Enrollment No./Seat No.:

## GUJARAT TECHNOLOGICAL UNIVERSITY DIPLOMA IN ENGINEERING - SEMESTER - II EXAMINATION - WINTER 2025

Subject Code: DI02000021

Date: 09-01-2026

Subject Name: Engineering Mathematics

Time: 10:30 AM TO 01:00PM

Total Marks: 70

Instructions:

1. Attempt all questions.
2. Make Suitable assumptions wherever necessary.
3. Figures to the right indicate full marks.
4. Use of programmable & Communication aids are strictly prohibited.
5. Use of only simple calculator is permitted in Mathematics.
6. English version is authentic.
7. Draw the question paper in English and Gujarati Both languages.
8. Q.1 Fill in the blanks/MCQs using appropriate choice from the given options.
9. ( યોGLYPH<c=3,font=/QWCAAA+Lohit-Gujarati>ય િવકGLYPH<c=7,font=/QWCAAA+Lohit-Gujarati>પ પસંદ કરી ખાલી જGLYPH<c=3,font=/QWCAAA+Lohit-Gujarati>યા પૂરો / બહુિવGLYPH<c=22,font=/QWCAAA+Lohit-Gujarati>GLYPH<c=7,font=/QWCAAA+Lohit-Gujarati>પ GLYPH<c=23,font=/QWCAAA+Lohit-Gujarati>GLYPH<c=24,font=/QWCAAA+Lohit-Gujarati> ોનાં જવાબ આપો )

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( ૧ )

(2)

(

૨

)

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(a)    0    (b)    2    (c)    -8    (d)    8

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Marks 14

(3)

```
If A = then = _______ (a) (b) (c) (d) ( ૩ ) GLYPH<c=28,font=/QWCAAA+Lohit-Gujarati> A = હોય તો = ________ (a) (b) (c) (d) (4) If  A = then cofactor of element 3 (i.e. ) is ________ (a)    -1    (b)    1    (c)    2    (d)    0 ( ૪ ) GLYPH<c=28,font=/QWCAAA+Lohit-Gujarati> A = હોય તો ઘટક 3  (i.e. ) નો સહ અવયવ __________ છે. (a)    -1    (b)    1    (c)    2    (d)    0 (5) = ________ (a)    0    (b)    2024    (c)    1    (d)    2026 ( ૫ ) = __________ (a)    0    (b)    2024    (c)    1    (d)    2026 (6) If then = ______
```

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( ૬ )

$$GLYPH<c=28,font=/QWCAAA+Lohit-Gujarati> હોય તો = ________ (a) (b) (c) (d) (7) = ________ (a) (b) (c) (d) ( ૭ ) = _________ (a) (b) (c) (d) (8) = _______ + c (a) (b) (c) (d) ( ૮ ) = _________ + c (a) (b) (c) (d) (9) = ___________ +c (a) (b) (c) (d) ( ૯ ) = _________ + c (a) (b) (c) (d) (10) = _________ (a) (b) (c) (d)$$

( ૧૦ ) = \_\_\_\_\_\_\_\_ (a) (b) (c) (d) (11) The order and degree of is \_\_\_\_\_\_\_  respectively. (a)  1 and 1  (b)  1 and 2  (c)  2 and 1  (d)  2 and2 ( ૧૧ ) િવકલ સમીકરણ ની ક1ા અને પ2રમાણ અનુ3મે \_\_\_\_\_\_\_\_\_\_\_ છે. (a)  1 and 1  (b)  1 and 2  (c)  2 and 1  (d)  2 and2 (12) The integrating factor of is \_\_\_\_\_\_\_ (a) (b) (c) (d) ( ૧૨ ) નો સંકGLYPH&lt;c=7,font=/QWCAAA+Lohit-Gujarati&gt;યકારક અવયવ \_\_\_\_\_\_\_\_\_ છે. (a) (b) (c) (d) (13) · = \_\_\_\_\_\_\_\_\_ (a) (b) (c) (d) ( ૧૩ ) = \_\_\_\_\_\_\_\_\_ (a) (b) (c) (d) (14) = \_\_\_\_\_\_ (a)    0    (b)    1    (c)    i      (d)    -i ( ૧૪ ) = \_\_\_\_\_\_ (a)    0    (b)    1    (c)    i      (d)    -i

Q.2A Attempt any two ( કોઇપણ બે ના જવાબ આપો )

(1)

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(2)

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Solve the differential equation

(

૨

)

(3)

(

૩

)

િવકલ સમીકરણ નો ઉકેલ મેળવો.

Q.2B Attempt any two ( કોઇપણ બે ના જવાબ આપો )

(1)

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(

૧

)

(2)

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(3)

Solve using matrices.

- ( ૩ ) સુરેખ સમીકરણ સંહ￵ત #ેણીકોની મદદ થી ઉકેલો.

08

## Q.3A Attempt any two ( કોઇપણ બે ના જવાબ આપો )

(1)

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(2)

( ૨ )

(3)

( ૩ )

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Q.3B Attempt any two ( કોઇપણ બે ના જવાબ આપો )

(1)

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Equation of motion of a moving particle is given by . Find velocity at second and acceleration at second.

ગ￵ત કરતા કણનું ગ￵તસૂ; છે. તો સેક&lt;ડે વેગ અને સેક&lt;ડે GLYPH&lt;c=23,font=/QWCAAA+Lohit-Gujarati&gt;વેગ મેળવો.

( ૧ )

(2)

(

૨

)

(3)

( ૩ )

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Evaluate:

08

Q.4A Attempt any two ( કોઇપણ બે ના જવાબ આપો )

(1)

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( ૧ )

(2)

( ૨ )

(3)

( ૩ )

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Q.4B Attempt any two ( કોઇપણ બે ના જવાબ આપો )

(1)

Evaluate:

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Find the area of the region enclosed by the curves and

વ3ો અને X અ1 થી ઘેરાયેલા GLYPH&lt;c=23,font=/QWCAAA+Lohit-Gujarati&gt;દેશનું 1ે;ફળ મેળવો.

Find the square root of  a complex number

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( ૧ )

(2)

( ૨ )

(3)

(

૩

)

08

Q.5A Attempt any two ( કોઇપણ બે ના જવાબ આપો )

(1)

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( ૧ )

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- (2) If then find the value of

(

૨

)

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If then find

(3)

( ૩ )

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Q.5B Attempt any two ( કોઇપણ બે ના જવાબ આપો )

(1)

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(

૧

)

(2)

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- ( ૨ ) િવકલ સમીકરણ નો ઉકેલ મેળવો.

(3)

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***

(

૩

)

08