BASIC MATHEMATICS USED IN PHYSICS ONLINE TEST - 03

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Created on November 01, 2021

Physics

BASIC MATHEMATICS USED IN PHYSICS TEST - 3

1 / 20

The unit vector parallel to the resultant of the vectors $\underset{A}{\rightarrow}$ = $4\hat{i}$ + $3\hat{j}$ + $6\hat{k}$ and $\underset{B}{\rightarrow}$ = - $\hat{i}$ + $3\hat{j}$ - $8\hat{k}$ is :
सदिश $\underset{A}{\rightarrow}$ = $4\hat{i}$ + $3\hat{j}$ + $6\hat{k}$ तथा $\underset{B}{\rightarrow}$ = $\hat{i}$ + $3\hat{j}$ - $8\hat{k}$ के परिणामी सदिश के समान्तर एकांक सदिश है

(1) $\frac{1}{7}\left [3\hat{i} + 6\hat{j}-2\hat{k}\right ]$

(2) $\frac{1}{7}\left [3\hat{i} + 6\hat{j}+2\hat{k}\right ]$

(3) $\frac{1}{49}\left [3\hat{i} + 6\hat{j}+2\hat{k}\right ]$

(4) $\frac{1}{49}\left [3\hat{i} + 6\hat{j}-2\hat{k}\right ]$

2 / 20

Given that A = B. What is the angle between ( $\underset{A}{\rightarrow}$ + $\underset{A}{\rightarrow}$ ) and ( $\underset{A}{\rightarrow}$ - $\underset{B}{\rightarrow}$ ) ?
यदि A = B हो, तो ( $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ ) व ( $\underset{A}{\rightarrow}$ - $\underset{B}{\rightarrow}$ ) के मध्य कोण है

(1) 30°

(2) 60°

(3) 90°

(4) 180°

3 / 20

The vector $\underset{B}{\rightarrow}$ = 5 $\hat{i}$ + 2 $\hat{j}$ - S $\hat{k}$ is perpendicular to the vector $\underset{A}{\rightarrow}$ = 3 $\hat{i}$ + $\hat{j}$ + 2 $\hat{k}$ if S=
यदि सदिश $\underset{B}{\rightarrow}$ 5 $\hat{i}$ +2 $\hat{j}$ -S $\hat{k}$ , एक अन्य सदिश A - 3 $\hat{i}$ + $\hat{j}$ + 2 $\hat{k}$ के लम्बवत् है, S का मान होगा

(1) 1

(2) 4.7

(3) 6.3

(4) 8.5

4 / 20

If vectors $\underset{P}{\rightarrow}$ , $\underset{Q}{\rightarrow}$ and $\underset{R}{\rightarrow}$ have magnitudes 5, 12 and13 units and $\underset{P}{\rightarrow}$ + $\underset{Q}{\rightarrow}$ = $\underset{R}{\rightarrow}$ , the angle between $\underset{Q}{\rightarrow}$ and $\underset{R}{\rightarrow}$ is :

सदिश $\underset{P}{\rightarrow}$ , $\underset{Q}{\rightarrow}$ और $\underset{R}{\rightarrow}$ के परिमाण क्रमश: 5, 12 और 13 इकाई हैं। यदि $\underset{P}{\rightarrow}$ + $\underset{Q}{\rightarrow}$ = $\underset{R}{\rightarrow}$ हो, तो $\underset{Q}{\rightarrow}$ व $\underset{R}{\rightarrow}$ के मध्य कोण होगा

(1) COS^-1

(2) COS^-1

(3) COS^-1

(4) COS^-1

5 / 20

The angle between the two vectors $\underset{A}{\rightarrow}$ = $3\hat{j}+4\hat{j}+5\hat{k}$ and $\underset{B}{\rightarrow}$ = $3\hat{i}+4\hat{j}-5\hat{k}$ will be :
सदिश $\underset{A}{\rightarrow}$ = $3\hat{j}+4\hat{j}+5\hat{k}$ तथा $\underset{B}{\rightarrow}$ = $3\hat{i}+4\hat{j}-5\hat{k}$ के मध्य कोण होगा

(1) zero

(2) 180°

(3) 90°

(4) 45°

6 / 20

The angle between vectors $\left ( \hat{i}+ \hat{j}\right )$ and e $\left (\hat{j} + \hat{k}\right )$ is :
सदिश $\left ( \hat{i}+ \hat{j}\right )$ व सदिश $\left (\hat{j} + \hat{k}\right )$ के मध्य कोण है

