Question types

Mathematical Methods question types

116 questions across 4 question groups — pick any mix to generate a Physics paper with step-by-step answer keys.

116
Questions
4
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5
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Sample Questions

Mathematical Methods questions

One sample from each question group in this chapter. Select any group above to see the full set with answer keys.

If $\vec{A}, \vec{B}$, and $\vec{C}$ are three vectors, then which of the following is not correct?
  • A
    $\vec{A} \cdot(\vec{B}+\vec{C})=\vec{A} \cdot \vec{B}+\vec{A} \cdot \vec{C}$
  • B
    $\overrightarrow{ A } \cdot \overrightarrow{ B }=\overrightarrow{ B } \cdot \overrightarrow{ A }$
  • $\vec{A} \times \vec{B}=\vec{B} \times \vec{A}$
  • D
    $\vec{A} \times(\vec{B} \times \vec{C})=\vec{A} \times \vec{B}+\vec{B} \times \vec{C}$

Answer: C.

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The magnitude of vector product of two unit vectors making an angle of 60° with each other is
  • A
    1
  • B
    2
  • C
    $\frac{3}{2}$
  • $\frac{\sqrt{3}}{2}$

Answer: D.

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For two vectors to be equal, they should have the
  • A
    same magnitude
  • B
    same direction
  • same magnitude and direction
  • D
    same magnitude but opposite direction

Answer: C.

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The resultant of two forces 10 N and 15 N acting along + x and – x-axes respectively, is
  • A
    25 N along + x-axis
  • B
    25 N along – x-axis
  • C
    5 N along + x-axis
  • 5 N along – x-axis

Answer: D.

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If $\overrightarrow{ P }$ is moving away from a point and $\overrightarrow{ Q }$ is moving towards a point then, can their resultant be found using parallelogram law of vector addition?
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Given: L.C. = 0.01 cm
To measure external diameter of hollow cylinder readings are taken as follows:

Image

[Note: The above table is made assuming zero error in Vernier callipers. If calliper has positive or negative zero error, the zero error correction needs to be introduced into observed reading.]

Image

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Determine the vector product of $\overrightarrow{ v _1}=2 \hat{i}+3 \hat{j}-\hat{k}$ and $\overrightarrow{ v _2}=\hat{i}+2 \hat{j}-3 \hat{k}$ are perpendicular to each other, determine the value of $a$.
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Show that vectors $\overrightarrow{ a }=2 \hat{ i }+3 \hat{ j }+6 \hat{ k }, \overrightarrow{ b }=3 \hat{ i }-6 \hat{ j }+2 \hat{ k }$ and $\overrightarrow{ c }=6 \hat{ i }+2 \hat{ j }-3 \hat{ k }$ are mutually perpendicular.
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On an open ground, a biker follows a track that turns to his left by an angle of $60^\circ$ after every $600 m.$ Starting from a given turn, specify the displacement of the biker at the third and sixth turn. Compare the magnitude of the displacement with the total path length covered by the motorist in each case.
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$\overrightarrow{ P }=\hat{ i }+ 2 \hat{ k }$ and $\overrightarrow{ Q }=2 \hat{ i }+\hat{ j }-2 \hat{ k }$ are two vectors, find the unit vector parallel to $\overrightarrow{ P } \times \overrightarrow{ Q }$ Also find the vector perpendicular to $P$ and $Q$ of magnitude 6 units.
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