(iii) Show that points P(-2, 3, 5) Q(1, 2, 3) and R(7, 0, -1) are collinear. [1] Observe the two graphs, Graph 1 and Graph 2 given below and answer the questions that follow. (iv) Two honeybees are flying parallel to each other in the garden to collect the nectar. The path traced by Y Y  ( ) ( ) the bees is given r = i + 2 j + 3k + λ 2i + 3 j + 4 k . X (0, 0) X (0, 0) Graph 1 Graph 2
Find the value of tan -1  2 sin  2 cos-1   (a) Write the above-mentioned equation in Cartesian
  2
   form.
(b) Find the equation of the path traced by the other
honeybee passing through the point (2, 4, 5).

Evaluate: ∫ ( log x ) dx
 x -3 0 
symmetric matrix? Question 9

(a) Statement 1 is true and Statement 2 is false. In subparts (i) to (xi) choose the correct options and (b) Statement 2 is true and Statement 1 is false. in subparts (xii) to (xv), answer the questions as (c) Both the statements are true. instructed. (d) Both the statements are false. 0 a  16 1x -1
If A =   , then A is: (iv) ∫ 2 dx is equal to:
0 0  0 x +1

Write the smallest equivalence relation from the set
cos x
A to A, where A = {1, 2, 3}. (i) Evaluate: ∫ dx
3cos x - 5
 0 1 -2 
 OR

For what value of x, is A =  -1 0 3  a skew

2] 5 10 2  2 x +1 3x 
Statement 1: If ‘A’ is an invertible matrix, then (A2)-1
of the differential equation (1 + x2) dy + (1 + y2)
= (A-1)2
dx = 0
Statement 2: If ‘A’ is an invertible matrix, then |A-1|

(a) Statement 1 is true and Statement 2 is false. In subparts (i) to (xi) choose the correct options and (b) Statement 2 is true and Statement 1 is false. in subparts (xii) to (xv), answer the questions as (c) Both the statements are true. instructed. (d) Both the statements are false. 0 a  16 1x -1
Which of the following is a homogenous differential -2
equation? (c) (d) 0
(a) (4x2 + 6y + 5) dy - (3y2 + 2x + 4) dx = 0