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Mathematics

11th Class CBSE Mathematics Compartment Exam 2019-20

11th Class CBSE Mathematics Compartment Exam 2019-20

School Name: Himalaya Public School, Sector 13, Rohini, Delhi 110085 India
Time: 3 hours
Maximum Marks: 80
Class: 11th
Date: 14/02/2020
Subject: Mathematics

General Instructions:

  • All questions are compulsory.
  • This question paper consists of 36 questions divided into four sections – A, B, C and D.
  • Section – A Comprises of 20 question of 1 marks each.
    Section – B Comprises of 6 question of 2 marks each.
    Section – C Comprises of 6 question of 4 marks each.
    Section – D Comprises of 4 question of 6 marks each.
  • There is no overall choice. However on internal choice has been Provided in there questions of 1 marks each, two questions of 2 marks each, two questions of 4 marks each and two questions of 6 marks each. You have to attempt only one of the alternative in all such questions.
  • Use of calculator is not Permitted.

11th Class CBSE Mathematics Compartment: Section A

Question 1 – Question 10 are Multiple choice type questions. Select the correct option.

Question: 1. If A = {1, 2} then the number of elements in P (A) will be

  1. 4
  2. 2
  3. 0
  4. None of these

Question: 2. If A = {1, 2} and B = {3, 4} then number of subsets that A × B have is

  1. 16
  2. 4
  3. 2
  4. None of these

Question: 3. Value of sin 31π/3 is

  1. ½
  2. √3/2
  3. -1/2
  4. -√3/2

Question: 4. If a Card is dream from well shuffled Pack of cards then Probability of Not getting an ace is

  1. 1/13
  2. 12/13
  3. 1/52
  4. 4/5

Question: 5. Arithmetic Mean between 15 and 35 is

  1. 50
  2. 25
  3. 5√21
  4. 20

Question: 6. Slope of line making an angle 120° with Positive direction of x axis is

  1. √3
  2. 1/√3
  3. – √3
  4. -1/√3

Question: 7. Equation of Parabola with vertex at (0,0) and focus at (6,0) is

  1. y² = -24 x
  2. x² = 24 y
  3. x² = -24 y
  4. y² = 24 x

Question: 8. Distance between the points p(1, -3, 4) and Q = (-4, 1, 2) is

  1. 5√3 units
  2. 3√5 units
  3. 7 units
  4. 5 units

Question: 9. Event ‘A but not B’ is represented by which of the following

  1. A – B
  2. A – B¹
  3. B – A
  4. B – A¹

Question: 10. Range of greatest integer function is given by which of the following

  1. Z
  2. R
  3. W
  4. N

Question 11 to Question 15 (Fill in the blanks)

Question: 11. If (2x, yx) = (y + 3, 0), then value of y is _______.

OR

Given set A = {2, 3, 4, 5, 6} and set B = {0, 1, 2, 3} write a relation R from A to B given by R = {(x, y): x + y = 8}.

Question: 12. Let U = {1, 2, 3, 4, 5, 6}, A = {2, 3} and B = {3, 4, 5} then A’ ∩B’ = ____.

Question: 13.

Blanks

Question: 14. Find the center and Radius of the circle: 2x² + 2y² = 9

Question: 15. If E and F are events such that P(E) = 1/4, P(F) = 1/2 and P(E and F) = 1/8, then P(E or F) is _____.

Q. 16 to 20. Answer the following questions:

Question: 16. Find the value of sin 765°.

OR

Prove that sin

Question: 17. Find the Multiplicative inverse of 2 + 3 i

OR

If Z1 = a + ib and Z2 = c + id are two complex Numbers. Then Find the Product Z1, Z2.

Question: 18. Find the equation of ellipse, if for are (± 3, 0) and a = 4.

Question: 19.
Evaluate1

Question: 20. Find the equation of line through (-2, 3) with slope as -4.

11th Mathematics Compartment Exam: Section B

Question: 21. In a survey of 60 people, It was find that 25 people read newspaper H, 26 read newspaper T, 26 read newspaper I, 9 read both H and I, 11 read both H and T 8 read both T and I, 3 read all the three newspapers. Find the number of people who read only newspaper H.

Question: 22.

Prove that

Question: 23. If P(n,r) = 336,  C(n,r) =56 find n and r

OR

In how many ways can the litters of word ‘ASSASSINATION’ be arranged so that all the sir are to gather?

Question: 24. Find equation of straight line that passes through the point (3,4) and perpendicular to line 3x + 2y + 5 = 0.

OR

Find the distance of the point (-1, 1) from the line 12(x + 6) = 5(y – 2).

Question: 25. Find the ratio in which the YZ plane divides the line segment formed by joining the points (-2, 4, -1) and (3, -5, 8).

Question: 26. 4 Cards are drain from a well shuffled deck of 52 Cards. What is the probability of obtaining 3 kings and one are.

11th Mathematics Compartment Exam: Section C

Question: 27. Prove that Cos 20°. Cos 40°. Cos 60°. Cos 80° = 1/16.

OR

Find the general solution fer the following equation Cos 3x + Cosx – Cos 2x = 0.

Question: 28. Prove the following by Principle of Mathematical Induction fer all n ∈ N.

32n+2 – 8n – is divisible by 8.

OR

Prove the following by Principle of Mathematical Induction fer all n ∈ N.

Principle 1

Question: 29. Solve the following system of inequalities graphically
x + 2y ≤ 10, x + y ≥ 1, xy ≤ 0, y ≥ 0, x ≥ 0.

Question: 30. Find the Sum of the series up to n terms
3 × 8 + 6 × 11 + 9 × 14 + ……..

Question: 31. Find the equation of the ellipse satisfying with given condition: Foci(0, + 4), e = 4/5

Question: 32. Find the derivatives of each of the following with respect to x:     [2+2 Marks]

Derivatives

11th Mathematics Compartment Exam: Section D

Question: 33. Convert the complex number

Complex number          in the polar form. [6]

Complex number (a)   [4 Marks]

(b) Solve the following quadratic equation x² – x + 2 = 0 [2 Marks]

Question: 34. (i) The coefficient of the (r – 1)th, rth and (r + 1)th terms in the expansion of (x + 1)n are in the ratio 1:3:5. Find n and r. [4 Marks]

(ii) Find the Middle term in the expansion of (3xx³/6)6. [2 Marks]

Question: 35. (i) find the Coordinates of foot of Perpendicular from the point (2,3) to the line y = 3x + 4.        [4 Marks]

(ii) Reduce the following equation into intercept form and find the intercepts on the axes
3x + 4y – 24 = 0        [2 Marks]

OR

(i) Find the equation of the lines through the prints (3,2) which makes an angle of 45° with the line x – 2y = 3            [4 Marks]

(ii) Find the angle between the lines √3x + y = 1 and x + √3y = 1            [2 Marks]

Question: 36. (i) Find the derivative of following from first principle f (x) = cos x. [4 Marks]

(ii) Evaluate:                  [2 Marks]

Evaluate

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