Board Paper of Class 12Science TermI 2021 Math Delhi(Set 4)  Solutions
General Instructions:
(i) This question paper comprises 50 questions out of which 40 questions are to be attempted as per instructions. All questions carry equal marks.
(ii) The question paper consists three Sections – Section A, B and C.
(iii) Section – A contains 20 questions. Attempt any 16 questions from Q.No. 1 to 20.
(iv) Section – B also contains 20 questions. Attempt any 16 questions from Q.No. 21 to 40.
(v) Section – C contains 10 questions including one Case Study. Attempt any 8 from Q.No. 41 to 50.
(vi) There is only one correct option for every Multiple Choice Question (MCQ). Marks will not be awarded for answering more than one option.
(vii) There is no negative marking.
(i) This question paper comprises 50 questions out of which 40 questions are to be attempted as per instructions. All questions carry equal marks.
(ii) The question paper consists three Sections – Section A, B and C.
(iii) Section – A contains 20 questions. Attempt any 16 questions from Q.No. 1 to 20.
(iv) Section – B also contains 20 questions. Attempt any 16 questions from Q.No. 21 to 40.
(v) Section – C contains 10 questions including one Case Study. Attempt any 8 from Q.No. 41 to 50.
(vi) There is only one correct option for every Multiple Choice Question (MCQ). Marks will not be awarded for answering more than one option.
(vii) There is no negative marking.
 Question 1
Differential of $\mathrm{log}\left[\mathrm{log}\left(\mathrm{log}{x}^{5}\right)\right]$ w.r.t x is
(a) $\frac{5}{x\mathrm{log}\left({x}^{5}\right)\mathrm{log}\left(\mathrm{log}{x}^{5}\right)}$
(b) $\frac{5}{x\mathrm{log}\left(\mathrm{log}{x}^{5}\right)}$
(c) $\frac{5{x}^{4}}{\mathrm{log}\left({x}^{5}\right)\mathrm{log}\left(\mathrm{log}{x}^{5}\right)}$
(d) $\frac{5{x}^{4}}{\mathrm{log}{x}^{5}\mathrm{log}\left(\mathrm{log}{x}^{5}\right)}$ VIEW SOLUTION
 Question 2
The number of all possible matrices of order 2 × 3 with each entry 1 or 2 is
(a) 16
(b) 6
(c) 64
(d) 24 VIEW SOLUTION
 Question 3
A function f : R$\to $R is defined as f(x) = ${x}^{3}+1$. Then the function has
(a) no minimum value
(b) no maximum value
(c) both maximum and minimum values
(d) neither maximum value nor minimum value VIEW SOLUTION
 Question 4
If sin y = x cos (a + y), then $\frac{dx}{dy}$ is
(a) $\frac{\mathrm{cos}a}{{\mathrm{cos}}^{2}(a+y)}$
(b) $\frac{\mathrm{cos}a}{{\mathrm{cos}}^{2}(a+y)}$
(c) $\frac{\mathrm{cos}a}{{\mathrm{sin}}^{2}y}$
(d) $\frac{\mathrm{cos}a}{{\mathrm{sin}}^{2}y}$ VIEW SOLUTION
 Question 5
The points on the curve $\frac{{x}^{2}}{9}+\frac{{y}^{2}}{25}=1,$ where tangent is parallel to xaxis are
(a) $\left(\pm 5,0\right)$
(b) $\left(0,\pm 5\right)$
(c) $\left(0,\pm 3\right)$
(d) $\left(\pm 3,0\right)$ VIEW SOLUTION
 Question 6
Three points P(2x, x + 3), Q(0, x) and R(x + 3, x + 6) are collinear, then x is equal to
(a) 0
(b) 2
(c) 3
(d) 1 VIEW SOLUTION
 Question 7
The principal value of ${\mathrm{cos}}^{1}\left(\frac{1}{2}\right)+{\mathrm{sin}}^{1}\left(\frac{1}{\sqrt{2}}\right)$ is
(a) $\frac{\mathrm{\pi}}{12}$
(b) $\frac{\mathrm{\pi}}{3}$
(c) $\mathrm{\pi}$
(d) $\frac{\mathrm{\pi}}{6}$ VIEW SOLUTION
 Question 8
If (x^{2} + y^{2})^{2} = xy, then $\frac{dy}{dx}$ is
