CBSE Class 12 Maths Question Paper 2020 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.
2. Section A – Questions no. 1 to 20 comprises of 20 questions of 1 mark each.
3. Section B – Questions no. 21 to 26 comprises of 6 questions of 2 mark each.
4. Section C – Questions no. 27 to 32 comprises of 6 questions of 4 mark each.
5. Section D – Questions no. 33 to 36 comprises of 4 questions of 6 mark 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.

SECTION - A

Question number 1 to 20 carry 1 mark each.

Question number 1 to 10 are multiple choice type questions. Select the correct option.

The value of p for which <math>p(\hat{i}+\hat{j}+\hat{k})</math> is a unit vector is

1. 0 (b) <math>\frac{1}{\sqrt{3}}</math> (d) <math>\sqrt{3}</math>

1. <math>\tan\left(\sin^{-1}\frac{3}{5} + \tan^{-1}\frac{3}{4}\right)</math> is equal to
2. <math>\frac{7}{24}</math> (b) <math>\frac{24}{7}</math> (d) <math>\frac{3}{4}</math>

1. The feasible region for an LPP is shown below: Let <math>z = 3x - 4y</math> be the objective function. Minimum of z occurs at

DATE: SUBJECT

CLASS:

CENTRE:

TOPIC

(4, 10)

(0, 8) (6, 8)

(6, 5)

(0, 0) (5, 0)

(c) <math>(5,0)</math> (d) <math>(4,10)</math>

(a) <math>(0,0)</math>

(b) <math>(0,8)</math>

1. If f and g are two functions from R to R defined as <math>f(x) = |x| + x</math> and <math>g(x) = |x| - x</math>, then <math>f \circ g(x)</math> for <math>x < 0</math> is
2. 4x (b) 2x (d) -4x

1. <math display="block">\int \frac{1}{x \log x} dx</math> is equal to
2. <math>\frac{(\log x)^2}{2} + c</math> (b) <math>\log |\log x| + c</math> (c) <math>\log |x \log x| + c</math> (d) <math>\frac{1}{\log x} + c</math>

1. The order of the differential equation of the family of circles touching x – axis at the origin is
2. 1 (b) 2 (d) 4

1. If <math>A = \begin{bmatrix} -2 & 0 & 0 \\ 0 & -2 & 0 \\ 0 & 0 & -2 \end{bmatrix}</math>, then the value of <math>\begin{vmatrix} adj & A \end{vmatrix}</math> is
2. 64 (b) 16

(d) -8

1. The image of the point <math>(2,-1,4)</math> in the YZ-plane is
2. <math>(0,-1,4)</math> (b) <math>(-2,-1,4)</math> (c) <math>(2,1,-4)</math>

1. The maximum value of slope of the curve <math>y = -x^3 + 3x^2 + 12x - 5</math> is
2. 15 (b) 12 (d) 0

1. The vector equation of XY-plane is
2. <math>\vec{r} \cdot \hat{k} = 0</math> (b) <math>\vec{r} \cdot \hat{j} = 0</math> (c) <math>\vec{r} \cdot \hat{i} = 0</math> (d) <math>\vec{r} \cdot \vec{n} = 1</math>

Fill in the blanks in question number 11 to 15.

1. The area of the parallelogram whose diagonals are <math>2\hat{i}</math> and <math>-3\hat{k}</math> is ______ square units.