2] (i) A building is to be constructed in the form of a triangular pyramid ABCD as shown in the figure. Let the angular points be A (0, 1, 2), B (3, 0, 1), C (4, 3, 6) and D (2, 3, 2) and let G be the point of intersection of the medians of ∆BCD. Using the above information, answer the following (a) What will be the length of vector ⃗⃗⃗⃗⃗⃗ AG ? (b) Find the area of ∆ABC. OR
What are the values of x for which the angle between the vectors?
2x 2 î + 3xĵ + k̂ and î - 2ĵ + x 2 k̂ is obtuse?

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