Maths-
General
Easy
Question
If θ is angle between pair of lines
, then ![cosec squared invisible function application theta equals](data:image/png;base64,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)
- 10
- 20
- 5
- 15
Hint:
First find the coefficient of y square and then obtain the angle between the pair of straight lines.
The correct answer is: 10
Given That:
If θ is angle between pair of lines
, then ![cosec squared invisible function application theta equals](data:image/png;base64,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)
>>> We first need to find the value of ![lambda](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAoAAAANCAYAAACQN/8FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAHZJREFUeNpjYEAAJiC+BcS2DEQAFiBeCsTCxCj2AOJaYhSCnHCOgUhwlBi3ZgBxCRDPxadIBYg3QNkHgZgHl9t2A7E4lF8NxGnYFDYDcSQS3xiID6MrsgTiNVg030cOU5A7TuII5C5k6xcCcRAOz+kB8XEGUgAA3BsQpUbmebIAAABPdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1pPiYjeDNCQjs8L21pPjwvbWF0aD6tkH33AAAAAElFTkSuQmCC)
>>> Since, it is a pair of straight lines. Then, the determinant should be equal to zero.
>>>![](https://1.bp.blogspot.com/-2OKIUFstxvs/XNUETKd1Q2I/AAAAAAAAACE/yhtL58FIB1orLvtv5YzmqXhXtdo86ZzgwCLcBGAs/s400/pairoflines.png)
>>> This gives
= 2.
>>> Therefore, now the angle between the pair of straight lines becomes:
tan
= ![fraction numerator 2 square root of n squared minus a b end root over denominator a plus b end fraction](data:image/png;base64,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)
tan
= ![1 third](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABIAAAAjCAYAAACZ6FpfAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAXQ/cXWQAAAKNJREFUeNpjYMAP1IC4FogvMFAIFgNxGhD/Z6ASGDVo1KBBYdB/LHgUDCbwn0w8CgYLcATibUD8DYh/APEtIJ4AxMKkGrQfiIOAmA1JzACId1DLpZ+oYYgSEN+gxABxIE6EhpMXNbJMAaVeEgTiACA+CcT21AgjHqhhVAE/qGGIHjTASQIHgTgUiFmAmAma0u8DcTypBtkC8RaoV35AU7oPPg0ArQs4erRAu/EAAABidEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1mcmFjPjxtbj4xPC9tbj48bW4+MzwvbW4+PC9tZnJhYz48L21hdGg+q+QgMwAAAABJRU5ErkJggg==)
>> We know that
![cos e c squared theta space equals space 1 plus c o t squared theta
space space space space space space space space space space space space space space space space equals space 1 plus fraction numerator 1 over denominator tan squared theta end fraction](data:image/png;base64,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)
>>> Therefore,![cos e c squared theta space equals space 1 plus space 9](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAIEAAAAVCAYAAABhV40FAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAU2v5G4wAAAuhJREFUeNrtWDFoFEEUXRYJFiFwhRxBRAgSREIIhOMIQQ4hWISwhICFhUU4sEghFjYpgoUciKVtEAuRgITDIohNkBCCCCIix5HmCBap0oQrjnAsnP/rOxnHP7Ose+Z22XnwOPbv3O7s/P/f/D+el030wC7xgHjNc8gtfOIa8YtbCocztwT5RoW455YhvxhHTTBhGTNPrBOPESzlIc53krhB/DqERNmHYnaI2xFrlhnwgu4gEEwoIwB8XF8itoY451fE+yhqzwu3iQ1iCetwgVglHhKLWVeAd8SxiHGccZc123vidAq6m/P4D+OzIevvEJ9JsrkHyfhOvKfdXyI20ZbxbyA8mF/2AZLTs0y8CEnqv6sijBnFJI/xTs7oAu5xAFyP+PgF4kvBvkVczFEQhJbO6o+uaoZ4QlzGTZba15qssoxO4XoK13NC1AURk+Ls/aaMuwG50gOAJ1jD+BHiIwSiek7QswTbJnFFsNchkXHOI2xMexCwn2YF+1Uk629wVj6wPGhbcYCqDG81W0fJVhM4u9c12w4c3cdT4vOE2da0OK6YIyVg2T+C2vrgEpKsqw5sR+yvbc1JHq7bmm0Z1fpdiwSdokBTbW2lePOhSoUEi+wLc7PZ0xgEg1ShCrbpM/CN9+uUtRNnUqb7XcNevolMnBSqdeljDpQxJbQzScCZvivYS1C1OM7K+nZgwkXiJ9VwMiAlULHu/X2cGyAKbVjEvp0EZcMzHhNXM6IE/zsIbhGf6EVUVE0QCNJfj5BkXSnm9OgTMIseNglGhQOZAoJyxAXBT9T09nkCrdoKnMc3X2gy2kIl76HPbqGtNKGKfUgq2B7iPQUoxk2hv6/hYGMM4+djfmRDCWxuJz8KxW0egmAXfu0HP/t2w9TFzSBLQzghELqBQ2R3A0pg2kND9PLjhrOEfYxpIlh0XMGZRYh2svoPHz+N7+hqLemwnT+ImiIOFpCMIbbvrRQcljk4ODg4ODg4OKQRPwBz5ti+6jL+PAAAAPh0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+Y29zPC9taT48bWk+ZTwvbWk+PG1zdXA+PG1pPmM8L21pPjxtbj4yPC9tbj48L21zdXA+PG1pPiYjeDNCODs8L21pPjxtbz4mI3hBMDs8L21vPjxtbz49PC9tbz48bW8+JiN4QTA7PC9tbz48bW4+MTwvbW4+PG1vPis8L21vPjxtbz4mI3hBMDs8L21vPjxtbj45PC9tbj48bXNwYWNlIGxpbmVicmVhaz0ibmV3bGluZSIvPjwvbWF0aD47ztcQAAAAAElFTkSuQmCC)
= 10.
