Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 1

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Assertion : A vector is a quantity that has both magnitude and direction and obeys the triangle law of addition.

Reason : The magnitude of the resultant vector of two given vectors can never be less than the magnitude of any of the given vector.

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Important Questions on Mathematical Tools in Physics

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 2

Assertion : If the rectangular components of a force are $8 N$ and $6 N,$ then the magnitude of the force is $10 N .$

Reason : If $|\vec{Δ}| |\vec{B}| =_{1}$ then ${|{\vec{A}}^{\times} \vec{B}|}^{2} + {|\vec{A \cdot B}|}^{2} = 1 .$

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 5

Assertion : If three vectors

\vec{A, B}

and

\vec{C}

satisfy the relation

\vec{A . B} = 0 \vec{A . C} = 0

then the vector

\vec{Λ}

is paraliel to

\vec{B} \times \vec{C} .

Reason :

\vec{A} ⊥ \vec{B}

and

\vec{A} ⊥ \vec{C}

hence

\vec{A}

is perpendicular to plane formed by

\vec{B}

and

\vec{C} .

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 6

f = 2 π \frac{x^{3} y^{5}}{\sqrt{z}}

then

\log f

is equal to :

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 7

(3) Which of following are true

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 8

If

y_{1} = A \sin θ_{1}

and

y_{2} = A \sin θ_{2}

then

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 9

R^{2} = A^{2} + B^{2} + 2 A B \cos θ

, if

| A | = | B |

, then the value of the magnitude of

R

is equivalent to:

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 10

Find value of

a

if distance between the points

(- 9 cm, a cm)

and

(3 cm, 3 cm)

is

13 cm .

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Alpha Question Bank for Medical: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise-2>Q 11

y = \ln x^{2} + \sin x F i n d \frac{d y}{d x} a n d \frac{d^{2} y}{d x^{2}}