CBSE Maths Class XII Compartment Paper 2009

SECTION-B

Questions number 11 to 22 carry 4 marks each.

Q.11 Three cards are drawn successively with replacement from a well shuffled deck of 52 playing cards. If getting a card of spade is considered a success, find the probability distribution of the number of successes.

Q.12 Find the equation of the plane that contains the point (1, -1, 2) and is perpendicular to each of the planes 2x + 3y – 2z = 5 and x + 2y – 3z = 8.

Q.13 Show that the points A(-2i + 3j + 5k), B(i + 2j + 3k) and C(7i – k) are collinear.

Q.14 Solve the differential equation : x log x (dy/dx) + y = 2 log x

Q.15 If the function defined by

is continuous at x = 2, find the value of a. Also discuss the continuity of f(x) at x = 3.

Q.16 Using the properties of determinants prove the following :

Q.17 Prove the following :

OR

Solve the following for x :

tan^-1 (x +1) + tan ^-1 (x -1) = tan^-1 (8/31) ; x > 0

Q.18 If y = e^{tan x}, prove that cos² x d²y/dx² – (1 + sin 2x) dy/dx = 0.

OR

If y = (x)^x + (cos x)^2x , find dy/dx

Q.19 If the function f : R → R is given by f(x) = (x+3)/2 and g : R → R is given by g(x) = 2x – 3, find

(i) fog and (ii) gof. Is f ^-1 = g ?

Q.20 Form the differential equation representing the family of ellipses having foci on x-axis and centre at the origin.

Q.21 Evaluate :

OR

Using properties of definite integrals, evaluate the following :

Q.22 Find the intervals^- in which the following function is :

(a) Increasing

(b) Decreasing

f(x) = x³ – 12x² + 36x + 17

OR

Find the equation of the tangent to the curve x² + 3y = 3, which is parallel to the line y – 4x + 5 = 0.