CBSE Paper 2020 Math Delhi (Set 3)

General Instructions:

Read the following instructions very carefully and strictly follow them:

1. This question paper comprises four sections – A, B, C and D.

This question paper carries 36 questions. All questions are compulsory.

1. Section A – Question no. 1 to 20 comprises of 20 questions of one mark each.
2. Section B – Question no. 21 to 26 comprises of 6 questions of two marks each.
3. Section C – Question no. 27 to 32 comprises of 6 questions of four marks each.
4. Section D – Question no. 33 to 36 comprises of 4 questions of six marks each.

1. There is no overall choice in the question paper. However, an internal choice has

been provided in 3 questions of one mark, 2 questions of two marks, 2 questions of four marks and 2 questions of six marks. Only one of the choices in such questions have to be attempted.

1. In addition to this, separate instructions are given with each section and question, wherever necessary.
2. Use of calculators is not permitted.

Question 1

If A is a skew symmetric matrix of order 3, then the value of |A| is

1. 3
2. 0

(c)9

1. 27

Solution:

Given: A is a skew symmetric matrix of order 3.

We know <math>|A'| = |A|</math> (where A' stands for A transpose) .....(1) In a skew symmetric matrix, <math>\Rightarrow A' = -A</math> <math>\Rightarrow |A'| = (-1)^n |A|</math> <math>\Rightarrow |A'| = (-1)^3 |A|</math> (Since <math>n=3</math>)

<math display="block">\Rightarrow |A'| = -|A| \qquad \dots (2)</math> From (1) and (2), we get <math>2|A| = 0</math> <math>\Rightarrow |A| = 0</math> Hence, the correct answer is option (b).

Question 2

If <math>\hat{i},~\hat{j},~\hat{k}</math> are unit vectors along three mutually perpendicular directions, then

1. <math>\hat{i}</math> . <math>\hat{j}=1</math>
2. <math>\hat{i} \, \times \, \hat{j} = 1</math>
3. <math>\hat{i}</math> . <math>\hat{k}=0</math>
4. <math>\hat{i} \times \hat{k} = 0</math>

Solution:

Given three unit vectors <math>\hat{i}</math>, <math>\hat{j}</math>, <math>\hat{k}</math> are mutually perpendicular.

Therefore, the angle between them will be right angle.

Consider

<math display="block">\hat{i} \cdot \hat{k} = \left| \hat{i} \right| \left| \hat{k} \right| \cos 90^{\circ} = 0</math>

Hence, the correct answer is option (c).

Question 3

A card is picked at random from a pack of 52 playing cards. Given that picked card is a queen, the probability of this card to be a card of spade is

1. 1/3
2. 4/13
3. 1/4
4. 1/2

Solution:

Given that the picked card is a queen.

Therefore,

Total number of outcomes=Total number of queens = 4 Since only one queen exists of spade.

Therefore,

Required Probability = <math>\frac{\text{Total number of favorable outcomes}}{\text{Total outcomes}}</math> Hence, the correct answer is option (c).

Question 4

If A is a <math>3 \times 3</math> matrix such that <math>|A| = 8</math>, then <math>|3A|</math> equals.

1. 8
2. 24 (c)72
3. 216