If the position vectors of $A, B, C, D$ are $\hat{i}+2\hat{j}+2\hat{k}, 2\hat{i}-\hat{j}, \hat{i}+\hat{j}+3\hat{k}$ and $4\hat{j}+5\hat{k}$ respectively,then the quadrilateral $ABCD$ is a

Who is known as the Father of Botany?

The transformed equation of $3x^2 + 3y^2 + 2xy = 2$,when the coordinate axes are rotated through an angle of $45^{\circ}$,is

Let $\overrightarrow{a}=a_1 \hat{i}+a_2 \hat{j}+a_3 \hat{k}$.
Assertion $(A)$: The identity $|\overrightarrow{a} \times \hat{i}|^2+|\overrightarrow{a} \times \hat{j}|^2+|\overrightarrow{a} \times \hat{k}|^2=2|\overrightarrow{a}|^2$ holds for $\overrightarrow{a}$.
Reason $(R)$: $\overrightarrow{a} \times \hat{i}=a_3 \hat{j}-a_2 \hat{k}$, $\overrightarrow{a} \times \hat{j}=a_1 \hat{k}-a_3 \hat{i}$, and $\overrightarrow{a} \times \hat{k}=a_2 \hat{i}-a_1 \hat{j}$.
Which of the following is correct?

Among $K$,$Mg$,$Au$,and $Cu$,the one which is extracted by heating its ore in air is

In a galvanometer,$5 \%$ of the total current in the circuit passes through it. If the resistance of the galvanometer is $G$,the shunt resistance $S$ connected to the galvanometer is