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 4x^{2} + 4y^{2} – 8x + 12y – 25 = 0

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

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

- 10
- 9
- 1
- cannot be predicted

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

- –39\over 4
- -33\over 4
- –20\over 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

- Rs 84.3
- Rs 118.5
- 0.84
- 1.18

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

- x
^{2}+ y^{2}+ 4y = 0 - x
^{2}+ y^{2}– 4y = 0 - x
^{2}+ y^{2}– 4y + 2= 0 - x
^{2}+ y^{2}+ 4y + 2= 0

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

- 32
- 162
- 8
- 486

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

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

(viii) The number of tangents that can be drawn from (1, 2) to the circle x^{2} + y^{2} = 5 is

- 0
- 1
- 2
- 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

- 10
- 12
- 22
- 26

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

- 3775
- 3557
- 3757
- 3575

**Question 2**

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

**Question 3 ( Anyone)**

- Using the binomial theorem expand (x + y)⁵+(x – y)⁵. Hence find the value of (√2 + 1)⁵ + (√2 – 1)⁵
- 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 a^{2} + b^{2}, ab + bc and b^{2} + c^{2} are also in GP.

**[4]**

**Question 5 ( Anyone)**

(a) Find the sum of the series: (3^{3} – 2^{3}) + (5^{3} – 4^{3}) + (7^{3} – 6^{3}) + … 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]**