CBSE Class 12 Maths Question Paper 2020 Set 2

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 numbers 1 to 20 carry 1 mark each.

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

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. The principal value of <math>\cot^{-1}(-\sqrt{3})</math> is
2. <math>-\frac{\pi}{6}</math> (b) <math>\frac{\pi}{6}</math> (d) <math>\frac{5\pi}{6}</math>

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

5. <math display="block">\int \frac{e^x (1+x)}{\cos^2(xe^x) dx}</math> is equal to

SUBJECT

DATE:

CLASS:

CENTRE: TOPIC

1. <math>\tan(xe^x) + c</math> (b) <math>\cot(xe^x) + c</math> (c) <math>\cot(e^x) + c</math> (d) <math>\tan[e^x(1+x)] + c</math>

1. The degree of the differential equation <math>x^2 \frac{d^2 y}{dx^2} = \left(x \frac{dy}{dx} - y\right)^3</math> is
2. 1 (b) 2 (c) 3

(d) 6

1. The value of p for which <math>p(\hat{i} + \hat{j} + \hat{k})</math> is a unit vector is
2. 0 (b) <math>\frac{1}{\sqrt{3}}</math> (c) 1 (d) <math>\sqrt{3}</math>

1. The coordinates of the foot of the perpendicular drawn from the point <math>\left(-2,8,7\right)</math> on the ZX-plane is
2. <math>(-2, -8, 7)</math> (b) <math>(2, 8, -7)</math> (c) <math>(-2, 0, 7)</math> (d) <math>(0, 8, 0)</math>

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>

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

(4, 10)

(0, 8) (6, 8)

(6, 5)

(0, 0) (5, 0)

1. <math>(0,0)</math> (b) <math>(0,8)</math> (c) <math>(5,0)</math> (d) <math>(4,10)</math>

Fill in the blanks in question numbers 11 to 15.

1. If <math>y = \tan^{-1} x + \cot^{-1} x</math>, <math>x \in R</math>, then <math>\frac{dy}{dx}</math> is equal to _____

(OR)

If <math>\cos(xy) = k</math>, where k is a constant and <math>xy \neq n\pi</math>, <math>n \in \mathbb{Z}</math>, then <math>\frac{dy}{dx}</math> is equal to ______.