If the rate of the reaction is equal to the rate constant,the order of the reaction is

$\lim _{x \rightarrow \infty}\left[\sqrt{x^2+2 x-1}-x\right]$ is equal to :

If $y=(1+x)(1+x^2)(1+x^4) \dots (1+x^{2^n})$,then $(\frac{dy}{dx})_{x=0}$ is equal to

The acute angle between the two lines whose direction ratios $(l, m, n)$ satisfy the equations $l+m-n=0$ and $l^2+m^2-n^2=0$ is

If pairs of straight lines $x^2-2 p x y-y^2=0$ and $x^2-2 q x y-y^2=0$ be such that each pair bisects the angle between the other pair,then

The line $x=\frac{\pi}{4}$ divides the area of the region bounded by $y=\sin x$,$y=\cos x$ and the $x$-axis $(0 \leq x \leq \frac{\pi}{2})$ into two regions of areas $A_1$ and $A_2$. Then $A_1 : A_2$ equals (in $: 1$)