CBSE Paper 2020 Math Delhi (Set 1)

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 square matrix of order 3, such that A (adj A) = 10 I, then |adj A| is equal to

1. 1
2. 10
3. 100
4. 101

Solution:

We know that <math>(adjA)A = |A|I</math> Writing determinants on both the sides, we get <math>|(adjA)A| = ||A|I|</math> <math>\Rightarrow |10I| = |A|</math> <math>\Rightarrow |A| = |10I| = 10</math>

Also, <math display="block">|adjA| = |A|^{n-1}</math> <math>\Rightarrow |adjA| = |10|^{3-1} = 100</math>

Hence, the correct answer is option (c).

Question 2

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
3. 72
4. 216

Solution:

Given that A is a <math>3 \times 3</math> matrix and <math>|A| = 8</math>.

We know that If <math>A=[a_{ij}]_{3\times 3}</math> then <math>|k,A|=k^3\,|A|</math>

When <math>k = 3</math>, then

<math>|3. A| = 3^3 |A| = 27 |A| = 27 \times 8 = 216</math>

Hence, the correct answer is option (d).

Question 3

If <math>y = Ae^{5x} + Be^{-5x}</math>, then <math>\frac{d^2y}{dx^2}</math> is equal to

1. 25y
2. 5y
3. -25y<br>(d) 15y

Solution:

Given <math>y = Ae^{5x} + Be^{-5x}</math>. Differentiating both sides w.r.t. x, we get <math>\frac{dy}{dx} = 5Ae^{5x} - 5Be^{-5x}</math> <math>\Rightarrow \frac{\mathrm{d}^2 y}{\mathrm{d}^2 x^2} = 25Ae^{5x} + 25Be^{-5x}</math> <math>\Rightarrow \frac{d^2y}{dx^2} = 25(Ae^{5x} + Be^{-5x}) = 25y</math> Hence, the correct answer is option (a).

Question 4

<math>\int x^2 e^{x^3} dx</math> equals

1. <math>\frac{1}{3} e^{x^3} + C</math>
2. <math>\frac{1}{2} e^{x^4} + C</math>