If $(x, y, z)$ is an arbitrary point lying on a plane $P$ which passes through the points $(42, 0, 0)$,$(0, 42, 0)$,and $(0, 0, 42)$,then the value of the expression $3 + \frac{x-11}{(y-19)^2(z-12)^2} + \frac{y-19}{(x-11)^2(z-12)^2} + \frac{z-12}{(x-11)^2(y-19)^2} - \frac{x+y+z}{14(x-11)(y-19)(z-12)}$ is:

Six identical conducting rods are joined as shown in the figure. Points $A$ and $D$ are maintained at temperatures $200\,^{\circ}C$ and $20\,^{\circ}C$,respectively. The temperature of junction $B$ will be ......... $^{\circ}C$.

The value of the integral $\int_0^4 \frac{dx}{1+x^2}$ obtained by using the Trapezoidal rule with $h=1$ is

The horizontal acceleration that should be given to a smooth inclined plane of angle $\theta = \sin^{-1}\left(\frac{1}{l}\right)$ to keep an object stationary on the plane, relative to the inclined plane is:

Which of the following statements is correct?

A linear octasaccharide $($molar mass $=1024 g mol ^{-1} )$ on complete hydrolysis produces three monosaccharides: ribose, $2-$deoxyribose and glucose. The amount of $2-$deoxyribose formed is $58.26 \%( w / w )$ of the total amount of the monosaccharides produced in the hydrolyzed products. The number of ribose unit$(s)$ present in one molecule of octasaccharide is $.....$
Use : Molar mass $($in g $mol ^{-1} )$: ribose $=150,2-$deoxyribose $=134$, glucose $=180$; Atomic mass $($in amu$): H =1, O =16$