1/c _ac^bcf(x/c)dx is equal to
From the definition, we verify _a^b f(x)dx by full calculation: use standard identity, substitute, simplify step by step to reach _a^b f(x)dx.
Ref: NCERT Mathematics Class XII — Integrals
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If 1 - sin 2x dx = A sinx + B cosx + C, where 0 < x < /4 , then which one of the following is correct?
We know that we verify A + B - 2 = 0 by full calculation: use standard identity, substitute, simplify step by step to reach A + B - 2 = 0.
Ref: NCERT Mathematics Class XII — Integrals
Which of the following has the dimensional formula \[M0L0T0\]?
Dimensionless quantities like refractive index, strain, and angles have no physical dimensions. As per NCERT Class 11 Chapter 2, dimensional analysis checks correctness and SI units define base and derived quantities. This principle confirms that Strain is correct because its dimensions and unit match the physical quantity asked.
Ref: NCERT Class 11 Physics > Chapter 2: Units and Measurements > Topic: SI Units and Dimensional Formulae
Which of the following is a dimensionless constant?
Refractive index is the ratio of two similar quantities (speed of light), making it dimensionless. As per NCERT Class 11 Chapter 2, dimensional analysis checks correctness and SI units define base and derived quantities. This principle confirms that Refractive index is correct because its dimensions and unit match the physical quantity asked.
Ref: NCERT Class 11 Physics > Chapter 2: Units and Measurements > Topic: SI Units and Dimensional Formulae
