Maths-
General
Easy
Question
What is the LCM of 8 and 15 :
- 120
- 60
- 130
- 140
The correct answer is: 120
![](data:image/png;base64,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)
LCM of 8 and 15 = 2 × 3 × 2 × 2 × 5 = 120
Related Questions to study
Maths-
Find angle x and y :
![](data:image/png;base64,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)
Find angle x and y :
![](data:image/png;base64,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)
Maths-General
Maths-
What is the LC M of 9 and 18:
What is the LC M of 9 and 18:
Maths-General
Maths-
Find the GCF of 9 and 16 :
Find the GCF of 9 and 16 :
Maths-General
Chemistry-
The correct statement about the following disaccharide is:
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655636/1/1188918/Picture321.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655636/1/1188918/Picture322.png)
The correct statement about the following disaccharide is:
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655636/1/1188918/Picture321.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655636/1/1188918/Picture322.png)
Chemistry-General
Chemistry-
A carbonyl compound P, which gives positive iodoform test, undergoes reaction with MeMgBr followed by dehydration to give an olefin Q. Ozonolysis of Q leads to a dicarbonyl compound R, which undergoes intramolecular aldol reaction to give predominantly S.
![table row cell P fraction numerator 1. M e M g B r over denominator 2. H to the power of plus end exponent comma H subscript 2 end subscript O end fraction Q fraction numerator 1. O subscript 3 end subscript over denominator 2. Z n comma H subscript 2 end subscript O end fraction R fraction numerator 1. O H to the power of minus end exponent over denominator 2. capital delta end fraction S end cell row cell 3. H subscript 2 end subscript S O subscript 4 end subscript comma capital delta end cell end table](data:image/png;base64,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)
The structures of the products Q and R, respectively, are:
A carbonyl compound P, which gives positive iodoform test, undergoes reaction with MeMgBr followed by dehydration to give an olefin Q. Ozonolysis of Q leads to a dicarbonyl compound R, which undergoes intramolecular aldol reaction to give predominantly S.
![table row cell P fraction numerator 1. M e M g B r over denominator 2. H to the power of plus end exponent comma H subscript 2 end subscript O end fraction Q fraction numerator 1. O subscript 3 end subscript over denominator 2. Z n comma H subscript 2 end subscript O end fraction R fraction numerator 1. O H to the power of minus end exponent over denominator 2. capital delta end fraction S end cell row cell 3. H subscript 2 end subscript S O subscript 4 end subscript comma capital delta end cell end table](data:image/png;base64,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)
The structures of the products Q and R, respectively, are:
Chemistry-General
Chemistry-
Consider the following reactions I and II,
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655007/1/1188868/Picture105.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655007/1/1188868/Picture106.png)
Products 'X' and 'Y' are respectively:
Consider the following reactions I and II,
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655007/1/1188868/Picture105.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655007/1/1188868/Picture106.png)
Products 'X' and 'Y' are respectively:
Chemistry-General
Chemistry-
In which of the following cases, the nitration will take place at meta-position?
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655564/1/1188862/Picture84.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655564/1/1188862/Picture85.png)
III) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655564/1/1188862/Picture86.png)
IV) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655564/1/1188862/Picture87.png)
In which of the following cases, the nitration will take place at meta-position?
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655564/1/1188862/Picture84.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655564/1/1188862/Picture85.png)
III) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655564/1/1188862/Picture86.png)
IV) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655564/1/1188862/Picture87.png)
Chemistry-General
Chemistry-
The correct order of decreasing basicity of the following compounds is:
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture52.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture53.png)
III) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture54.png)
IV) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture55.png)
The correct order of decreasing basicity of the following compounds is:
I) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture52.png)
II) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture53.png)
III) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture54.png)
IV) ![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655588/1/1188847/Picture55.png)
Chemistry-General
Chemistry-
Phenol . gives two polymers on condensation with formaldehyde:
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655569/1/1188831/Picture38.png)
X and Y are :
Phenol . gives two polymers on condensation with formaldehyde:
![](https://mycourses.turito.com/tokenpluginfile.php/c161933dbfaab094c54655ab71e9b8f0/1/question/questiontext/655569/1/1188831/Picture38.png)
X and Y are :
Chemistry-General
Chemistry-
X and Yare:
X and Yare:
Chemistry-General
Chemistry-
Chemistry-General
Maths-
Simplify : 2m-3 =17
Simplify : 2m-3 =17
Maths-General
Physics-
In the figure is shown Young’s double slit experiment. Q is the position of the first bright fringe on the right side of O. P is the 11th fringe on the other side, as measured from Q. If the wavelength of the light used is
, then
will be equal to
![](data:image/png;base64,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)
In the figure is shown Young’s double slit experiment. Q is the position of the first bright fringe on the right side of O. P is the 11th fringe on the other side, as measured from Q. If the wavelength of the light used is
, then
will be equal to
![](data:image/png;base64,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)
Physics-General
Physics-
When one of the slits of Young’s experiment is covered with a transparent sheet of thickness 4.8 mm, the central fringe shifts to a position originally occupied by the 30th bright fringe. What should be the thickness of the sheet if the central fringe has to shift to the position occupied by 20th bright fringe
When one of the slits of Young’s experiment is covered with a transparent sheet of thickness 4.8 mm, the central fringe shifts to a position originally occupied by the 30th bright fringe. What should be the thickness of the sheet if the central fringe has to shift to the position occupied by 20th bright fringe
Physics-General
Physics-
Figure here shows P and Q as two equally intense coherent sources emitting radiations of wavelength 20 m. The separation PQ is 5.0 m and phase of P is ahead of the phase of Q by 90o. A, B and C are three distant points of observation equidistant from the mid-point of PQ. The intensity of radiations at A, B, C will bear the ratio
![](data:image/png;base64,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)
Figure here shows P and Q as two equally intense coherent sources emitting radiations of wavelength 20 m. The separation PQ is 5.0 m and phase of P is ahead of the phase of Q by 90o. A, B and C are three distant points of observation equidistant from the mid-point of PQ. The intensity of radiations at A, B, C will bear the ratio
![](data:image/png;base64,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)
Physics-General