All India JEE Group

The identity element for the binary operation * defined by a * b =   , where a, b are the elements of a set of non-zero rational numbers, is​
  • a)
    1
  • b)
    1/2
  • c)
    0
  • d)
    2
Correct answer is option 'D'. Can you explain this answer?

Shail Saha answered  •  6 hours ago
Understanding the Binary Operation *
The binary operation defined is a * b = ab/2, where a and b are non-zero rational numbers. To find the identity element, we need to determine an element e such that for any non-zero rational number a, the following holds true:
a * e = a and e * a = a.
Finding the Identity Element
1. Setting Up the Equation
We star
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The number of five digits telephone numbers having atleast one of their digits repeated is
  • a)
    90000
  • b)
    100000
  • c)
    30240
  • d)
    69760
Correct answer is option 'D'. Can you explain this answer?

Nilotpal Goyal answered  •  14 hours ago
Understanding the Problem
To find the number of five-digit telephone numbers with at least one repeated digit, we can use the complementary counting method. This method involves calculating the total number of combinations and subtracting the combinations that have no repeated digits.
Total Number of Five-Digit Telephone Numbers
- The total number of five-digit telepho
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Characteristics and features of optical telescopes?

Mihir Rane answered  •  18 hours ago
Characteristics of Optical Telescopes
Optical telescopes are essential tools for astronomers, designed to collect and magnify light from celestial objects. Their key characteristics include:
  • Light Gathering Power: The ability to collect light is crucial; larger apertures capture more light, enabling observation of fainter objects.
  • Resolution: This det... more
  • Magnification: The power of a telescope to enlarge the appearance of distant objects, which is a function of the focal length of the telescope and the eyepiece used.

Types of Optical Telescopes
Optical telescopes come in several types, each with unique features:
  • Refracting Telescopes: Utilize lenses to bend light; known for high-quality images but can be bulky and expensive as aperture increases.
  • Reflecting Telescopes: Use mirrors to gather light; more cost-effective for large apertures and less prone to chromatic aberration.
  • Catadioptric Telescopes: Combine lenses and mirrors; offer compact designs with excellent image quality, suitable for both amateur and professional use.

Additional Features
Optical telescopes also include various features that enhance their usability:
  • Mounting Systems: Various types of mounts (altazimuth or equatorial) allow for smooth tracking of celestial objects.
  • Finderscopes: Small auxiliary scopes that help locate objects in the night sky, making observations easier.
  • Camera Attachments: Many telescopes can be fitted with cameras for astrophotography, allowing for detailed images of celestial phenomena.

These characteristics and features make optical telescopes invaluable for exploring and understanding our universe.

The chance of getting a doublet with 2 dice is
  • a)
    2/3
  • b)
    1/6
  • c)
    5/6
  • d)
    5/36
Correct answer is option 'B'. Can you explain this answer?

Jyoti Patel answered  •  19 hours ago
Understanding the Problem
When rolling two dice, a "doublet" occurs when both dice show the same number. There are six possible doublets: (1,1), (2,2), (3,3), (4,4), (5,5), and (6,6).
Total Outcomes
- Each die has 6 faces.
- The total number of outcomes when rolling two dice is:
- 6 (for the first die) * 6 (for the second die) = 36 possible outcomes.
<
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Let  defined as f(x) = 1/ x where x ∈ N is not an onto function. Which one of the following sets should be replaced by N such that the function f will become onto?​
  • a)
    R0
  • b)
    W
  • c)
    Z
  • d)
    None of these
Correct answer is option 'A'. Can you explain this answer?

Harshitha Shah answered  •  yesterday
Understanding the Function f(x) = 1/x
The function f is defined as f : N → R - {0}, where f(x) = 1/x for x in the natural numbers N. This function maps each natural number to a positive real number.
Why f is Not Onto
- Definition of Onto: A function is onto if every element in the codomain (R - {0}) has a pre-image in the domain (N).
- Range of f: T
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Which of the following do not show disproportionation reaction?
, and
  • a)
    , and
  • b)
    only
  • c)
    and
  • d)
    only
Correct answer is option 'C'. Can you explain this answer?

Ambition Institute answered  •  2 days ago
being most electronegative element cannot exhibit any positive oxidation state. In
chlorine is present in its highest oxidation state i.e
. Therefore it does not show disproportionation reaction.

The acceleration of a particle, starting from rest, varies with time according to relation ,
A= -a omega^2sin omega t .Find the displacemnt of this particle at a time (t).?

