Maths-
General
Easy
Question
In the following figure, the value of x =
![](data:image/png;base64,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)
- 15°
- 25°
- 20°
- 30°
The correct answer is: 15°
Related Questions to study
maths-
In the given figure, 2b-a=65° and BOC=90° the measure of ![left floor A O B comma left floor C O D equals](data:image/png;base64,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)
![](data:image/png;base64,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)
In the given figure, 2b-a=65° and BOC=90° the measure of ![left floor A O B comma left floor C O D equals](data:image/png;base64,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)
![](data:image/png;base64,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)
maths-General
maths-
In the following figure, x =
![](data:image/png;base64,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)
In the following figure, x =
![](data:image/png;base64,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)
maths-General
maths-
In the given figure, the value of x =
![](data:image/png;base64,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)
In the given figure, the value of x =
![](data:image/png;base64,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)
maths-General
maths-
In the adjacent figure, the value of x =
![](data:image/png;base64,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)
In the adjacent figure, the value of x =
![](data:image/png;base64,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)
maths-General
maths-
In the given figure if
then x =
![](data:image/png;base64,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)
In the given figure if
then x =
![](data:image/png;base64,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)
maths-General
maths-
Which value of x will make AOB a straight line ?
![](data:image/png;base64,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)
Which value of x will make AOB a straight line ?
![](data:image/png;base64,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)
maths-General
maths-
In the figure, if
, then EFD is
![](data:image/png;base64,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)
In the figure, if
, then EFD is
![](data:image/png;base64,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)
maths-General
maths-
AB is parallel to CD. If
and
then
![](data:image/png;base64,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)
AB is parallel to CD. If
and
then
![](data:image/png;base64,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)
maths-General
maths-
In the figure, if ![Error converting from MathML to accessible text.](data:image/png;base64,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)
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)
In the figure, if ![Error converting from MathML to accessible text.](data:image/png;base64,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)
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)
maths-General
maths-
If
where
are constants, then
If
where
are constants, then
maths-General
Maths-
If ![fraction numerator sin to the power of 4 space theta over denominator a end fraction plus fraction numerator cos to the power of 4 begin display style space end style theta over denominator b end fraction equals fraction numerator 1 over denominator a plus b end fraction text then end text fraction numerator sin to the power of 8 begin display style text end text end style theta over denominator a cubed end fraction plus fraction numerator cos to the power of 8 begin display style space end style theta over denominator b cubed end fraction equals](data:image/png;base64,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)
