Are you preparing for the TGT or PGT Physics exams in 2025? Vector Algebra is a game-changer for mastering physics concepts, from Mechanics to Electromagnetism. Whether you’re aiming for a teaching position in Uttar Pradesh or anywhere in India, nailing this topic is crucial for success in competitive exams.

At Physics Scholar, we’ve created this free 35-MCQ practice test to make your prep seamless and effective. Available in bilingual format (English and Hindi), this test covers key Vector Algebra concepts like vector addition, dot and cross products, unit vectors, and their real-world applications. Each question is crafted to match the 2025 TGT/PGT syllabus, helping you build confidence and skills.

This test is designed to feel like the real exam, with one question per page to improve focus and time management. Once you’re done, download our detailed solutions PDF (in English and Hindi) to review your answers, learn from mistakes, and solidify your understanding. Take the first step toward acing your 2025 TGT/PGT Physics exam—start this free test today!

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If the sum of two vectors is maximum, then angle between them will be ? / यदि दो सदिशों का योग अधिकतम हो, तो उनके बीच कोण है-

(a) 0º

(b) 90º

(d) 180º

Two vectors $\vec{A}$ and $\vec{B}$ are such that $|\vec{A}+\vec{B}| = |\vec{A} - \vec{B}|$, then what is the angle between $\vec{A}$ and $\vec{B}$? दो सदिश $\vec{A}$ व $\vec{B}$ इस प्रकार हैं कि $|\vec{A} + \vec{B}| = |\vec{A} - \vec{B}|$ तो $\vec{A}$ व $\vec{B}$ के बीच कोण है-

(a) 0º

(b) 90º

(d) 180º

Which of the following combinations of forces cannot have their resultant zero? निम्न में से कौन से बलों के संयोजन का परिणामी शून्य नहीं हो सकता-

(a) 10, 10, 10

(b) 10, 10, 20

(d) 10, 20, 40

If $\vec{A}$ and $\vec{B}$ are perpendicular then which of the following statement is correct? यदि $\vec{A}$ व $\vec{B}$ एक दूसरे के लम्बवत् हो, तो निम्न में से कौन सा कथन सत्य है-

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

$\vec{A}\times\vec{B}=0$

$\vec{A}+\vec{B}=0$

$\vec{A}-\vec{B}=0$

If $\vec{P} \times \vec{Q} = \vec{R}$, then which of the following statements is incorrect?

(a) $\vec{R} \perp (\vec{P} + \vec{Q})$

(b) $\vec{R} \perp (\vec{P} $

(d) $\vec{R} \perp (\vec{P} \times \vec{Q})$

Angle between vector $(\hat{i} + \hat{j})$ and $(\hat{j} + \hat{k})$ is:

(a) 90°

(b) 180°

(d) 60°

Vector $\vec{A} \times \vec{B}$ is:

Parallel to vector A

Parallel to vector B

Parallel to vectors A and B

Perpendicular to vectors A and B

Unit vector in the direction of $\vec{A} = \hat{i} + 2\hat{j} + 3\hat{k}$ is:

$\frac{\hat{i} + 2\hat{j} + 3\hat{k}}{\sqrt{14}}$

$\frac{\hat{i} + 2\hat{j} + 3\hat{k}}{6}$

$\frac{\hat{i} + 2\hat{j} + 3\hat{k}}{14}$

$\frac{\hat{i} + 2\hat{j} + 3\hat{k}}{\sqrt{6}}$

A particle is displaced through $3\hat{i} + 5\hat{j} +7\hat{k}$ metre by a force $3\hat{i} + \hat{j} -2\hat{k}$ newton. Work done by the force on the particle is : एक कण को $3\hat{i} + \hat{j} -2\hat{k}$ न्यूटन बल द्वारा $3\hat{i} + 5\hat{j} +7\hat{k}$ मी. विस्थापित किया जाता है। बल द्वारा कण पर किया गया कार्य है -

(a) 28 joule/जूल

(b) 10 joule/जूल

(d) 0 joule/जूल

10.

What is the maximum number of components into which a vector can be split? किसी सदिश को अधिकतम कितने घटकों में नियोजित किया जाता है -

Infinite/अनन्त

11.

If two numerically equal forces P and P acting at a point produce a resultant force of magnitude P itself, then the angle between the two original forces is: किसी बिन्दु पर कार्यरत दो समान परिमाण के बल P व P के परिणामी बल का परिमाण P है तो दोनो प्रारम्भिक सदिशों के बीच कोण होगा।

(a) 0º

(b) 60º

(d) 120º

12.