>>>> Therefore, the value of
is 10.
>>> = 2.
>>> tan =
>>> = 10.
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chemistry-
In the structure the configurations at chiral centers are:
![](data:image/png;base64,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)
In the structure the configurations at chiral centers are:
![](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAG0AAAB8CAYAAABjcj5oAAAGh0lEQVR4nO2dMUzbTBTH/6k6METKkA5YLAkZ6FQVsXToEDBLUJBYujo7HUiFO3Tq2MWoCnMG0qVDF6pYsACuZIYuEKkbslSyhDA2ioXYrkPl+xICBIOT431+P8lScOLc434625e8l0sIIQQYUjxRHQATHpZGEJZGEJZGEJZGEJZGEJZGEJZGEFLSGo0Gnj17hkQigUQiAdu2Ua1W4bouFhcX5f6NjQ0AQKlUkvtKpZLi6CNEEKFerwsAol6vy32GYYh0Oi2Oj49Ft9sVuq4Ly7L6jjMMQxiGMe5wRwqJkdZut7G2tgbLslAsFuX+Wq2Gra0ttFotJJNJTE1NDRz74sWLcYY6Fp6qDuAuHB0dodPpYGFhYeC5XolxgcRIOzk5QSqVwuTk5NDXmqYpr2OJRAKmaY4hwvFCQloYLMuCEEJulmWpDilySEibmZlBp9PB+fm56lAeBSSkzc3NIZVK4eDgYOA527Zh27aCqNRBQpqmaVhdXYVpmnIOBvybtzmOg2KxCN/30Wq1Bo799evXte/pui48zxtZzCNF8ZQjFMFcLdh0XRfdblfO0YL9wVzNMAy5r3eu5nme8DxPmKYpzs7OVP079yYhRHzTDXZ3d1EoFFSHERoSp8dePnz4gMvLywe/j+u62NzcRKPRiCCq8UJupGWzWTiOg0wm8+D3Cm5gqE3QSXwiEjU7OzvQNA0XFxdYWlpSHU5oYiktEDU7O6s4kvtB7prGsDSSsDSCsDSCsDSCsDSCsDSCsDSCsDSCsDSCsDSCsDSCPAEA3/fjlVY9ItrtNnK5nOyzXC6HdrsNIOI+Dr7CppJWnclkxOnpqeowBrgubf3qvqj6WJ4e45RWHTU3pa0Xi0VYloW1tTW02+3I+pivaRFwW9r6wsICOp0Ojo6OImtv4EtQ0zQHUqkNw5CPm80mms1mZAGE5fLyEj9//lQWw8TEBF69etW377a09cnJSaRSKZycnMhROKyPhzEgzbIsrK+vy783Njb6cge3t7fx/fv3OzcQNX/+/EGlUsHExISS9jOZDF6+fPmg9of18TBCpxuUy2WUy+Wwh0VGNpvF169fI0nsiYretHVN0/qeOz8/R6fTwczMTGTt8TUtAm5LWz84OEAqlcLc3Fxk7UlpYdOqmf/QNA2VSgWmafbVFdi2DdM0UalUoGladH3cO3/AHdOqVfJY52lCCHF2diamp6dln01PT8u08yj7ONbJqlThaxpBWBpBWBpBWBpBWBpBWBpBWBpBWBpBWBpBWBpBWBpBWBpBWBpBWBpByEnLZDJKE4seA+SkMSyNJCyNICyNICyNICyNICyNIFxUSJCnwL/atO3tbaysrKBQKMjigFqtJl/Y+5hRCxcVPpCrK00F2+LiInzfH0mbfE17ILOzs2g2m9B1HfV6HUIIdLtdAMDbt29H0uaAtDis1TJqkskkyuUyDg8PZaF8lAxIG7ZWy7t37wZOBePcfvz4gfn5eWXtZ7PZO3Xst2/f8Pr16756teCGr1qtIpfL3fsUGvr0+Pnz5z6p497y+Twcx1HW/unp6Y19s7y8LOUC/Tdvvu9jZWUF+/v7+PTpEw4PD7G3t4dkMjl6aczNBNe0oBCp93dEgjt0Xddlvdp94aLCEfHmzRv8/v070l81CHgK9A/d/f19AMD6+jpKpRK+fPkiX8xztbszNTWFdDo9kveWk+u9vb2BJ2u1Gou6B77v4/3795HXWkvuVC/6iMjn88JxHNVhSI6Pj0U6ne5bbQqAXBW4l95S3d6fYwoLufLd+fl5fPz4Efl8XnUoyuC7R4KwNIKwNIKwNIKwNIKwNIKwNIKwNIKwNIKwNIKwNIKwNIKwNIKwNIKwNIKwNIKwNIKwNIKwNIKQk/b8+fNrF+KJE+QSexiCI40hJu1qAZ9t26hWq3BdN17lxw9J1Bwn1625aRiGTAqlsqZpFJAYaTetuVmr1bC1tYVWqxWr8uPQi96p4LY1N3slxgUSI+22NTevEofyYxLSwjCs/Pj/AAlpvWtuMkSk3bbmpm3bfUs6xgES0jRNw+rqKkzTlHMw4N+8zXEcFIvF0OXHruvC87yRxTxSFE85QhHM1YJN13XR7XZDr7fpeZ7wPE+YpinX7KRErD973N3dRaFQUB1GaEicHkeB67rY3NxEo9FQHUpoYj3SghsYahN0Ep+IRM3Ozg40TcPFxQWWlpZUhxOaWI80qsT2mkYZlkYQlkYQlkYQlkaQv4bXAL2zfqeNAAAAAElFTkSuQmCC)
chemistry-General
chemistry-
