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Mathematical Methods (Std 11) — MH-CET Physics MCQs with Solutions
Free MH-CET Physics Mathematical Methods (Std 11) MCQs with step-by-step solutions covering Scalars & Vectors, Addition & Subtraction of Vectors, Resolution of Vectors & Components, Scalar (Dot) Product, Vector (Cross) Product, Derivatives & Integrals in Physics. Practise online on Prepizo — no login needed.
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Sample 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 · 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.
Q3 — 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.
Q4 — 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.
Q5 — 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.
Q6 — 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: $|\vec{A}| = \sqrt{3^2 + 4^2} = \sqrt{25} = 5$.
Q7 — 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: $\sqrt{36 + 64} = \sqrt{100} = 10$.
Q8 — 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: $\sqrt{64 + 36} = 10$.
Q9 — 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.
Q10 — 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.
Q11 — 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.
Q12 — Addition & Subtraction of Vectors · easy · theory
The parallelogram law gives the resultant of two vectors as:
A. The shorter diagonal always
B. The perimeter of the parallelogram
C. The diagonal of the parallelogram drawn from their common point ✓ Correct
D. The side of the parallelogram
Solution: The magnitude is $\sqrt{A^2 + B^2 + 2AB\cos\theta}$.
Q13 — Addition & Subtraction of Vectors · easy · theory
Vector addition is commutative, meaning that:
A. $\vec{A} + \vec{B} = 0$
B. $\vec{A} + \vec{B} = \vec{A} - \vec{B}$
C. $\vec{A} \times \vec{B} = \vec{B} \times \vec{A}$
D. $\vec{A} + \vec{B} = \vec{B} + \vec{A}$ ✓ Correct
Solution: The order in which vectors are added does not affect the resultant.
Q14 — Addition & Subtraction of Vectors · easy · theory
The resultant of two vectors is maximum when the angle between them is:
A. $0^\circ$ ✓ Correct
B. $45^\circ$
C. $90^\circ$
D. $180^\circ$
Solution: With $\cos 0^\circ = 1$, the magnitudes simply add.
Q15 — Addition & Subtraction of Vectors · easy · theory
The resultant of two vectors is minimum when the angle between them is:
A. $90^\circ$
B. $270^\circ$
C. $0^\circ$
D. $180^\circ$ ✓ Correct
Solution: Opposite vectors partly cancel, leaving the difference of the magnitudes.
Q16 — Addition & Subtraction of Vectors · easy · theory
Subtraction of a vector $\vec{B}$ from $\vec{A}$ is carried out by:
A. Adding $-\vec{B}$ to $\vec{A}$ ✓ Correct
B. Adding $\vec{B}$ to $\vec{A}$
C. Multiplying $\vec{A}$ by $\vec{B}$
D. Dividing $\vec{A}$ by $\vec{B}$
Solution: Vector subtraction is simply addition of the reversed vector.
Q17 — Addition & Subtraction of Vectors · easy · numerical
Two vectors of magnitudes $3$ and $4$ act at $90^\circ$. Their resultant is:
A. $7$
B. $1$
C. $12$
D. $5$ ✓ Correct
Solution: $R = \sqrt{9 + 16} = 5$.
Q18 — Addition & Subtraction of Vectors · easy · numerical
Two vectors of magnitudes $3$ and $4$ act in the same direction. Their resultant is:
A. $1$
B. $12$
C. $7$ ✓ Correct
D. $5$
Solution: With $\theta = 0^\circ$ the magnitudes add directly.
Q19 — Addition & Subtraction of Vectors · easy · numerical
Two vectors of magnitudes $3$ and $4$ act in opposite directions. Their resultant is:
A. $5$
B. $1$ ✓ Correct
C. Zero
D. $7$
Solution: With $\theta = 180^\circ$ the magnitudes subtract.
Q20 — Addition & Subtraction of Vectors · easy · numerical
The maximum possible resultant of two vectors of magnitudes $6$ and $8$ is:
A. $48$
B. $14$ ✓ Correct
C. $2$
D. $10$
Solution: The maximum occurs when they are parallel: $6 + 8 = 14$.
Q21 — Addition & Subtraction of Vectors · easy · numerical
The minimum possible resultant of two vectors of magnitudes $6$ and $8$ is:
A. $2$ ✓ Correct
B. $14$
C. $10$
D. Zero
Solution: The minimum occurs when they are antiparallel: $|8 - 6| = 2$.
Q22 — Addition & Subtraction of Vectors · easy · numerical
Two vectors each of magnitude $10$ act in exactly opposite directions. Their resultant is:
A. $10$
B. Zero ✓ Correct
C. $14.14$
D. $20$
Solution: Equal and opposite vectors cancel completely.
Q23 — Resolution of Vectors & Components · easy · theory
Resolution of a vector means:
A. Adding it to another vector
B. Splitting it into components along chosen directions ✓ Correct
C. Reversing its direction
D. Finding its magnitude
Solution: It is the reverse process of vector addition.
Q24 — Resolution of Vectors & Components · easy · theory
The rectangular components of a vector $\vec{A}$ making an angle $\theta$ with the $x$-axis are:
A. $A\tan\theta$ and $A$
B. $A$ and $A\tan\theta$
C. $A\sin\theta$ and $A\cos\theta$
D. $A\cos\theta$ and $A\sin\theta$ ✓ Correct
Solution: The angle is measured from the $x$-axis, so the horizontal component carries the cosine.
Q25 — Resolution of Vectors & Components · easy · theory
The magnitude of a vector in terms of its rectangular components is:
A. $A_xA_y$
B. $A_x + A_y$
C. $\sqrt{A_x^2 + A_y^2}$ ✓ Correct
D. $\sqrt{A_x^2 - A_y^2}$
Solution: The components form the perpendicular sides of a right triangle whose hypotenuse is the vector.
Q26 — Resolution of Vectors & Components · easy · numerical
A vector has equal $x$ and $y$ components. The angle it makes with the $x$-axis is:
A. $90^\circ$
B. $60^\circ$
C. $45^\circ$ ✓ Correct
D. $30^\circ$
Solution: $\tan\theta = \dfrac{A_y}{A_x} = 1$, so $\theta = 45^\circ$.
Q27 — Scalar (Dot) Product · easy · theory
The scalar product of two vectors is defined as:
A. $AB\cos\theta$, which is a scalar ✓ Correct
B. $\dfrac{A}{B}\cos\theta$
C. $AB\tan\theta$
D. $AB\sin\theta$, which is a vector
Solution: It projects one vector onto the other and multiplies by the magnitude.
Q28 — Scalar (Dot) Product · easy · theory
The result of a scalar product of two vectors is:
A. A vector perpendicular to both
B. A scalar ✓ Correct
C. Always zero
D. A vector in the plane of the two
Solution: This is why it is also called the dot product.
Q29 — Scalar (Dot) Product · easy · theory
The scalar product is commutative, meaning that:
A. $\vec{A}\cdot\vec{B} = \vec{B}\cdot\vec{A}$ ✓ Correct
B. $\vec{A}\cdot\vec{B} = 0$
C. $\vec{A}\cdot\vec{B} = -\vec{B}\cdot\vec{A}$
D. $\vec{A}\cdot\vec{B} = \vec{A} \times \vec{B}$
Solution: The cosine of the angle is the same whichever vector is taken first.
Q30 — Scalar (Dot) Product · easy · theory
Work done by a force is an example of a:
A. Scalar product of force and velocity
B. Vector sum
C. Scalar product of force and displacement ✓ Correct
D. Vector product of force and displacement
Solution: $W = \vec{F}\cdot\vec{s} = Fs\cos\theta$.