The projection of \(\overrightarrow{\mathbf{a}}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}+5 \hat{\mathbf{k}}\) on \(\overrightarrow{\mathbf{b}}=2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+\hat{\mathbf{k}}\) is

If \(A=\left[\begin{array}{ccc}0 & x & 16 \\ x & 5 & 7 \\ 0 & 9 & x\end{array}\right]\) is singular, then the possible values of \(x\) are

The simplified form of \( i^{n}+i^{n+1}+i^{n+2}+i^{n+3} \) is

\(\tan^{-1}\left(\dfrac{1}{1 + 1 \cdot 2}\right) + \tan^{-1}\left(\dfrac{1}{1 + 2 \cdot 3}\right) + \ldots + \tan^{-1}\left(\dfrac{1}{1 + n(n+1)}\right) = \)

If \(3 x+y+k=0\) is a tangent to the circle \(x^{2}+y^{2}=10\), the values of \(k\) are

If \(u=\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)\) and \(v=\tan ^{-1}\left(\frac{2 x}{1-x^2}\right)\) then \(\frac{d u}{d v}\) is

The negation of the statement "All continuous functions are differentiable"

What does sthe sample of given base sequence represent?
5'-GAATTC-3'
3'-CTTAAG-5

Which of the following system in an octahedral complex has maximum unpaired electrons?

\(\Lambda^0_{m(\text{NH}_4\text{OH})}\) is equal to ____

For Freundlich adsorption isotherm, a graph of \(\log (x / m)\) vs \(\log (p)\) gives a straight line. The slope of line and its \(Y\)-axis intercept respectively are

If \(z=x+i y\), then the equation \(|z+1|=|z-1|\) represents

Match List-I with List-II for the following reaction pattern
Glucose \(\xrightarrow{\text { Reagent }}\) Product \(\longrightarrow\) Structural prediction
\begin{array}{|l|l|l|l|}\hline & \text{List - I (Reagents)} & & \text{List-II (Structural prediction)} \\\hline \text{a}. & \text{Acetic anhydride} & \text{(i)} & \text{Glucose has an aldehyde group} \\\hline \text{b.} & \text{Bromine water} & \text{(ii)} & \text{Glucose has a straight chain of six carbon atoms} \\\hline \text{c.} & \text{Hydroiodic acid} & \text{(iii)} & \text{Glucose has five hydroxyl group} \\\hline \text{d.} & \text{Hydrogen cyanide} & \text{(iv)} & \text{Glucose has a carbonyl group} \\\hline\end{array}

Choose the correct answer from the options given below.