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

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

(b) $\frac{3}{2}(\hat{\mathrm{i}}+\hat{\mathrm{j}}) $

(d) $ \frac{7}{2}(\hat{\mathrm{i}}+\hat{\mathrm{j}}) $

13.

Given that $\vec{A}+\vec{B}+\vec{C}=0 $ Which of the following options is correct? दिया है, $\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}+\overrightarrow{\mathrm{C}}=0 $ निम्न में से कौन सा कथन सत्य है।

(a)$|\overrightarrow{\mathrm{A}}|+|\overrightarrow{\mathrm{B}}|=|\overrightarrow{\mathrm{C}}| $

(b)$|\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}}|=|\overrightarrow{\mathrm{C}}| $

(d)$|\overrightarrow{\mathrm{A}}-\overrightarrow{\mathrm{B}}|=|\overrightarrow{\mathrm{C}}| $

14.

What is the angle between $( \vec{A}+\vec{B} )$ and $( \vec{A} \times\vec{B} )$ ?$(\overrightarrow{\mathrm{A}}+\overrightarrow{\mathrm{B}} )$ तथा $(\overrightarrow{\mathrm{A}} \times \overrightarrow{\mathrm{B}} )$ के बीच कोण है -

(a) 0

(b) $( \pi / 4 )$

(d) $( \pi )$

15.

Resultant of three non-coplanar non-zero vectors $\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}} $ and $\overrightarrow{\mathrm{c}} $ तीन असमतलीय तथा अशून्य सदिशों $ \vec{a}, \vec{b} $ व $ \vec{c} $ का परिणामी-

(a) Always lies in the plane containing $( \vec{a}+\vec{b} )$ / हमेशा $( \vec{a}+\vec{b} )$ के तल में स्थित होता है

(b) Always lies in the plane containing $( \vec{a}-\vec{b} )$ / हमेशा $( \overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}} )$ के तल में स्थित होता है

(d) Cannot be zero/शून्य नहीं हो सकता है।

16.

A body is moving with a velocity v in the east direction. If it travels with the same velocity in the north direction, then resultant velocity is : एक कण v वेग से पूर्व दिशा में गतिमान है। यदि यह उसी वेग से उत्तर दिशा में गतिमान हो, तो परिणामी वेग होगा -

$ \mathrm{v} / \sqrt{2} $

$ \sqrt{2} \mathrm{v} $

17.

If $\vec{A} \cdot (\vec{B} \times \vec{C}) = 0$, what can be inferred about vectors $\vec{A}$, $\vec{B}$, and $\vec{C}$?

अगर $\vec{A} \cdot (\vec{B} \times \vec{C}) = 0$, तो $\vec{A}$, $\vec{B}$, और $\vec{C}$ के बारे में क्या निष्कर्ष निकाला जा सकता है?

(a) $\vec{A}$, $\vec{B}$, and $\vec{C}$ are coplanar / सहतली हैं

(b) $\vec{A}$, $\vec{B}$, and $\vec{C}$ are collinear / रेखीय हैं

(d) None / कोई नहीं

18.

The scalar triple product $\vec{A} \cdot (\vec{B} \times \vec{C})$ represents what? स्केलर ट्रिपल प्रोडक्ट $\vec{A} \cdot (\vec{B} \times \vec{C})$ किसे दर्शाता है?

(a) Area of triangle / त्रिभुज का क्षेत्रफल

(b) Volume of parallelepiped / समान्तर षट्फलक का आयतन

(d) None / कोई नहीं

19.

What is the divergence ($\nabla \cdot \vec{A}$) of a constant vector $\vec{A}$? स्थिर वेक्टर $\vec{A}$ का डाइवर्जेंस ($\nabla \cdot \vec{A}$) क्या है?

(a) Unity / एक

(b) Zero / शून्य

(d) None / कोई नहीं

20.

What is $\nabla \cdot (\nabla \times \vec{A})$? $\nabla \cdot (\nabla \times \vec{A})$ क्या है?

(a) Zero / शून्य

(b) Constant / स्थिर

(d) None / कोई नहीं

21.

The vector field $\vec{A}$ is solenoidal if: वेक्टर क्षेत्र $\vec{A}$ सोलोनॉयडल है यदि:

(a) $\nabla \times \vec{A} = 0$

(b) $\nabla \cdot \vec{A} = 0$

(d) None / कोई नहीं

22.

In which case does the scalar triple product equal zero? किस स्थिति में स्केलर ट्रिपल प्रोडक्ट शून्य होगा?

(a) When vectors are perpendicular / जब वेक्टर लम्बवत होते हैं

(b) When vectors are collinear / जब वेक्टर रेखीय होते हैं

(d) None / कोई नहीं

23.

