BASIC MATHEMATICS USED IN PHYSICS ONLINE TEST - 04

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Created on November 01, 2021

Physics

BASIC MATHEMATICS USED IN PHYSICS TEST - 4

1 / 20

If | $\underset{A}{\rightarrow}$ × $\underset{B}{\rightarrow}$ |= $\sqrt{3}$ $\underset{A}{\rightarrow}$ . $\underset{B}{\rightarrow}$ , then the value of | $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ | is :
यदि | $\underset{A}{\rightarrow}$ × $\underset{B}{\rightarrow}$ | = $\sqrt{3}$ $\underset{A}{\rightarrow}$ . $\underset{B}{\rightarrow}$ हो, तो | $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ | का मान होगा

(1) $\left [ A^{2} + B^{2} +\frac{AB}{\sqrt{3}}\right ]^{\frac{1}{2}}$

(2) A + B

(3) $\left ( A^{2}+B^{2}+\sqrt{3} A B \right )^{\frac{1}{2}}$

(4) $\left ( A^{2}+B^{2}+AB \right )\frac{1}{2}$

2 / 20

A force $\underset{F}{\rightarrow}$ = ( $3\hat{i}+4\hat{j}$ )N acts on a body and displaces it by $\underset{S}{\rightarrow}$ = ( $3\hat{i}+4\hat{j}$ )m . The work done (W = $\underset{F}{\rightarrow}$ . $\underset{S}{\rightarrow}$ )r by the force is :
$\underset{F}{\rightarrow}$ = ( $3\hat{i}+4\hat{j}$ ) N का एक वल एक वस्तु पर कार्य करता है तथा $\underset{S}{\rightarrow}$ – ( $3\hat{i}+4\hat{j}$ ) m से विस्थापित करता है। बल द्वारा किया गया कार्य (W= $\underset{F}{\rightarrow}$ . $\underset{S}{\rightarrow}$ ) है :

(1) 10J

(2) 12J

(3) 19J

(4) 25J

3 / 20

If three vectors satisfy the relation $\underset{A}{\rightarrow}$ . $\underset{B}{\rightarrow}$ = O and $\underset{A}{\rightarrow}$ . $\underset{C}{\rightarrow}$ = O , then $\underset{A}{\rightarrow}$ can be parallel to
तीन सदिश यदि सम्बन्धों $\underset{A}{\rightarrow}$ . $\underset{B}{\rightarrow}$ = 0 औ $\underset{A}{\rightarrow}$ . $\underset{C}{\rightarrow}$ =0 को संतुष्ट करते हैं। तो सदिश $\underset{A}{\rightarrow}$ निम्न में से किसके समान्तर हो सकता है ?

(1) $\underset{C}{\rightarrow}$

(2) $\underset{B}{\rightarrow}$

(3) $\underset{B}{\rightarrow}$ × $\underset{C}{\rightarrow}$

(4) $\underset{B}{\rightarrow}$ . $\underset{C}{\rightarrow}$

4 / 20

The magnitude of the vector product of two vectors $\underset{A}{\rightarrow}$ and $\underset{B}{\rightarrow}$ may not be :
सदिश $\underset{A}{\rightarrow}$ व $\underset{B}{\rightarrow}$ के सदिश गुणनफल का परिमाण नहीं हो सकता है

(1) Greater than AB
AB से अधिक

(2) Less than AB
AB से कम

(3) Equal to AB
AB के बराबर

(4) Equal to zero
शून्य

5 / 20

The vectors $\underset{A}{\rightarrow}$ and $\underset{B}{\rightarrow}$ are such tha | $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ | = | $\underset{A}{\rightarrow}$ - $\underset{B}{\rightarrow}$ |. The angle between vectors $\underset{A}{\rightarrow}$ and $\underset{B}{\rightarrow}$ is -
सदिश $\underset{A}{\rightarrow}$ तथा $\underset{B}{\rightarrow}$ इस प्रकार है कि | $\inline \underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ |= | $\underset{A}{\rightarrow}$ - $\underset{B}{\rightarrow}$ | तो सदिश $\underset{A}{\rightarrow}$ तथा $\underset{B}{\rightarrow}$ के मध्य कोण होगा

