ARMY PUBLIC SCHOOL NO-2 ROORKEE

FIRST PERIODIC TEST, 2024-25

Time: - 2Hrs CLASS – 11 ,SUBJECT:-MATHEMATICS (SCIENCE STREAM) M.M.:60
General Instructions:-
Read the following instructions very carefully and strictly follow them:
1. This question paper comprises of two parts- A & B, Part A carries 40 questions & part B carries 17 questions overall. All
questions are compulsory.
2. Part A- Question no.01 to 20 comprises of 20 Multiple Choice Questions of 1mark each.
3. Part B comprises of 5 Sections- A, B, C, D & E
4. Section A-Question no.1 to 4 comprises of 4 questions of one mark each.
5. Section B-Question no.5 to 8 comprises of 4 questions of two marks each.
6. Section C-Question no.9 to 12 comprises of 4 questions of three marks each.
7. Section D-Question no.13 & 14 comprises of 2 questions of five marks each.
8. Section E-Question no.15 & 16 comprises of 2 questions of three marks each.
9. There will be negative marking for each wrong attempt in Part-A. For every wrong attempt 1 marks will be deducted however
for any un attempted question neither marks will be awarded nor will be deducted
10. There is no overall choice. However, an internal choice has been provided in one question of each section of Part-B except for
Section E.
11. In addition to this, separate instructions are given with each section and question, wherever necessary.
12. Please write down the Serial Number of the question before attempting it.
13. Reference figure or construction must be drawn using pencil subject to scale wherever required.
14. Use of Calculator is not permitted.

1. The function ′t′ which maps temperature in degree Celsius into temperature in degree Fahrenheit is
9
defined by t(C) = C +32. Then t(28) is :
5
(a) 83.2 (b) 83.7 (c) 82.4 (d) 82
2. The range of the real function f(x)=−|x| is:
(a) R (b) (-∞,0] (c) (-∞,0) (d) Z
x 2 5 1
3. If ( 3 +1, y− 3 )= ( 3 , 3 ), then the values of x and y are:
(a) x=2, y=1 resp. (b) x=3, y=2 resp. (c) x=3, y=3 resp. (d) x=2, y=3 resp.
4. For a relation R: A  B if all the elements of set B have a pre-image in set A then
(a) Domain= Range (b) Domain = Codomain (c) Range= Codomain (d) None of these
2
x + 2 x +1
5. The domain of the function f(x)= 2 .
x −8 x+12
(a) R−{2,6} (b) {-1,-1} (c) R−{-1,-1} (d) R−{2,6}
6. Which of the following given sets is finite?
(a) The set of numbers which are multiple of 5 (b) The set of circles passing through the origin (0,0)
(c) The set of animals living on the earth (d) The sets of lines which are parallel to x axis
7. If A⊂B then which of the following is incorrect?
(a) A−B=∅ (b) A∪B=A (c) A∪B=B (d) A∩B=A
8. A - B can also also be considered as:
(a) (A∪B)′ (b) A∪B′ (c) (A∩B)′ (d) A∩B′
9. Total number of proper subsets of a set having ‘n’ elements is given by:
(a) 2n (b) 2n−1 (c) 2n × n (d) 2n−1
10. How many 3-digit even numbers cab be formed from the digits 1, 2, 3, 4, 5, 6 if the digits can be
repeated?
(a) 108 (b) 109 (c) 110 (d) 111
1 1 x
11. + = Then x is equal to:
6! 7! 8!
(a) 62 (b) 63 (c) 64 (d) 65
12. Given 5 flags of different colours, how many different signals can be generated if each signal
requires the use of 2 flags, one below the other?
(a) 20 (b) 21 (c) 22 (d) 23
 19 π
13. tan =
3
1
(a) (b) √ 3 (c)1 (d) None of these
√3
14. If x lies in 4th Quadrant then x/2 lies in
(a) 1st Quadrant (b) 2nd Quadrant (c) 3rd Quadrant (d) 4th Quadrant
15. sin 7650 =

