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 angular diameter of the moon be 30’, how far from the eye a coin of diameter 2.2 cm be kept to hide the moon?
2. Find the equation of hyperbola satisfying given condition foci (5,0) and (-5, 0) and transverse axis of length 8.
3. Find the derivative with respect to x
OR
Find the derivative with respect to x
4. Solve
5. If sin 𝑥 + cos 𝑥 = 0 and 𝑥 lies in the fourth quadrant, find sin 𝑥 and cos 𝑥
6. Find r, if: 15Cr : 15Cr-1 = 11:5
SECTION – B
7. Solve the following system of inequalities graphically: 2 𝑥 + 𝑦 – 3 ≥ 0, 𝑥 – 2 𝑦 + 1 ≤ 0
OR
A plumber can be paid under two schemes as given below:
Scheme I: ₹ 600 and ₹ 50 per hour.
Scheme II: ₹170 per hour
If the job takes 𝑥 hours, for what values of 𝑥 does the scheme I give the plumber the better wages?
8. Find the equation of the circle which passes through the origin and cuts off intercepts 3 and 4 on positive part of 𝑥-axis and 𝑦-axis respectively.
OR
Find the equation of the ellipse whose vertices are (0, ±6) and eccentricity is 1/3.
9. The probability of two events A and B are 0.25 and 0.50 respectively. The probability of their simultaneous occurrence is 0.14. Find the probability that neither A nor B occurs.
10. Two cards are drawn from a well shuffled pack of 52 cards. Find the probability:
(i) one is black, other is red
(ii) both are king
(iii) both are face cards.
SECTION – C
11. Prove that sin2 A + sin2 (A + π/3) + sin2 (A – π/3) = 3/2
12. Find the coordinates of the point in xz – plane which is the point of intersection of the plane and the line joining the points (2, 4, 5) and (3, 5, -4)
OR
If the points A (1, 0, -6), B (-3, p, q) and C (-5, 9, 6) are collinear, find the values of p & q.
13. Differentiate tan (2x + 3) using 1st Principle.
CASE BASED/DATA BASED
14. Due to restrictions of COVID 19 there was no celebration of New Year party in past two years. This year the government of India allowed with protocol. Abhilash a student of class XI invites his classmates to celebrate New party at his house with protocol of COVID 19. He invites his four friends named Bianca, Cabana, Derek and Esha for the party. After the party they took group photographs of all of them standing in a row.
Based on above information answer the following:
(i) How many different photographs can be clicked?
(ii) In how many of these photographs Abhilash be standing in the middle?
(iii) In how many of these photographs would Abhilash and Bianca be next to each other?
(iv) In how many of these photographs would Abhilash and Derek be not standing together?