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is the ans 1/2?

the no of points may vary depending on how u plot the points.

however,

the minimum no of points is 0 ( bcoz u can draw a circle , an ellipse , a parabola , two curves of a hyperbola & 2 lines that do not intersect )

the maximum no of points is 37 (i'm not too sure but somewhere near this no)

the ellipse & circle intersect at 2 points

now a parabola drawn can intersect tha above two conics at 6 points (at the maximum)

now hyperbola drawn can intersect the above three conics at 12 points (each of the 2 curves of hyperbola at 6 points each)

now apair of straight lines drawn can intersect the above & themselves at 17 points(each line intersects the above 4 conics at 8 points & the lines can intersect each other at one point at the maximum)

thus 2+6+12+17=37(at the max)

thus max no of points =37

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thank u

the volume of a solid formed by rotating a curve around x-axis is

_[a]

^[b] y² dx

in this case it is

V=

_[0]

^[1] x⁶ dx

=

[ x⁷/ 7]₀¹ =

/7 cubic units

the ans is not pi/2

i'm pretty sure about it

pls rate me

the value of _[1]

^[a] [x] f '(x) dx , a>1, where [x] dentes greatest integer not exceeding x is

1) af([a]) - { f(1)+f(2)+...f(a)}

2) af(a) - { f(1)+f(2)+...f(a)}

3) [a] f(a) - { f(1)+f(2)+...f(a)}

4) [a]f([a]) - { f(1)+f(2)+...f(a)}

pls give ,me the answer with the solution

hey there is a simpler method (reduction formula)

_[0]

^[pi/2] sinⁿ x dx = (n-1/n).(n-3/n-2).(n-5/n-4)....2/3        if n is odd

                          = (n-1/n).(n-3/n-2).(n-5/n-4).....(1/2).pi/2   if n is even

eg.

_[0]

^[pi/2] sin⁵ x dx = (4/5).(2/3) (this it sooo simple isnt it)

for sin² x

_[0]

^[pi/2] sin² x dx=(1/2).(pi/2)

note: this method is applicable only for 0 to pi/2 .for other limits like 0 to pi or 0 to pi/4 use substitution method.
eg
for 0 to pi take t=x/2 & proceed

for 0 to pi/4 take t=2x & proceed

for 0 to pi/6 take t=3x & proceed.....

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what is the relation between the refractive index of a material of prism & its angle of minimum deviation?(is it directly proportional or inversely proportional? & what is the exact relation)

answer to Q1

the water starts boiling.

bcoz there is no atmosphere on the moon.

consequently the pressure is very low .

generally water boils when the pressure inside the bottle becomes equal to atmospheric pressure. (the temperature at which this happens corresponds to the boiling point of water(100 degree C) )

when the bottle is on the earth water will not boil at 30⁰ C as the pressure in the bottle is lower than atmospheric pressure.

but on the moon the atmospheric pressure is low & hence the boiling point of water is reduced. hence it boils at 30 degree C.

please rate me if my ans was useful

thank u guys

what is the method to find the colour of a metal ion by knowing the electronic configuration & the no of unpaired electrons in it. eg. how do i determine that Cu²⁺
is blue while Mn⁷⁺ is purple