Step 1: Analyzing the Possessive Form.
In the sentence, the subject "mother's" is singular, indicating that it belongs to one mother. Hence, the correct possessive form should be "mother's."
Step 2: Analyzing the Options.
- (A) My mother's official car is parked elsewhere: This is the correct sentence as it correctly uses the possessive form "mother's."
- (B) My mothers' official car is parked elsewhere: This is incorrect because the possessive form "mothers'" indicates multiple mothers, which does not match the context.
- (C) My mother's official car is parked everywhere: While this sentence is grammatically correct, it doesn't convey the intended meaning of the original sentence, which specifies the location of the car ("elsewhere").
- (D) My mother's official cars is parked elsewhere: This is incorrect because "cars" is plural, while "mother's" is singular. Hence, it creates a subject-verb agreement error.
Step 3: Conclusion.
The correct answer is (A) My mother's official car is parked elsewhere, as it is grammatically correct and fits the context.
A weight of $500\,$N is held on a smooth plane inclined at $30^\circ$ to the horizontal by a force $P$ acting at $30^\circ$ to the inclined plane as shown. Then the value of force $P$ is:
A steel wire of $20$ mm diameter is bent into a circular shape of $10$ m radius. If modulus of elasticity of wire is $2\times10^{5}\ \text{N/mm}^2$, then the maximum bending stress induced in wire is: