Select the correct option with respect to the age pyramids shown in the image.
- A$a$ - Expanding,$b$ - Stable,$c$ - Declining
- B$a$ - Stable,$b$ - Expanding,$c$ - Declining
- C$a$ - Stable,$b$ - Declining,$c$ - Expanding
- D$a$ - Declining,$b$ - Stable,$c$ - Expanding
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Wires $P$ and $Q$ have the same resistance at ordinary (room) temperature. When heated,the resistance of $P$ increases and that of $Q$ decreases. We conclude that
$A$ tower subtends angles $\alpha, 2 \alpha$ and $3 \alpha$ respectively at points $A, B$ and $C$,all lying on a horizontal line through the foot of the tower. Then $\frac{A B}{B C}$ is equal to:
Some physical quantities are given in List-$I$ and their related units are given in List-$II$. Match the correct pairs.
List-$I$ List-$II$ $(A)$ Magnetic field intensity $(i)$ $Wb$ $(B)$ Magnetic flux (ii) $Wb \cdot m^{-2}$ $(C)$ Magnetic pole strength (iii) $A \cdot m$ $(D)$ Magnetic induction (iv) $A \cdot m^{-1}$
| List-$I$ | List-$II$ |
| $(A)$ Magnetic field intensity | $(i)$ $Wb$ |
| $(B)$ Magnetic flux | (ii) $Wb \cdot m^{-2}$ |
| $(C)$ Magnetic pole strength | (iii) $A \cdot m$ |
| $(D)$ Magnetic induction | (iv) $A \cdot m^{-1}$ |
$\sum_{k=1}^{2n+1} (-1)^{k-1} k^2$ is equal to
If the circle $x^2+y^2+4x-6y+c=0$ bisects the circumference of the circle $x^2+y^2-6x+4y-12=0$,then $c$ is equal to
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