Which of the following is not a homogeneous function?
Let \(\overline{\mathrm{a}}\) and \(\overline{\mathrm{c}}\) be unit vectors at an angle \(\frac{\pi}{3}\) with each other. If \((\overline{\mathrm{a}} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})) \cdot(\overline{\mathrm{a}} \times \overline{\mathrm{c}})=5\), then \([\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]=\)
The maximum value and minimum value of the volume of the parallelopiped having coterminous edges \(\hat{\mathrm{i}}+x \hat{\mathrm{j}}+\hat{\mathrm{k}}, \hat{\mathrm{j}}+x \hat{\mathrm{k}}\) and \(x \hat{\mathrm{i}}+\hat{\mathrm{k}}\) are respectively
A particular solution of \(\frac{\mathrm{d} y}{\mathrm{~d} x}=(x+9 y)^2\), when \(x=0, y=\frac{1}{27}\) is
If \(\mathrm{f}(x)=\cos (\log x)\) then \(\mathrm{f}\left(x^2\right) \cdot \mathrm{f}\left(y^2\right)-\frac{1}{2}\left[\mathrm{f}\left(\frac{x^2}{y^2}\right)+\mathrm{f}\left(x^2 y^2\right)\right]\) has the value
The shortest distance between the lines \(\bar{r}=(4 \hat{i}-\hat{j})+\lambda(\hat{i}+2 \hat{j}-3 \hat{k})\) and \(\bar{r}=(\hat{i}-\hat{j}+2 \hat{k})+\mu(2 \hat{i}+4 \hat{j}-5 \hat{k})\) is
\[ \mathop {\lim }\limits_{x \to \infty } \frac{\mathrm{e}^{x^4}-1}{\mathrm{e}^{x^4}+1}= \]
If a random variable X follows the Binomial distribution \(B(10, \quad p)\) such that \(5 \mathrm{P}(\mathrm{X}=0)=\mathrm{P}(\mathrm{X}=1)\), then the value of \(\frac{\mathrm{P}(\mathrm{X}=5)}{\mathrm{P}(\mathrm{X}=6)}\) is equal to
Identify the reagent ' \(R\) ' used in the following reaction.
Ketone \(\xrightarrow{\mathrm{R}}\) Semicarbazone
Identify substrate ' \(A\) ' in the following reaction.
\(\mathrm{A}+\mathrm{CO}_2 \xrightarrow[6 \text { atm }]{398 \mathrm{~K}}\) Sodium salicylate \(\xrightarrow{\mathrm{H}_3 \mathrm{O}^{+}}\)Salicylic acid
Calculate the total number of tetrahedral and octahedral voids in 0.4 mol compound having such voids in it.
Which carbon atom of glucopyranose numbered from \(\mathrm{C}-1\) to \(\mathrm{C}-6\) is anomeric?
Calculate molality of the solution containing nonvolatile solute if boiling point elevation of the solution is 0.2 K
\[ \left[\mathrm{K}_{\mathrm{b}}=0.52 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right] \]
Identify the product when magnesium burns in air.
What is the number of chiral carbon atoms present in 3,4-Dibromohexane?
If standard emf of cell \(\mathrm{Zn}_{(\mathrm{s})}\left|\mathrm{Zn}_{(\mathrm{1M})}^{+2}\right| \mathrm{Ag}_{(\mathrm{1M})}^{+1} \mid \mathrm{Ag}_{(\mathrm{s})}\) is 1.55 V .
What is electrical work done under standard conditions?
Identify the major product formed when 2-Methylhexan-3-ol is heated with concentrated sulphuric acid.
What is the value of pH of a NaOH solution that dissociates \(2 \%\) in its 0.01 M solution?
What is the coordination number of Pt in cisplatin?
If a reaction occurs in following two steps
i. \(2 \mathrm{ClO}^{-} \longrightarrow \mathrm{ClO}_2^{-}\)
ii. \(\mathrm{ClO}_2^{-}+\mathrm{ClO}^{-} \longrightarrow \mathrm{ClO}_3^{-}+\mathrm{Cl}^{-}\)
Find the reaction intermediate.
Which amino acid from following is NOT synthesized in our body?
The mass of an atom present in unit cell is \(4.4 \times 10^{-23} \mathrm{~g}\) and the product of density and volume of unit cell is \(1.792 \times 10^{-22} \mathrm{~g}\). What is the type of cubic unit cell?
Which of the following statements is false about interhalogen compounds?
If \(\mathrm{E}^*\left(\mathrm{Mg}^{+2}{ }_{(\mathrm{aq})} \mid \mathrm{Mg}_{(\mathrm{s})}\right)=-2.37 \mathrm{~V}\).
What is potential for \(\mathrm{Mg}_{(\mathrm{s})} \rightarrow \mathrm{Mg}^{+2}(0.1 \mathrm{M})+2 \mathrm{e^-}\) at 298 K ?
Calculate the temperature of 0.05 M sucrose solution in Kelvin if the osmotic pressure of the solution is 1.5 atm .
\[ \left[\mathrm{R}=0.0821 \mathrm{dm}^3 \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right] \]