Which of the following compound are meso forms?
![](data:image/png;base64,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)
Which of the following compound are meso forms?
![](data:image/png;base64,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)
chemistry-General
chemistry-
The number of enantiomers of the compound
is:
The number of enantiomers of the compound
is:
chemistry-General
chemistry-
Following stereo-structure of tartaric acid represents:
![](data:image/png;base64,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)
Following stereo-structure of tartaric acid represents:
![](data:image/png;base64,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)
chemistry-General
Maths-
The transformed equation of
when the axes are rotated through an angle 36° is
>>> Given equation is x2+y2=r2. After rotation
>>> x=Xcos36∘−Ysin36∘ and y=Xsin36o+Ycos36∘
∴X2(cos236o+sin236o)+Y2(sin236o+cos236o)=r2
>>> ⇒X2+Y2=r2
The transformed equation of
when the axes are rotated through an angle 36° is
Maths-General
>>> Given equation is x2+y2=r2. After rotation
>>> x=Xcos36∘−Ysin36∘ and y=Xsin36o+Ycos36∘
∴X2(cos236o+sin236o)+Y2(sin236o+cos236o)=r2
>>> ⇒X2+Y2=r2
maths-
When axes rotated an angle of
the transformed form of
is
When axes rotated an angle of
the transformed form of
is
maths-General
Maths-
The transformed equation of
when the axes are rotated through an angle 90° is
>>> Therefore, the equation becomes =1.
The transformed equation of
when the axes are rotated through an angle 90° is
Maths-General
>>> Therefore, the equation becomes =1.
maths-
The arrangement of the following in ascending order of angle to eliminate xy term in the following equations
A) ![2 x squared plus 5 x y plus 2 y squared plus 5 x plus 7 y plus 1 equals 0](data:image/png;base64,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)
B) ![2 x squared minus square root of 3 x y plus 3 y squared equals 9](data:image/png;base64,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)
C) ![9 x squared plus 2 square root of 3 x y end root plus 5 y squared equals 10](data:image/png;base64,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)
The arrangement of the following in ascending order of angle to eliminate xy term in the following equations
A) ![2 x squared plus 5 x y plus 2 y squared plus 5 x plus 7 y plus 1 equals 0](data:image/png;base64,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)
B) ![2 x squared minus square root of 3 x y plus 3 y squared equals 9](data:image/png;base64,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)
C) ![9 x squared plus 2 square root of 3 x y end root plus 5 y squared equals 10](data:image/png;base64,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)
maths-General