Goa Board Class 12 Question Paper 2022 Mathematics and Statistics

2022 XI 14 0230 Seat No.

Time : 1½ Hours FIRST-TERM MATHEMATICS &
STATISTICS
Subject Code

H 4 6 0 6

Total No. of Questions : 40 (Printed Pages : 16) Maximum Marks : 40

INSTRUCTIONS : (i) Every question has four choices A, B, C and D and only

one of them is the correct answer.

(ii) On the OMR sheet darken completely with a ball point

pen ONLY ONE bubble you consider as the most

appropriate answer.

(iii) Multiple markings are invalid.

(iv) Use Blue or Black ball point pen only.

(v) Do not fold the OMR sheet or use white ink.

(vi) For each question, you will be awarded ONE mark, if

you have darkened only the bubble corresponding to

the correct answer. In all other cases, you will get zero

mark. There is no negative mark.

(vii) Once the bubble is filled it is not possible to change

the answer.

(viii) Only one OMR sheet will be provided. Hence sufficient

care must be taken while darkening the bubble.

H-4606 [FT] 1 P.T.O.

1. Let f, g be real valued function defined as f ( x) 3x2 5 x and g( x) 2 x . The
value of ( f o g)(2) is .................... .

(A) 48

(B) 58

(C) 68

(D) 78

2. A function is said to have removable type of discontinuity at x = a
if ..................... .

(A) lim f ( x) f (a) lim f ( x)
x a x a

(B) lim f ( x) lim f ( x)
x a x a

(C) lim f ( x) f (a) lim f ( x)
x a x a

(D) lim f ( x) lim f ( x) f (a)
x a x a

xn 1
, if x 1
3. The function f ( x) x 1 is continuous at x = 1, then the value
k , if x 1

of k is .................... .

(A) n

(B) 1

(C) –1

(D) –n

H-4606 [FT] 2

2 x dy
4. If y , then at x = 1 is ...................... .
3 dx

(A) 3/2

(B) 2/3

(C) +1/3

(D) 3

x2 4x 5
5. If f ( x) ; x 1 is continuous at x = 1, then f(1) is .................... .
x 1

(A) 10

(B) 8

(C) 6

(D) 4

6. A square matrix is invertible i.e. A–1 exist if and only if matrix A
is ...................... .

(A) Singular matrix

(B) Skew-symmetric matrix

(C) Non-singular matrix

(D) Symmetric matrix

7. The derivative of 8x with respect to x is ...................... .

8x
(A)
log 8

(B) 8x
(C) 8 x log x

(D) 8 x log 8

H-4606 [FT] 3 P.T.O.

d2 y
8. If y 7 2 x log x , then is ........................ .
dx2

2
(A)
y

2
(B)
x

2
(C)
x

2
(D)
y

2 6 8
9. For A 5 3 8 , (A')' = ..................... .
11 9 7

(A) A'

(B) Zero matrix

(C) A

(D) Identity matrix

0 2 3
10. Matrix A 2 0 1 is skew-symmetric matrix, then the value of
x 1 0

x is ..................... .

(A) –3

(B) –2

(C) –1

(D) 0

H-4606 [FT] 4

7 1
11. Matrix is a singular matrix, then the value of is .................... .
2

2
(A)
7
7
(B)
2

2
(C)
7

7
(D)
2

2 3 x 3
12. If , then the value of x is ..................... .
4 5 2x 5

(A) 1

(B) 2

(C) 3

(D) 4

13. Let * be a binary operation on the Q 0, set of all non-zero rational
2ab
numbers defined by a * b a, b Q0 , then identity element in
3
Q0 is .................. .

3
(A)
2

3
(B)
2

2
(C)
3

2
(D)
3

H-4606 [FT] 5 P.T.O.

dy
14. If x x y , then .................... .
dx

(A) y(1 log x)

(B) (1 log x)

(C) x x (log x x)

(D) (log x x)

3 2
15. If A , then Adjoint of A is ................... .
7 1

1 2
(A)
7 3

3 2
(B)
7 1

7 1
(C)
3 2

2 3
(D)
1 7

16. If R is a relation defined on Z, the set of all integers given by
R {( x, y) : x y is multiple of 5}, then R is ................... .

(A) Reflexive and Symmetric

(B) Symmetric and Transitive

(C) Reflexive and Transitive

(D) An Equivalence Relation

H-4606 [FT] 6

2 x 3sin x
, x 0
17. The function f ( x) 3 x 2sin x is continuous at x = 0, then the
4k , x 0

value of k is .................... .

(A) 4

(B) 1

(C) –1

1
(D)
4

2 3 3 4
18. If X , then matrix X = ..................... .
4 2 5 1

5 7
(A)
1 1

5 7
(B)
1 1

5 7
(C)
1 1

5 1
(D)
7 1

1 1 2
19. For matrix A 0 2 3 , the co-factor of –2 is .................. .
3 2 4

(A) –3

(B) –2

(C) 2

(D) 3

H-4606 [FT] 7 P.T.O.

dy
20. If x y 5 , then ................... .
dx

x
(A)
y

x
(B)
y

y
(C)
x

y
(D)
x
i j
21. The matrix A aij of order 2 × 2, where elements are given by aij
j
is .................. .

