CBSE EXAMINATION PAPER-2021

In a game of Archery, each ring of the Archery target is valued. The centremost ring is worth 10 points and rest of the rings are allotted points 9 to 1 in sequential order moving outwards. Archer A is likely to earn 10 points with a probability of 0·8 and Archer B is likely the earn 10 points with a probability of 0·9.

Based on the above information, answer the following questions : If both of them hit the Archery target, then find the probability that

A coin is tossed twice. The following table shows the probability distribution of number of tails:

(a) Find the value of K. (b) Is the coin tossed biased or unbiased? Justify your answer.

The foot of a perpendicular drawn from the point (-2, -1, -3) on a plane is (1, -3, 3). Find the equation of the plane.

Find all the possible vectors of magnitude 5√3 which are equally inclined to the coordinate axes.

Evaluate:

Find the area of the region {(x, y) : x² ≤ y ≤ x + 2}, using integration.

Find the ∫ 1/+ e ˣ +1 dx.

Evaluate

If 𝑎⃗, 𝑏⃗ and 𝑐⃗ (2𝑎⃗+𝑏⃗+2𝑐⃗) is equally inclined to both 𝑎⃗ and 𝑐⃗. Also, find the angle between 𝑎⃗ and (2𝑎⃗+𝑏⃗+2𝑐⃗).

Check whether the lines x-1/2=y - 2/3=z-3/4 and x-4/5=y-1/2 = z are skew or not.

Find the equations of the planes passing through the line of intersection of the planes 𝑟⃗⋅(𝑖̂+3𝑗̂)=6and 𝑟⃗⋅(3𝑖̂−𝑗̂−4𝑘̂) =0, which are at a distance of 1 unit from the origin. 

Find the particular solution of the differential equation x dy/dx + y+1/1+x² = 0, given that y(1) = 0.

Evaluate