Goa Board Class 12 Question Paper June 2019 Mathematics Vocational

2019 VI 10 1430 Seat No.

Time : 2 Hours Mathematics (Vocational)

Subject Code

V 3 1 1

Total No. of Questions : 5 (Printed Pages : 4) Maximum Marks : 50

INSTRUCTIONS : (i) Answer each question on a fresh page.

(ii) Write the number of questions and sub-questions

clearly.

(iii) All questions are compulsory.

(iv) Figures to the right indicate full marks.

(v) Use of logarithmic table is allowed.

(vi) Graph paper will be supplied on request.

1. (A) If 1

2 3 2
A= and B = ,
4 5 3

find (AB)T.

(B) Construct a backward difference table for the following data : 2

x 0 2 4 6 8 10

f(x) 10 14 17 21 27 35

Find 3y 2y .
6 and 8

[V-311] 1 P.T.O.

(C) Find 3

1 1
lim 2 2
.
1 2x 3x 2 6x x 1
x
2

(D) Solve the following L.P.P. by Graphical method : 4

Max. : Z = 5x + 7y

Subject to : 4x + 2y < 12

3x + 6y < 18

with x > 0, y > 0.

dy
2. (A) If y = (2x2 + 8)2, find . 1
dx

(B) If 2

2 1
A= ,
1 2

Show that A2 – 4A + 3I = O.

(C) Evaluate : 3

x · sin 5 x dx.

(D) If 4

cot x tan x
y tan x cot x ,

dy
find .
dx
[V-311] 2

3. (A) Evaluate : 1

5x 2
6 dx.

(B) Three cards are drawn from a well shuffled pack of 52 playing cards.

Find the probability of getting a picture card and two aces. 2

(C) Evaluate : 3

3
x
dx.
0
3 x x

(D) Find the regression line of x on y for the following data : 4

x 2 3 4 5 6

y 3 5 7 9 11

Also, find x when y = 4.

4. (A) If 1

4 5

2 k

is a singular matrix, find k.

(B) Evaluate : 2

x2 1
3
dx.
x 3x 5

(C) Evaluate : 3

10
x2 3 dx
4

by using trapezoidal rule when n = 6.

[V-311] 3 P.T.O.

(D) Find the inverse of : 4

1 2 1

1 1 1 .

1 4 1

5. (A) Evaluate : 1

tan2 7 x dx.

(B) Differentiate : 2

5 1
3 x2 4x 1 3
1 2x

with respect to x.

(C) Form a differential equations : 3

y = Ae4x + Be–4x + x2.

(D) Given that f(2) = 1, f(6) = 5, f(8) = 9 use Lagrange’s interpolation formula

to obtain f(4). 4

[V-311] 4