Which of the following pair of straight lines intersect at right angles?

If four letters are chosen from the letters of the word ASSIGNMENT and are arranged in all possible ways to form 4 letter words (with or without meaning), then total number of such words that can be formed is

If $\left[x\right]$ represents the greatest integer not greater than $x,$ then $\left[{\left(1+\frac{1}{100000}\right)}^{100000}\right]=$

In a triangle ABC, if \(\mathrm{A}, \mathrm{B}\) and C are in arithmetic progression, \(rr_3=r_1 r_2\) and \(c=10\), then \(a^2+b^2+c^2=\)

Let ' \(\mathrm{O}\) ' be the origin, \(\mathrm{A}\) and \(\mathrm{B}\) be two points with position vectors \(-3 \hat{i}-3 \hat{j}+4 \hat{k}\) and \(4 \hat{i}-4 \hat{j}-3 \hat{k}\) respectively. Let \(P\) be a point such that the line drawn through \(P\) parallel to \(\overrightarrow{\mathrm{OB}}\) meets \(\mathrm{OA}\) in \(\mathrm{L}\) and another line through \(\mathrm{P}\) parallel to \(\overrightarrow{\mathrm{OA}}\) meets \(\mathrm{OB}\) in \(\mathrm{M}\). If \(\mathrm{L}\) divides \(\mathrm{OA}\) in the ratio \(2: 3\) and \(\mathrm{M}\) divides \(\mathrm{OB}\) in the ratio \(3: 2\), then the distance from 0 to \(\mathrm{P}\) is

If the lines represented by the equation $2x^2-pxy+2y^2=0$ are real then the value of ' $p$ ' lies in the interval

If \(\int f(x) d x=\psi(x)\), then \(\int x^5 f\left(x^3\right) d x=\)

If \(x \sqrt{1+y}+y \sqrt{1+x}=0\), then \(\frac{d y}{d x}\) is equal to

The circumcentre of the triangle with vertices \((-2,3)\), \((2,-1),(4,0)\) is

2.0 g of \(\mathrm{H}_2\) diffuses through a porous container in 10 minutes. How many grams of \(\mathrm{O}_2\) would diffuse from the same container in the same time under similar conditions?

The two enantiomers of secondary butyl chloride differ from each other in which one of the following properties?

100 mL of 0.1 M HA (weak acid) and 100 mL of 0.2 M NaA are mixed. What is the pH of resultant solution? ( \(\mathrm{K}_{\mathrm{a}}\) of HA is \(10^{-5} ; \log 2=0.3\) )

The number of half lives elapsed before \(93.75 \%\) of a radioactive sample has decayed is