Rajveer Chauhan answered  •  2 days ago
Understanding the Problem
The acceleration of the particle is given by the equation:
A = -a ω² sin(ωt).
The particle starts from rest, indicating that its initial velocity (v(0)) is zero.
Step 1: Finding Velocity
To find the velocity (v) as a function of time (t), we integrate the acceleration with respect to time:
- v(t) = ∫A dt
- v(t) = ∫(-a ω²
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The of a particle starting from rest, varies with time according to the relation?

Jatin Iyer answered  •  2 days ago
Understanding Particle Motion
When analyzing the motion of a particle starting from rest, it is essential to consider how its velocity changes over time. The relationship between position, velocity, and time can be described in various ways, often involving equations of motion.
1. Initial Conditions
- The particle starts from rest, meaning its initial velocity (u) is 0
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A non-conducting sphere has uniform charge density in it. The electric field at a point inside the sphere will be _______ 
  • a)
    Zero
  • b)
    Only due to the charge inside that point
  • c)
    Only due to the charge outside that point
  • d)
    Due to the entire charge of the sphere
Correct answer is option 'B'. Can you explain this answer?

Tejas Malik answered  •  2 days ago
Understanding the Electric Field Inside a Non-Conducting Sphere
When analyzing the electric field within a uniformly charged non-conducting sphere, we must consider the principles of electrostatics.
Gauss's Law
- Gauss's Law states that the electric flux through a closed surface is proportional to the charge enclosed within that surface.
- For a point inside the s
... more

Filippo Brunelleschi is not known for --------
  • a)
    Architecture
  • b)
    Sculpture
  • c)
    Writing
  • d)
    Mechanical engineering
Correct answer is option 'C'. Can you explain this answer?

Dhruv Ghosh answered  •  3 days ago
Overview of Filippo Brunelleschi
Filippo Brunelleschi was a pivotal figure of the Renaissance, renowned primarily for his contributions to architecture and engineering. His innovative approaches and designs significantly shaped the architectural landscape of Italy.
Contributions to Architecture
- Dome of Florence Cathedral: Brunelleschi is best known for designi
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How does electric field strength change with distance from a short dipole?
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'D'. Can you explain this answer?

Learners Habitat answered  •  3 days ago
The electric field strength of a short dipole decreases as the distance from the dipole increases.
This relationship follows an inverse cube law, meaning the field strength is proportional to 1/r³ (where r is the distance).
As you move further away, the field becomes weaker more rapidly compared to point charges.
The dipole's field pattern is directional, meaning the field lines spread out from the positive to the negative charge.
Tab Home asked a question

DIRECTION: Read the following passage carefully and answer the questions given below it.
The likelihood of at least 600,000 deaths being caused annually in India by fine particulate matter pollution in the air is cause for worry, even if the data released by the World Health Organisation are only a modelled estimate. The conclusion that so many deaths could be attributed to particulate matter 2.5 micrometres or less in size is, of course, caveated, since comprehensive measurement of PM2.5 is not yet being done and the linkages between pollution, disease and deaths need further study. What is not in doubt is that residents in many urban areas are forced to breathe unhealthy levels of particulates, and the smallest of these - PM10 and less - can penetrate and get lodged deep in the lungs.
The WHO Global Burden of Disease study has been working to estimate pollution-linked health impacts, such as stroke and ischaemic heart disease, acute lower respiratory infection and chronic obstructive pulmonary disease. Data on fine particulates in India show that in several locations the pollutants come from burning of biomass, such as coal, fuel wood, farm litter and cow dung cakes. In highly built-up areas, construction debris, road dust and vehicular exhaust add to the problem. The Prime Minister launched an Air Quality Index last year aimed at improving pollution control. The new data, which the WHO says provide the best evidence available on the terrible toll taken by particulates, should lead to intensified action. A neglected aspect of urban air pollution control is the virtual discarding of the Construction and Demolition Waste Management Rules, notified to sustainably manage debris that is dumped in the cities, creating severe particulate pollution.
The Environment Ministry has highlighted the role that debris can play as a resource. Municipal and government contracts are, under the rules, required to utilise up to 20 per cent materials made from construction and demolition waste, and local authorities must place containers to hold debris. This must be implemented without delay. Providing cleaner fuels and scientifically designed cookstoves to those who have no option but to burn biomass, would have a big impact on reducing particulate matter in the northern and eastern States, which are the worst-hit during winter, when biomass is also used for heating.
Greening the cities could be made a mission, involving civil society, with a focus on landscaping open spaces and paving all public areas to reduce dust. These measures can result in lower PM10 and PM2.5 levels.
Comprehensive measurement of these particulates is currently absent in many cities, a lacuna that needs to be addressed.
Q. As per the given passage, which of the following is/are the measures for lowering particulate matter in the atmosphere?
(I) Making cleaner fuels available
(II) Landscaping open areas
(III) Providing cooking stoves designed scientifically
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