(1) 90°

(2) 60°

(3) 75°

(4) 45°

6 / 20

If $\underset{A}{\rightarrow}$ × $\underset{B}{\rightarrow}$ = $\underset{O}{\rightarrow}$ and $\underset{B}{\rightarrow}$ × $\underset{C}{\rightarrow}$ = $\underset{O}{\rightarrow}$ , then the angle between $\underset{A}{\rightarrow}$ and $\underset{C}{\rightarrow}$ may be :
यदि $\underset{A}{\rightarrow}$ x $\underset{B}{\rightarrow}$ = $\underset{O}{\rightarrow}$ और $\underset{B}{\rightarrow}$ x $\underset{C}{\rightarrow}$ = $\underset{O}{\rightarrow}$ है, $\underset{A}{\rightarrow}$ और $\underset{C}{\rightarrow}$ के मध्य कोण हो सकता है.

(1) zero

(2) $\frac{\pi }{4}$

(3) $\frac{\pi }{2}$

(4) None

7 / 20

Which of the following vector identities is false ?
निम्नलिखित में से कौनसी समीकरण असत्य है

(1) $\underset{P}{\rightarrow}$ + $\underset{Q}{\rightarrow}$ = $\underset{Q}{\rightarrow}$ + $\underset{P}{\rightarrow}$

(2) $\underset{P}{\rightarrow}$ + $\underset{Q}{\rightarrow}$ = $\underset{Q}{\rightarrow}$ × $\underset{P}{\rightarrow}$

(3) $\underset{P}{\rightarrow}$ . $\underset{Q}{\rightarrow}$ = $\underset{Q}{\rightarrow}$ . $\underset{P}{\rightarrow}$

(4) $\underset{P}{\rightarrow}$ × $\underset{Q}{\rightarrow}$ ≠ $\underset{Q}{\rightarrow}$ × $\underset{P}{\rightarrow}$

8 / 20

What is the projection of( $3\hat{i}+4\hat{k}$ ) on the y-axis ?
सदिश ( $3\hat{i}+4\hat{k}$ ) का y-अक्ष पर प्रक्षेप क्या है ?

(1) 3

(2) 4

(3) 5

(4) zero

9 / 20

If | $\underset{A}{\rightarrow}$ × $\underset{B}{\rightarrow}$ |=| $\underset{A}{\rightarrow}$ . $\underset{B}{\rightarrow}$ |, then the angle between $\underset{A}{\rightarrow}$ and $\underset{B}{\rightarrow}$ will be :
यदि | $\underset{A}{\rightarrow}$ × $\underset{B}{\rightarrow}$ = | $\underset{A}{\rightarrow}$ . $\underset{B}{\rightarrow}$ | तो $\underset{A}{\rightarrow}$ और $\underset{B}{\rightarrow}$ के मध्य कोण होगा:

(1) 30°

(2) 45°

(3) 60°

(4) 75°

10 / 20

Two vectors $\underset{A}{\rightarrow}$ and $\underset{B}{\rightarrow}$ are such that $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ = $\underset{A}{\rightarrow}$ - $\underset{B}{\rightarrow}$ . Then select incorrect alternative
दो सदिश $\underset{A}{\rightarrow}$ एवं $\underset{B}{\rightarrow}$ ऐसे है कि $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ = $\underset{B}{\rightarrow}$ - $\underset{A}{\rightarrow}$ , तो गलत कथन चुनिए :

(1) $\underset{A}{\rightarrow}$ . $\underset{B}{\rightarrow}$ = 0

(2) $\underset{A}{\rightarrow}$ × $\underset{B}{\rightarrow}$ = $\underset{O}{\rightarrow}$

