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Class XI – Mathematics – 1 – Sample

Practice Paper

TERM II (2021 – 2022)

Class – XI

Mathematics (041)

Time: 2 hours                                                                                    Maximum Marks: 40

General Instructions:

1. This question paper contains three sections – A, B and C. Each part is compulsory. 

2. Section – A has 6 short answer type (SA1) questions of 2 marks each. 

3. Section – B has 4 short answer type (SA2) questions of 3 marks each. 

4. Section – C has 4 long answer type questions (LA) of 4 marks each. 

5. There is an internal choice in some of the questions. 

6. Q14 is a case-based problem.

SECTION – A

1. If in two circles arcs of the same length subtend angles 600 and 750at the centre, find the ratio of their radii.

OR

If cot x = -5/12, x lies in second quadrant, find the value of other five trigonometric functions.

2. Solve the inequation:

3. Solve the system of inequations graphically.

2x+y ≥ 8. x+2y ≥8,  x+y ≤  6

4. Find the lengths of the medians of the triangle with vertices A (0,0,6), B (0,4,0) and C (6,0,0)

5. Find the derivative of : 

6. A fair coin with 1 marked on one face and 6 on other and a fair die are both tossed, find the probability that the sum of numbers that turns up is (i) 3   (ii) 12

SECTION – B

7. The minute hand of a watch is 35 cm long. How far does it move in 9 minutes?

OR

Prove that: – (cosA – cosB)2 +(sinA – sinB)2 = 4 sin2(A-B)/2

8. How many different words can be formed with the letters of the word “EQUATION” so that

(i) The words begin with E?

(ii) The words begin with E and end with N?

(iii) The words begin and end with a consonant?

9. Find the area of the triangle formed by the lines joining the vertex of the parabola, x2 = 12y to the ends of the latus rectum.

OR

If foci of a hyperbola are (0, ±5) and length of semi transverse axis is 3 units, then find the equation of hyperbola.

10. If x lies in the first quadrant and cosx = 8/17 then prove that: –

SECTION – C

11.

12. Find the number of words with or without meaning which can be made using all the letters of the word “AGAIN”. If these words are written as in a dictionary, what will be the 50th word?

OR

How many numbers greater than 1000000 can be formed by using the digits 1, 2, 0, 2, 4, 2, 4?

13. In a relay race there are five teams A, B, C, D and E.

(a) What is the probability that A, B and C finish first, second and third, respectively.

(b) What is the probability that A, B and C are first three to finish (in any order)

(Assume that all finishing orders are equally likely)

CASE BASED

Rakesh wishes to install 2 handpumps in his field for watering. He moves in the field while watering in such a way that sum of distances between the Rakesh and each handpump is always 26 metres. Also, the distance between handpumps is 10 metres.

Based on the above information, answer the following questions:

(i) Name the curve along which Rakesh moves.

(ii) Find the equation of curve traced by Rakesh.

(iii) Find the eccentricity of the curve along which Rakesh moves.

(iv) Find the co-ordinates of handpumps.