To solve this problem, we need to determine the cost price of the first pendant given certain conditions about losses and gains on selling two pendants together, resulting in neither a profit nor a loss overall.

1. Let the cost price of the first pendant be \(x\) rupees. Consequently, the cost price of the second pendant will be \((1200 - x)\) rupees since the total cost of both pendants is ₹1,200.
2. The first pendant is sold at a loss of 10%. Thus, the selling price of the first pendant is:

\text{Selling Price}_1 = x - \frac{10}{100} \cdot x = 0.9x

1. The second pendant is sold at a gain of 14%. Therefore, the selling price of the second pendant is:

\text{Selling Price}_2 = (1200 - x) + \frac{14}{100} \cdot (1200 - x) = 1.14 \cdot (1200 - x)

1. We know that on the whole, there is neither a gain nor a loss, which implies that the total selling price of both pendants is equal to their total cost price:

\begin{align*} 0.9x + 1.14 \cdot (1200 - x) &= 1200 \\ \end{align*}

1. Simplifying the equation, we have:

\begin{align*} 0.9x + 1368 - 1.14x &= 1200 \\ -0.24x + 1368 &= 1200 \\ 1368 - 1200 &= 0.24x \\ 168 &= 0.24x \\ x &= \frac{168}{0.24} \\ x &= 700 \end{align*}

1. Therefore, the cost price of the first pendant is ₹700.

Thus, the correct answer is ₹700, which matches the given correct option.