If $\vec{A}=\vec{B}$ then which of the following is NOT correct

$\hat{A}=\hat{B}$

$|\vec{A}|=|\vec{B}|$

$B\hat{A}=A\hat{B}$

$\vec{A}+\vec{B}=\hat{A}+\hat{B}$

24.

The expression $ \left( \frac{1}{\surd{2}}\hat{i}+\frac{1}{\surd{2}}\hat{j} \right) $ is a

unit vector

null vector

vector of magnitude $\surd{2}$

scalar

25.

Moment of inertia is

Scalar

Vector

Neither Scalar nor Vector

Some times Scalar and some time Vector

26.

Which of the following physical quantites is neither Scalars nor Vectors

moment of inertia

specific heat

latent heat

density

modulus of elasticity

All Above

27.

For the figure

$\vec{A}+\vec{B}=\vec{C}$

$\vec{B}+\vec{C}=\vec{A}$

$\vec{C}+\vec{A}=\vec{B}$

$\vec{A}+\vec{B}+\vec{C}=0$

28.

If vectors P, Q and R have magnitude 5, 12 and 13 units and $\vec{P}+\vec{Q}=\vec{R}$, the angle between Q and R is

$cos^{-1}(\frac{5}{12})$

$cos^{-1}(\frac{5}{13})$

$cos^{-1}(\frac{12}{13})$

$cos^{-1}(\frac{7}{13})$

29.

If the magnitude of sum and difference of two vectors is the same, the angle between them is

0°

30°

45°

90°

30.

Which of the following statement is wrong

$|\vec{A}\times\vec{B}|=|\vec{B}\times\vec{A}|$

$\vec{A}\times\vec{B} \perp \vec{A}$

$\vec{A}\times\vec{B}=\vec{B}\times\vec{A}$

$|\vec{A}\times\vec{A}|=0$

31.

The angle between the vectors $(-2\hat{i}+3\hat{j}+\hat{k})$ and $(\hat{i}+2\hat{k})-4\hat{k})$ is

0°

45°

90°

180°

32.

Dot product of two mutual perpendicular vector is

infinity

none of them

33.

If $\vec{A}\times\vec{B}=\vec{C}$, then choose right option

$\vec{A}\times\vec{B} \perp\vec{C}$ (always)
$\vec{B} \perp \vec{C}$ (always)
$\vec{A} \perp \vec{C}$ (always)
$\vec{A}.\vec{B} \perp\vec{C}$ (always)

only 1 , 2 & 3

only 2 & 3

only 4

only 1

34.

Match the following Quantities with their Type

Physical Quantities	Type of Quantity

(A) Pressure

(1) Scalar

(B) Velocity

(2) Vector

(3) Tensor

(D) Energy

(a) A-1, B-2, C-3, D-1

(b) A-2, B-1, C-3, D-2

(d) A-1, B-3, C-2, D-1

35.

Match the following Physical Quantities with their Type

Physical Quantities	Type of Quantity

(A) Temperature

(1) Scalar

(B) Force

(2) Vector

(3) Tensor

(D) Electric Field

(a) A-3, B-1, C-2, D-3

(b) A-1, B-3, C-1, D-2

(d) A-1, B-2, C-3, D-2

TGT PGT Physics [Free] Practice Test: Units & Measurements

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Why Vector Algebra Is a Must for TGT PGT Physics

Vector Algebra is the backbone of physics, helping you tackle problems involving direction and magnitude. From calculating the resultant force in Mechanics to solving electric field problems in Electromagnetism, vectors are everywhere in TGT and PGT exams.

You’ll face questions like:

“What is the angle between two vectors if their cross product is zero?”
“Resolve a vector into its components at a 45-degree angle.”

Mastering these concepts not only helps you score on direct vector questions but also strengthens your foundation for advanced topics like Kinematics, Dynamics, and more. Our 25-MCQ test includes a mix of easy, medium, and tough questions, all in English and Hindi, to ensure you’re ready for any challenge in the 2025 exams.

What Makes This Practice Test Special?

Bilingual Questions: Available in English and Hindi to suit your preference and ensure accessibility.
Exam-Like Experience: One question per page to mimic the real TGT/PGT exam environment.
Comprehensive Coverage: Includes vector operations, scalar vs. vector quantities, and practical applications.
Detailed Solutions: Download a bilingual solutions PDF to understand each answer and improve.
Free & Accessible: No cost, no hassle—just high-quality prep at your fingertips.

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Free TGT PGT Physics Practice Test: Vector Algebra – 35 Must-Do MCQs for 2025 Exams

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