MHTCET 20 Apr 2026 Shift 2 Paper

Concept:Validity of vector expressions depends on whether dot and cross products are applied to vectors only.Explanation:For A: $(\vec{a} \times \vec{b}) \cdot \vec{c}$.$\vec{a} \times \vec{b}$ is a vector, so its dot product with $\vec{c}$ is valid.Thus A is meaningful.For B: $\vec{a} \times (\vec{b} \cdot \vec{c})$.$\vec{b} \cdot \vec{c}$ is a scalar, but cross product requires two vectors.Thus B is meaningless.For C: $\vec{a} \cdot (\vec{b} \cdot \vec{c})$.Here $\vec{b} \cdot \vec{c}$ is a scalar, and dot product is defined only between vectors.Thus C is meaningless.For D: $|\vec{a}|(\vec{b} \cdot \vec{c})$.Both $|\vec{a}|$ and $\vec{b} \cdot \vec{c}$ are scalars, so their product is valid.Thus D is meaningful.For E: $(\vec{a} \cdot \vec{b}) \times (\vec{b} \cdot \vec{c})$.Both factors are scalars, and cross product is not defined for scalars.Thus E is meaningless.So meaningful expressions are A and D, while B, C, and E are meaningless.Therefore, the statement "B and E are meaningful" is incorrect.Answer:Option A: B and E are meaningful is not correct.