AP EAMCET Engineering 20 Apr 2019 Shift 2 Paper

As the physical quantity is obtained from the ratio of thermal conductivity and universal gravitational constant therefore, the dimensional formula of it is,
‌

[k]

[G]

‌‌=‌

[M1L1T−3K−1]

[M−1L3T−2]

‌‌=[M2L−2T−1K−1]
Compare the above dimensional formula with the given dimensional formula,
[M2aL4bT2cKd]=[M2L−2T−1K−1]
‌Thus, ‌a=1,b=−‌

1

2

,c=−‌

1

2

‌ and ‌d=‌

1

2

The values of required expression is calculated as
‌

a+b

c+b

−d=‌

1− 1 2

−‌ 1 2 −‌ 1 2

−(−1)
‌

a+b

c+b

−d=‌

1

2