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The area(in $\text{sq.units}$) enclosed between the region $x+y\le 6,x^2+y^2\le 6y$ and $y^2\le 8x$ is

Using
properties of determinants, prove that:

If $x,y,z$ are real numbers such that $x+y+z=4$ and $x^2+y^2+z^2=6,$ then the range of $x$ is

Let f: R$\to$ Rbe defined by $f\left(x\right)=\frac{1}{x}\forall xϵR,$ then f is.....

The length of normal to the curve $x=a\left(\theta +\sin \theta \right),y=a\left(1-\cos \theta \right)\mathrm{at}\theta =\frac{\pi }{2}$ is .

Let $A,B,C,D$ are any four points in space. If $|\overrightarrow{AB}\times \overrightarrow{CD}+\overrightarrow{BC}\times \overrightarrow{AD}+\overrightarrow{CA}\times \overrightarrow{BD}|=\lambda \times$(Area of $△ABC$), then the value of $\lambda$ is:

On heating, arsine $\left(As{H}_3\right)$ decomposes according to first order kinetics as follows:

$2As{H}_3\left(g\right)\to 2As\left(s\right)+3H_2\left(g\right)$

The total pressure measured at constant temperature and constant volume varies with time as given:

Let $x+\sin y=2020$ and $x+2020\cos y=2019$ where $0\le y\le \frac{\pi }{2}.$ If $[.]$ denotes the greatest integer function, then the value of $[x+y]$ is

Solve the equation

Set of value(s) of $\theta$ for which ${\sin }^{3}3\theta =0$ is

$\int f^{\prime }(ax+b)\left[f\right(ax+b){]}^{n}dx.$

If $\overrightarrow{a}=-\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k}\text{and}\overrightarrow{b}=2\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{k},$ then the vector $\overrightarrow{c}$ satisfying the conditions

$1)\text{coplanar with}\overrightarrow{a}\text{and}\overrightarrow{b}$

$2)\text{perpendicular to}\overrightarrow{b}$

$3)\overrightarrow{a}\cdot \overrightarrow{c}=7$ is

The angle between the lines $2x=3y=-z\text{and}6x=-y=-4z$ is

"If X then Y unless Z" is represented by which of the following formulas in propostional logic?

$("\rightharpoondown ")$ is negation , "$\wedge$" is conjuntion , and "$\to$" is implication)

1. 1572

If ABCDEF is a regular hexagon with $\overrightarrow{AB}=\overrightarrow{a}$ and $\overrightarrow{BC}=\overrightarrow{b}$,then $\overrightarrow{CE}$

If $\frac{5}{x-2}<5,x\ne 2$, then the interval(s) in which $x$ can be lie is/are

The line passing through the extremity A of the major axis and extremity B of the minor axis of the ellipse $x^2+9y^2=9$ meets its auxiliary circle at the point M. Then, the area (insqunits) of the triangle with vertices at A, M and the origin O is

If $x,y,z$ are real numbers such that $x+y+z=4$ and $x^2+y^2+z^2=6,$ then the range of $x$ is

The letters of the word ASHISH are permuted and are arranged in an alphabetical order as in an English dictionary. Then, the rank of the word ASHISH is _____

If α
and β are different complex
numbers with
= 1, then find.

If $\alpha and\beta$ are the roots of the equation $4x^2+3x+7=0$, then $\frac{1}{\alpha }+\frac{1}{\beta }=$

The value of $\sum _{r=1}^n\frac{r{}^n{C}_r}{{}^n{C}_{r-1}}$ is

Find the value of n so that may be the geometric mean between a and b.

1. 1

Evaluate $\int \frac{x\mathrm{dx}}{(x-1)(x^2+4)}$

Let $f\left(x\right)=[x^3-3],$ where $[.]$ denotes the greatest integer function. Then the number of points in the interval $(1,2)$ where the function is discontinuous, is

A variable line passes through a fixed point $(x_1,y_1)$ and meets the axes at $A$ and $B$. If the rectangle $OAPB$ be completed, the locus of P is, ($O$ being the origin of the system of axes)

If $si{n}^{-1}\left(\frac{2a}{1+a^2}\right)+si{n}^{-1}\left(\frac{2b}{1+b^2}\right)=2ta{n}^{-1}x$, then x is equal to

What is the condition for a function y = f(x) to be a Strictly decreasing function.