(a)
1
(b)
1
(c)
√3 (d) 1
√2 2 2
16. A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?
(a) 12 π (b) 2 π (c) 20 π (d) 15 π
17. Value of i(iota) is ____________
(a) -1 (b) 1 (c) (-1)1/2 (d) (-1)1/4
18. (x+3) + i(y-2) = 5+i2, find the values of x and y.
(a) x=8 and y=4 (b) x=2 and y=4 (c) x=2 and y=0 (d) x=8 and y=0
19. 1/z is _________________ for complex number z.
(a) additive inverse (b) additive identity element
(c) multiplicative identity element (d) multiplicative inverse
20. The value of √ −25+3 √ −4 +2 √−9 is
(a) 13i (b) -13i (c) 17i (d) -17i

PART-B
Section-A
1. Convert these sets into roster form:
−1 9
(i) B = { x : x is an integer ; <x< }
2 2
(ii) E = { x : x is a month of a year not having 31 days }
2. A coin is tossed 3 times and the outcomes are recorded. How many possible outcomes are there?
3. Convert 250 into radian.
OR
Find the angle in radian through which a pendulum swings if its length is 7575 cm and the tip
describes an arc of length 10 cm.
4. Express i−39 in the form a+ib.

Section-B

5. If U= {1,2,3,4,5,6,7,8,9} , A = {2,4,6,8} and B={2,3,5,7} . Verify both De morgan’s law for set A & B .
6. Draw the graph of any rational function.
OR
Draw the graph of any polynomial functions.

√
2 2
7. If x – i y =
a− ⅈb prove that ( x 2 + y 2 )2= a +b .
2 2
c− ⅈd c +d
8. Find the real numbers x & y if ( x − i y )( 3 + 5 i) is the conjugate of −6−24 i .

Section-C

9. Let A, B and C be the set such that A∪B = A∪C and A∩B = A∩C. Show that B = C .

Let A and B be sets. If A∩X = B∩X = ∅ and A∪X = B∪X for some set X, show that A=B.
OR

2 ) : x ∈ R } be a function from R to R. Determine the range of f .

2
x
10. {
Let f = (x ,
1+ x
sin x−sin 3 x
11. Prove that 2 2 = 2sinx.
sin x −cos x
12. Reduce ( 1−41 ⅈ − 1+2 ⅈ )( 3−4
5+ ⅈ )
ⅈ
to the standard form.

Section-D

13. (i) Prove that cos 6x =32 cos6x-48 cos4x+18 cos2x-1. (2)
(ii) Prove that cot x cot 2x-cot 2x cot 3x-cot 3x cot x=1. (2)
(iii) Prove that cos22x-cos26x=sin 4x sin 8x. (1)

14. (i) Find r if 5Pr = 2 6Pr-1 . (3)

(ii) In how many ways can a student choose a programme of 5 courses if 9 courses are available
and 2 specific courses are compulsory for every student? (2)
OR
(i) How many words, with or without meaning, each of 2 vowels and 3 consonants can be formed
from the letters of the word DAUGHTER? (2)
(ii) In an examination, a paper consists of 12 Qs divided into 2 parts i.e., Part I and Part II,
containing 5 and 7 Qs, respectively. A student is required to attempt 8 Qs in all, selecting at
least 3 from each part. In how many ways can a student select the Qs? (3)

Section-E
15. Case Study-1

Five students Ajay, Shyam, Yojana, Rahul and Akansha are sitting in a playground in a line.
(a) Find the total number of ways for sitting arrangement of five students. (1)
(b) Find the total number of ways in which Ajay and Yojana can sit together. (1)
(c) Find the total number of ways in which Rahul and Yojana not sit together. (1)

16. Case Study-2

5
If tan x= & x lies in III rd quadrant
12
(i) sin 2x
(ii) cos2x
(iii) cos 4x .