The relationship between the focal length and the radius of curvature of a spherical mirror is a fundamental concept in optics. We will use this relationship to determine how the radius of curvature changes when the focal length is doubled.
A) increase to double — As derived in the step-by-step explanation, if the focal length doubles, the radius of curvature also doubles because \(R = 2f\).
The question asks to identify the Indian organization responsible for advising people on fuel conservation while driving. This requires knowledge of prominent government or semi-government bodies involved in energy conservation and awareness campaigns.
Correct Option: D) PCRA stands for Petroleum Conservation Research Association. It is a non-profit organization set up under the aegis of the Ministry of Petroleum & Natural Gas, Government of India. Its primary objective is to promote fuel conservation and efficiency in various sectors, including transport, industry, agriculture, and households. PCRA regularly conducts campaigns and provides advice on how to save petrol/diesel while driving through various educational initiatives and public awareness programs like 'Saksham'.
We are given the ratio of the present ages of Shinjan and Aamya, and the ratio of their ages after 10 years. We need to find Aamya's present age. We can set up algebraic equations based on the given ratios and solve for the unknown ages.
Let the present age of Shinjan be \(S\) years.
Let the present age of Aamya be \(A\) years.
The ratio of their present ages is 3 : 4.
\[ \frac{S}{A} = \frac{3}{4} \]\[ 4S = 3A \]\[ S = \frac{3A}{4} \quad \text{(Equation 1)} \]After 10 years, Shinjan's age will be \(S + 10\) years.
After 10 years, Aamya's age will be \(A + 10\) years.
The ratio of their ages after 10 years will be 5 : 6.
\[ \frac{S + 10}{A + 10} = \frac{5}{6} \]\[ 6(S + 10) = 5(A + 10) \]\[ 6S + 60 = 5A + 50 \]Substitute \(S = \frac{3A}{4}\) into the equation from Step 3:
\[ 6\left(\frac{3A}{4}\right) + 60 = 5A + 50 \]\[ \frac{18A}{4} + 60 = 5A + 50 \]\[ \frac{9A}{2} + 60 = 5A + 50 \]Rearrange the equation to solve for \(A\):
\[ \frac{9A}{2} - 5A = 50 - 60 \]\[ \frac{9A - 10A}{2} = -10 \]\[ \frac{-A}{2} = -10 \]\[ -A = -20 \]\[ A = 20 \]Aamya's present age \(A = 20\) years.
Shinjan's present age \[S = \frac{3 \times 20}{4} = \frac{60}{4} = 15\] years.
Present ratio: \(15 : 20 = 3 : 4\). (Correct)
After 10 years:
Shinjan's age: \(15 + 10 = 25\) years.
Aamya's age: \(20 + 10 = 30\) years.
Ratio after 10 years: \(25 : 30 = 5 : 6\). (Correct)
The present age of Aamya is 20 years.
B) 20
The problem asks us to find the measure of angle SQR in a rectangle PQRS, given the measure of angle QPR. We will use the properties of a rectangle, specifically that all angles are 90 degrees and opposite sides are parallel, which implies that alternate interior angles formed by a transversal are equal.
A) 64° — As derived in the step-by-step explanation, by using the properties of a rectangle (diagonals are equal and bisect each other, forming isosceles triangles, and all angles are 90 degrees), we find that \( \text{m}\angle PQS = 26^\circ \). Since \( \text{m}\angle PQR = 90^\circ \), then \( \text{m}\angle SQR = 90^\circ - \text{m}\angle PQS = 90^\circ - 26^\circ = 64^\circ \).
The question asks about the nitrogenous wastes removed by the human kidney. We need to identify the primary nitrogenous excretory products in humans and determine which ones are filtered and excreted by the kidneys.
Therefore, the main nitrogenous wastes removed by the human kidney are urea and uric acid.
D) Urea and uric acid — Humans convert highly toxic ammonia into less toxic urea in the liver, which is then excreted by the kidneys. Uric acid, a product of purine metabolism, is also excreted by the kidneys. These are the two primary nitrogenous wastes removed by the human kidney.
The problem presents a series of number pairs and asks us to find the missing number in the last pair based on the relationship observed in the preceding pairs. We need to identify the pattern connecting the first and second numbers, and the third and fourth numbers, and then apply that same pattern to the fifth number to find the sixth.
Correct Option: D) 36
The question describes a single displacement reaction where iron (Fe) reacts with copper sulfate (CuSO₄) to form iron sulfate (FeSO₄) and copper (Cu). We need to determine the underlying chemical principle that explains why this reaction occurs.
\[ \text{Fe(s)} + \text{CuSO}_4\text{(aq)} \rightarrow \text{FeSO}_4\text{(aq)} + \text{Cu(s)} \]
In this reaction, iron (Fe) replaces copper (Cu) from its compound (copper sulfate). This is a classic example of a single displacement reaction.
Correct Option: C) Iron displaces copper because iron is more reactive than copper. This statement correctly explains why the reaction occurs, based on the reactivity series of metals.
To identify the reproductive parts of a flower, we need to recall the basic structure of a typical angiosperm flower and the function of each part in the reproductive process.
Correct Option: A) stamens and pistil
The question asks to identify which function is NOT typically handled by District Administration in India. We need to evaluate each option based on the common responsibilities of district-level governance.
A) Postal Services — Postal services are administered by the Central Government through India Post, a department under the Ministry of Communications. They do not fall under the administrative control of the District Administration.
This is a work-rate problem. The total amount of work done is constant (knitting one dozen sweaters). We need to find out how many hours per day are required if the number of days is reduced. The total work can be expressed as the product of the number of people, days, and hours per day. Since the number of people (Bina and Neena) is constant, we can use the inverse proportionality between days and hours per day to solve this problem.
Calculate the total work in terms of 'person-hours':
Initially, Bina and Neena work for 8 days, 10 hours per day. Since the number of people is constant, we can consider the total work as the product of days and hours per day.
This '80 hours' represents the total effort required to knit one dozen sweaters.
Determine the required hours per day for the new duration:
Now, they need to finish the same work (80 hours of effort) in 5 days. Let the new number of hours per day be \(x\).
Solve for \(x\):
\[ x = \frac{80}{5} \] \[ x = 16 \text{ hours/day} \]Thus, they should work 16 hours per day to finish the work in 5 days.
C) 16 — The calculation shows that 16 hours per day are required to complete the work in 5 days.