(3) $\underset{A}{\rightarrow}$ = $\underset{O}{\rightarrow}$

(4) $\underset{B}{\rightarrow}$ = $\underset{O}{\rightarrow}$

11 / 20

Area of a parallelogram, whose diagonals are 3 $\hat{i}$ + $\hat{j}$ - 2 $\hat{k}$ and $\hat{i}$ - 3 $\hat{j}$ + 4 $\hat{k}$ will be :
यदि समान्तर चतुर्भुज के दो विकर्ण क्रमशः (B $\hat{i}$ + $\hat{j}$ –2 $\hat{k}$ ) और ( $\hat{i}$ – 3 $\hat{j}$ + 4 $\hat{k}$ ) हो तो उसका क्षेत्रफल होगा -

(1) 14 unit

(2) 5 $\sqrt{3}$ unit

(3) 10 $\sqrt{3}$ unit

(4) 20 $\sqrt{3}$ unit

12 / 20

If $\underset{A}{\rightarrow}$ = $3\hat{i}$ + $4\hat{j}$ r and $\underset{B}{\rightarrow}$ = $6\hat{i}$ + $8\hat{j}$ and A and B are the magnitudes of $\underset{A}{\rightarrow}$ and $\underset{B}{\rightarrow}$ , then which of the following is not true ?
यदि $\underset{A}{\rightarrow}$ = $3\hat{i}$ + $4\hat{j}$ और $\underset{B}{\rightarrow}$ = $6\hat{i}$ + $\underset{8j}{\rightarrow}$ हो, तो निम्नलिखित में से कौनसा कथन सत्य नहीं है। यहाँ $\underset{A}{\rightarrow}$ और $\underset{B}{\rightarrow}$ क्रमश: सदिशों A तथा B के परिमाण है

(1) $\underset{A}{\rightarrow}$ × $\underset{B}{\rightarrow}$ = $\underset{O}{\rightarrow}$

(2) $\frac{A}{B}$ = $\frac{1}{2}$

(3) $\underset{A}{\rightarrow}$ . $\underset{B}{\rightarrow}$ = 48

(4) A = 5

13 / 20

A vector $\underset{A}{\rightarrow}$ points vertically upward and $\underset{B}{\rightarrow}$ points towards north. The vector product $\underset{A}{\rightarrow}$ × $\underset{B}{\rightarrow}$ is
यदि सदिश $\underset{A}{\rightarrow}$ उर्ध्वाधर ऊपर की ओर इंगित है तथा $\underset{B}{\rightarrow}$ उत्तर की ओर इंगित है, तो सदिश गुणनफल $\underset{A}{\rightarrow}$ × $\underset{B}{\rightarrow}$ की दिशा है

(1) zero
शून्य सदिश के समान

(2) along west
पश्चिम की ओर

(3) along east
उत्तर की ओर

(4) vertically downward
उर्ध्वाधर नीचे की ओर

14 / 20

A vector $\underset{_{F1}}{\rightarrow}$ is along the positive X-axis. If its vector product with another vector $\underset{_{F2}}{\rightarrow}$ is zero then $\underset{_{F2}}{\rightarrow}$ may be :-

एक सदिश $\underset{_{F1}}{\rightarrow}$ धनात्मक X-अक्ष के अनुदिश है। यदि किसी अन्य सदिश $\underset{_{F2}}{\rightarrow}$ के साथ इसका सदिश गुणनफल शून्य हो, तो निम्न में से कौन $\underset{_{F2}}{\rightarrow}$ , हो सकता है ?