(1) 90°

(2) 180°

(3) 0°

(4) 60°

7 / 20

The vector sum of two forces is perpendicular to their vector difference. In that case, the force :
दो बलों का सदिश योग उनके सदिश अंतर के लम्बवत् है। इस स्थिति में :

(1) Are equal to each other.
दोनों बल समान हैं।

(2) Are equal to each other in magnitude.
दोनों बलों के परिमाण समान हैं।

(3) Are not equal to each other in magnitude.
दोनों बलों के परिमाण समान नहीं है।

(4) Cannot be predicted.
दोनों बलों के बारे में कुछ कहना संभव नहीं है।

8 / 20

What is the projection of $\underset{A}{\rightarrow}$ on $\underset{B}{\rightarrow}$ ?
सदिश $\underset{A}{\rightarrow}$ का $\underset{B}{\rightarrow}$ पर प्रक्षेप क्या है ?

(1) $\underset{A}{\rightarrow}$ . $\underset{B}{\rightarrow}$

(2) $\underset{A}{\rightarrow}$ . $\hat{B}$

(3) $\underset{B}{\rightarrow}$ . $\underset{A}{\rightarrow}$

(4) $\hat{A}$ . $\hat{B}$

9 / 20

The vector $\underset{P}{\rightarrow}$ = $a\hat{i}+a\hat{j}+3\hat{k}$ r and $\underset{Q}{\rightarrow}$ = $a\hat{i}-2\hat{j}-\hat{k}$ are perpendicular to each other. The positive value of a is :
यदि सदिश $\underset{P}{\rightarrow}$ = $a\hat{i}+a\hat{j}+3\hat{k}$ औ $\underset{Q}{\rightarrow}$ = $a\hat{i}-2\hat{j}-\hat{k}$ परस्पर लम्बवत् हो, तो a का धनात्मक मान है।

(1) 3

(2) 2

(3) 1

(4) zero

10 / 20

The magnitudes of vectors $\underset{A}{\rightarrow}$ , $\underset{B}{\rightarrow}$ and $\underset{C}{\rightarrow}$ are respectively 12, 5 and 13 units and $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ = $\underset{C}{\rightarrow}$ ,then the angle between $\underset{A}{\rightarrow}$ and $\underset{B}{\rightarrow}$ is :
सदिश $\underset{A}{\rightarrow}$ , $\underset{B}{\rightarrow}$ और $\underset{C}{\rightarrow}$ के परिमाण क्रमश: 12, 5 और 13 इकाई है। यदि $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ = $\underset{C}{\rightarrow}$ हो, तो $\underset{A}{\rightarrow}$ व $\underset{B}{\rightarrow}$ के मध्य कोण होगा

(1) 0

(2) π/3

(3) π /2

(4) π /4

11 / 20

A vector perpendicular to (4 $\hat{i}$ - 3 $\hat{j}$ ) may be :
(4 $\hat{i}$ -3 $\hat{j}$ ) के लम्बवत् सदिश है

(1) 4 $\hat{i}$ + 3 $\underset{j}{\rightarrow}$

(2) 7 $\hat{k}$

(3) 6 $\hat{i}$

(4) 3 $\hat{i}$ - 4 $\hat{j}$

12 / 20

A force (3 $\hat{i}$ +2 $\hat{j}$ ) N displaces an object through a distance (2 $\hat{i}$ -3 $\hat{j}$ ) m. The work (W = $\underset{F}{\rightarrow}$ · $\underset{S}{\rightarrow}$ ) done is :
(3 $\hat{i}$ + 2 $\hat{j}$ ) N का एक बल, एक वस्तु को (2 $\hat{i}$ -3 $\hat{j}$ ) m तक विस्थापित करता है। तो किया गया कार्य (W = $\underset{F}{\rightarrow}$ . $\underset{S}{\rightarrow}$ ) है

(1) zero

(2) 12J

(3) 5J

(4) 13J

13 / 20

The angle that the vector $\underset{A}{\rightarrow}$ = $2\hat{i}+3\hat{j}$ makes with y-axis is :
सदिश $\underset{A}{\rightarrow}$ = $2\hat{i}+3\hat{j}$ का Y-अक्ष के साथ कोण है

(1) tan-1 (3/2)

(2) tan-1 (2/3)

(3) sin-1 (2/3)

