KENDRIYA VIDYALAYA SANGATHAN GURUGRAM REGION
HALF YEARLY Examination 2024-25
11 - Mathematics (Code- 041) Time: 3 Hours MM-80
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 18 MCQ’s and 02 Assertion-Reason based questions of 1 mark each.
3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each.
4. Section C has 6 Short Answer (SA)-type questions of 3 marks each.
5. Section D has 4 Long Answer (LA)-type questions of 5 marks each.
6. Section E has 3 source based/case based/passage based/integrated units of assessment (4 marks each)
with sub parts.
SECTION A (Multiple Choice Questions)
Each question carries 1 mark
The number of the proper subset of {a, b, c} is:
(A) 3 (B) 8
1 (C) 6 (D) 7 1
1
If set A has 3 elements and set B has 6 elements then
2 (𝐴) 6 ≤ 𝑛(𝐴 ∩ 𝐵) ≤ 9 (𝐵) 6 ≤ 𝑛(𝐴 ∪ 𝐵) ≤ 9
(𝐶) 0 ≤ 𝑛(𝐴 ∩ 𝐵) ≤ 2 (𝐷) 3 ≤ 𝑛(𝐴 ∩ 𝐵) ≤ 6
If f(x) = −|x|. Choose the correct option from the following: 1
(A) Domain is set of negative real numbers (B) Range is set of real numbers
3 (C) Range is set of all negative integers (D) Range is (-∞, 0]
1
If 𝑓(𝑥) = 𝑥 𝑎𝑛𝑑 𝑔(𝑥) = |𝑥| , 𝑡ℎ𝑒𝑛 (𝑓 + 𝑔)(𝑥)𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜
4 (A) 0 for all 𝑥 ∈ 𝑅 (B) 2x for all 𝑥 ∈ 𝑅
2𝑥 , 𝑓𝑜𝑟 𝑥 ≥ 0 0 , 𝑓𝑜𝑟 𝑥 ≥ 0
(C) { (D) {
0 , 𝑓𝑜𝑟 𝑥 < 0 2𝑥 , 𝑓𝑜𝑟 𝑥 < 0
The radian measure of 520°.is
5 13𝜋 26𝜋 17𝜋 6𝜋 1
(A) 9 (B) 9 (C) (D)
9 9
The greatest value of 𝑠𝑖𝑛𝑥 𝑐𝑜𝑠𝑥 is 1
6 1
(𝐴) (𝐵) 2 (𝐶) √2 (𝐷) 1
2
The smallest positive integer for which (1 + 𝑖)2𝑛 = (1 − 𝑖)2𝑛 is 1
7
(a) 1 (b) 2 (c) 4 (d) 8
If 𝑥 = −1 + 𝑖 , 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑥 2 + 2𝑥 − 1 𝑖𝑠 1
8 (𝐴) − 3 (𝐵) 0 (𝐶) 1 (𝐷) − 1
Solution set of the inequality 5𝑥 − 1 > 3𝑥 + 7 𝑖𝑠 1
9 (𝐴) (−4, ∞) (𝐵) (−∞, −4) (𝐶) (4, ∞) (𝐷) (−4, −∞)
Number of words from the letters of the words BHARAT in which B and H will never come together 1
is:
10 a) 210 b) 240 c) 422 d) 400
If 𝑛𝐶12 = 𝑛𝐶8 , then 𝑛 is equal to
11 (A) 12 (B) 6 (C) 4 (D) 20 1
The total number of terms in the expansion of (𝑥 + 𝑎)51 − (𝑥 − 𝑎)51 after simplification:
HALF YEARLY Examination 2024-25
11 - Mathematics (Code- 041) Time: 3 Hours MM-80
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 18 MCQ’s and 02 Assertion-Reason based questions of 1 mark each.
3. Section B has 5 Very Short Answer (VSA)-type questions of 2 marks each.
4. Section C has 6 Short Answer (SA)-type questions of 3 marks each.
5. Section D has 4 Long Answer (LA)-type questions of 5 marks each.
6. Section E has 3 source based/case based/passage based/integrated units of assessment (4 marks each)
with sub parts.
SECTION A (Multiple Choice Questions)
Each question carries 1 mark
The number of the proper subset of {a, b, c} is:
(A) 3 (B) 8
1 (C) 6 (D) 7 1
1
If set A has 3 elements and set B has 6 elements then
2 (𝐴) 6 ≤ 𝑛(𝐴 ∩ 𝐵) ≤ 9 (𝐵) 6 ≤ 𝑛(𝐴 ∪ 𝐵) ≤ 9
(𝐶) 0 ≤ 𝑛(𝐴 ∩ 𝐵) ≤ 2 (𝐷) 3 ≤ 𝑛(𝐴 ∩ 𝐵) ≤ 6
If f(x) = −|x|. Choose the correct option from the following: 1
(A) Domain is set of negative real numbers (B) Range is set of real numbers
3 (C) Range is set of all negative integers (D) Range is (-∞, 0]
1
If 𝑓(𝑥) = 𝑥 𝑎𝑛𝑑 𝑔(𝑥) = |𝑥| , 𝑡ℎ𝑒𝑛 (𝑓 + 𝑔)(𝑥)𝑖𝑠 𝑒𝑞𝑢𝑎𝑙 𝑡𝑜
4 (A) 0 for all 𝑥 ∈ 𝑅 (B) 2x for all 𝑥 ∈ 𝑅
2𝑥 , 𝑓𝑜𝑟 𝑥 ≥ 0 0 , 𝑓𝑜𝑟 𝑥 ≥ 0
(C) { (D) {
0 , 𝑓𝑜𝑟 𝑥 < 0 2𝑥 , 𝑓𝑜𝑟 𝑥 < 0
The radian measure of 520°.is
5 13𝜋 26𝜋 17𝜋 6𝜋 1
(A) 9 (B) 9 (C) (D)
9 9
The greatest value of 𝑠𝑖𝑛𝑥 𝑐𝑜𝑠𝑥 is 1
6 1
(𝐴) (𝐵) 2 (𝐶) √2 (𝐷) 1
2
The smallest positive integer for which (1 + 𝑖)2𝑛 = (1 − 𝑖)2𝑛 is 1
7
(a) 1 (b) 2 (c) 4 (d) 8
If 𝑥 = −1 + 𝑖 , 𝑡ℎ𝑒𝑛 𝑡ℎ𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑥 2 + 2𝑥 − 1 𝑖𝑠 1
8 (𝐴) − 3 (𝐵) 0 (𝐶) 1 (𝐷) − 1
Solution set of the inequality 5𝑥 − 1 > 3𝑥 + 7 𝑖𝑠 1
9 (𝐴) (−4, ∞) (𝐵) (−∞, −4) (𝐶) (4, ∞) (𝐷) (−4, −∞)
Number of words from the letters of the words BHARAT in which B and H will never come together 1
is:
10 a) 210 b) 240 c) 422 d) 400
If 𝑛𝐶12 = 𝑛𝐶8 , then 𝑛 is equal to
11 (A) 12 (B) 6 (C) 4 (D) 20 1
The total number of terms in the expansion of (𝑥 + 𝑎)51 − (𝑥 − 𝑎)51 after simplification:
