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

The volume of a sphere is increasing in volume at the rate of 3*π*
cm^{3} / sec .

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)

Differential equations are equations containing functions y = f(x), g(x) and derivatives of y with respect to x.

a line when intersect another line or axis two kind of angle form ,as an assumption we take positive side of axis, to define the direction of line we take angle made from all three axis.and we take cos not other trigonometric function like sin,tan because we can define Direction cosines of a line are coefficient of i,j,k of a unit vector along that line.