Sample Question Paper M.Sc. (Mathematics Education) Number of Questions: 51 Time Allowed: 1 hr. Booklet Contains pages: Maximum Marks: 85 DO NOT OPEN THE TEST BOOKLET UNTIL ASKED TO DO SO BY THE INVIGILATOR Particulars to be filled by the applicant Name of the candidate Roll No. Date of Examination Candidate’s Signature Signature of Invigilator ______________________________________ INSTRUCTIONS TO THE CANDIDATES 1. If your roll no. is 34567, then please enter your roll no. in OMR sheet as 2. Each question carries a weightage of 5/3 marks. 3. There is no negative marking. 4. Use only BLUE or BLACK BALL POINT PEN for completely darkening the answer circle. For Example: 5. Rough work is to be done only on the Test Booklet and not on the answer sheet. 6 . Any unfair means like copying, helping others, possession of any objectionable written/printed material, calculator, mobile phone, cordless phone, communication device, pager, scanner or other device (whether or not such materials/devices are used in the entrance examination) will lead to disqualifications from examination. 7. Candidates should hand over the answer sheet (OMR sheet) to the invigilator at the end of the examination. 8. Applicant shall carry this question booklet after the examination is over. 9. The answer keys of this test will be posted on the website of University of Delhi (http://du.ac.in), CIC (http://ducic.ac.in) and Jamia Millia Islamia (http://jmi.ac.in) The applicant must check the result of Entrance Test and Schedule of Interview of shortlisted candidates displayed on notice board of Cluster Innovation Centre, University of Delhi or on the websites of University of Delhi (http://du.ac.in), CIC (http://ducic.ac.in ) & Jamia Millia Islamia (http://jmi.ac.in). No separate communication will be made regarding this. 1 SHEET FOR ROUGH WORK
2 1.
Which of the following values is not possible?
!!! !
A. 𝑠𝑖𝑛𝜃 = !!! !
!!! !
B. 𝑐𝑜𝑠𝜃 = !!! ! , 𝑡 ≠ ±1
!!! !
C. 𝑡𝑎𝑛𝜃 = !!! !
!!! !
D. 𝑠𝑒𝑐𝜃 = !!! ! , 𝑡 > 1
2. Which of the following is not true?
A. 0 ∈ {0, 0 }
B. {0} ∈ {0, 0 }
C. {0} ⊂ {0, 0 }
D. 0 ⊂ {0, 0 }
3. In a class of 40 students, everyone opts for either NSS or NCC. If 25 opt for NSS and 30
opt for NCC, how many students opt for only NSS?
A. 15
B. 5
C. 10
D. 20
4. The diagram given below shows that
!
A.
B.
C.
D.
a"
1"
2"
b!
3"
c"
4"
f:A"
"""B"
f is a one – one function from A to B
f is an onto function from A to B
f is a bijective function from A to B
f is not a function
3 5. The graph given below represents the function
A.
B.
C.
D.
sin x +1
cos x + 1
sin (x + 1)
cos (x + 1)
6. Sum of the first 10 terms of the series 2 + 8 + 18 + 32 + ⋯ is
A.
B.
C.
D.
55 2
110
110 2
55
7. The figure given below is to be coloured using three different colours: red, green and blue
in such a way so that no two triangles having the same side have the same colour. The
number of ways this can be done is
A.
B.
C.
D.
1
6
24
48
4 8. The vertices of a triangle are A (1, - 1), B (2, 1) and C (6 , 5) . The length of the median
through A is
A. 5
B. 2.5
C. 5
D. 2 5
Directions for questions 9 – 12 : Consider the curves
C1 : y2 – 4 a x = 0, a > 0
C2 : x2 + y2 + x + y = 0
C3 : x2 – 2 x + y = 0
C4 : y – a x = 0, a < 0
9. The curve/s which lie/s in the 2nd and 4th quadrant only is/are
A. C1 only
B. C2 only
C. C4 only
D. C1 and C3 only
10. The conic/s with eccentricity 1 is/ are
A.
B.
C.
D.
C1 only
C2 only
C4 only
C1 and C3 only
11. The curve/s that lie/s on the right of y – axis is/ are
A.
B.
C.
D.
C1 only
C2 only
C4 only
C1 and C3 only
12. The conic/s with eccentricity 0 is/ are
A.
B.
C.
D.
C1 only
C2 only
C4 only
C1 and C3 only
5 13. Two variables X and Y are related to each other by the relation ax + by + c = 0 where
𝑎𝑏 > 0. Then the correlation coefficient between X and Y is
A.
B.
!
!
−
!
!
C. 1
D. −1
14. The equation 𝑥 −
A.
