Board Paper of Class 12Commerce 2020 Math Delhi(Set 3)  Solutions
General Instructions:
Read the following instructions very carefully and strictly follow them :
(i) This question paper comprises four sections – A, B, C and D.
This question paper carries 36 questions. All questions are compulsory.
(ii) Section A – Question no. 1 to 20 comprises of 20 questions of one mark each.
(iii) Section B – Question no. 21 to 26 comprises of 6 questions of two marks each.
(iv) Section C – Question no. 27 to 32 comprises of 6 questions of four marks each.
(v) Section D – Question no. 33 to 36 comprises of 4 questions of six marks each.
(vi) 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.
(vii) In addition to this, separate instructions are given with each section and question, wherever necessary.
(viii) Use of calculators is not permitted.
Read the following instructions very carefully and strictly follow them :
(i) This question paper comprises four sections – A, B, C and D.
This question paper carries 36 questions. All questions are compulsory.
(ii) Section A – Question no. 1 to 20 comprises of 20 questions of one mark each.
(iii) Section B – Question no. 21 to 26 comprises of 6 questions of two marks each.
(iv) Section C – Question no. 27 to 32 comprises of 6 questions of four marks each.
(v) Section D – Question no. 33 to 36 comprises of 4 questions of six marks each.
(vi) 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.
(vii) In addition to this, separate instructions are given with each section and question, wherever necessary.
(viii) Use of calculators is not permitted.
 Question 1
If A is a skew symmetric matrix of order 3, then the value of A is
(a) 3
(b) 0
(c) 9
(d) 27 VIEW SOLUTION
 Question 2
If $\hat{i},\hat{j},\hat{k}$ are unit vectors along three mutually perpendicular directions, then
(a) $\hat{i}.\hat{j}=1$
(b) $\hat{i}\times \hat{j}=1$
(c) $\hat{i}.\hat{k}=0$
(d) $\hat{i}\times \hat{k}=0$ VIEW SOLUTION
 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
(a) $\frac{1}{3}$
(b) $\frac{4}{13}$
(c) $\frac{1}{4}$
(d) $\frac{1}{2}$ VIEW SOLUTION
 Question 4
If A is a 3 × 3 matrix such that A = 8, then 3A equals.
(a) 8
(b) 24
(c) 72
(d) 216 VIEW SOLUTION
 Question 5
$\int {x}^{2}{e}^{{x}^{3}}dx\mathrm{equals}$
(a) $\frac{1}{3}{e}^{{x}^{3}}+\mathrm{C}$
(b) $\frac{1}{3}{e}^{{x}^{4}}+\mathrm{C}$
(c) $\frac{1}{2}{e}^{{x}^{3}}+\mathrm{C}$
(d) $\frac{1}{2}{e}^{{x}^{2}}+\mathrm{C}$ VIEW SOLUTION
 Question 6
If $y={\mathrm{log}}_{e}\left(\frac{{x}^{2}}{{e}^{2}}\right),$ then $\frac{{d}^{2}y}{d{x}^{2}}$equals
(a) $\frac{1}{x}$
(b) $\frac{1}{{x}^{2}}$
(c) $\frac{2}{{x}^{2}}$
(d) $\frac{2}{{x}^{2}}$ VIEW SOLUTION
 Question 7
A die is thrown once. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then P(A∪B) is
(a) $\frac{2}{5}$
(b) $\frac{3}{5}$
(c) 0
(d) 1 VIEW SOLUTION
 Question 8
ABCD is a rhombus whose diagonals intersect at E. Then $\overrightarrow{\mathrm{EA}}+\overrightarrow{\mathrm{EB}}+\overrightarrow{\mathrm{EC}}+\overrightarrow{\mathrm{ED}}$ equals
(a) $\overrightarrow{0}$
(b) $\overrightarrow{\mathrm{AD}}$
(c) $2\overrightarrow{\mathrm{BC}}$
(d) $2\overrightarrow{\mathrm{AD}}$ VIEW SOLUTION
 Question 9
The distance of the origin (0, 0, 0) from the plane –2x + 6y – 3z = –7 is
(a) 1 unit
(b) $\sqrt{2}$ units
(c) $2\sqrt{2}$ units
(d) 3 units VIEW SOLUTION
 Question 10
The graph of the inequality 2x + 3y > 6 is
VIEW SOLUTION
(a) half plane that contains the origin.
(b) half plane that neither contains the origin nor the points of the line 2x + 3y = 6.
(c) whole XOY – plane excluding the points on the line 2x + 3y = 6.
(d) entire XOY plane.
 Question 11
Fill in the blank.
If A and B are square matrices each of order 3 and A = 5, B = 3, then the value of 3 AB is __________ VIEW SOLUTION
 Question 12
Fill in the blank.
The least value of the function $f\left(x\right)=ax+\frac{b}{x}\left(a>0,b0,x0\right)$ is __________. VIEW SOLUTION
 Question 13
Fill in the blank.
The vector equation of a line which passes through the points (3, 4, –7) and (1, –1, 6) is _________.OR
Fill in the blank.
The line of shortest distance between two skew lines is ______ to both the lines. VIEW SOLUTION
 Question 14
Fill in the blank.
The integrating factor of the differential equation x $\frac{dy}{dx}+2y={x}^{2}$ is _________.OR
Fill in the blank.
The degree of the differential equation $1+{\left(\frac{dy}{dx}\right)}^{2}=x$ is _____________. VIEW SOLUTION
 Question 15
Fill in the blank.
A relation in a set A is called ________ relation, if each element of A is related to itself. VIEW SOLUTION
 Question 16
Find the cofactors of all the elements of $\left[\begin{array}{cc}1& 2\\ 4& 3\end{array}\right]$. VIEW SOLUTION
 Question 17
Let f(x) = xx, for all x ∈ R check its differentiability at x = 0. VIEW SOLUTION
 Question 18
Find the value of ${\mathrm{sin}}^{1}\left[\mathrm{sin}\left(\frac{17\mathrm{\pi}}{8}\right)\right]$. VIEW SOLUTION
 Question 19
Find the value of $\underset{1}{\overset{4}{\int}}\leftx5\rightdx.$ VIEW SOLUTION
 Question 20
If f(x) = x^{4} – 10, then find the approximate value of f(2.1).
OR
Find the slope of the tangent to the curve y = 2 sin^{2} (3x) at $x=\frac{\mathrm{\pi}}{6}$. VIEW SOLUTION
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