Chemistry-
General
Easy
Question
Which of the following molecule has the lowest average speed at 273K?
- CO
- CH4
- CO2
- C2H6
The correct answer is: CO2
Related Questions to study
chemistry-
In the below experiment, the value of P is
![](data:image/png;base64,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)
In the below experiment, the value of P is
![](data:image/png;base64,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)
chemistry-General
biology
Digestion of hormonal vesicle by lysosome is called -
Digestion of hormonal vesicle by lysosome is called -
biologyGeneral
chemistry-
Glycerol on oxidation with bismuth nitrate mainly gives:
Glycerol on oxidation with bismuth nitrate mainly gives:
chemistry-General
chemistry-
Anisole is the product obtained from phenol by the reaction known as
Anisole is the product obtained from phenol by the reaction known as
chemistry-General
chemistry-
Propan-2-ol on reacting with
produces:
Propan-2-ol on reacting with
produces:
chemistry-General
chemistry-
Proof spirit contains about:
Proof spirit contains about:
chemistry-General
physics-
A convex lens makes a real image 4 cm long on a screen. When the lens is shifted to a new position without disturbing the object, we again get a real image on the screen which is 16 cm tall. The length of the object must be
A convex lens makes a real image 4 cm long on a screen. When the lens is shifted to a new position without disturbing the object, we again get a real image on the screen which is 16 cm tall. The length of the object must be
physics-General
physics-
The slit of a collimator is illuminated by a source as shown in the adjoining figures. The distance between the slit S and the collimating lens L is equal to the focal length of the lens. The correct direction of the emergent beam will be as shown in figure
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)
The slit of a collimator is illuminated by a source as shown in the adjoining figures. The distance between the slit S and the collimating lens L is equal to the focal length of the lens. The correct direction of the emergent beam will be as shown in figure
![](data:image/png;base64,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)
physics-General
physics-
Two similar plano-convex lenses are combined together in three different ways as shown in the adjoining figure. The ratio of the focal lengths in three cases will be
![](data:image/png;base64,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)
Two similar plano-convex lenses are combined together in three different ways as shown in the adjoining figure. The ratio of the focal lengths in three cases will be
![](data:image/png;base64,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)
physics-General
physics-
White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected then the emerging ray in air contains
![](data:image/png;base64,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)
White light is incident on the interface of glass and air as shown in the figure. If green light is just totally internally reflected then the emerging ray in air contains
![](data:image/png;base64,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)
physics-General
physics-
A ray of light is incident at an angle i from denser to rare medium. The reflected and the refracted rays are mutually perpendicular. The angle of reflection and the angle of refraction are respectively r and r’, then the critical angle will be
![](data:image/png;base64,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)
A ray of light is incident at an angle i from denser to rare medium. The reflected and the refracted rays are mutually perpendicular. The angle of reflection and the angle of refraction are respectively r and r’, then the critical angle will be
![](data:image/png;base64,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)
physics-General
physics-
A fish is a little away below the surface of a lake. If the critical angle is
, then the fish could see things above the water surface within an angular range of
where
![](data:image/png;base64,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)
A fish is a little away below the surface of a lake. If the critical angle is
, then the fish could see things above the water surface within an angular range of
where
![](data:image/png;base64,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)
physics-General
physics-
A ray of light passes through four transparent media with refractive indices
as shown in the figure. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486791/1/932122/Picture26.png)
A ray of light passes through four transparent media with refractive indices
as shown in the figure. The surfaces of all media are parallel. If the emergent ray CD is parallel to the incident ray AB, we must have
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/486791/1/932122/Picture26.png)
physics-General
chemistry-
The acidic character of
alcohols,
and
is of the order
The acidic character of
alcohols,
and
is of the order
chemistry-General
chemistry-
Ethanol is more soluble in water but ether is less soluble because:
Ethanol is more soluble in water but ether is less soluble because:
chemistry-General