The problem asks us to find the next number in the given series: 17, 23, 27, 29, ?. We need to identify the pattern or rule governing the sequence of numbers.
The differences are 6, 4, 2. This sequence of differences is decreasing by 2 each time (\(6 - 2 = 4\), \(4 - 2 = 2\)).
Following this pattern, the next difference should be \(2 - 2 = 0\).
To find the next term, we add the predicted difference to the last known term:
\[ \text{Next term} = 29 + 0 = 29 \]C) 29. The pattern of differences between consecutive terms is 6, 4, 2, ... which implies the next difference is 0. Adding 0 to the last term (29) gives 29.
The question asks about the representation of a Gram Panchayat by a Sarpanch. This is a fundamental concept in the Indian Panchayati Raj system. Understanding the structure and leadership of Gram Panchayats is key to answering this question.
Therefore, each Gram Panchayat is represented by a single Sarpanch.
Correct Option: B) One
The question asks about the primary motivation behind the Chipko Andolan. To answer this, we need to recall the historical context and goals of this movement, specifically what natural resource it aimed to protect.
Correct Option: D) a renewable resource
The question asks about the nature of the magnetic field produced by a long solenoid carrying current. We need to recall the properties of the magnetic field inside and outside a solenoid based on Ampere's Law and practical observations.
A) uniform inside the solenoid — As explained above, for a long solenoid, the magnetic field lines inside are parallel and equally spaced, indicating a uniform magnetic field. This is a fundamental property of solenoids.
The question asks for the name of the supercomputer installed at IIT Roorkee under Phase II of the National Supercomputing Mission (NSM) in March 2022. This requires knowledge of specific supercomputer installations under India's NSM program.
D) PARAM Ganga is the correct answer. The supercomputer PARAM Ganga was designed and installed by the Centre for Development of Advanced Computing (C-DAC) at IIT Roorkee in March 2022, as part of Phase II of the National Supercomputing Mission (NSM).
The question asks about the product of an energy-efficient electrocatalyst system designed by CeNS scientists in March 2022, specifically involving the electrolysis of urea. This is a factual question related to scientific advancements.
D) hydrogen. The news report from March 2022 highlighted that scientists at CeNS developed an electrocatalyst system for the energy-efficient production of hydrogen through the electrolysis of urea. This method is advantageous because urea is an abundant and inexpensive source, and its electrolysis requires less energy compared to water electrolysis for hydrogen generation.
Ramesh buys a radio for Rs 4,000. He sells it at a profit of 10% to Mohan. Mohan spends Rs 500 on it. Then he sells it at a profit of 12% to Ritwik. The cost price of the radio to Ritwik is:
This problem involves calculating the cost price of an item through a series of transactions, each involving a profit percentage and an additional expense. We need to calculate the selling price at each stage to determine the final cost for Ritwik.
Calculate the selling price of the radio by Ramesh to Mohan:
Ramesh buys the radio for Rs 4,000 and sells it at a profit of 10%.
\[ \text{Profit} = \text{Cost Price} \times \frac{\text{Profit Percentage}}{100} \] \[ \text{Profit} = 4000 \times \frac{10}{100} = 400 \] \[ \text{Selling Price (Ramesh to Mohan)} = \text{Cost Price} + \text{Profit} \] \[ \text{Selling Price (Ramesh to Mohan)} = 4000 + 400 = 4400 \]So, Mohan buys the radio for Rs 4,400.
Calculate Mohan's effective cost price:
Mohan spends Rs 500 on the radio.
\[ \text{Mohan's Effective Cost Price} = \text{Purchase Price} + \text{Additional Expense} \] \[ \text{Mohan's Effective Cost Price} = 4400 + 500 = 4900 \]Calculate the selling price of the radio by Mohan to Ritwik:
Mohan sells the radio at a profit of 12% on his effective cost price.
\[ \text{Profit for Mohan} = \text{Mohan's Effective Cost Price} \times \frac{\text{Profit Percentage}}{100} \] \[ \text{Profit for Mohan} = 4900 \times \frac{12}{100} = 49 \times 12 = 588 \] \[ \text{Selling Price (Mohan to Ritwik)} = \text{Mohan's Effective Cost Price} + \text{Profit for Mohan} \] \[ \text{Selling Price (Mohan to Ritwik)} = 4900 + 588 = 5488 \]Determine the cost price for Ritwik:
The price at which Mohan sells the radio to Ritwik is the cost price for Ritwik.
\[ \text{Cost Price for Ritwik} = 5488 \]D) 5,488 is the correct cost price of the radio for Ritwik.
To find the equilibrium income, we use the aggregate demand-aggregate supply (AD-AS) model. In a simple Keynesian model, equilibrium occurs when aggregate demand (AD) equals aggregate supply (AS), or equivalently, when total income (Y) equals aggregate expenditure (AE). Aggregate expenditure is the sum of consumption (C) and investment (I).
Thus, the equilibrium income is 175.
D) 175 — This is the correct equilibrium income derived from the given consumption and investment functions.
The question asks about the relationship between the angle of deviation and the wavelength of light when white light undergoes dispersion through a prism. We need to recall the phenomenon of dispersion and how the refractive index of a material varies with the wavelength of light, which in turn affects the angle of deviation.
B) inversely proportional to the wavelength. As derived from Cauchy's formula and the deviation formula for a prism, a longer wavelength corresponds to a smaller refractive index, which in turn leads to a smaller angle of deviation. Thus, the angle of deviation is inversely proportional to the wavelength.
To solve this problem, we need to follow a series of steps for each given number:
The given numbers are: 167, 876, 567, 187, 873.
Step 1: Subtract 11 from each number.
The new list of numbers is: 156, 865, 556, 176, 862.
Step 2: Reverse the digits of each new number.
The list of numbers after reversing digits is: 651, 568, 655, 671, 268.
Step 3: Arrange these numbers in ascending order.
Original order of reversed numbers: 651, 568, 655, 671, 268
Ascending order: 268, 568, 651, 655, 671
Step 4: Compare positions.
Let's list the original numbers, their transformed values, and their positions:
| Original Number | Transformed Number (after -11 and reverse) | Original Position in Transformed List | Position in Ascending Order |
|---|---|---|---|
| 167 | 651 | 1st | 3rd |
| 876 | 568 | 2nd | 2nd |
| 567 | 655 | 3rd | 4th |
| 187 | 671 | 4th | 5th |
| 873 | 268 | 5th | 1st |
Only one number, 568 (which originated from 876), retains its position. It was the 2nd number in the list of transformed numbers (651, 568, 655, 671, 268) and it is also the 2nd number in the ascending order list (268, 568, 651, 655, 671).
C) One
Only one number (876, which transforms to 568) retains its position when the transformed numbers are arranged in ascending order.