Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 2>Q 46

EASY

JEE Main/Advance

IMPORTANT

Earn 100

The magnitude of sum of three vectors $\vec{A}, \vec{B}$ and $\vec{C}$ representing the sides of a cube of length $A$ is equal to $A$ .

(Take, $\sqrt{3} = 1.73$ )

50% studentsanswered this correctly

Important Questions on Mathematical Tools in Physics

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 2>Q 47

If

\vec{A} = 3 \hat{i} + 4 \hat{j}

and

\vec{B} = 7 \hat{i} + 24 \hat{j}

, then the vector having the same magnitude as

\vec{B}

and parallel to

\vec{A}

has sum of coefficient of

\hat{i}, \hat{j}

as _____.

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 2>Q 48

If

\vec{A} ‖ \vec{B}

, then magnitude of

\vec{A} \times \vec{B}

is equal to _____.

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 2>Q 49

The magnitude of area of the parallelogram formed by the adjacent sides of vectors

\vec{A} = 3 \hat{i} + 2 \hat{j}

and

\vec{B} = 2 \hat{i} - 4 \hat{k}

is

\sqrt{a}

units. The value of

a

is _____

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 2>Q 50

If

\vec{A}

is _____to

\vec{B}

, then

\vec{A} \cdot \vec{B} = 0

.

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 2>Q 51

The vector

\vec{A} = \hat{i} + \hat{j}

, where

\hat{i}

and

\hat{j}

are unit vectors along

x

-axis and

y

-axis, respectively, makes an angle of _____ degree with the

x

-axis.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 4>Q 1

Two vectors

\vec{A}

and

\vec{B}

are defined as

\vec{A} = α \hat{i}

and

\vec{B} = α (\cos ω t \hat{i} + \sin ω t \hat{j}),

where

α

is a constant and

ω = \frac{π}{6} rad s^{- 1} .

If

| \vec{A} + \vec{B} | = \sqrt{3} | \vec{A} - \vec{B} |

at time

t = τ

for the first time, the value of

τ

in second is _____.

MEDIUM

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 4>Q 2

If $g (x) = \frac{x^{2} - 4}{x + 0.5}$ and $g^{'} (x) = \frac{x^{2} + x + n}{(x + 0.5)^{2}}$ . Find $n$ by derivative of functions using quotient rule.

EASY

JEE Main/Advance

IMPORTANT

Alpha Question Bank for Engineering: Physics>Chapter 2 - Mathematical Tools in Physics>Exercise - 4>Q 3

Suppose $u$ and $v$ are differentiable functions of $x$ and $u (1) = 2, u^{'} (1) = 0, v (1) = 5, v^{'} (1) = - 1$ .
Find the value of the following derivative at, $x = 1$ .

\frac{d}{d x} (u v)