Maths

Let m and M be respectively the minimum and maximum values of |cosx, 1+sin²x, sin2x; 1+cos²x, sin²x, sin2x; cos²x, sin²x, 1+sin2x|. Then the ordered pair (m,M) is equal to:

Two families with three members each and one family with four members are to be seated in a row. In how many ways can they be seated so that the same family members are not separated?

The negation of the Boolean expression p∨(¬p∧q) is equivalent to:

The shortest distance between the lines (x-1)/0 = (y+1)/-1 = z/1 and x+y+z+1=0, 2x-y+z+3=0 is:

If {p} denotes the fractional part of the number p, then {3²⁰⁰/8}, is equal to

If Σᵢ₌₁ⁿ(xᵢ-a)=n and Σᵢ₌₁ⁿ(xᵢ-a)²=na, (n,a>1) then the standard deviation of n observations x₁,x₂,.,xₙ is:

lim(x→1) ∫₁ˣ (t-1)² cos(t²)dt / ((x-1)sin(x-1))

If the value of (1 + 2/3 + 6/3² + 10/3³ + .upto ∞) / (log?.?(1/3 + 1/3² + 1/3³ + .upto ∞)) is l, then l² is equal to……….

The position of a moving car at time t is given by f(t)=at²+bt+c, t>0, where a,b and c are real numbers greater than 1. Then the average speed of the car over the time interval [t?,t?] is attained at the point:

If α, β are roots of the equation x² + 5√2x + 10 = 0, α > β and P? = α? - β? for each positive integer n, then the value of (P?P? + 5√2P?P?)/(P?P? + 5√2P?²) is equal to……….