CBSE 12th Mathematics Delhi Set 1 - 2023
Paper was held on Tue, Mar 14, 2023 5:00 AM
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## Mathematics

Let $$A=\{3,5\}$$. Then number of reflexive relations of $$A$$ is:
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$$\sin \left[\frac{\pi}{3}+\sin ^{-1}\left(\frac{1}{2}\right)\right]$$ is equal to:
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If for a square matrix $$\mathrm{A}, A^2-A+I=\mathrm{O}$$, then $$\mathrm{A}^{-1}$$ equals:
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$$\text { If } A=\left[\begin{array}{ll} 1 & 0 \\ 2 & 1 \end{array}\right], B=\left[\begin{array}{ll} x & 0 \\ 1 & 1 \en View Question$$\text { If }\left|\begin{array}{lll} \alpha & 3 & 4 \\ 1 & 2 & 1 \\ 1 & 4 & 1 \end{array}\right|=0 \text {, then the v
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The derivative of $$x^{2 x}$$ w.r.t. $$x$$ is:
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The function $$f(x)=[x]$$, where $$[x]$$ denotes the greatest integer less than or equal to $$x$$, is continuous at:
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If $$x=A \cos 4 t+B \sin 4 t$$, then $$\frac{d^2 x}{d t^2}$$ is equal to:
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The interval in which the function $$f(x)=2 x^3+9 x^2 +12 x-1$$ is decreasing is :
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$$\int \frac{\sec x}{\sec x-\tan x} d x$$ equals:
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$$\int_\limits{-1}^1 \frac{|x-2|}{x-2} d x, x \neq 2 \text { is equal to: }$$
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The sum of the order and the degree of the differential equation $$\frac{d}{d x}\left(\left(\frac{d y}{d x}\right)^3\rig View Question Two vector$$\vec{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k} \quad$$and$$\vec{b}=b_1 \hat{i}+b_2 \hat{j}+b_3 \hat{k}$$are View Question The magnitude of the vector$$6 \hat{i}-2 \hat{j}+3 \hat{k}$$is : View Question If a line makes angles of$$90^{\circ}, 135^{\circ}$$and$$45^{\circ}$$with the$$x, y$$and$$z$$axes respectively, View Question The angle between the lines$$2 x=3 y=-z$$and$$6 x=-y=-4 z$$is: View Question If for any two events$$\mathrm{A}$$and$$\mathrm{B}, P(A)=\frac{4}{5}$$and$$P(A \cap B)=\frac{7}{10}$$, then$$P(B /
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Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is:
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Assertion (A): Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least o
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Assertion (A): $$\int_\limits2^8 \frac{\sqrt{10-x}}{\sqrt{x}+\sqrt{10-x}} d x=3$$ Reason (R): $$\int_\limits a^b f(x) d View Question Write the domain and range (principle value branch) of the following functions:$$f(x)=\tan ^{-1} x$$View Question (a) If$$f(x)=\left\{\begin{array}{ll}x^2, & \text { if } x \geq 1 \\ x, & \text { if } x OR (b) Find the value(s) of '\$
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Sketch the region bounded by the lines $$2 x+y=8, y=2, y=4$$ and the $$y$$-axis. Hence, obtain its area using integratio
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(a) If the vectors $$\vec{a}$$ and $$\vec{b}$$ are such that $$|\vec{a}|=3,|\vec{b}|=\frac{2}{3}$$ and $$\vec{a} \times View Question Find the vector and the cartesian equations of a line that passes through the point$$A(1,2,-1)$$and parallel to the li View Question$$\text { If } A=\left[\begin{array}{ccc} 1 & 2 & 3 \\ 3 & -2 & 1 \\ 4 & 2 & 1 \end{array}\right] \text {, then show tha
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(a) Differentiate $$\quad \sec ^{-1}\left(\frac{1}{\sqrt{1-x^2}}\right) \quad$$ w.r.t. $$\sin ^{-1}\left(2 x \sqrt{1-x^2 View Question (a) Evaluate:$$\int_\limits0^{2 \pi} \frac{1}{1+e^{\sin x}} d x$$OR$$\text { (b) Find: } \int \frac{x^4}{(x-1)\left(x
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Find the area of the following region using integration: $$\left\{(x, y): y^2 \leq 2 x \text { and } y \geq x-4\right\} View Question (a) Find the coordinates of the foot of the perpendicular drawn from the point$$P(0,2,3)$$to the line$$\frac{x+3}{5}=
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Find the distance between the lines: \begin{aligned} & \vec{r}=(\hat{i}+2 \hat{j}-4 \hat{k})+\lambda(2 \hat{i}+3 \hat{ View Question (a) The median of an equilateral triangle is increasing at the rate of2 \sqrt{3} \mathrm{~cm} / \mathrm{s}$$. Find th View Question Evaluate :$$\int_\limits0^{\frac{\pi}{2}} \sin 2 x \tan ^{-1}(\sin x) d x$$View Question Solve the following Linear Programming Problem graphically : Maximize:$$P=70 x+40 y$$Subject to:$$\begin{aligned} \ma
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(a) In answering a question on a multiple choice test, a student either knows the answer or guesses. Let $$\frac{3}{5}$$
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Case Study I An organization conducted bike race under two different categories-Boys and Girls. There were 28 participan
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Case Study II Gautam buys 5 pens, 3 bags and 1 instrument box and pays a sum of ₹ 160. From the same shop. Vikram buys 2
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Case Study III An equation involving derivatives of the dependent variable with respect to the independent variables is
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