The p.d.f. of a continuous r.v. \(\mathrm{X}\) is given by \(\mathrm{f}(x)=\frac{x}{8}, 0 < x < 4\) \(=0\), otherwise, then \(\mathrm{P}(\mathrm{X} \leq 2)\) is

The equation \(x^3+x-1=0\) has

The rational form of a number \(1 \cdot \overline{41}\) is

The solution set of the constraints \(|x-y| \leqslant 1, x, y \geqslant 0\) is

If \(|\vec{a}|=4,|\vec{b}|=5\), then the values of \(k\) for which \(\vec{a}+k \vec{b}\) is perpendicular to \(\vec{a}-k \vec{b}\) are

\(\int e^{\tan x}\left(\sec ^2 x+\sec ^3 x \sin x\right) d x=\)

Let \(\overline{\mathrm{a}}, \overline{\mathrm{b}}, \overline{\mathrm{c}}\) be three non-coplanar vectors and \(\overline{\mathrm{p}}, \overline{\mathrm{q}}, \overline{\mathrm{r}}\) defined by the relations
\(\overline{\mathrm{p}}=\frac{\overline{\mathrm{b}} \times \overline{\mathrm{c}}}{[\overline{\mathrm{a}} \overline{\mathrm{~b}} \overline{\mathrm{c}}]}, \overline{\mathrm{q}}=\frac{\overline{\mathrm{c}} \times \overline{\mathrm{a}}}{[\overline{\mathrm{a}} \overline{\mathrm{~b}} \overline{\mathrm{c}}]}, \overline{\mathrm{r}}=\frac{\overline{\mathrm{a}} \times \overline{\mathrm{b}}}{[\overline{\mathrm{a}} \overline{\mathrm{~b}} \overline{\mathrm{c}}]}\)
then the value of the expression \((\bar{a}+\bar{b}) \cdot \bar{p}+(\bar{b}+\bar{c}) \cdot \bar{q}+(\bar{c}+\bar{a}) \cdot \bar{r}\) is equal to

A string of mass \(0 \cdot 1 \mathrm{~kg}\) is under a tension \(1 \cdot 6 \mathrm{~N}\). The length of the string is \(1 \mathrm{~m}\). A
transverse wave starts from one end of the string. The time taken by the wave to
reach the other end is

In the following sequence of reactions, the alkene affords the compound $\mathrm{B}$.
${\text{CH}}_3\text{CH}={\text{CHCH}}_3\stackrel{{\text{O}}_3}{⟶}\text{A}\underset{\text{Z}\mathrm{n}}{\overset{{\text{H}}_2\text{O}}{⟶}}$
 The compound $\mathrm{B}$ is:

Which from following cations forms least stable complex with same ligand?

If \(y \sqrt{1-x^{2}}+x \sqrt{1-y^{2}}=1, \quad\) then \(\frac{d y}{d x}=\)

What is the number of moles of propane-1,2,3-triol formed when \(n\) mole of triglyceride is hydrolysed ?

The modulus of the square root of the conjugate of \(-7+24 \sqrt{-1}\) is ....