St. Thomas’ Day School | Class 11 Unit 2 Examination | 12 Dec 2023

School	:	St. Thomas’s Day School
Class	:	11
Exam	:	Unit 2
Subject	:	Mathematics
Date	:	12 Dec 2023
Time	:	2 hour
Marks	:	50

St. Thomas’s Day School

Class 11 | Unit 2 Examination

Question 1

Choose the correct option for the following:

(i) Find the centre of the circle 4x² + 4y² – 8x + 12y – 25 = 0

1. (-1, 3/2)
2. (1, -3/2)
3. (-4, 6)
4. (4, -6)

(ii) The number of terms in the expansion of (2x – 3/x³)¹⁰

1. 10
2. 9
3. 1
4. cannot be predicted

(iii) The 10th term of the sequence -3, -21\over 4, -11\over 2, – 3\over 4, …

1. –39\over 4
2. -33\over 4
3. –20\over 4
4. 33\over 4

(iv) If the price of a commodity in 2001 is Rs 54 and in 2011 is Rs 64. The price relative to the commodity is

1. Rs 84.3
2. Rs 118.5
3. 0.84
4. 1.18

(v) The equation of the circle with the centre (0, 2) and radius 2 is

1. x² + y² + 4y = 0
2. x² + y² – 4y = 0
3. x² + y² – 4y + 2= 0
4. x² + y² + 4y + 2= 0

(vi) The fifth term of the sequence 2, 6, 18 … Is

1. 32
2. 162
3. 8
4. 486

(vii) If n is even in the expansion of (a + b)ⁿ the middle term is

1. n^th term
2. n\over 2^th term
3. ({n\over2}-1)^th term
4. ({n\over2}+1)^th term

(viii) The number of tangents that can be drawn from (1, 2) to the circle x² + y² = 5 is

1. 0
2. 1
3. 2
4. more than 2

(ix) If the n^th term of an arithmetic progression is 3x – 4 then the 10^th term of the AP is

1. 10
2. 12
3. 22
4. 26

(x) The sum of AP 2, 5, 8 … up to 50 terms is

1. 3775
2. 3557
3. 3757
4. 3575

Question 2

1. Find the equation of the circle whose centre is C (-2, 3) and which touches the line x-y+7=0
2. Using the Binomial Theorem find the value of (98)⁵ OR Find the fourth term from the end of the expansion ({3\over x^2}-{x^3\over 3})⁹
3. Using the Binomial Theorem proves that 6ⁿ-5n always leaves a remainder 1 when divided by 25 for all n ∈ N
4. The radius of the circle x² + y² – 2x + 3y + k = 0 is 2? Find the value of k.

Question 3 (Anyone)

1. Using the binomial theorem expand (x + y)⁵+(x – y)⁵. Hence find the value of (√2 + 1)⁵ + (√2 – 1)⁵
2. Find the equation of the circle which is concentric with the circle x² + y² – 6x + 7 = 0 and touch the line x + y – 3 = 0

[4]

Question 4

If a. b. c are in GP. Prove that a² + b², ab + bc and b² + c² are also in GP.

[4]

Question 5 (Anyone)

(a) Find the sum of the series: (3³ – 2³) + (5³ – 4³) + (7³ – 6³) + … n terms.

(b) Evaluate: \sum_{k=1}^{n}{(3^k - 2^k)} [4]

Question 6

If the second, third and fourth terms in the expansion of (x+a)ⁿ are 240, 720, and 1080 respectively. Find the value of x, a, n. [4]

Question 7

Find the consumer price index number for 2011 on the base of 2010 from the following data using the method of weighted relatives. [4]

Items	Weight	2010	2011
A	20	200	320
B	14	400	420
C	15	100	120
D	18	40	60
E	10	20	28

 

Question 8

Assuming a four-yearly cycle calculate the trend by the method of moving average from the following data. Alsoplot them on a graph paper.

Year	Value
1984	112
1985	180
1986	99
1987	154
1988	170
1989	87
1990	105
1991	100
1992	82
1993	189

OR

(b) In an influenza epidemic the number of cases diagnosed were

Date (March)	Number of Cases
1	20
2	45
3	55
4	82
5	75
6	27
7	46
8	30
9	31
10	48
11	43
12	55
13	40

Calculate the 3-year moving average and display them and the original figure on the same graph. [6]

Question 9

Show that the points(7,1), (-2,4), (5,5), (6,4) are concyclic. Also find the radius, centre and equation of the circle. [6]