A bag contains books numbered 1 to 20 . Three books are drawn from the bag with replacement. The probability that largest number on the book is 7 .

\(\int_0^2 \frac{2 x-2}{2 x-x^2} d x\) is equal to

In a hyperbola, if the length of transverse axis is twice that of the conjugate axis, then the distance between its directrices is..... units.

The area (in sq units) of the triangle formed by the normal drawn at the point \((1,0)\) on the curve \(\mathrm{x}=\mathrm{e}^{\sin \mathrm{y}}\) with the coordinate axes is

The value of \(\lambda\) with \(|\lambda| < 16\) such that \(2 x^2-10 x y+12 y^2+5 x+\lambda y-3=0\) represents a pair of straight lines, is

If the equation to the locus of points equidistant from the points \((-2,3),(6,-5)\) is \(a x+b y+c=0\), where \(a>0\), then the ascending order of \(a, b, c\) is

If \(2 \cosh 2 x+10 \sinh 2 x=5\), then \(x=\)

If the equation of the tangent drawn at \((h, k)\) to the hyperbola \(\frac{(\mathrm{x}-1)^2}{1}-\frac{(\mathrm{y}-2)^2}{2}=1\) is \(\mathrm{x}=2\), then \(\mathrm{h}+\mathrm{k}=\)

\(\int \sin ^5 x \cdot \cos ^5 x d x=\)

The source of vitamin, whose deficiency causes scurvy is

If $a,b$ and $c$ are the roots of $x^3+4x+1=0,$ then $\frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}=$

Identify antihistamines from the following:
\(\begin{array}{cccc}
\hline \text { Serotonin } & \text { Dimetane } & \text { Phenelzine } & \text { Seldane } \\
\hline 1 & 2 & 3 & 4 \\
\hline
\end{array}\)

The formation of oxide ion \(\mathrm{O}^{2-}\) from oxygen atom requires an exothermic reaction, followed by an endothermic step as shown below. The process of formation of \(\mathrm{O}^{2-}\) in gas phase is unfavorable \(\left(\Delta H^{\ominus}=+\right.\) ve \()\), even though it has stable configuration of the nearest noble gas neon. This is because
\(\begin{aligned} & \mathrm{O}(g)+e^{-} \longrightarrow \mathrm{O}^{-}(g) ; \Delta H^{\ominus}=-141 \mathrm{~kJ} \mathrm{~mol}^{-1} \\ & \mathrm{O}^{-}(g)+e^{-} \longrightarrow \mathrm{O}^{2-}(g) ; \Delta H^{\ominus}=+760 \mathrm{~kJ} \mathrm{~mol}^{-1}\end{aligned}\)