Which of the following molecules has the highest dipole moment?

  • A
    $BF_3$
  • B
    $NH_3$
  • C
    $NF_3$
  • D
    $B_2H_6$

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If the ionic product of water $(K_w)$ is $1.96 \times 10^{-14}$ at $35^{\circ} C$,what is its value at $10^{\circ} C$?

$A$ series combination of resistor $(R)$ and capacitor $(C)$ is connected to an $A$.$C$. source of angular frequency $\omega$. Keeping the voltage same,if the frequency is changed to $\omega / 3$,the current becomes half of the original current. Then the ratio of the capacitive reactance and resistance at the former frequency is

Consider a system of three charges $\frac{q}{3}, \frac{q}{3}$ and $\frac{-2q}{3}$ placed at points $A, B$ and $C$,respectively,as shown in the figure. Take $O$ to be the centre of the circle of radius $R$ and angle $\angle CAB = 60^{\circ}$.

Observe the following lists. Then the correct match for List-$I$ from List-$II$ is:
List-$I$List-$II$
$(A)$ $[\mathbf{a} \mathbf{b} \mathbf{c}]$$1. |\mathbf{a}||\mathbf{b}|\cos(\mathbf{a}, \mathbf{b})$
$(B)$ $(\mathbf{c} \times \mathbf{a}) \times \mathbf{b}$$2. (\mathbf{a} \cdot \mathbf{c})\mathbf{b} - (\mathbf{a} \cdot \mathbf{b})\mathbf{c}$
$(C)$ $\mathbf{a} \times (\mathbf{b} \times \mathbf{c})$$3. \mathbf{a} \cdot \mathbf{b} \times \mathbf{c}$
$(D)$ $\mathbf{a} \cdot \mathbf{b}$$4. |\mathbf{a}||\mathbf{b}|$
$5. (\mathbf{b} \cdot \mathbf{c})\mathbf{a} - (\mathbf{a} \cdot \mathbf{b})\mathbf{c}$

Which one of the following items gives its correct total number?

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