Board Paper of Class 12-Science 2020 Math Delhi(Set 3) - Solutions

• 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 $y={\log }_e\left(\frac{x^2}{e^2}\right),$ 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
  (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.

  VIEW SOLUTION

• 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 $f\left(x\right)=ax+\frac{b}{x}\left(a>0, b>0, x>0\right)$ 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) = x|x|, for all x ∈ R check its differentiability at x = 0. VIEW SOLUTION

• Question 18
  Find the value of ${\sin }^{-1 }\left[\sin \left(-\frac{17\mathrm{\pi }}{8}\right)\right]$. VIEW SOLUTION

• Question 19
  Find the value of $\underset{1}{\overset{4}{\int }}\left|x-5\right|dx.$ VIEW SOLUTION

• Question 20
  If f(x) = x⁴ – 10, then find the approximate value of f(2.1).
  

  OR

  
  Find the slope of the tangent to the curve y = 2 sin² (3x) at $x=\frac{\mathrm{\pi }}{6}$. VIEW SOLUTION