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

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

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

$$\text { If } A=\left[\begin{array}{ll} 1 & 0 \\ 2 & 1 \end{array}\right], B=\left[\begin{array}{ll} x & 0 \\ 1 & 1 \en

$$\text { If }\left|\begin{array}{lll} \alpha & 3 & 4 \\ 1 & 2 & 1 \\ 1 & 4 & 1 \end{array}\right|=0 \text {, then the v

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

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

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

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

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

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

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

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

The magnitude of the vector $$6 \hat{i}-2 \hat{j}+3 \hat{k}$$ is :

If a line makes angles of $$90^{\circ}, 135^{\circ}$$ and $$45^{\circ}$$ with the $$x, y$$ and $$z$$ axes respectively,

The angle between the lines $$2 x=3 y=-z$$ and $$6 x=-y=-4 z$$ is:

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 /

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

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

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

Write the domain and range (principle value branch) of the following functions: $$f(x)=\tan ^{-1} x$$

(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 '$

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

(a) If the vectors $$\vec{a}$$ and $$\vec{b}$$ are such that $$|\vec{a}|=3,|\vec{b}|=\frac{2}{3}$$ and $$\vec{a} \times

Find the vector and the cartesian equations of a line that passes through the point $$A(1,2,-1)$$ and parallel to the li

$$\text { If } A=\left[\begin{array}{ccc} 1 & 2 & 3 \\ 3 & -2 & 1 \\ 4 & 2 & 1 \end{array}\right] \text {, then show tha

(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

(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

Find the area of the following region using integration: $$\left\{(x, y): y^2 \leq 2 x \text { and } y \geq x-4\right\}$

(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}=

Find the distance between the lines: $$\begin{aligned} & \vec{r}=(\hat{i}+2 \hat{j}-4 \hat{k})+\lambda(2 \hat{i}+3 \hat{

(a) The median of an equilateral triangle is increasing at the rate of $$2 \sqrt{3} \mathrm{~cm} / \mathrm{s}$$. Find th

Evaluate : $$\int_\limits0^{\frac{\pi}{2}} \sin 2 x \tan ^{-1}(\sin x) d x$$

Solve the following Linear Programming Problem graphically : Maximize: $$P=70 x+40 y$$ Subject to: $$\begin{aligned} \ma

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

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

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

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