Maths-
General
Easy
Question
In
![R to the power of 2 end exponent left parenthesis blank s i n blank 2 A plus blank s i n blank 2 B plus blank s i n blank 2 C right parenthesis equals](data:image/png;base64,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)
- 1
The correct answer is: ![2 capital delta](data:image/png;base64,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)
Given ![R to the power of 2 end exponent left parenthesis blank s i n blank 2 A plus blank s i n blank 2 B plus blank s i n blank 2 C right parenthesis equals](data:image/png;base64,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)
(
AsinBsin
)
![equals 4 a to the power of 2 end exponent cross times fraction numerator a over denominator 2 a end fraction cross times fraction numerator b over denominator 2 a end fraction cross times fraction numerator c over denominator 2 a end fraction equals fraction numerator a b c over denominator 2 R end fraction equals 2 capital delta.](data:image/png;base64,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)
Related Questions to study
maths-
then the general solution of
=
then the general solution of
=
maths-General
maths-
Solution of
is
Solution of
is
maths-General
maths-
The general solution of
is
The general solution of
is
maths-General
maths-
If ![Sin space A equals Sin space B comma Cos space A equals Cos space B text then end text A equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAARUAAAAPCAYAAADK1FurAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAA/BJREFUeNrtWl9kHEEcHnEiqi9RFXWqVERE1L1URR6qVFVF1FEVFVVHH6oqqlSe+lB5qaqqvkRF5SFCVVRFlKqoE32JioiIUFVRlZeqOHFOuf5+d99dp5O93Zm9293Z6358ZCZ7u/vN78/8ZmaFqKKDOEXcJZaIeeKIOIiyCBYTAd47So1F4m/iN+IX4lviMY3fnSA+Jm7inbeJD4lHRHSYCOEZtuj2a7cwY8ZaW7IB7xJTYJa4HPIAXYUDpdpMYy9xTenjAHnp8btR4irxIhKigEPniO8icsKgbWSTblO7/YxZUgncloWIBXYT14nviZfbTCPrmVP6sg59MgYwM3Zb5IRh2Mgm3aZ2K8coqYRhy0p5N+yjlKu1r8AZuFz8SDxu+Pxp4hjxOvF5m2l8QLyv9M1iJnYbj1sG2kakpcImZnsVJ1GZ7UNT2UIb2aTbxG5lhU7+c4n4ycN/eHx3cA1XRF0xjrdKaVnAIHYaBhwLfIR1MOMGhOpiiLiIv3swWF5B70WbNL7CbMClfIY4o7GW5QSY1rz/GYzZINqDaA8p1602CDqbbGSTblO7uVUq7HtLxH4X/2E9W0gQ/MybxCcxjrd61ueX+068bRBw55S+DswcOkjB6HKm/SwNfqsRhcZtafALHhVKDSUDTa/FwQ1nbr9R+vZ9LivCtJFNuk3t5pZU5jT8ZwHVg4wfMY+3f0qwXyjVjmouDfyuI7nEvKf0TRmWwDZr7JD2crg6Oo9n9rUwuPYcKq9O9Kt7BCsOjmuTjWzR7cdubn7SpXF9AZWDqrEd4q0+qJMOWb+VAdePLKnirKge3QVSjoWskUvaD0rfNZSvbtg0WCeXDQL0MPEF7t9noY1s0e3HbuUm+3XGKc7xVg+6YoABl3d5yaCPLcPSOIa1uIxxOLgb+Pj7TotnbBmTDRwsahvZotuP3ZpNKnwkfaiJJVYc4q2yDt0JKOB4E+qpy//nRXW3PM4aGc+wkSZjRqMU59n6q9D70Ir3FkYdSv4Fj2RastBGNuj2a7eS+PtdjR//4dOeXEBJJZJ4y2MQ05JxF/EyrQ44dph1lKSNkPMYBNs1yptvtQ0+3rvhnfs1ZYadx73U7wWyCLBx6foetPPSdadFdQd/AO1TaA97jO+yhTaKWreJ3VSsNUg6uv7Ti/e/gDaf7szGON4qx0wLWArUPmHPaq4DTUXyUd2Ix/tw4G/HWKNc0tZKzCISSNphlnBKKowMZuQ9XMP3m3MIHB7PLejaaHCv2nvwZ+dLHtVAVDaKWreJ3VTwqcxuk/7DiXIF77rhUInFKd4SRIywlnsJEiT4D5DBrJRKhiJBggStQFoc/D4hQYLY4g+UnARqFk3CCgAAASR0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+U2luPC9taT48bW8+JiN4QTA7PC9tbz48bWk+QTwvbWk+PG1vPj08L21vPjxtaT5TaW48L21pPjxtbz4mI3hBMDs8L21vPjxtaT5CPC9taT48bW8+LDwvbW8+PG1pPkNvczwvbWk+PG1vPiYjeEEwOzwvbW8+PG1pPkE8L21pPjxtbz49PC9tbz48bWk+Q29zPC9taT48bW8+JiN4QTA7PC9tbz48bWk+QjwvbWk+PG10ZXh0PiYjeEEwO3RoZW4mI3hBMDs8L210ZXh0PjxtaT5BPC9taT48bW8+PTwvbW8+PC9tYXRoPuEcbgIAAAAASUVORK5CYII=)
If ![Sin space A equals Sin space B comma Cos space A equals Cos space B text then end text A equals](data:image/png;base64,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)
maths-General
maths-
In
(B-C) ![equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAJCAYAAADU6McMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAIzv8arAAAABZJREFUeNpjYMAE/4nAQwgMM+8MYQAAvYER7yMcYioAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPj08L21vPjwvbWF0aD4wTGvlAAAAAElFTkSuQmCC)
In
(B-C) ![equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAABEAAAAJCAYAAADU6McMAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAIzv8arAAAABZJREFUeNpjYMAE/4nAQwgMM+8MYQAAvYER7yMcYioAAABJdEVYdE1hdGhNTAA8bWF0aCB4bWxucz0iaHR0cDovL3d3dy53My5vcmcvMTk5OC9NYXRoL01hdGhNTCI+PG1vPj08L21vPjwvbWF0aD4wTGvlAAAAAElFTkSuQmCC)
maths-General
maths-
If
then principal value of ![theta](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=)
If
