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MATHEMATICS
(Three hours)
(Candidates are allowed additional 15 minutes for only reading the paper
...
)
--------------------------------------------------------------------------------------------------------------------The Question Paper consists of three sections A, B and C
...

Section B: Internal choice has been provided in two questions of four marks each
...

All working, including rough work, should be done on the same sheet as, and adjacent to
the rest of the answer
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Mathematical tables and graph papers are provided
...


(ii)

Find the domain and range of the function 𝑓(𝑥) = [𝑆𝑖𝑛𝑥]
...


(iv)

For what value of 𝑘 will the equations 𝑥 2 − 𝑘𝑥 − 21 = 0 𝑎𝑛𝑑 𝑥 2 − 3𝑘𝑥 + 35 = 0
have one common root
...


(vii)

Prove that sin 20° sin 40° sin 80° =

𝑥−𝑛

, where 𝑚 ≠ 𝑛
...

|𝑥−2|

(ix)

Show that lim

(x)

Find the point on the curve 𝑦 2 = 4𝑥, the tangent at which is parallel to the straight
line 𝑦 = 2𝑥 +4
...


……………………………………………………………………………………………………………
SPECIMEN PAPER ISC 2018 – CLASS XI

Question 2

[4]

Draw the graph of the function 𝑦 = |𝑥 − 2| + |𝑥 − 3|
...

OR
In a ∆𝐴𝐵𝐶 prove that 𝑏 cos 𝐶 + 𝑐 cos 𝐵 = 𝑎
Question 4

[4]

Find the locus of a complex number, Z= x+iy, satisfying the relation |

𝑧−3𝑖
𝑧+3𝑖

| ≤ √2
...

Question 5

[4]

Find the number of words which can be formed by taking four letters at a time from the
word “ COMBINATION”
...
In how many
ways can this be done when the committee consists of:
(i) exactly 3 girls
(ii) at least 3 girls and
(iii) atmost three girls
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1
1
1
𝑛
+
+
+ … … … … … …
...

1
...
3 3
...


OR
Find the sum of the terms of the binomial expansion to infinity:
2

2
...
5
...
8 + 4
...
12 + ⋯ … …
...

Question 9

[4]

Reduce the equation 𝑥 + 𝑦 + √2 = 0 to the normal form ( +𝑦 𝑆𝑖𝑛𝛼 = 𝑝) and find the
values of 𝑝 𝑎𝑛𝑑 𝛼
...

Question 11

[6]

In a ∆𝐴𝐵𝐶 prove that cot 𝐴 + cot 𝐵 + cot 𝐶 =

𝑎2 +𝑏 2 +𝑐 2
4∆

[6]

Question 12
Find the nth term and deduce the sum to n terms of the series:
4 + 11 + 22 + 37 + 56 + ⋯ … …
OR
If (p+q)th term and (p-q)th terms of G
...

Question 13

[6]

If 𝑥 is real, prove that the value of the expression

(𝑥−1)(𝑥+3)
(𝑥−2)(𝑥+4)

cannot be between

4/9 and 1
...


1
1
[ (4𝑛−𝑝)!] [ (2𝑛+𝑝)!]
3
3

Question 14

[6]

Calculate the standard deviation of the following distribution:
Age

20-25

25-30

30-35

35-40

40-45

45-50

No
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[2]

(b) Construct the truth table (~ 𝑝 ⋀ ∼ 𝑞)⋁(𝑝 ⋀ ∼ 𝑞)
...
”
Question 16

[4]

Show that the point (1, 2, 3) is common to the lines which join A(4, 8, 12) to B(2, 4, 6)
and C(3, 5, 4) to D(5, 8, 5)
...


Question 17

[4]

Find the equation of the hyperbola whose focus is (1, 1), the corresponding directrix
2𝑥 + 𝑦 − 1 = 0 𝑎𝑛𝑑 𝑒 = √3
...


Question 18

[6]

Show that the equation 16𝑥 2 − 3𝑦 2 − 32𝑥 − 12𝑦 − 44 = 0 represents a hyperbola
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……………………………………………………………………………………………………………
SPECIMEN PAPER ISC 2018 – CLASS XI

SECTION C (20 Marks)
Question 19
(i)

Two sample sizes of 50 and 100 are given
...
I
...


[2]

(ii)

Calculate Spearman’s Rank Correlation for the following data and interpret the
result:

[4]

Marks in Mathematics

36 48 27 36 29 30 36 39 42 48

Marks in Statistics

27 45 24 27 31 33 35 45 41 45
OR

Find Karl Pearson’s Correlation Coefficient from the given data:

[4]

x

21

24

26

29

32

43

25

30

35

37

y

120

123

125

128

131

142

124

129

134

136

……………………………………………………………………………………………………………
SPECIMEN PAPER ISC 2018 – CLASS XI

Question 21
Find the consumer price index for 2007 on the basis of 2005 from the following data
using weighted average of price relative method:
Items

Food

Rent

Cloth

[4]

Fuel

Price in 2005(Rs)

200

100

150

50

Price in 2007(Rs)

280

200

120

100

Weighted

30

20

20

10

Question 22
Using the following data

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