Mathematics - Online Test

Since given there are four alternatives in which one or more are correct,we have to consider the following four cases

The candidate choose 1 correct answer, 2 correct answers,3 correct answers or 4 correct answers.

1 correct answer can be chosen in 4C1 ways = 4 ways

 2 correct answer can be chosen in 4C2 ways= 6 ways

 3 correct answers can be chosen in  4C3ways  = 4 ways

4 correct answers can be chosen in4C4 ways = 1 way

 Hence the totalnumber of ways = 4 + 6 + 4+ 1=15ways

Equation of circle is x2+y2+6x−6y+5=0

x2+6x+y2−6y=−5

Applying completing the square method

(x+3)2+(y−3)2=(13−−√)2

Comparing the above equation with(x−h)2+(y−k)2=(r)2   we get center as (-3,3) and radius as 13−−√   .

As centre of the circlre lies on diameter , it will satisfy the equation of diameter, so on putting (-3,3) in equation of diameter we get

2(−3)−(3)+λ=0

=> −6−3−λ=0

=>λ=9

The distance of the point ( 3, 4, 5) from X- axis is

let L be the foot of perpendicular from the point ( 3, 4, 5) to X axis ,then coordinate of L will be (3,0,0)       [ because on X axis y and z coordinate are zero]

then distance of the point ( 3, 4, 5) from X- axis i.e. from L (3,0,0) is given by (3−3)2+(4−0)2+(5−0)2−−−−−−−−−−−−−−−−−−−−−−−√= 41−−√