In the following figure, triangle ABC is an equilateral triangle and triangle CDE is a right angled triangle. If the length of side AE is 20 units, then what will be the length of side DB?
We need to find the length of side DB in the given figure where triangle ABC is equilateral and triangle CDE is right-angled. Using properties of these triangles, we can determine the unknown side.
Correct Option: C) 14 units
This question asks us to identify implicit assumptions in a given statement, which is an advertisement. An assumption is something taken for granted or supposed in advance. We need to analyze what must be true for the advertisement to be meaningful and effective.
Analyze the Statement: The statement is an advertisement by a pharma company claiming to cure diabetes in 6 months with a daily capsule.
Evaluate Assumption I: "Reader is interested in curing diabetes."
Evaluate Assumption II: "The company is a pharmaceutical manufacturer."
Conclusion: Both assumptions I and II are necessary for the advertisement to make sense and achieve its purpose.
D) Both I and II are implicit. As explained above, for an advertisement for a diabetes cure to be effective, it must assume that readers are interested in such a cure (Assumption I). Furthermore, the advertisement explicitly identifies the advertiser as a "pharma company" which inherently implies it is a pharmaceutical manufacturer (Assumption II).
To find the molecular mass of ozone, we need to know its chemical formula and the atomic mass of the elements it contains. Ozone is an allotrope of oxygen, meaning it is composed solely of oxygen atoms. We will use the standard atomic mass of oxygen to calculate the molecular mass.
Substitute the value:
\[ \text{Molecular mass of ozone} = 3 \times 16 \text{ u} = 48 \text{ u} \]B) 48u — The molecular mass of ozone (\(O_3\)) is calculated by multiplying the atomic mass of oxygen (16 u) by the number of oxygen atoms (3), resulting in \(3 \times 16 \text{ u} = 48 \text{ u}\).
This is a work and time problem. We need to calculate the individual work rates of Parimal and his sister, and then use these rates to determine the total time taken under the given conditions where Parimal's sister leaves before the work is completed.
Calculate Parimal's work rate:
Parimal takes 81 days to complete the work alone. So, Parimal's one day's work is:
\[ \text{Parimal's work rate} = \frac{1}{81} \text{ part/day} \]Calculate the combined work rate of Parimal and his sister:
Together, they take 54 days to complete the work. So, their combined one day's work is:
\[ \text{Combined work rate} = \frac{1}{54} \text{ part/day} \]Calculate Parimal's sister's work rate:
The sister's work rate can be found by subtracting Parimal's work rate from their combined work rate:
\[ \text{Sister's work rate} = \text{Combined work rate} - \text{Parimal's work rate} \] \[ \text{Sister's work rate} = \frac{1}{54} - \frac{1}{81} \]To subtract, find a common denominator, which is 162 (LCM of 54 and 81):
\[ \text{Sister's work rate} = \frac{3}{162} - \frac{2}{162} = \frac{1}{162} \text{ part/day} \]Set up the equation for the work done:
Let \(T\) be the total number of days taken to complete the work. Parimal's sister left 9 days before the completion of the work. This means Parimal worked for all \(T\) days, and his sister worked for \((T - 9)\) days.
The total work done is the sum of the work done by Parimal and his sister:
\[ \text{Total Work} = (\text{Parimal's work rate} \times \text{Days Parimal worked}) + (\text{Sister's work rate} \times \text{Days Sister worked}) \] \[ 1 = \left(\frac{1}{81} \times T\right) + \left(\frac{1}{162} \times (T - 9)\right) \]Solve for \(T\):
Multiply the entire equation by the common denominator, 162, to eliminate fractions:
\[ 162 \times 1 = 162 \times \frac{T}{81} + 162 \times \frac{(T - 9)}{162} \] \[ 162 = 2T + (T - 9) \] \[ 162 = 3T - 9 \] \[ 162 + 9 = 3T \] \[ 171 = 3T \] \[ T = \frac{171}{3} \] \[ T = 57 \text{ days} \]B) 57
The total number of days taken to paint the house is 57 days.
The general formula of alkanes is:
The question asks for the general formula of alkanes. Alkanes are saturated hydrocarbons, meaning they consist only of carbon and hydrogen atoms, and all carbon-carbon bonds are single bonds. We need to recall or derive the general formula for this class of organic compounds.
B) \(C_nH_{2n+2}\) is the correct general formula for alkanes. This formula represents saturated acyclic hydrocarbons where \(n\) is the number of carbon atoms.
The question asks to identify the incorrect statement about rhizoids. We need to evaluate each option based on the characteristics of rhizoids, especially in bryophytes.
Correct Option: C) They have fully developed stem, root and leaves.
This statement is incorrect because bryophytes, which possess rhizoids, are non-vascular plants and lack true roots, stems, and leaves. Their plant body is relatively undifferentiated compared to vascular plants.
The question asks about the primary authority responsible for determining and regulating interest rates for banks in India. This involves understanding the roles of key financial institutions and government bodies.
A) Reserve Bank of India
The Reserve Bank of India (RBI) is the central bank of India and is primarily responsible for formulating, implementing, and monitoring the monetary policy. A key objective of monetary policy is to maintain price stability while keeping in mind the objective of growth. The RBI achieves this by controlling the money supply and credit conditions in the economy, a major part of which involves determining and regulating interest rates. It sets policy rates like the repo rate, which directly influences the lending and deposit rates of commercial banks.
Who was honored with the 53rd Jnanpith Award for the year 2017?
Akhlaq Mohammad Khan 'Shahryar'
Kedarnath Singh
Shankha Ghosh
Krishna Sobti
The question asks to identify the recipient of the 53rd Jnanpith Award for the year 2017. This requires knowledge of the Jnanpith Award laureates for specific years.
Correct Option: D) Krishna Sobti was awarded the 53rd Jnanpith Award for the year 2017. She was a renowned Hindi fiction writer and essayist, known for her experimental and original style.
Which option figure will be formed by rotating the following figure?
The question asks which option figure will be formed by rotating the given figure. We need to analyze the orientation and position of elements in the figure to determine the correct option.
Correct Option: B) …
This is a blood relation question. To solve such problems, we break down the relationship described into smaller, more manageable parts, starting from the subject and working our way through the chain of relations. We then identify the final relationship with respect to the target person.
B) Maternal uncle — As derived, the brother of Varun's mother is Varun's maternal uncle. Since Varun's sister shares the same mother, he is also her maternal uncle.