DELHI PUBLIC SCHOOL, GURGAON

MONDAY TEST – I (2024-2025)

SUBJECT: APPLIED MATHEMATICS (241)
CLASS: XI, (12/08/2024)

Time: 1 hr 20 mins. M.M: 40

No. of Pages: 03
General Instructions:
1. This Question paper contains - five sections A, B, C, D and E. Each section is compulsory.
However, there are internal choices in some questions.
2. Section A has 9 MCQ’s and 01 Assertion-Reason based question of 1 mark each.
3. Section B has 2 Very Short Answer type questions of 2 marks each.
4. Section C has 4 Short Answer type questions of 3 marks each.
5. Section D has 2 Long Answer type questions of 5 marks each.
6. Section E has 01 case study based question of 4 marks with sub parts of value of two marks each.

SECTION A
(Multiple Choice Questions)
This section comprises of multiple-choice questions of 1 mark each.

Q1. How many three digits even numbers can be formed from the digits 1, 2,3,4,5 if the digits (1)
can be repeated?
(a) 120 (b)10 (c) 100 (d) 50

Q2. If nC9 = nC8 , then find nC17 (1)

(a) 1 (b) 10 (c) 9 (d) 5

Q3. Let 𝐴 = {𝑥, 𝑦, 𝑧} and 𝐵 = {1,2}. Find the number of relations from A to B. (1)

(a) 10 (b) 12 (c) 64 (d) 40

Q4. Let 𝑓 = {(1,1), (2,3), (0, −1), (−1, −3)} be a function from Z to Z defined by 𝑓(𝑥) = 𝑎𝑥 + 𝑏 for
some integers 𝑎, 𝑏. Find the values of 𝑎 𝑎𝑛𝑑 𝑏. (1)

(a) 𝑎 = 2, 𝑏 = −2 (b) 𝑎 = −2, 𝑏 = −3 (c) 𝑎 = 2, 𝑏 = −1 (d) 𝑎 = −2, 𝑏 = 4

Q5. If 𝐴 × 𝐵 = {(𝑎, 1), (𝑏, 3), (𝑎, 3), (𝑏, 1), (𝑎, 2), (𝑏, 2)}. Find set B. (1)
(a) {1,2} (b) {2,3} (c) {𝑎, 𝑏} (d) {1,2,3}

Q6. Find the equation of line perpendicular to the line 𝑥 − 7𝑦 + 5 = 0 and having 𝑥 intercept 3. (1)

(a) 7𝑥 + 𝑦 = 21 (b) 7𝑥 − 𝑦 = 21 (c) 𝑥 + 7𝑦 = 21 (d) 𝑥 + 𝑦 = 21

Q7. If 𝑅 = {(𝑥, 𝑦): 𝑥, 𝑦 ∈ 𝑊, 𝑥 2 + 𝑦 2 ≤ 4} then domain of R is (1)

(a) {0,1,2,3} (b) {0,1,2} (c) {0,2} (d) {0,2,3}

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Q8. If the points (𝑥, −1), (2,1) and (4,5) are collinear, then the value of 𝑥 is (1)
1
(a) 1 (b) 5 (c) 10 (d)
2

Q9. In how many ways can 3 prizes be distributed among 4 boys when a boy may get any number
of prizes? (1)
(a) 60 (b) 64 (c) 16 (d) 20
ASSERTION-REASON BASED QUESTION
In the following question, a statement of assertion (A) is followed by a statement of Reason (R).
Choose the correct answer out of the following choices.
(a) Both A and R are true and R is the correct explanation of A.
(b) Both A and R are true but R is not the correct explanation of A.
(c) A is true but R is false.
(d) A is false but R is true

Q10. Assertion (A) :If the line passing through (4,-5) and (7,-2) is parallel to the line joining (1)
(-2,3) and (𝑥, 7), then 𝑥 = −2.
Reason (R) : If two lines are parallel, then their slopes are equal.

SECTION B
This section comprises of very short answer type-questions of 2 marks each.

Q11. Find the domain for which the function 𝑓(𝑥) = 2𝑥 2 − 1 and 𝑔(𝑥) = 1 − 3𝑥 are equal. (2)
OR

Let 𝐴 = {1,2,3,4,6}.Let R be the relation on A is defined by

{(𝑎, 𝑏): 𝑎, 𝑏 𝐴, 𝑏 is exactly divisible by 𝑎}
(i) Write R in roster form
(ii) Find the range of R

𝑛! 𝑛!
Q12. Find the value of 𝑛 if 2!(𝑛−2)! ∶ = 2: 1 (2)
4!(𝑛−4)!

SECTION C
This section comprises of short answer type questions of 3 marks each.

1 1
Q13. If 𝑓(𝑥) = 𝑥 + 𝑥 , Prove that [𝑓(𝑥)]3 = 𝑓(𝑥 3 ) + 3𝑓 (𝑥) (3)

Q14. Find the equation of the line parallel to 𝑦 axis and drawn through the point of intersection of
the lines 𝑥 − 7𝑦 + 5 = 0 and 3𝑥 + 𝑦 = 0. (3)

OR
Find equation of the line passing through the point (3,4) and cutting off intercepts on the axes
whose sum is14.
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 𝑥 𝑦
Q15. Find the equation of a line drawn perpendicular to the line 4 + 6 = 1 through the point, where
it meets the y axis. (3)

Q16. How many words each of 3 vowels and 2 consonants can be formed from the letters of the (3)
word ‘INVOLUTE’.
SECTION D
This section comprises of long answer-type questions of 5 marks each.

Q17. The slope of a line is double of the slope of another line. If the tangent of the angle between (5)
1
them is 3 , Find the slope of the lines.

OR
A line perpendicular to the line segment joining the points (1,0) and (2,3) divides it in the ratio
1:𝑛. Find the equation of the line.

Q18. Find the domain and range of the following functions: (5)

(i) 𝑓(𝑥) = √9 − 𝑥 2
|𝑥−1|
(ii) 𝑓(𝑥) = 𝑥−1

SECTION E
This section comprises of a case study question of 4 marks. It has two sub parts
of two marks each.

Q19. Ram is walking along the sides of a triangular park whose two vertices are B (-4,1) and
C (2,11). When he reaches to the third vertex A, he realizes that point A is dividing the line
segment joining the points (3,1) and (6,4) in the ratio 2:1.

Based on the above information answer the following:

(a) What are the coordinates of third vertex A? (2)

(b) What is the equation of line passing through B and C? (2)

OR
What is the equation of line passing through A and parallel to BC?

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