%' is a symbol, 'N' is a letter, '9' is a number. This matches the pattern. So, N is the first such letter.N 9 *
(No)9 * M
(No)* M S
(No)M S 3
(No)S 3 U
(No)3 U =
(No)U = L
(No)= L 8
Here, '=' is a symbol, 'L' is a letter, '8' is a number. This matches the pattern. So, L is the second such letter.L 8 Y
(No)8 Y @
(No)Y @ G
(No)@ G &
(No)G & 3
Here, '&' is a symbol, 'G' is a letter, '3' is a number. This matches the pattern. So, G is the third such letter.& 3 E
(No)3 E >
(No)E > 5
(No)> 5 &
(No)5 & R
(No)& R 3
Here, '&' is a symbol, 'R' is a letter, '3' is a number. This matches the pattern. So, R is the fourth such letter.R 3 !
(No)3 ! K
(No)! K #
(No)K # 7
(No)# 7 %
(No)7 % H
(No)% H =
(No)H = Y
(No)= Y 6
(No)C) 4 is the correct option because we found 4 letters (N, L, G, R) that are immediately preceded by a symbol and immediately followed by a number.
To solve this problem, we need to compare the original position of each digit in the given number with its position after arranging all the digits in ascending order. We will list the original number, then sort its digits, and finally identify digits that retain their original position.
C) Two
The problem involves distributing a sum of money among four members in a given ratio. We are given a relationship between the shares of two members (C and D) and need to find the share of one specific member (D). We will use a common multiplier for the ratio parts to represent each member's share and then form an equation based on the given difference.
Let the shares of A, B, C, and D be \(4x\), \(7x\), \(9x\), and \(3x\) respectively, where \(x\) is a common multiplier.
According to the problem, C gets Rs 720 more than D. We can write this as an equation:
\[ \text{C's share} - \text{D's share} = 720 \]Substitute the expressions for C's and D's shares into the equation:
\[ 9x - 3x = 720 \]Simplify the equation:
\[ 6x = 720 \]Solve for \(x\):
\[ x = \frac{720}{6} \]\[ x = 120 \]Now that we have the value of \(x\), we can find D's share. D's share is \(3x\).
\[ \text{D's share} = 3 \times 120 \]\[ \text{D's share} = 360 \]Correct Option: C) Rs 360
To find the selling price, we first need to calculate the total cost incurred by Mahesh, which includes the production cost and the transportation cost. Once the total cost is determined, we can calculate the selling price by adding a 15% profit margin to this total cost.
Calculate the production cost:
The cost incurred by Mahesh to produce an item in the factory was Rs 2,000.
\[ \text{Production Cost} = \text{Rs } 2,000 \]Calculate the transportation cost:
He spent 10% of the production cost on transportation.
\[ \text{Transportation Cost} = 10\% \text{ of Production Cost} \]\[ \text{Transportation Cost} = 0.10 \times 2,000 \]\[ \text{Transportation Cost} = \text{Rs } 200 \]Calculate the total cost incurred:
The total cost is the sum of the production cost and the transportation cost.
\[ \text{Total Cost} = \text{Production Cost} + \text{Transportation Cost} \]\[ \text{Total Cost} = 2,000 + 200 \]\[ \text{Total Cost} = \text{Rs } 2,200 \]Calculate the selling price:
He sold the item at a price that was 15% above the total cost incurred.
\[ \text{Selling Price} = \text{Total Cost} + 15\% \text{ of Total Cost} \]\[ \text{Selling Price} = \text{Total Cost} \times (1 + 0.15) \]\[ \text{Selling Price} = 2,200 \times 1.15 \]\[ \text{Selling Price} = \text{Rs } 2,530 \]Correct Option: B) Rs 2,530
To solve this problem, we need to establish relationships between Cost Price (CP), Marked Price (MP), and Selling Price (SP) using the given discount and profit percentages. We will first find the Selling Price in terms of Marked Price and Cost Price, then equate these expressions to find the ratio of Marked Price to Cost Price, and finally calculate the percentage by which Marked Price is more than Cost Price.
Relate Selling Price (SP) to Marked Price (MP) using discount:
Given a 30% discount on the Marked Price, the Selling Price is 70% of the Marked Price.
Relate Selling Price (SP) to Cost Price (CP) using profit:
Given a 10% profit, the Selling Price is 110% of the Cost Price.
Equate the two expressions for SP:
Since both expressions represent the same Selling Price, we can equate them:
Find the ratio of MP to CP:
Rearrange the equation to find the ratio \(\frac{\text{MP}}{\text{CP}}\):
Calculate the percentage by which MP is more than CP:
The percentage increase is given by \(\frac{\text{MP} - \text{CP}}{\text{CP}} \times 100\%\). We can rewrite this as \[\left(\frac{\text{MP}}{\text{CP}} - 1\right) \times 100\%\].
Correct Option: A) 57.14%
The question asks to identify the British Parliamentary Act that defined the powers and responsibilities of the various organs of the East India Company. We need to recall the major constitutional acts passed by the British Parliament concerning India and their primary objectives.
Correct Option: B) Regulating Act of 1773. This Act was the first significant step taken by the British Parliament to control and regulate the affairs of the East India Company in India. It laid down the foundation of central administration in India and defined the powers and responsibilities of the Company's various organs, including the Governor-General of Bengal and the Court of Directors.
The question asks to identify the body responsible for fiscal policy. To answer this, one needs to understand the definitions and roles of fiscal policy and monetary policy, and which institutions in India are responsible for each.
Correct Option: A) the Government. Fiscal policy involves decisions on government spending and taxation, which are the direct responsibilities of the government.
The product of the roots of the quadratic equation 6 - 5x² - 8x = 0 is:
\( \frac{-8}{5} \)
\( \frac{8}{5} \)
\( \frac{6}{5} \)
\( \frac{-6}{5} \)
To find the product of the roots of a quadratic equation, we first need to express the equation in its standard form, which is \(ax^2 + bx + c = 0\). Once in standard form, the product of the roots is given by the formula \( \frac{c}{a} \).
Rearrange the given equation into standard form:
The given equation is \(6 - 5x^2 - 8x = 0\).
The standard form of a quadratic equation is \(ax^2 + bx + c = 0\).
Rearranging the terms, we get:
Identify the coefficients a, b, and c:
Comparing \( -5x^2 - 8x + 6 = 0 \) with \( ax^2 + bx + c = 0 \), we identify the coefficients:
Apply the formula for the product of the roots:
For a quadratic equation \(ax^2 + bx + c = 0\), if \(\alpha\) and \(\beta\) are the roots, then the product of the roots is given by:
Calculate the product of the roots:
Substitute the values of \(c\) and \(a\) into the formula:
Correct Option: D) \( \frac{-6}{5} \)
The question asks to identify the term for workers who own and operate their own enterprise to earn a living. We need to analyze each option to see which one best fits this description.
Correct Option: D) self-employed workers — These are individuals who undertake work for themselves rather than being employed by someone else. They own and operate their own business or enterprise, directly earning their livelihood from it, which aligns perfectly with the definition provided.