Class 11th

The value of λ and µ for which the system of linear equations
x+y+z=2
x+2y+3z=5
x+3y+λz=µ
has infinitely many solutions are, respectively:

A clock has a continuously moving second's hand of 0.1 m length. The average acceleration of the tip of the hand (in units of ms?²) is of the order of:

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:

A satellite is in an elliptical orbit around a planet P. It is observed that the velocity of the satellite when it is farthest from the planet is 6 times less than that when it is closest to the planet. The ratio of distances between the satellite and the planet at closest and farthest points is:

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?

What is the Markovnikov Rule?

An insect is at the bottom of a hemispherical ditch of radius 1 m. It crawls up the ditch but starts slipping after it is at height h from the bottom. If the coefficient of friction between the ground and the insect is 0.75, then h is: (g = 10 ms?²)

Which technique is used to identify an alkene?

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:

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