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 the angles of a triangle are in the ratio 3: 4: 5, then find the smallest angle in degree and the greatest angle in radians.
OR
If the arcs of the same lengths in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii.
2. Prove that cos 20° cos 40° cos 80° = 1/8.
3. Solve the linear inequality:
4. If the letters of the word ‘EXAMINATION’ are arranged in all possible ways as listed in dictionary. How many words are there in the list in which the first word start with ‘A’?
5. Differentiate tan2x using first principle.
6. From a group of 2 boys and 3 girls, two children are selected at random. Consider the following events:
(i) A: Event that both the selected children are girls
(ii) B: Event that the selected group consists of one boy and one girl
(iii) C: Event that at least one boy is selected
Which pairs of events are mutually exclusive?
SECTION – B
7. Solve the following system of inequalities graphically: x – 2y ≤ 3, 3x + 4y ≥ 12, x ≥ 0, x – y ≥ 1
8. Find the equation of the parabola whose focus is at (–1, –2) and the directrix is the line x – 2y + 3 = 0.
OR
Find the equation of ellipse with centre at origin, major axis along x-axis, foci (± 2, 0) and passing through the point (2, 3).
9. Find the equation of the circle which passes through the points (2, –2) and (3, 4) and whose centre lies on x + y = 1.
10. Find the ratio in which YZ-plane divides the line segment joining points (–2, 4, 7) and (3, –5, 8). Also, find the coordinates of the point of intersection.
OR
If the origin is the centroid of the triangle PQR with vertices P(2a, 2, 6), Q(–4, 3b, –10) and R(8, 14, 2c), then find the values of a, b and c.
SECTION – C
11. A group consists of 4 girls and 7 boys. In how many ways can a team of 5 members be selected if the team has (i) No girl?
(ii) Atleast one boy and one girl?
(iii) Atleast 3 girls?
OR
If nCr : nCr + 1 = 1 : 2 and nCr + 1 : nCr + 2 = 2 : 3, then find the values of n and r.
12. If A, B, C, D be the angles of a cyclic quadrilateral, taken in order, prove that
(i) cos A + cos B + cos C + cos D = 0
(ii) cos(180° + A) + cos(180° + B) + cos(180° + C) – sin(90° + D) = 0.
13. Find the derivative of
(i) (6x3 + 9x)(5x + 10)
(ii) (5x + 4)/(x – 3)
CASE BASED
14. Nishtha and Naira are sisters. They purchased two dice of different colour. Nishtha selected the red coloured dice and Naira selected the black coloured dice. They and were playing with two dice. They decided to threw both the dice simultaneously and note down the sum of numbers which come up on two dice.
(i) Find the probability that the sum is even.
(ii) Find the probability that the sum is multiple of 3.