(1) $4\hat{j}$

(2) ( $\hat{i}+\hat{j}$ )

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

(4) - $\underset{i}{\rightarrow}$

15 / 20

The angle between vectors ( $\underset{A}{\rightarrow}$ × $\underset{B}{\rightarrow}$ )r and ( $\underset{B}{\rightarrow}$ × $\underset{A}{\rightarrow}$ ) is:
सदिश ( $\underset{A}{\rightarrow}$ x $\underset{B}{\rightarrow}$ ) और ( $\underset{B}{\rightarrow}$ x $\underset{A}{\rightarrow}$ ) के मध्य कोण होता है:

(1) π rad

(2) $\frac{\pi }{2 }$ rad

(3) $\frac{\pi }{4 }$ rad

(4) zero

16 / 20

Two vectors $\underset{P}{\rightarrow}$ and $\underset{Q}{\rightarrow}$ are inclined to each other at angle θ. Which of the following is the unit vector perpendicular to $\underset{P}{\rightarrow}$ and $\underset{Q}{\rightarrow}$ ?
दो सदिशों $\underset{P}{\rightarrow}$ और $\underset{Q}{\rightarrow}$ के मध्य कोण θ है। कौन $\underset{P}{\rightarrow}$ तथा $\underset{Q}{\rightarrow}$ के लम्बवत् एकांक सदिश है

(1) $\frac{\underset{P}{\rightarrow} \times \underset{Q}{\rightarrow}}{P.Q}$

(2) $\frac{\hat{P}\times \hat{Q}}{\sin \theta }$

(3) $\frac{\hat{P}\times \hat{Q}}{PQ\sin \theta }$

(4) $\frac{\hat{P}\times \hat{Q}}{PQ\sin \theta }$

17 / 20

If a vector $\left ( 2\hat{i}+3\hat{j}+ 8\hat{k}\right )$ is perpendicular to the vector $\left ( 4\hat{j}-4\hat{i}+\alpha \hat{k} \right )$ ), then the value of α is :
यदि सदिश $\left ( 2\hat{i}+3\hat{j}+ 8\hat{k}\right )$ व सदिश $\left ( 4\hat{j}-4\hat{i}+\alpha \hat{k} \right )$ परस्पर लम्बवत् हो, तो α का मान होगा :

(1) 1

(2) 1/2

(3) 1/2

(4) 1

18 / 20

If $\hat{i}$ , $\hat{j}$ and $\hat{k}$ are unit vectors along X, Y & Z axis respectively, then tick the wrong statement :
यदि $\hat{i}$ , $\hat{j}$ और $\hat{k}$ क्रमश: x Y औरz अक्षों के अनुदिश एकांक सदिश हैं, तो गलत कथन है -

(1) $\hat{i}.\hat{i}$ =1

(2) $\hat{i}$ × $\hat{j}$ = $\hat{k}$

(3) $\hat{i}$ . $\hat{j}$ = 0

(4) $\hat{i}$ × $\hat{k}$ = - $\hat{i}$

19 / 20

What is the value of ( $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ )· ( $\underset{A}{\rightarrow}$ × $\underset{B}{\rightarrow}$ ) ?
( $\underset{A}{\rightarrow}$ + $\underset{B}{\rightarrow}$ ) • ( $\underset{A}{\rightarrow}$ x $\underset{B}{\rightarrow}$ ) का मान होगा

(1) 0

(2) A² B²

(3) A² + B² + 2AB

(4) none of these

20 / 20

If the vectors ( $\hat{i}$ + $\hat{j}$ + $\hat{k}$ ) and 3 $\hat{i}$ form two sides of a triangle, then area of the triangle is :
यदि सदिश ( $\hat{i}$ + $\hat{j}$ + $\hat{k}$ ) और 3 $\hat{i}$ त्रिभुज की दो भुजाओं को निरूपित करते हैं, तो त्रिभुज का क्षेत्रफल होगा:

(1) $\sqrt{3}$ unit

(2) $\sqrt[2]{3}$ unit

(3) $\frac{3}{\sqrt{2}}$ unit

(4) $\sqrt[3]{2}$ unit

Your score is

The average score is 13%

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