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

Applying completing the square method

Comparing the above equation with we get center as (-3,3) and radius as .

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

=>

=>

This function exists only if cosx−1≥0 ⇒cosx≥1 ⇒cosx>1 OR cosx=1 since maximum value of cosine function is 1 so, cos x >1 is not possible so, cosx=1 cosx=cos2nπ ⇒x=2nπ(n∈I)

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 =

{tex}A \cap (A \cup B)' = \phi {/tex} since {tex}(A \cup B)'{/tex} Set represent the element which are not belongs to it,so there is no common element with the set A.So the answer is null set

If n is a rational number, which is not a whole number, then the number of terms in the expansion of is