The formal charge of the O-atoms in the ion is:

The incentre of the triangle formed by the links x=0, y=0 and 3x+4y=12 is at

In order to answer this question, we used the formula for the coordinates of a triangle's in-center when the lengths of its sides a, b, and c are known, as well as the coordinates of its vertices. The incentre is (1,1).

Two vertices of a triangle are (3,-2) and (-2,3) and its orthocentre is (-6,1). Then its third vertex is

 2x+y-4=0 and the x-y+7=0 are the equations that pass through the third vertex.

If in triangle , circumcenter  and orthocenter  then the co-ordinates of mid-point of side opposite to  is :

>>> The orthocenter, centroid and circumcenter of any triangle are collinear. And the centroid divides the distance from orthocenter to circumcenter in the ratio $2:1$.
>>> Also, the centroid $(G)$ divides the medians $(AD)$ in the ratio $2:1.$
>>> ∴D(h, k)=(1,​)

A triangle ABC with vertices A(-1,0), B(-2,3/4)&C(-3,-7/6) has its orthocentre H. Then the orthocentre of triangle BCH will be

ABC is an equilateral triangle such that the vertices B and C lie on two parallel lines at a distance 6 If A lies between the parallel lines at a distance 4 from one of them then the length of a side of the equilateral triangle is

$>>>\; acos\theta =6$ ----(1)
$>>>\; a(sin(30-\theta ))=4$ ----(2)
>>> a = 

If the point  lies between the region corresponding to the acute angle between the lines x-3y=0 and x-6y=0 then

>>> L11  L22 <0
>>>   (1+cos)² -6sin -6sincos -3sin-3sincos+18sin² < 0

If  be any point on a line then the range of  for which the point ' P ' lies between the parallel lines x+2y=1 and 2x+4y=15 is

((1+)+2() -1).() < 0

is any point in the interior of the quadrilateral formed by the pair of lines  and the two lines 2x+y-2=0 and 4x+5y=20 then the possible number of positions of the points ' P ' is

If the point ,lies in the region corresponding to the acute angle between the lines 2y=x and 4y=x then - .....

u ≡ x - 2y = 0 and v ≡ x - 4y = 0
>>>    S(x, y) ≡ x² - 6xy + 8y² = 0
>>>     ( a - 2 )( a - 4 ) < 0

Consider A(0,1) and B(2,0) and P be a point on the line 4x+3y+9=0, co-ordinates of P such  is maximum is

 Hence the point is (, ).

Assertion (A): The lines represented by  and x+ y=2 do not form a triangle
Reason (R): The above three lines concur at (1,1)

Both Assertion and Reason are correct and the Reason is the correct explanation of Assertion.

In Bohr’s hydrogen atom, the electronic transition emitting light of longest wavelength is:

P₁,P₂,P₃, be the product of perpendiculars from (0,0) to    respectively then:

P1 = 1;
P2 = ;
P3 = ;
>>> Therefore, we can say that P1>P2>P3.

If θ is angle between pair of lines , then 

>>>  = 2.
>>> tan = 
>>>  = 10.

If the pair of lines  intersect on the x-axis, then 2fgh=