This problem can be solved using the division algorithm, which states that for any integers \(a\) (dividend) and \(d\) (divisor) with \(d > 0\), there exist unique integers \(q\) (quotient) and \(r\) (remainder) such that \(a = dq + r\), where \(0 \le r < d\). We will set up two equations based on the given information and then solve for the divisor.
Let the original number be \(N\) and the divisor be \(D\). According to the first condition, when \(N\) is divided by \(D\), the remainder is 16. Let the quotient be \(q_1\). Using the division algorithm:
\[ N = Dq_1 + 16 \quad \text{(Equation 1)} \]According to the second condition, when twice the original number (\(2N\)) is divided by the same divisor \(D\), the remainder is 3. Let the quotient be \(q_2\). Using the division algorithm:
\[ 2N = Dq_2 + 3 \quad \text{(Equation 2)} \]Substitute Equation 1 into Equation 2:
\[ 2(Dq_1 + 16) = Dq_2 + 3 \]\[ 2Dq_1 + 32 = Dq_2 + 3 \]Rearrange the terms to isolate the divisor \(D\):
\[ 32 - 3 = Dq_2 - 2Dq_1 \]\[ 29 = D(q_2 - 2q_1) \]From this equation, we can see that \(D\) must be a divisor of 29. Since 29 is a prime number, its only positive divisors are 1 and 29.
Also, recall from the division algorithm that the remainder must be less than the divisor. From Equation 1, the remainder is 16, so \(D > 16\). From Equation 2, the remainder is 3, so \(D > 3\). Both conditions imply \(D > 16\).
Considering the divisors of 29 (which are 1 and 29) and the condition \(D > 16\), the only possible value for \(D\) is 29.
A) 29 is the correct answer because it satisfies both conditions: it is a divisor of 29 and is greater than 16 (the first remainder).
To find the currents through resistors connected in parallel, we use Ohm's Law. In a parallel circuit, the voltage across each component is the same as the source voltage. We will calculate the current for each resistor individually using its resistance and the battery voltage.
When resistors are connected in parallel, the voltage across each resistor is the same and equal to the source voltage.
Using Ohm's Law, \(I = \frac{V}{R}\), the current through resistor A (\(I_A\)) is:
\[ I_A = \frac{V}{R_A} = \frac{6 \, \text{V}}{20 \, \Omega} = 0.3 \, \text{A} \]Similarly, the current through resistor B (\(I_B\)) is:
\[ I_B = \frac{V}{R_B} = \frac{6 \, \text{V}}{40 \, \Omega} = 0.15 \, \text{A} \]The currents in A and B are \(0.3 \, \text{A}\) and \(0.15 \, \text{A}\) respectively.
Correct Option: D) 0.3 A and 0.15 A
The question asks to identify the main defect of Dobereiner's triads. We need to recall the key characteristics and limitations of Dobereiner's classification system.
B) He was unable to make more than three triads of the elements. This is the main defect because Dobereiner could only identify a limited number of triads (e.g., Li, Na, K; Ca, Sr, Ba; Cl, Br, I). This classification system was not universally applicable to all then-known elements, which was its biggest drawback and led to its eventual replacement by more comprehensive classification methods.
The question asks for the correct formula for aggregate demand (AD). Aggregate demand represents the total demand for all goods and services produced in an economy over a given period. It is typically broken down into its main components based on different sectors of the economy.
Correct Option: C) AD = C + I + G
This formula correctly represents the components of aggregate demand in a closed economy, where:
The question asks to identify the institution responsible for initiating the 'Waste to Wealth Creation' program for women in Sundarban, West Bengal. This requires knowledge of recent initiatives by financial and governmental bodies in India, particularly those focused on skill development and economic empowerment.
A) Small Industries Development Bank of India (SIDBI) is the correct answer. SIDBI launched the 'Waste to Wealth Creation' program for women in Sundarban, West Bengal, as part of its mission to promote sustainable livelihoods and empower women through skill development and entrepreneurship.
This problem involves tracking movement in different directions. We can solve this by breaking down Neetu's journey into horizontal (East-West) and vertical (North-South) components. We will assign positive values for East and North, and negative values for West and South. By summing up the displacements in each direction, we can find the net displacement from the starting point.
A) 51 m, North. As calculated, the final position is 51 m North of the starting point.
Identify the amendment of the Indian Constitution from the following, which is related to the Panchayati Raj institutions?
73rd Amendment
71st Amendment
72nd Amendment
74th Amendment
The question asks to identify the constitutional amendment related to Panchayati Raj institutions. This requires knowledge of major constitutional amendments and their subjects.
Correct Option: A) 73rd Amendment
The 73rd Constitutional Amendment Act, passed in 1992, gave constitutional status to the Panchayati Raj institutions. It mandated the establishment of a three-tier system of Panchayats at the village, intermediate, and district levels (except in states with populations below 20 lakhs). It also provided for regular elections, reservation of seats for Scheduled Castes, Scheduled Tribes, and women, and the establishment of State Election Commissions and State Finance Commissions.
The question asks to identify the group that contains ONLY biodegradable substances. Biodegradable substances are those that can be decomposed by natural processes and microorganisms (like bacteria and fungi) into simpler, harmless substances. Non-biodegradable substances, on the other hand, cannot be broken down by natural means or take a very long time to decompose.
B) Grass, wood, orange peels — All these items are organic materials that are easily broken down by microorganisms and natural processes, making them biodegradable.
To find a single equivalent discount for successive discounts, we can assume an initial price (e.g., Rs. 100) and apply each discount one by one. Alternatively, we can use the formula for equivalent discount for two successive discounts and extend it for three.
Discount amount = \(10\%\) of Rs. \(100 = \frac{10}{100} \times 100 = \text{Rs. } 10\)
Price after first discount = \(100 - 10 = \text{Rs. } 90\)
Discount amount = \(15\%\) of Rs. \[90 = \frac{15}{100} \times 90 = \frac{1350}{100} = \text{Rs. } 13.50\]
Price after second discount = \(90 - 13.50 = \text{Rs. } 76.50\)
Discount amount = \(20\%\) of Rs. \[76.50 = \frac{20}{100} \times 76.50 = \frac{1530}{100} = \text{Rs. } 15.30\]
Final price after all discounts = \(76.50 - 15.30 = \text{Rs. } 61.20\)
Total discount = Original Price - Final Price
Total discount = \(100 - 61.20 = \text{Rs. } 38.80\)
Equivalent discount percentage = \[\frac{\text{Total Discount}}{\text{Original Price}} \times 100\%\]
\[\text{Equivalent discount percentage} = \frac{38.80}{100} \times 100\% = 38.8\%\]For two successive discounts \(d_1\) and \(d_2\), the equivalent discount is \(d = d_1 + d_2 - \frac{d_1 d_2}{100}\).
Both methods yield the same result.
Correct Option: D) 38.8%
The question asks about the function of olfactory receptors. To answer this, one needs to recall the basic sensory organs and their corresponding receptors.
Therefore, olfactory receptors are directly involved in the perception of smell.
Correct Option: A) smell — Olfactory receptors are specialized sensory cells located in the nasal cavity that detect odor molecules, enabling the perception of smell.