In the given figure `oversetharr( PQ)` is a line. Ray `oversetharr(OR)` is perpendicular to line `oversetharr (PQ). Oversetharr(OS )`is another ray lying between rays `oversetharr(OP) and oversetharr(OR)`. Prove that,`angleROS = 1/2 ( angleQOS - anglePOS)`.

In the given figure bar(PQ) is a line. Ray bar(OR) is perpendicular to line bar(PQ) . bar(OS) is another ray lying between rays bar(OP) and bar(OR) . Prove that angleROS = (1)/(2) angleQOS − anglePOS

State whether the following statements are true or false : Line oversetharr(AB) is the same as the line oversetharr(BA) .

In the given figure lines oversetharr(XY) and oversetharr(MN) intersect at O. If anglePOY = 90^@ and a:b =2:3 find c.

IF the d.r.'s of oversetharr(OA),oversetharr(OB) are (1, -2, -1), (3, -2, 3) then the d.c.'s of the normal to the plane oversetharr(AOB) are

If A, B, C are the points (0, 4, 1), (2, 3, -1), (4, 5, 0) respectively, then angle between oversetharr(AB) " and " oversetharr(BC) is

The only electron in the hydrogen atom resides under ordinary conditions on the first orbit. When energy is supplied, the electron moves to higher energy orbit depending on the amount of energy absorbed. When this electron returns to any of the lower orbits, it emits energy. Lyman series is formed when the electron returns to the lowest orbit while Balmer series is formed when the electron returns to second orbit. Similarly, Paschen, Brackett and Pfund series are formed when electron returns to the third, fourth orbits from higher energy orbits respectively (as shown in figure) Maximum number of lines produced when an electron jumps from nth level to ground level is equal to (n(n-1))/(2) . For example, in the case of n = 4, number of lines produced is 6. (4 rarr 3, 4 rarr 2, 4 rarr 1, 3 rarr 2, 3 rarr 1, 2 rarr 1) . When an electron returns from n_(2) to n_(1) state, the number of lines in the spectrum will be equal to ((n_(2) - n_(1))(n_(2)-n_(1) +1))/(2) If the electron comes back from energy level having energy E_(2) to energy level having energy E_(2) then the difference may be expressed in terms of energy of photon as E_(2) - E_(1) = Delta E, lambda = (h c)/(Delta E) . Since h and c are constant, Delta E corresponds to definite energy, thus each transition from one energy level to another will prouce a higher of definite wavelength. THis is actually observed as a line in the spectrum of hydrogen atom. Wave number of the line is given by the formula bar(v) = RZ^(2)((1)/(n_(1)^(2)) - (1)/(n_(2)^(2))) Where R is a Rydberg constant (R = 1.1 xx 10^(7)) (i) First line of a series : it is called .line of logest wavelength. or .line of shortest energy.. (ii) Series limit of last of a series : It is the line of shortest wavelength or line of highest energy. The wave number of electromagnetic radiation emitted during the transition of electron in between two levels of Li^(2+) ion whose principal quantum numbers sum if 4 and difference is 2 is

Name the following from the figure. 1.Any five points.2.Any five line segments.3.Any three rays.4.Any two lines.

A ray of light is incident along a line which meets another line 7x-y+1=0 , at the point (0,1). The ray is then reflected from this point along the line y+2x=1 . Then the equation of the line of incidence of the ray of light is

Construct triangleABC , right angle at angleA and BC 6 cm, AB-5 cm.Step (1) Draw a line segment of P AB=5 cm.Step (2) Join, B, C to the required triangleABC . Step (3) Draw a rough sketch of triangleABC with given measurements. Step (4) Construct a ray bar(AX) perpendicular to AB at A.Step (5) Draw an are from B with radius 6cm to intersect bar(AX) at C.