# 11th Class CBSE Mathematics Compartment Exam 2019-20

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February 17, 2020
11th Class, CBSE Question Papers, English
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**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

- 4
- 2
- 0
- None of these

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

- 16
- 4
- 2
- None of these

#### Question: 3. Value of sin 31π/3 is

- ½
- √3/2
- -1/2
- -√3/2

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

- 1/13
- 12/13
- 1/52
- 4/5

#### Question: 5. Arithmetic Mean between 15 and 35 is

- 50
- 25
- 5√21
- 20

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

- √3
- 1/√3
- – √3
- -1/√3

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

*y*² = -24 *x*
*x*² = 24 *y*
*x*² = -24 *y*
*y*² = 24 *x*

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

- 5√3 units
- 3√5 units
- 7 units
- 5 units

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

- A – B
- A – B¹
- B – A
- B – A¹

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

- Z
- R
- W
- N

**Question 11 to Question 15 (Fill in the blanks)**

**Question: 11.** If (2x, *y* – *x*) = (*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.**

**Question: 14.** Find the center and Radius of the circle: 2*x*² + 2*y*² = 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

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

#### OR

#### If Z_{1} = a + ib and Z_{2} = c + id are two complex Numbers. Then Find the Product Z_{1}, Z_{2}.

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

**Question: 19.**

**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.**

**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 3*x* + 2*y* + 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 3*x* + Cos*x* – Cos 2*x* = 0.

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

#### 3^{2n+2} – 8n – is divisible by 8.

#### OR

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

**Question: 29.** Solve the following system of inequalities graphically

*x* + 2*y* ≤ 10, *x* + *y* ≥ 1, *x* – *y* ≤ 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]

**11th Mathematics Compartment Exam: ****Section D**

**Question: 33.** Convert the complex number

#### in the polar form. [6]

#### [4 Marks]

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

**Question: 34.** (i) The coefficient of the (*r* – 1)^{th}, *r*^{th} 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 (3*x* – *x*³/6)^{6}. [2 Marks]

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

#### (ii) Reduce the following equation into intercept form and find the intercepts on the axes

3*x* + 4*y* – 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* – 2*y* = 3 [4 Marks]

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

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

#### (ii) Evaluate: [2 Marks]