(4) cos-1 (3/2)

14 / 20

If $\hat{n}$ = a $\hat{i}$ + b $\hat{j}$ is perpendicular to the vector ( $\hat{i}$ + $\hat{j}$ ), then the value of a and b may be :
यदि सदिश $\hat{n}$ = a $\hat{i}$ + b $\hat{j}$ , सदिश ( $\hat{i}$ + $\hat{j}$ ) के लम्बवत् है, तो a व b के मान होगें

(1) 1, 0

(2) 2, 0

(3) 3, 0

(4) $\frac{1}{\sqrt{2}}$ ,- $\frac{1}{\sqrt{2}}$

15 / 20

The resultant of $\underset{A}{\rightarrow}$ and $\underset{B}{\rightarrow}$ is perpendicular to $\underset{A}{\rightarrow}$ . What is the angle between $\underset{A}{\rightarrow}$ and $\underset{B}{\rightarrow}$ ?
$\underset{A}{\rightarrow}$ व $\underset{B}{\rightarrow}$ का परिणामी $\underset{A}{\rightarrow}$ के लम्बवत् है, तो $\underset{A}{\rightarrow}$ व $\underset{B}{\rightarrow}$ के मध्य कोण कितना होगा ?

(1) cos^-1 $\left ( \frac{A}{B} \right )$

(2) cos^-1 $\left ( -\frac{A}{B} \right )$

(3) sin^-1 $\left ( \frac{A}{B} \right )$

(4) sin^-1 $\left ( -\frac{A}{B} \right )$

16 / 20

What is the component of (3 $\hat{i}$ + 4 $\hat{j}$ ) along ( $\hat{i}$ + $\hat{j}$ ) ?
सदिश ( 3 $\hat{i}$ +4 $\hat{j}$ ) का सदिश ( $\hat{i}$ + $\hat{j}$ ) के अनुदिश घटक क्या होगा ?

(1) $\frac{1}{2}\left (\hat{j} + \hat{i}\right )$

(2) $\frac{2}{3}\left (\hat{j} + \hat{i}\right )$

(3) $\frac{5}{7}\left (\hat{j} + \hat{i}\right )$

(4) $\frac{7}{2}\left (\hat{j} + \hat{i}\right )$

17 / 20

If $\underset{P}{\rightarrow}$ . $\underset{Q}{\rightarrow}$ = PQ, then angle between $\underset{P}{\rightarrow}$ and $\underset{Q}{\rightarrow}$ is :
यदि $\underset{P}{\rightarrow}$ . $\underset{Q}{\rightarrow}$ = PQ हो, तो $\underset{P}{\rightarrow}$ व $\underset{Q}{\rightarrow}$ के मध्य कोण होगा

(1) 0°

(2) 30°

(3) 45°

(4) 60°

18 / 20

What is the angle between $\underset{A}{\rightarrow}$ and the resultant of ( $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ ) and ( $\underset{A}{\rightarrow}$ - $\underset{B}{\rightarrow}$ ) ?
सदिश ( $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ ) और सदिश ( $\underset{A}{\rightarrow}$ - $\underset{B}{\rightarrow}$ ) के परिणामी तथा $\underset{A}{\rightarrow}$ के मध्य कोण क्या है ?

(1) 0°

(2) tan^-1

(3) tan^-1

(4) tan^-1

19 / 20

If $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ r is a unit vector along x-axis and $\underset{A}{\rightarrow}$ = $\hat{i}-\hat{j}+\hat{k}$ , then what is $\underset{B}{\rightarrow}$ ?
यदि $\underset{A}{\rightarrow}$ = $\hat{i}-\hat{j}+\hat{k}$ है, ( $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ ) x-अक्ष के अनुदिश एकांक सदिश है, तो $\underset{B}{\rightarrow}$ होगा

(1) $\hat{j}+\hat{k}$

(2) $\hat{j}-\hat{k}$

(3) $\hat{i}+\hat{j}+\hat{k}$

(4) $\hat{i}+\hat{j}-\hat{k}$

20 / 20

Forces 3N, 4N and 12N act at a point in mutually perpendicular directions. The magnitude of the resultant force is :
3N, 4N व 12N के बल, एक बिन्दु पर, परस्पर लम्बवत् दिशाओं में कार्यरत हैं, तो परिणामी बल का परिमाण होगा

(1) 19N

(2) 13 N

(3) 11 N

(4) 5 N

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