CBSE 12th Mathematics Delhi Set 1 - 2023

Paper was held on
Tue, Mar 14, 2023 5:00 AM

## Mathematics

Let $$A=\{3,5\}$$. Then number of reflexive relations of $$A$$ is:

View Question $$\sin \left[\frac{\pi}{3}+\sin ^{-1}\left(\frac{1}{2}\right)\right]$$ is equal to:

View Question If for a square matrix $$\mathrm{A}, A^2-A+I=\mathrm{O}$$, then $$\mathrm{A}^{-1}$$ equals:

View Question $$\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

View Question The derivative of $$x^{2 x}$$ w.r.t. $$x$$ is:

View Question The function $$f(x)=[x]$$, where $$[x]$$ denotes the greatest integer less than or equal to $$x$$, is continuous at:

View Question If $$x=A \cos 4 t+B \sin 4 t$$, then $$\frac{d^2 x}{d t^2}$$ is equal to:

View Question The interval in which the function $$f(x)=2 x^3+9 x^2 +12 x-1$$ is decreasing is :

View Question $$\int \frac{\sec x}{\sec x-\tan x} d x$$ equals:

View Question $$\int_\limits{-1}^1 \frac{|x-2|}{x-2} d x, x \neq 2 \text { is equal to: }$$

View Question 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 /

View Question Five fair coins are tossed simultaneously. The probability of the events that atleast one head comes up is:

View Question Assertion (A): Two coins are tossed simultaneously. The probability of getting two heads, if it is known that at least o

View Question 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 '$

View Question 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

View Question (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

View Question (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

View Question 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}=

View Question 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 of $$2 \sqrt{3} \mathrm{~cm} / \mathrm{s}$$. 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

View Question (a) In answering a question on a multiple choice test, a student either knows the answer or guesses.
Let $$\frac{3}{5}$$

View Question Case Study I
An organization conducted bike race under two different categories-Boys and Girls. There were 28 participan

View Question 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

View Question Case Study III
An equation involving derivatives of the dependent variable with respect to the independent variables is

View Question