Goa Board Class 11 Sample Paper Maths

Sample Paper
&
Question Paper Pattern
2022
2023

GOA BOARD

Model question paper for online exam
Sub: Mathematics Time: 1 hr
Std: XI Commerce Marks: 20

INSTRUCTIONS: Questions 1 – 2 are MCQ type and carry 1 mark each; question 3 – 4 are
VSA type and carry 1 mark each; question 5 – 9 are SA type and carry 2
marks each; question 10 – 11 are LA type and carry 3 marks each.
Questions 1 – 2 carry 1 mark each.
Q.1. If A is the subsets of the universal set U, then A ∩ ( A∪ ∅ ) = __________________

(i) A (ii) B (iii) ∅ (iv) ∪
Q.2. Common difference of an arithmetic progression for which a 1=5 and a 6=30 is

____________
(i) 5 (ii) 10 (iii) 15 (iv) 20
Questions 3 – 4 carry 1 mark each.

Q.3. If A = { x : x ∈ N } and B = { x : x ∈ N , x 2 + 4 x−5=0 } , then find A ∩ B
Q.4. Solve 2 x−2<5 x +1

Questions 5 – 9 carry 2 marks each.
Q.5. In a school, 150 students were found to be drinking tea and 225 drinking coffee and
100 were drinking both tea and coffee. Find how many students were drinking tea or
coffee.

Q.6. For the set A= { x : x =2n , n ∈ N ,1 ≤ n ≤ 5 } and B= { x : x=2 n , n ∈ N ,1 ≤ n ≤ 5 } ,

Find A∪ B and A∩B

Q.7. Solve the inequation
5 x−2 7 x−3 x
− >
3 5 4
Q.8. Insert 3 numbers between 2 and 32 such that the resulting sequence is a G.P.
Q.9. Find the nth term of an A.P. whose 6th term is 12 and the 8th term is 22.
Questions 10 & 11 carry 3 marks each.

Q.10. Determine the number of terms in the A. P. 3, 7, 11, . . . , 407. Also, find their sum.

OR
Find the sum of all odd numbers between 100 and 200
Q.11. Solve the following system of linear inequations graphically
2 x+ y ≤6 ;
3 x+ 4 y ≤ 12 ;
x ≥0 ;
y≥ 0 .

BLUE PRINT
SUB: MATHEMATICS DURATION: 1 HOUR
STD: XI COMMERCE MARKS: 20

SR Content objectives t
N area o
O t
a
l
Knowledge Understanding Application Skill
Type MCQ VS S L MC VSA SA L M VS SA LA M VS S LA
A A A Q A CQ A C A A
Q
MARKS 1 1 2 3 1 1 2 3 1 1 2 3 1 1 2 3
1. SETS 1(A) 3 6(E) 5
(A) (A)
2. LINEAR 4(E) 7(A) 11
INEQUAL (A)
ITIES
3 SEQUEN 2(A) 8(E), 10
CES 9(A) (O)
&SERIES (D)
12 5 3

OBJECTIVES: DIFFICULTY LEVEL:
KNOWLEDGE - 0 EASY: 5 MKS (25%)
UNDERSTANDING- 12 MKS(60%) AVERAGE: 12 MKS(60%)
APPLICATION – 5 MKS(25%) DIFFICULT: 3 MKS(15%)
SKILL – 3 MKS(15%)

EXPECTED TIME FOR DIFFERENT TYPES OF QUESTION:

S.NO. FORM OF QUESTION Approx. time for Number of Approx. time for
each question in questions(n) each form of
mins(t) quest. In mins.
(n x t)
1. MCQ (1 mk each) 2 min 2 4
2. VSA(1 mk each) 3 min 2 6
3 SA(2 mks each) 6 min 5 30
4. LA(3 mks each) 8 min 2 16
11 56 min.
(4 min. for re-
checking)

Model question paper for online exam

Sub: Mathematics Time: 1 hr

Std : XI Science Marks: 20

INSTRUCTIONS : Questions 1- 2 are MCQ type and carry 1 mark each ; questions 3 – 4 are
VSA type and carry 1 mark each ; question 5 to 9 are SA type and carry 2
marks each; questions 10 & 11 are LA type and carry 3 marks each.

Questions 1- 2 carry 1 mark each.

Q. 1. Select and write the correct alternative.

A = { x / x is prime number } , B = { x/x2 – x - 6 =0 , x Z } , then A ∩ B is --------

i) ɸ ii) {3} iii) {2} iv) { 3, 2}

3 (𝑥−2) 5(2−𝑥)
Q.2. The set of values of xR such that ≤ is ______
5 3

i) [2,∞) ii) ( -∞,2] iii) ) ( -∞,-2) iv) ) [-2,∞)

Questions 3 – 4 carry 1 mark each.

Q.3. A = {1, ɸ} , then write the Power set of A.

Q.4. If the n th term of the sequence 9, 5, 1, -3……. is -35 . Find the value of n.

Question 5 to 9 carry 2 marks each.

Q.5. The sum of the 3rd and 4th term of a G.P is 60 and product of its first 3 terms is 1000. If
the first term is positive then find its 7th term.

Q.6. If five times the 5th term is equal to 10 times the 10th term of an A.P , then calculate its
15th term.

Q.7. Write the linear inequalities for the following shaded region.

Q.8. In a School there are 800 students appearing for Public Exam . If 25% of the students
answer Mathematics, 15% answer Biology and 40 students answer both Mathematics
and Biology. How many students answer Mathematics or Biology.

Q.9. A= { x/ x= 3n , n N, n≤6} ,B= { x/ x= 9n , n N, n≤6} . write A∩B in roster form.

Questions 10 & 11 carry 3 marks each

Q. 10. Solve the following system of linear inequations graphically.

X + 2y ≤ 8

-x + y ≥ 1

X–y ≤ 0

x, y ≥0

Q 11. A person saves Rs 500 in each of 4 months of his service . In each of the subsequent
months his saving increases by 50 more than the saving of immediate previous month.
In how many months his total earnings will be 13050?

OR

A square is drawn by joining the mid points of a given square . A third square is drawn
inside the 2nd square in the same way and the process continues. The side of the first
square is 20 cm. how many such squares can we construct so that the sum of their areas
is 775?