If ![fraction numerator sin to the power of 4 space theta over denominator a end fraction plus fraction numerator cos to the power of 4 begin display style space end style theta over denominator b end fraction equals fraction numerator 1 over denominator a plus b end fraction text then end text fraction numerator sin to the power of 8 begin display style text end text end style theta over denominator a cubed end fraction plus fraction numerator cos to the power of 8 begin display style space end style theta over denominator b cubed end fraction equals](data:image/png;base64,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)
Maths-General
Maths-
and the equation
has at least one solution then the value of (a+b)
and the equation
has at least one solution then the value of (a+b)
Maths-General
Chemistry
Correct order for stability of carbocation is
![](data:image/png;base64,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)
Correct order for stability of carbocation is
![](data:image/png;base64,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)
ChemistryGeneral
maths-
If ![x equals sec space theta plus tan space theta comma y equals cosec space theta minus cot space theta text then end text y equals](data:image/png;base64,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)
If ![x equals sec space theta plus tan space theta comma y equals cosec space theta minus cot space theta text then end text y equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAVMAAAAPCAYAAABZcCxMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAABHJJREFUeNrtW1FkXEEUfVatVVEiKioqRFVVrP5ERD6qVEVFrFDVj6go/az+9iOqqlQ/8tWfiqiKCBVRVVGqIioiRK1YK0o/qioq7EdUxArTe3fvi5fJvDfz3puZdt/O4dA3O9nZe++ZO3fmTT2vPTEMXAL+Aq4CB52NDs7HxuxjTirZxCAJJEfPZ4HfDYxTawMbnY5ax8c1C/bVXDJtL5SBPVzbR2BR8yrLWthGh+z5mFmwj7lk2sQ94HNB+1P6TCf6gCvAfXK0yNl3gD+BB8DXwELINmSV+vwATkjGvU7fxWMBeFOjKBlHHmPADWAd+I3sEI1xi6qBA7LzvMLYaWycBd4WtD8EPjOwhYyK3SiwSj6qks+ypCObvpLpUYd9UWP4z/i36xI9y+KVdG7Y1HYDX4HdgedJ4MsYSYMpBm4zZHIEtxjb5CDcZtwHTnN9rgB3gSXqcxE4L7FvBjguaMftzA2LlSn+zssBH1cEf4tieQHsDfRbVRg3jY13acwgTlPC79IYf1nsBmmi9NNzPz0PZUhHqtDlqzjVYVL7oipTLMiWgZci9KwSr6Rzw5a2jzAS+PG4On02VAVjJdEZ8fkSrVBB7HDPi8AHMcetRjim+x9t83NUUfB/e02hn24bsXJ4y7U9Bk5pjr8sdotUbfHV17sM6ci2r5gF+6KS6byCnlXilXRu2NL2MXwCXqUzky5DY+AquyZwnI8/gqDtCZ7PxBgzJ/iOqPa0K1Qc8TJNZ09JbfTRxVXJ/kuHgub4y2KHn+e5trzAhnbQkS5fMcP2yXRbUOivEq+kc8OWtk+cIWCWLyomgaSlcAdtJ6q0dVH53qTJyqMgiSrtAVrdkya+JP2maHtxGNM2ZsHG/cC/p0kPtheasM/rGdKRLr2p+opZsI+lbE8TL/afaPsIw+Sw6YjVXjceec2z2iBqdJ4Rhd2YFYV/1cMTlPqTFpPpKzrzKRioTHXY+MVrvtjpo5U7ZyDmstipVlutrCPbvmIW7EubTFXilSaZ2tB2AzjAezIGV/tNg9t82XkHvsWT3SCYiXnW1UFHF0F00gTMG0im9ZBg7Rnc5uuw8Y3XfKmDZ1wThmIui92id/LFUilkkreqjmz7qq6YPNLYFzaGqp5V4pUmmdrQduP8YJlLnniIPWchmaLzVri2C7Ry+G8Oe8kRfPLHayLjFEC8EzcrGasSECa+VVz3Th7e60qm5ZDqfjsgGPzNePVsxzt+py+NYFRtXKDvKwmOedCPWwZjLovdAMXfv/FQpOfhDOnItq/KMXabSe0LG0NVzyrxSjM3jGs7T6tYT8iEGzF0DoQ8pCR+LuSMZo36VDzxFRi8NrJBfcpe9DUZX2hlWkG3FPqnAb5x/C0IcpFW+Tr9dtxWPaG+OgSjamNYMi1Ru0nfqMRulBaeOsW/1KY60uWrMD3qtC9sjDh6lsUrzdywpW2HNoToEvYYVSIODlmD07aDsWoHV/5TXDtWeEPOPQ4ZhNO2gxHgsQ5/pw//98wH5xqHDMK4tv8CwZhX4D8kWmgAAAFtdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPng8L21pPjxtbz49PC9tbz48bWk+c2VjPC9taT48bW8+JiN4QTA7PC9tbz48bWk+JiN4M0I4OzwvbWk+PG1vPis8L21vPjxtaT50YW48L21pPjxtbz4mI3hBMDs8L21vPjxtaT4mI3gzQjg7PC9taT48bW8+LDwvbW8+PG1pPnk8L21pPjxtbz49PC9tbz48bWk+Y29zZWM8L21pPjxtbz4mI3hBMDs8L21vPjxtaT4mI3gzQjg7PC9taT48bW8+JiN4MjIxMjs8L21vPjxtaT5jb3Q8L21pPjxtbz4mI3hBMDs8L21vPjxtaT4mI3gzQjg7PC9taT48bXRleHQ+JiN4QTA7dGhlbiYjeEEwOzwvbXRleHQ+PG1pPnk8L21pPjxtbz49PC9tbz48L21hdGg+wHBoFwAAAABJRU5ErkJggg==)
maths-General
Maths-
For all values of
, the values of
lie in the interval
For all values of
, the values of
lie in the interval
Maths-General