2 3/2
(A)
3 2

2 3/2
(B)
3 2

3/2 2
(C)
2 3

2 3/2
(D)
3 2

22. If two rows (or columns) of a determinant are identical, then the value of
the determinant is ...................... .

(A) 0

(B) 1

(C) 2

(D) 3

H-4606 [FT] 8

dy
23. If x at 2 , y 2 at , then
dx
at t 1 is .................... .

(A) 1

(B) 2

(C) 3

(D) 4

24. The instantaneous rate of change of total cost at any level of output is
called .................... .

(A) Marginal cost

(B) Average cost

(C) Total cost

(D) None of the above

25. The binary operation * on Q defined by a * b a b ab for a, b Q . Set of
all rational numbers, then the value of 2 * 3 is ..................... .

(A) 10

(B) 11

(C) 12

(D) 13

26. The amount of the interest on the face value charged by banker or bill
broker, in order to make cash payment before the maturity of the bill against
its holding is called ...................... .

(A) True Discount

(B) Banker’s Discount

(C) Banker’s Gain

(D) Present Value

H-4606 [FT] 9 P.T.O.

27. In a partnership deed, on admission of a new partner the premium

for goodwill brought by the new partner is shared among old partners

in ........................ .

(A) New profit sharing ratio

(B) Gaining ratio

(C) Old profit sharing ratio

(D) Sacrificing ratio

28. Harpreet and Manpreet invested Rs. 10,000 and Rs. 5,000 in a partnership

business. Each partner is to receive 6% on the capital invested. If the total

profit after a year was Rs. 12,000. The net profit of that year is .............. .

(A) Rs. 11,000

(B) Rs. 11,100

(C) Rs. 11,200

(D) Rs. 11,300

29. If Heena and Leena are partners and invested Rs. 1,260 and Rs. 840

respectively, then the share of Heena in a profit of Rs. 1,210 after a

year is ...................... .

(A) Rs. 8,480

(B) Rs. 7,260

(C) Rs. 726

(D) Rs. 121

H-4606 [FT] 10

30. The difference between Total Revenue and Total Cost is called ................ .

(A) Break-even point

(B) Profit

(C) Marginal Revenue

(D) Average Cost

3 2
31. The revenue function is 21x x . Where x is the number of units
2
demanded, then ...................... number of units demanded to receive maximum
revenue.

(A) 5

(B) 6

(C) 7

(D) 8

32. The manufacturing cost of an item consists of Rs. 900 as overheads, the

x2
material cost Rs. 3 per item and labour cost is Rs. for x items produced.
10
Then the total cost for 10 items produced is ..................... .

(A) Rs. 640

(B) Rs. 740

(C) Rs. 840

(D) Rs. 940

H-4606 [FT] 11 P.T.O.

33. A bill of Rs. 10,00,000 due 10 months hence discounted now at a simple
interest of 6% p.a., then banker’s discount on a bill of exchange is .............. .

(A) Rs. 40,000

(B) Rs. 50,000

(C) Rs. 60,000

(D) Rs. 70,000

34. The banker’s discount and banker’s gain on a certain bill of exchange is due
after certain time are Rs. 1,150 and Rs. 50 respectively, then the true
discount is ..................... .

(A) Rs. 1,300

(B) Rs. 1,200

(C) Rs. 1,100

(D) Rs. 1,000

35. Amit and Sumit contribute as capital Rs. 40,000 and Rs. 35,000 respectively.
Amit is paid honorarium of Rs. 1,000 per month for one year and profit share
Rs. 8,000. Sumit is paid goodwill amount of Rs. 5,000 fixed and profit share
Rs. 10,000. The present worth of Amit is ...................... .

(A) Rs. 40,000

(B) Rs. 50,000

(C) Rs. 60,000

(D) Rs. 70,000

H-4606 [FT] 12

36. The revenue function for a certain product is represented by the equation

20 x 5 x2 3 x3 where x is the number of units demanded. Then the
marginal revenue when 2 units are sold is ....................... .

(A) Rs. 2

(B) Rs. 4

(C) Rs. 6

(D) Rs. 8

37. The cost of producing and marketing x units of a certain product

is given by c 3 x2 10 x 600 , then its Average Cost when 10 units
produced is .................... .

(A) Rs. 4,000

(B) Rs. 3,000

(C) Rs. 2,000

(D) Rs. 1,000

38. If the bill is drawn on 1st March, 2022 and its period is 4 months, then the

legal due date of the bill is ...................... .

(A) 1st July, 2022

(B) 2nd July, 2022

(C) 3rd July, 2022

(D) 4th July, 2022

H-4606 [FT] 13 P.T.O.

39. A bill of certain amount drawn on March 4th at 5 months is discounted on

June 10 of the same year. The period from the date of discounting to the

due date, t is .................... .

(A) 88 days

(B) 78 days

(C) 68 days

(D) 58 days

40. Shashi and Jack invested Rs. 15,000 and Rs. 18,000 in a hardware business.
At the end of year, their net loss was Rs. 2,640. The amount of loss borne

by Shashi is ........................ .

(A) Rs. 1,000

(B) Rs. 1,200

(C) Rs. 1,400

(D) Rs. 1,600

H-4606 [FT] 14

Space For Rough Work

H-4606 [FT] 15 P.T.O.

Space For Rough Work

H-4606 [FT] 16