then principal value of ![theta](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAAsAAAANCAYAAAB/9ZQ7AAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJNJREFUeNpjYMAE1kC8DoifAvFBIDZnwAHMoQqZoHxRIL6LS/EFIJZGE9sBxHroCl2AeD4WA5YDsRe64GwgDsKiGOQsN3TBa0D8HwcWR1YI8tAnLKZiFQfp3ItFsSkQr8EVZOigHogT0QV5oMGGDASB+BwQs2EL4ytAnAdlawDxcSD2wRUhelDTfwHxJSD2Y6AEAAAtDR3FA6PhyAAAAE90RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+JiN4M0I4OzwvbWk+PC9tYXRoPpXIFCkAAAAASUVORK5CYII=)
maths-General
maths-
If then
If then
maths-General
maths-
If
and
are acute angles such that
and
then ![A equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAANCAYAAABVRWWUAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJBJREFUeNpjYMAPChjoDMKB+BcQs9DLQkEgvgTEu4E4gF6WzgTiSCCOB+Ip9LDQEoi3QNniQHyXgPr/RGC8ABR/Z4BYFknsHBBr0NKX9UBcgibWCsRZtLJQA+ordGAPxJtoFbyH8WiiSdZJA+IJeOSXA7EXNS2UhOZJHjxqkgk4imSwCoh9CKiRBuJbDEMZAABr7iyLEy33WQAAAFN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PG1vPj08L21vPjwvbWF0aD6je85bAAAAAElFTkSuQmCC)
If
and
are acute angles such that
and
then ![A equals](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAB0AAAANCAYAAABVRWWUAAAACXBIWXMAAA7EAAAOxAGVKw4bAAAABGJhU0UAAAAMyZLetQAAAJBJREFUeNpjYMAPChjoDMKB+BcQs9DLQkEgvgTEu4E4gF6WzgTiSCCOB+Ip9LDQEoi3QNniQHyXgPr/RGC8ABR/Z4BYFknsHBBr0NKX9UBcgibWCsRZtLJQA+ordGAPxJtoFbyH8WiiSdZJA+IJeOSXA7EXNS2UhOZJHjxqkgk4imSwCoh9CKiRBuJbDEMZAABr7iyLEy33WQAAAFN0RVh0TWF0aE1MADxtYXRoIHhtbG5zPSJodHRwOi8vd3d3LnczLm9yZy8xOTk4L01hdGgvTWF0aE1MIj48bWk+QTwvbWk+PG1vPj08L21vPjwvbWF0aD6je85bAAAAAElFTkSuQmCC)
maths-General
physics-
Three persons
and
of same mass travel with same speed
such that each one faces the other always. After how much time will they meet each other?
![](data:image/png;base64,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)
Three persons
and
of same mass travel with same speed
such that each one faces the other always. After how much time will they meet each other?
![](data:image/png;base64,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)
physics-General
physics-
Figure given shows the distance–time graph of the motion of a car. It follows from the graph that the car is
![](data:image/png;base64,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)
Figure given shows the distance–time graph of the motion of a car. It follows from the graph that the car is
![](data:image/png;base64,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)
physics-General
physics-
A rocket is fired upwards. Its engine explodes fully is 12s. The height reached by the rocket as calculated from its velocity-time graph is
![](data:image/png;base64,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)
A rocket is fired upwards. Its engine explodes fully is 12s. The height reached by the rocket as calculated from its velocity-time graph is
![](data:image/png;base64,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)
physics-General
physics-
In the relation
P is pressure, Z is distance, k is Boltzmann constant and
is the temperature. The dimensional formula of β b will be:
In the relation
P is pressure, Z is distance, k is Boltzmann constant and
is the temperature. The dimensional formula of β b will be:
physics-General
maths-
The number of values of k for which the system of equations
has infinite number of solutions is
The number of values of k for which the system of equations
has infinite number of solutions is
maths-General
maths-
The value of λ such that the system ![x minus 2 y plus z equals negative 4 comma 2 x minus y plus 2 z equals 2 comma x plus y plus lambda z equals 4](data:image/png;base64,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)
has no solution is
The value of λ such that the system ![x minus 2 y plus z equals negative 4 comma 2 x minus y plus 2 z equals 2 comma x plus y plus lambda z equals 4](data:image/png;base64,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)
has no solution is
maths-General
maths-
Let
If AB is a scalar
multiple of B, then ![x plus y equals](data:image/png;base64,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)
Let
If AB is a scalar
multiple of B, then ![x plus y equals](data:image/png;base64,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)
maths-General