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Four resistors $A, B, C$ and $D$ form a Wheatstone bridge as shown in the figure. The bridge is balanced when $C = 100 \Omega$. If $A$ and $B$ are interchanged,the bridge balances for $C = 121 \Omega$. The value of $D$ is (in $\Omega$)

Suppose $\overrightarrow{a}=\lambda \hat{i}-7 \hat{j}+3 \hat{k}$ and $\overrightarrow{b}=\lambda \hat{i}+\hat{j}+2 \lambda \hat{k}$. If the angle between $\overrightarrow{a}$ and $\overrightarrow{b}$ is greater than $90^{\circ}$,then $\lambda$ satisfies the inequality

Product $A$ is

If $\overline{a}=\frac{1}{\sqrt{10}}(3 \hat{i}+\hat{k})$ and $\overline{b}=\frac{1}{7}(2 \hat{i}+3 \hat{j}-6 \hat{k})$,then the value of $(2 \overline{a}-\overline{b}) \cdot [(\overline{a} \times \overline{b}) \times (\overline{a}+2 \overline{b})]$ is

The $AT/GC$ ratio in human beings is (where $A=$ adenine,$T=$ thymine,$G=$ guanine,$C=$ cytosine).

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