Goa Board Class 12 Question Paper Mar 2019 Mathematics _Voc_

2019 III 09 1000 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

1 a
A=
3 7

then find A + AT where AT is the transpose of A.

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

x 12 22 32 42 52 62

y –3 –5 –2 0 5 7

Find 3y 5y
32 and 62.

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

(C) If f is continuous on [–2, 7] where 3

2 x2 ax 2b 2 x 0

f x 7x 3 0 x 3

4 ax 3b 3 x 7

Find the value of a and b.

(D) Solve the following linear programming problem using Graphical

method : 4

Minimize : Z = x + 4y

Subject to : x + 3y > 3

2x + y > 2

x > 0 and y > 0.

dy
2. (A) If y = x4 + 4x + 44, find . 1
dx

(B) If 2

2 5 3 2 x
1
A= 1 7 ,B= 5 1 ,C= ,X= y ,
0
5 6 1 4 z

find the values of x, y and z if X = (4A – 7B)C.

(C) Evaluate : 3

x3 log x dx.

[V-311] 2

(D) If 4

x a sin cos , y a cos sin ,

dy
find .
dx

3. (A) Evaluate : 1

sin 3 x 5 e 3x 5
dx.

(B) A ten rupees gems packet contains 6 red gems, 3 blue gems, 5 yellow

gems, 3 purple gems and 3 pink gems. If two gems are drawn at random

from the packet, find the probability that one is red and the other is

a yellow gem. 2

(C) Evaluate : 3

1
1
dx.
0 x 1 x

(D) Find the coefficient of correlation for the following data : 4

x 1 2 3 4 5

y 4 5 6 7 8

4. (A) If 1

4 b
A = and |A| = 4
2 3

find the value of b.

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

(B) Evaluate : 2

1 1
dx.
x log x x

(C) Evaluate : 3

8
x 3 dx
0

using trapezoidal rule for 8 strips.

(D) Solve the following using matrix method : 4

2x + y – z + 2 = 0, 3x – z = 5, 4y + 3z = 9.

5. (A) Evaluate : 1

x 2cot x . cosec x dx.

dy
(B) If y = x3 log (sin x), find . 2
dx

(C) Form the differential equation : 3

y = Ae2x + Be–2x + x2,

where A and B are arbitrary constants.

(D) Given that f(0) = 4, f(2) = 6, f(4) = 8. Using Lagrange’s inverse interpolation

formula find the value of x when f(x) = 7. 4

[V-311] 4