ECAT MCQs

Use the Pythagorean theorem for perpendicular components.
Magnitude = √(3²+4²)=5.

The x-component is A cosθ.
10 cos60° = 10×0.5 = 5.

The y-component is A sinθ.
10 sin30° = 10×0.5 = 5.

Vectors in the same direction add directly.
The resultant is 12+7 = 19 N.

Precision describes repeatability.
Measurements can be precise without being accurate.

Accuracy describes agreement with the true or accepted value.
Systematic error can reduce accuracy.

Systematic errors often arise from calibration or method bias.
Repeated measurements do not automatically remove them.

Random errors cause scatter around a central value.
Repeated measurements and averaging can reduce their effect.

Leading zeros are not significant, but trailing zeros after a decimal are.
Thus 4, 5, and the final zero are significant.

Vector addition replaces multiple vectors with an equivalent single vector.
Its direction and magnitude depend on the original vectors.

Perpendicular vector components form a right triangle.
The resultant magnitude is found from the sum of squared components.

Let the son's age be x and father's age 3x.
Then 3x + 10 = 2(x + 10), giving x = 10.