(a) $\frac{y+4x({x}^{2}+{y}^{2})}{4y({x}^{2}+{y}^{2})x}$
(b) $\frac{y4x({x}^{2}+{y}^{2})}{x+4({x}^{2}+{y}^{2})}$
(c) $\frac{y4x({x}^{2}+{y}^{2})}{4y({x}^{2}+{y}^{2})x}$
(d) $\frac{4y({x}^{2}+{y}^{2})x}{y4x({x}^{2}+{y}^{2})}$ VIEW SOLUTION
 Question 9
If a matrix A is both symmetric and skew symmetric, then A is necessarily a
(a) Diagonal matrix
(b) Zero square matrix
(c) Square matrix
(d) Identity matrix VIEW SOLUTION
 Question 10
Let set X = {1, 2, 3} and a relation R is defined in X as : R = {(1, 3), (2, 2), (3, 2)}, then minimum ordered pairs which should be added in relation R to make it reflexive and symmetric are
(a) {(1, 1), (2, 3), (1, 2)}
(b) {(3, 3), (3, 1), (1, 2)}
(c) {(1, 1), (3, 3), (3, 1), (2, 3)}
(d) {(1, 1), (3, 3), (3, 1), (1, 2)}
VIEW SOLUTION
 Question 11
A Linear Programming Problem is as follows :
Minimise z = 2x + y
subject to the constraints x ≥ 3, x ≤ 9, y ≥ 0
x – y ≥ 0, x + y ≤ 14
The feasible region has
(a) 5 corner points including (0, 0) and (9, 5)
(b) 5 corner points including (7, 7) and (3, 3)
(c) 5 corner points including (14, 0) and (9, 0)
(d) 5 corner points including (3, 6) and (9, 5) VIEW SOLUTION
 Question 12
The function $f\left(x\right)=\left\{\begin{array}{l}\frac{{e}^{3x}{e}^{5x}}{x},\mathrm{if}x\ne 0\\ k,\mathrm{if}x=0\end{array}\right.$ is continuous at x = 0 for the value of k, as
(a) 3
(b) 5
(c) 2
(d) 8 VIEW SOLUTION
 Question 13
If C_{ij} denotes the cofactor of element p_{ij} of the matrix $\mathrm{P}=\left[\begin{array}{ccc}1& 1& 2\\ 0& 2& 3\\ 3& 2& 4\end{array}\right]$, then the value of C_{31} ∙ C_{23} is
(a) 5
(b) 24
(c) –24
(d) –5 VIEW SOLUTION
 Question 14
The function y = x^{2}e^{–x }is decreasing in the interval
(a) (0, 2)
(b) (2, ∞)
(c) (–∞, 0)
(d) (–∞, 0) ∪ (2, ∞) VIEW SOLUTION
 Question 15
If R = {(x, y); x, y ∊ Z, x^{2 }+ y^{2} ≤ 4} is a relation in set Z, then domain of R is
(a) {0, 1, 2}
(b) {–2, –1, 0, 1, 2}
(c) {0, –1, –2}
(d) {–1, 0, 1} VIEW SOLUTION
 Question 16
The system of linear equations
5x + ky = 5
3x + 3y = 5
will be consistent if
(a) k $\ne $ –3
(b) k = –5
(c) k = 5
(d) k$\ne $ 5 VIEW SOLUTION
 Question 17
The equation of the tangent to the curve y (1 + x^{2}) = 2 – x, where it crosses the xaxis is
(a) x – 5y = 2
(b) 5x – y = 2
(c) x + 5y = 2
(d) 5x + y = 2 VIEW SOLUTION
 Question 18
If $\left[\begin{array}{cc}3c+6& ad\\ a+d& 23b\end{array}\right]=\left[\begin{array}{cc}12& 2\\ 8& 4\end{array}\right]$ are equal, then value of ab – cd is
(a) 4
(b) 16
(c) –4
(d) –16 VIEW SOLUTION
 Question 19
The principal value of ${\mathrm{tan}}^{1}\left(\mathrm{tan}\frac{9\mathrm{\pi}}{8}\right)$ is
(a) $\frac{\mathrm{\pi}}{8}$
(b) $\frac{3\mathrm{\pi}}{8}$
(c) $\frac{\mathrm{\pi}}{8}$
(d) $\frac{3\mathrm{\pi}}{8}$
VIEW SOLUTION
 Question 20
For two matrices P = $\left[\begin{array}{cc}3& 4\\ 1& 2\\ 0& 1\end{array}\right]$ and Q^{T} = $\left[\begin{array}{ccc}1& 2& 1\\ 1& 2& 3\end{array}\right]$ P – Q is
(a) $\left[\begin{array}{cc}2& 3\\ 3& 0\\ 0& 3\end{array}\right]$
(b) $\left[\begin{array}{cc}4& 3\\ 3& 0\\ 1& 2\end{array}\right]$
(c) $\left[\begin{array}{cc}4& 3\\ 0& 3\\ 1& 2\end{array}\right]$
(d) $\left[\begin{array}{cc}2& 3\\ 0& 3\\ 0& 3\end{array}\right]$ VIEW SOLUTION
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