Scalars & Vectors — MH-CET Physics MCQs with Solutions
Free MH-CET Physics Scalars & Vectors MCQs with step-by-step solutions (21 questions). Part of Mathematical Methods (Std 11). Practise online on Prepizo — no login needed.
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Questions with solutions
Q1 — Scalars & Vectors · easy · theory
A scalar quantity is one that has:
A. Magnitude only ✓ Correct
B. Direction only
C. Magnitude and direction
D. Neither magnitude nor direction
Solution: Mass, time, work and temperature are scalars; they add by ordinary arithmetic.
Q2 — Scalars & Vectors · medium · theory
A vector quantity is one that has:
A. Magnitude only
B. Direction only
C. Magnitude and direction but adds arithmetically
D. Magnitude, direction and obeys the laws of vector addition ✓ Correct
Solution: Electric current has both magnitude and direction yet is a scalar, because it does not add by the triangle law.
Q3 — Scalars & Vectors · easy · theory
Two vectors are said to be equal if they have:
A. The same point of application
B. The same direction only
C. The same magnitude and the same direction ✓ Correct
D. The same magnitude only
Solution: Equal vectors need not act at the same point; a vector can be shifted parallel to itself.
Q4 — Scalars & Vectors · easy · theory
A unit vector is a vector whose:
A. Magnitude equals that of the original vector
B. Magnitude is one and which specifies a direction ✓ Correct
C. Direction is undefined
D. Magnitude is zero
Solution: Dividing any vector by its own magnitude produces the unit vector along it.
Q5 — Scalars & Vectors · medium · theory
A null vector is a vector whose:
A. Magnitude is infinite
B. Magnitude is zero and whose direction is indeterminate ✓ Correct
C. Magnitude is one
D. Direction is along the $x$-axis
Solution: It results, for example, when a vector is added to its own negative.
Q6 — Scalars & Vectors · easy · theory
The negative of a vector $\vec{A}$ is a vector that has:
A. A magnitude smaller than $\vec{A}$
B. The same magnitude but the opposite direction ✓ Correct
C. Zero magnitude
D. The same direction but the opposite magnitude
Solution: Adding $\vec{A}$ and $-\vec{A}$ gives the null vector.
Q7 — Scalars & Vectors · easy · theory
The position vector of a point gives:
A. Its location relative to a chosen origin ✓ Correct
B. The force acting on it
C. Its mass
D. Its speed relative to the origin
Solution: It is drawn from the origin to the point in question.
Q8 — Scalars & Vectors · medium · theory
Collinear vectors are vectors that:
A. Have equal magnitudes
B. Act along the same line or along parallel lines ✓ Correct
C. Always sum to zero
D. Are always perpendicular
Solution: Their resultant is found by ordinary addition or subtraction of magnitudes.
Q9 — Scalars & Vectors · easy · numerical
The magnitude of the vector $3\hat{i} + 4\hat{j}$ is:
A. $7$
B. $5$ ✓ Correct
C. $1$
D. $25$
Solution: $|\vec{A}| = \sqrt{3^2 + 4^2} = \sqrt{25} = 5$.
Q10 — Scalars & Vectors · easy · numerical
The magnitude of the vector $6\hat{i} + 8\hat{j}$ is:
A. $48$
B. $14$
C. $10$ ✓ Correct
D. $2$
Solution: $\sqrt{36 + 64} = \sqrt{100} = 10$.
Q11 — Scalars & Vectors · medium · numerical
The unit vector along $3\hat{i} + 4\hat{j}$ is:
A. $\dfrac{3\hat{i} + 4\hat{j}}{7}$
B. $\dfrac{3\hat{i} + 4\hat{j}}{25}$
C. $3\hat{i} + 4\hat{j}$
D. $\dfrac{3\hat{i} + 4\hat{j}}{5}$ ✓ Correct
Solution: Dividing by the magnitude $5$ gives a vector of unit length in the same direction.
Q12 — Scalars & Vectors · medium · numerical
The magnitude of the vector $\hat{i} + \hat{j} + \hat{k}$ is:
A. $3$
B. $1$
C. $\sqrt{3}$ ✓ Correct
D. $\sqrt{2}$
Solution: $\sqrt{1 + 1 + 1} = \sqrt{3}$.
Q13 — Scalars & Vectors · medium · numerical
The magnitude of the vector $2\hat{i} - 3\hat{j} + 6\hat{k}$ is:
A. $5$
B. $7$ ✓ Correct
C. $49$
D. $11$
Solution: $\sqrt{4 + 9 + 36} = \sqrt{49} = 7$.
Q14 — Scalars & Vectors · medium · numerical
The unit vector along $2\hat{i} + 3\hat{j} + 6\hat{k}$ is obtained by dividing it by:
A. $5$
B. $7$ ✓ Correct
C. $11$
D. $49$
Solution: Its magnitude is $\sqrt{4 + 9 + 36} = 7$.
Q15 — Scalars & Vectors · medium · numerical
The magnitude of the vector $5\hat{i} - 12\hat{j}$ is:
A. $169$
B. $13$ ✓ Correct
C. $7$
D. $17$
Solution: $\sqrt{25 + 144} = \sqrt{169} = 13$.
Q16 — Scalars & Vectors · easy · numerical
The magnitude of the vector $8\hat{i} + 6\hat{j}$ is:
A. $10$ ✓ Correct
B. $14$
C. $48$
D. $2$
Solution: $\sqrt{64 + 36} = 10$.
Q17 — Scalars & Vectors · medium · numerical
The magnitude of the vector $\hat{i} + 2\hat{j} + 2\hat{k}$ is:
A. $3$ ✓ Correct
B. $\sqrt{5}$
C. $9$
D. $5$
Solution: $\sqrt{1 + 4 + 4} = \sqrt{9} = 3$.
Q18 — Scalars & Vectors · easy · numerical
Which of the following is a scalar quantity?
A. Work ✓ Correct
B. Angular velocity
C. Displacement
D. Torque
Solution: Work is the scalar product of force and displacement, so the result is a pure number with units.
Q19 — Scalars & Vectors · medium · numerical
Which of the following is a vector quantity?
A. Power
B. Work
C. Electric current
D. Torque ✓ Correct
Solution: Torque is the cross product $\vec{r} \times \vec{F}$ and has a definite direction along the axis.
Q20 — Scalars & Vectors · easy · numerical
The magnitude of a null vector is:
A. One
B. Infinite
C. Zero ✓ Correct
D. Indeterminate
Solution: Its direction, however, is indeterminate.
Q21 — Scalars & Vectors · easy · numerical
The magnitude of any unit vector is:
A. Zero
B. Exactly one ✓ Correct
C. Equal to that of the original vector
D. Infinite
Solution: By definition a unit vector carries direction information only.