B.
C.
D.
!
!!!
=2−
!
!!!
has
exactly two roots
exactly one root
infinitely many roots
no roots
15. Let A =
a
0
0
b
and B
=
1
3
2
4
where a, b ∈N. Then,
A. there exists infinitely many matrices B such that AB = BA
B. there exist more than one but finite number of matrices B such that AB = BA
C. there exist exactly one matrix B such that AB = BA
D. there cannot exist a matrix B such that AB = BA
16. The determinant of a 3 x 3 matrix A is 4. Then the determinant of matrix B = 2 A2 is
A.
B.
C.
D.
128
32
16
8
17. The equation of the curve, whose slope at any point different from the origin is 𝑦 + 𝑦𝑥 is
A.
B.
C.
D.
y = xex + C
y = C xex
xy = C ex
y + xex = C
6 18. If R and S are any two arbitrary events then
A.
B.
C.
D.
P (R ∪
P (R ∩
P (R ∩
P (R ∪
S) ≤ P (R) + P(S)
S) ≥ P (R) + P(S)
S) = P (R) + P(S)
S) = P (R) + P(S)
19. In the following figure a square is circumscribed by a circle that is inscribed in a bigger
square. If the side of the smaller square is ‘a’, then the area of the shaded portion is
𝑎!
A.
!!!
!
!!!
𝑎!
!
! !!!
B.
𝑎
C.
!
!!!
𝑎!
!
D.
20. If the graph of the function 𝑦 = 𝑓(𝑥) is symmetrical about the line 𝑥 = 2, then
𝑓
𝑓
𝑓
𝑓
A.
B.
C.
D.
𝑥 + 2 = 𝑓(𝑥 − 2)
2 + 𝑥 = 𝑓(2 − 𝑥)
𝑥 = 𝑓(−𝑥)
𝑥 = −𝑓(−𝑥)
21. Let 𝑓 𝑥 =
!
!!!"#$
!!!!
,
𝑥≠
!
!
, 𝑥 ∈ 0,
𝑓( ! ) is
A.
B.
C.
D.
1
1/2
−1/2
−1
7 !
!
, if
!
𝑓 𝑥 is continuous in 0, ! , then
22. Inverse function of 𝑦 = 2𝑥 − 3 is
!!!
A.
B.
C.
D.
!
!!!
!
1
2𝑥−3
1
− 2𝑥+3
23. Value of
A.
B.
C.
D.
!/!
!"# !
𝑑𝑥
!
!"# !! !"# !
is
𝜋/2
𝜋/4
𝜋/6
𝜋/8
24. Rohit scored 65% in English, 70% in Hindi and 85% in Mathematics. If marks of Science
is also added, then his average score cannot be less than
A.
B.
C.
D.
55%
60%
75%
65%
25. Here is the solution given by a student:
lim𝑥→3
𝑥2 −9
(!!!)
=
Following are possible options related to error in the solution
(i)
dropping the limit sign
(ii)
ignoring the common terms
(iii)
(iv)
!
!
≠0
solution has no error
Which of the following options are correct?
A.
B.
C.
D.
Only (i), (ii) and (iii)
Only (i) and (ii)
Only (iii)
Only (iv)
8 32 −9
(!!!)
!
= =0
!
26. If ‘a’ and ‘b’ are two real numbers then the relation 𝑎𝑏 = 𝑎. 𝑏 is:
A.
B.
C.
D.
Never true
Always true
True when ‘a’ and ‘b’ are integers
True when ‘a’ and ‘b’ are positive real numbers
27. When the given sheet of paper X is folded to form a die, the resultant die will be
(X)
A.
B.
C.
D.
(1)
(2)
(3)
(1) only
(2) only
(1) and (3) only
All of (1), (2), (3) and (4)
28. The number represented by the question mark (?) in the figure given below is
A.
B.
C.
D.
22
12
28
16
9 (4)
29. A square piece of paper is folded and punched as shown in the figure
When the paper is unfolded it will closely resemble
FIGURE 1
A. FIGURE 1
B. FIGURE 2
C. FIGURE 3
D. FIGURE 4
FIGURE 2
FIGURE 3
FIGURE 4
30. What number must be replaced by the question mark (?) in the figure below so that the
numbers in each triangle follow the same pattern?
A.
B.
C.
D.
10
30
9
12
31. What are the minimum numbers of straight lines needed to make the following figure?
A.
B.
C.
D.
12
18
14
16
10 32. You want to select monitor of your class. Which of the following criteria will you follow:
A.
B.
C.
D.
Democratic choice
Physical built
High achiever
Pleasant personality
33. The book, “Towards New Education” has been written by:
A.
