The interval in which the function $$f(x)=x^x,x>0$$, is strictly increasing is

The area enclosed by the curves $x y+4 y=16$ and $x+y=6$ is equal to :

The area of the region enclosed by the parabolas $$y=4x-x^2$$ and $$3y=(x-4{)}^2$$ is equal to :

The area of the region $$\left\{(x,y):y^2\le 4x,x0,x\ne 3\right\}$$ is

The area (in square units) of the region bounded by the parabola $$y^2=4(x-2)$$ and the line $$y=2x-8$$, is :

The area (in square units) of the region enclosed by the ellipse $$x^2+3y^2=18$$ in the first quadrant below the line $$y=x$$ is

The parabola $$y^2=4x$$ divides the area of the circle $$x^2+y^2=5$$ in two parts. The area of the smaller part is equal to :

One of the points of intersection of the curves $$y=1+3x-2x^2$$ and $$y=\frac{1}{x}$$ is $$\left(\frac{1}{2},2\right)$$. Let the area of the region enclosed by these curves be $$\frac{1}{24}(l\sqrt{5}+\mathrm{m})-\mathrm{n}{\log }_{\mathrm{e}}(1+\sqrt{5})$$, where $$l,\mathrm{m},\mathrm{n}\in \mathbf{N}$$. Then $$l+\mathrm{m}+\mathrm{n}$$ is equal to

The area (in sq. units) of the region described by $$\left\{(x,y):y^2\le 2x\text{, and }y\ge 4x-1\right\}$$ is

The area of the region in the first quadrant inside the circle $$x^2+y^2=8$$ and outside the parabola $$y^2=2x$$ is equal to :

The area enclosed between the curves $$y=x|x|$$ and $$y=x-|x|$$ is :

If the area of the region $$\left\{(x, y): \frac{\mathrm{a}}{x^2} $\le$ y $\le$ \frac{1}{x}, 1 $\le$ x $\le$ 2,0

Let the area of the region enclosed by the curves $$y=3x,2y=27-3x$$ and $$y=3x-x\sqrt{x}$$ be $$A$$. Then $$10A$$ is equal to

Match List - I with List - II. table { width: 100%; border-collapse: collapse; } table, th, td { border: 1px solid black; } th, td { padding: 10px; text-align: center; } th { background-color: blue; color: white; } List I (Number) List II (Significant figure) (A) 1001 (I) 3 (B) 010.1 (II) 4 (C) 100.100 (III) 5 (D) 0.0010010 (IV) 6 Choose the correct answer from the options given below :

10 divisions on the main scale of a Vernier calliper coincide with 11 divisions on the Vernier scale. If each division on the main scale is of 5 units, the least count of the instrument is :

The dimensional formula of angular impulse is :

The radius $(\mathrm{r})$, length $(l)$ and resistance $(\mathrm{R})$ of a metal wire was measured in the laboratory as $$\begin{array}{rl}& \mathrm{r}=(0.35\pm 0.05)\mathrm{cm}\\ & \\ & \mathrm{R}=(100\pm 10)\mathrm{ohm}\\ & \\ & l=(15\pm 0.2)\mathrm{cm}\end{array}$$ The percentage error in resistivity of the material of the wire is :

Given below are two statements : Statement (I) : Planck's constant and angular momentum have same dimensions. Statement (II) : Linear momentum and moment of force have same dimensions. In the light of the above statements, choose the correct answer from the options given below :

Given below are two statements : one is labelled as Assertion (A) and the other is labelled as Reason (R). Assertion (A) : In Vernier calliper if positive zero error exists, then while taking measurements, the reading taken will be more than the actual reading. Reason (R) : The zero error in Vernier Calliper might have happened due to manufacturing defect or due to rough handling. In the light of the above statements, choose the correct answer from the options given below :

Consider two physical quantities $$A$$ and $$B$$ related to each other as $$E=\frac{B-x^2}{At}$$ where $$E,x$$ and $$t$$ have dimensions of energy, length and time respectively. The dimension of $$AB$$ is