Board Paper of Class 12-Humanities 2023 Math Delhi(Set 3) - Solutions
General Instructions:
Read the following instructions very carefully and follow them:
(i) This question paper contains 38 questions. All questions are compulsory.
(ii) Question paper is divided into FIVE Sections-Section A, B, C, D and E.
(ii) In Section A - Question Number 1 to 18 are Multiple Choice Questions (MCQ) type and Question Number 19 & 20 are Assertion-Reason based questions of 1 mark each.
(iv) In Section B - Question Number 21 to 25 are Very Short Answer (VSA) type questions of 2 marks each.
(v) In Section C - Question Number 26 to 31 are Short Answer (SA) type questions, carrying 3 marks each.
(vi) In Section D - Question Number 32 to 35 are Long Answer (LA) type questions carrying 5 marks each.
(vii) In Section E - Question Number 36 to 38 are case study based questions carrying 4 marks each where 2 VSA type questions are of 1 mark each and 1 SA type question is of 2 marks. Internal choice is provided in 2 marks question in each case-study.
(viii) There is no overall choice. However, an internal choice has been provided in 2 questions in Section B - 3 questions in Section C, 2 questions in
Section-D and 2 questions in Section - E.
(ix) Use of calculators is NOT allowed.
- Question 1
Let R be a relation in the set N given by
R = {a, b): a = b − 2, b > 6}.
Then
(a) (8, 7) ∊ R
(b) (6, 8) ∊ R
(c) (3, 8) ∊ R
(d) (2, 4) ∊ R VIEW SOLUTION
- Question 2
If and A = AT, where AT is the transpose of the matrix A, then
(a) x = 0, y = 5
(b) x = y
(c) x + y = 5
(d) x = 5, y = 0 VIEW SOLUTION
- Question 3
- Question 4
If for a square matrix, A, A2 − A + I = O, then A−1 equals
(a) A
(b) A + I
(c) I − A
(d) A − I VIEW SOLUTION
- Question 5
- Question 6
- Question 7
- Question 8
The function f(x) = [x], where [x] denotes the greatest integer less than or equal to x, is continuous at
(a) x = 1
(b) x = 1.5
(c) x = −2
(d) x = 4 VIEW SOLUTION
- Question 9
The function f(x) = x3 + 3x is increasing in interval
(a) (−∞, 0)
(b) (0, ∞)
(c)
(d) (0, 1) VIEW SOLUTION
- Question 10
- Question 11
equals
(a) sec x − tan x + c
(b) sec x + tan x + c
(c) tan x − sec x + c
(d) −(sec x + tan x) + c VIEW SOLUTION
- Question 12
The order and the degree of the differential equation respectively are:
(a)
(b) 3, 1
(c) 3, 3
(d) 1, 2 VIEW SOLUTION
- Question 13
- Question 14
Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is
(a)
(b)
(c)
(d) VIEW SOLUTION
- Question 15
If for any two events A and B, P(A) and P(A ∩ B), then P(B/A) is equal to
(a)
(b)
(c)
(d) VIEW SOLUTION
- Question 16
The angle between the lines 2x = 3y = −z and 6x = −y = −4z is
(a) 0°
(b) 30°
(c) 45°
(d) 90° VIEW SOLUTION
- Question 17
If a line makes angles of 90°, 135° and 45° with the x, y and z axes respectively, then its direction cosines are
(a)
(b)
(c)
(d) VIEW SOLUTION
- Question 18
- Question 19
Assertion (A):
Reason (R):
(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 and (R) is false.
(d) (A) is false, but (R) is true. VIEW SOLUTION
- Question 20
Assertion (A): Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least one head comes up, is .
Reason (R): Let E and F be two events with a random experiment, then
(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 and (R) is false.
(d) (A) is false, but (R) is true. VIEW SOLUTION
-
Board Paper of Class 12-Humanities 2023 Math Delhi(Set 1) - Solutions
-
Board Paper of Class 12-Humanities 2023 Math Delhi(Set 2) - Solutions
-
Board Paper of Class 12-Humanities Term-II 2022 Math Delhi(Set 1) - Solutions
-
Board Paper of Class 12-Humanities Term-II 2022 Math Delhi(Set 2) - Solutions
-
Board Paper of Class 12-Humanities Term-II 2022 Math Delhi(Set 3) - Solutions
-
Board Paper of Class 12-Humanities Term-I 2021 Math Delhi(Set 4) - Solutions
-
Board Paper of Class 12-Humanities 2020 Math Delhi(Set 1) - Solutions
-
Board Paper of Class 12-Humanities 2020 Math Delhi(Set 2) - Solutions
-
Board Paper of Class 12-Humanities 2020 Math Delhi(Set 3) - Solutions
-
Board Paper of Class 12-Humanities 2019 Math Delhi(Set 1) - Solutions
-
Board Paper of Class 12-Humanities 2019 Math Delhi(Set 2) - Solutions
-
Board Paper of Class 12-Humanities 2019 Math Delhi(Set 3) - Solutions
-
Board Paper of Class 12-Humanities 2019 Math Abroad(Set 3) - Solutions
-
Board Paper of Class 12-Humanities 2018 Maths Delhi(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2018 Maths Delhi(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2018 Maths Delhi(SET 3) - Solutions
-
Board Paper of Class 12-Humanities 2018 Maths - Solutions
-
Board Paper of Class 12-Humanities 2018 Maths - Solutions
-
Board Paper of Class 12-Humanities 2017 Maths Delhi(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2017 Maths Delhi(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2017 Maths Delhi(SET 3) - Solutions
-
Board Paper of Class 12-Humanities 2017 Maths All India(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2017 Maths All India(SET 3) - Solutions
-
Board Paper of Class 12-Humanities 2017 Maths Abroad(SET 3) - Solutions
-
Board Paper of Class 12-Humanities 2016 Maths Delhi(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2016 Maths Delhi(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2016 Maths Delhi(SET 3) - Solutions
-
Board Paper of Class 12-Humanities 2016 Maths All India(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2016 Maths Abroad(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2015 Maths Delhi(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2015 Maths Delhi(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2015 Maths Delhi(SET 3) - Solutions
-
Board Paper of Class 12-Humanities 2015 Maths All India(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2015 Maths Abroad(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2014 Maths Delhi(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2014 Maths All India(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2014 Maths Delhi(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2014 Maths Abroad(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2014 Maths Delhi(SET 3) - Solutions
-
Board Paper of Class 12-Humanities 2013 Maths Delhi(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2013 Maths Delhi(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2013 Maths Delhi(SET 3) - Solutions
-
Board Paper of Class 12-Humanities 2013 Maths All India(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2013 Maths All India(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2012 Maths Delhi(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2012 Maths Delhi(SET 3) - Solutions
-
Board Paper of Class 12-Humanities 2012 Maths All India(SET 3) - Solutions
-
Board Paper of Class 12-Humanities 2011 Maths Delhi(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2011 Maths Abroad(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2011 Maths Delhi(SET 3) - Solutions
-
Board Paper of Class 12-Humanities 2010 Maths Delhi(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2010 Maths All India(SET 2) - Solutions
-
Board Paper of Class 12-Humanities 2008 Maths Delhi(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2007 Maths Delhi(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2006 Maths Delhi(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2005 Maths Delhi(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2005 Maths All India(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2004 Maths Delhi(SET 1) - Solutions
-
Board Paper of Class 12-Humanities 2004 Maths All India(SET 1) - Solutions