B.
C.
D.
Rabindranath Tagore
Mahatma Gandhi
J. Krishnamurthy
Swami Vivekananda
34. The role of National Assessment and Accreditation Council (NAAC) is to:
A.
B.
C.
D.
assess and accredit institutions of higher learning
provide funding for research
grant affiliation
grant approval
35. The latest National Level document which suggest framework for teaching of mathematics
at school level is:
A. Position paper on teaching of mathematics by NCERT in 2005
B. Formative Assessment teacher’s manual for Mathematics by CBSE
C. National Knowledge Commission report
D. Mathematics Lab Manuals by CBSE
36. Jawahar Navodaya Vidayalayas are established to provide quality education to:
A.
B.
C.
D.
Economically weaker children from cities
Talented children from rural areas
Academically weaker children
Only for primary grade children
37. The larger aim of education should be
A.
B.
C.
D.
To prepare students for examination
To prepare students for future jobs
To prepare students for vocational skills
To prepare students for life
38. PISA stands for:
A.
B.
C.
D.
Program for International Student Assessment
Program for Indian Student Assessment
Performance of International Students Assessment
Performance of Indian Students Assessment
11 39. Right to Education Act provides for the:
A. free and compulsory education till completion of primary education in a neighborhood
school
B. free and compulsory education till completion of elementary education in a
neighborhood school
C. free and compulsory education to children from disadvantaged groups
D. free and compulsory education to all child
40. The first “National Policy Statement on Education” came into existence on:
A.
B.
C.
D.
1968
1986
1992
1947
41. The mission “Sarva Shiksha Abhiyan (SSA)” stands for:
A.
B.
C.
D.
Universalization of Elementary Education (UEE)
Education for Disabled
Inclusive Education
Integrated Education
42. What is common among Rahul Gandhi, Narendra Modi, Arvind Kejriwal and Mayawati?
A.
B.
C.
D.
All are science graduates.
All are born in independent India.
All are former Chief Minister.
All have won Lok Sabha election at least once.
43. Which of the following is NOT TRUE about Google?
A. Google is an American multinational corporation specializing in Internet-related
services and products.
B. Google was founded by Larry Page and Sergey Brin while they were Ph.D. students at
Stanford University.
C. Google’s mission statement is "to organize the world's information and make it
universally accessible and useful".
D. Google search engine was launched on September 15, 1990.
44. Identify the INCORRECT statement.
A. National Capital Region (NCR) of Delhi includes the neighbouring cities of Alwar,
Baghpat, Gurgaon, Sonepat, Faridabad, Ghaziabad, Noida and Greater Noida.
B. University of Delhi was established in 1922.
C. Presently, E. Sreedharan is Managing Director of Delhi Metro Rail Corporation.
D. The walls of Red Fort are made up of red sandstone.
12 45. This Indian mathematician was born on 22 December 1887 and made extraordinary
contributions to mathematical analysis, number theory, infinite series, and continued
fractions. It was in recognition of his/her contribution to mathematics the Government of
India decided to celebrate his/her birthday as the National Mathematics Day every year.
This genius died in 1920 at the age of 32. Identify the great Indian mathematician with
above description.
A. Srinivasa Ramanujan
B. Aryabhata
C. Sundararaman Ramanan
D. Radhanath Sikdar
46. Which of the following fundamental constant’s value is NOT correctly depicted?
A.
B.
C.
D.
Speed of light = 3.00 X 108 m/s
Acceleration due to gravity = 980 m/s2
Electronic charge = 1.60 X 10-19 coulomb
Avogadro’s Number = 6.02 X1023 molecules/mole
Directions for questions 47 – 49 :
Complete the following sentences with the best option that reflects the sentences’ overall
meaning.
47. Normally a thunderstorm lasts about forty five minutes, but under certain conditions the
storm may _ _ _ _ , becoming even more severe, for as long as four hours.
A. wane
B. moderate
C. persist
D. dispense
48. If you are trying to make a strong impression on your audience, you cannot do so by being
understated, tentative, or _ _ _ _ _.
A. hyperbolic
B. restrained
C. passionate
D. suspicious
49. Some students are _ _ _ _ and want to take only the courses for which they see immediate
value.
A. theoretical
B. impartial
C. pragmatic
D. idealistic
13 Directions for questions 50 – 51 : Pick up the appropriate antonym for the capitalized word.
50. INDUSTRIOUS
A.
B.
C.
D.
Stupid
Harsh
Indolent
Inexpensive
51. GRANDIOSE
A.
B.
C.
D.
Docile
Unimposing
Uncommunicative
Magnificent
14