Chemistry-
General
Easy
Question
Assertion: All minerals are ores.
Reason: Ores are minerals from which metal can be extracted conveniently and economically.
- Statement–1 is True, Statement–2 is True; Statement–2 is a correct explanation for Statement–1.
- Statement–1 is True, Statement–2 is True; Statement–2 is not a correct explanation for Statement–1.
- Statement–1 is True, Statement–2 is False
- Statement–1 is False, Statement–2 is True
The correct answer is: Statement–1 is False, Statement–2 is True
All ores are minerals while all minerals are not ore.
ores are mineral from which metal can be extracted conveniently and economically.
Related Questions to study
Physics-
Consider the mechanical vibrating systems shown in figure
. The vibrations are simple harmonic in
![](data:image/png;base64,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)
Consider the mechanical vibrating systems shown in figure
. The vibrations are simple harmonic in
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)
Physics-General
Physics-
The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is
![](data:image/png;base64,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)
The mass M shown in the figure oscillates in simple harmonic motion with amplitude A. The amplitude of the point P is
![](data:image/png;base64,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)
Physics-General
Physics-
The displacement of a particle performing simple harmonic motion is given by,
where distance is in cm and time is in second. The amplitude of motion is
The displacement of a particle performing simple harmonic motion is given by,
where distance is in cm and time is in second. The amplitude of motion is
Physics-General
Physics-
Two simple harmonic motions are represented by
The ratio of their amplitudes is
Two simple harmonic motions are represented by
The ratio of their amplitudes is
Physics-General
Physics-
A 1000 Hz sound wave in air strikes the surface of a lake and penetrates into water. If speed of sound in water is
,the frequency and wavelength of waves in water are
A 1000 Hz sound wave in air strikes the surface of a lake and penetrates into water. If speed of sound in water is
,the frequency and wavelength of waves in water are
Physics-General
Physics-
Which of the following functions represent a wave?
Which of the following functions represent a wave?
Physics-General
Physics-
The Speed of sound in a mixture of 1 mole of helium and 2 moles of oxygen at
is
The Speed of sound in a mixture of 1 mole of helium and 2 moles of oxygen at
is
Physics-General
Physics-
A sound absorber the sound level by 20 dB. The intensity decreases by a factor of
A sound absorber the sound level by 20 dB. The intensity decreases by a factor of
Physics-General
Physics-
An object producing a pitch of 400 Hz flies past a stationary person. The object was moving in a straight line with a velocity
. What is the change in frequency noted by the person as the person as the object files past him?
An object producing a pitch of 400 Hz flies past a stationary person. The object was moving in a straight line with a velocity
. What is the change in frequency noted by the person as the person as the object files past him?
Physics-General
Physics-
A police car moving at
, changes a motorcyclist. The police man sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle, if it is given that he does not observe any beats.
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)
A police car moving at
, changes a motorcyclist. The police man sounds his horn at 176 Hz, while both of them move towards a stationary siren of frequency 165 Hz. Calculate the speed of the motorcycle, if it is given that he does not observe any beats.
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)
Physics-General
Physics-
A motor cycle starts from rest and accelerates along a straight path at
. At the starting point of the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was rest? (Speed =330
)
A motor cycle starts from rest and accelerates along a straight path at
. At the starting point of the motor cycle gone when the driver hears the frequency of the siren at 94% of its value when the motor cycle was rest? (Speed =330
)
Physics-General
Physics-
A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is
is
![](data:image/png;base64,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)
A piston fitted in cylindrical pipe is pulled as shown in the figure. A tuning fork is sounded at open end and loudest sound is heard at open length 13cm, 41 cm and 69 cm, the frequency of tuning fork if velocity of sound is
is
![](data:image/png;base64,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)
Physics-General
Physics-
An open organ pipe is closed suddenly with the result that the second overtone of the closed pipe is found to be higher in frequency by 100 than the first overtone of the original pipe. Then the fundamental frequency of the open pipe is
An open organ pipe is closed suddenly with the result that the second overtone of the closed pipe is found to be higher in frequency by 100 than the first overtone of the original pipe. Then the fundamental frequency of the open pipe is
Physics-General
Physics-
In an experiment with sonameter a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. tension of the string remaining constant the frequency of the second tuning fork is
In an experiment with sonameter a tuning fork of frequency 256 Hz resonates with a length of 25 cm and another tuning fork resonates with a length of 16 cm. tension of the string remaining constant the frequency of the second tuning fork is
Physics-General
Physics-
A uniform wire of length L, diameter D and density S is stretched under a tension T. the correct relation between its fundamental frequency f, the length L and the diameter D is
A uniform wire of length L, diameter D and density S is stretched under a tension T. the correct relation between its fundamental frequency f, the length L and the diameter D is
Physics-General