Two springs have spring constants $K_A$ and $K_B$ such that $K_A > K_B$. If both springs are stretched by the same extension $x$,the work required will be:
- AMore in spring $A$
- BMore in spring $B$
- CEqual in both
- DNothing can be said
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One die and a coin (both unbiased) are tossed simultaneously. The probability of getting $5$ on the top of the die and tail on the coin is
Names of units of some physical quantities are given in List-$I$ and their dimensional formulae are given in List-$II$. Match the correct pairs in the lists:
$A$. $Pa \cdot s$ $(i)$ $[L^2 \ T^{-2} \ K^{-1}]$ $B$. $N \cdot m \cdot K^{-1}$ $(ii)$ $[M \ L \ T^{-3} \ K^{-1}]$ $C$. $J \cdot kg^{-1} \cdot K^{-1}$ $(iii)$ $[M \ L^{-1} \ T^{-1}]$ $D$. $W \cdot m^{-1} \cdot K^{-1}$ $(iv)$ $[M \ L^2 \ T^{-2} \ K^{-1}]$
| $A$. $Pa \cdot s$ | $(i)$ $[L^2 \ T^{-2} \ K^{-1}]$ |
| $B$. $N \cdot m \cdot K^{-1}$ | $(ii)$ $[M \ L \ T^{-3} \ K^{-1}]$ |
| $C$. $J \cdot kg^{-1} \cdot K^{-1}$ | $(iii)$ $[M \ L^{-1} \ T^{-1}]$ |
| $D$. $W \cdot m^{-1} \cdot K^{-1}$ | $(iv)$ $[M \ L^2 \ T^{-2} \ K^{-1}]$ |
If the lines $2x - 3y = 5$ and $3x - 4y = 7$ are two diameters of a circle of radius $7$,then the equation of the circle is
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