Solved question paper for MATH-1 May-2018 (DIPLOMA 1st-2nd)

Solved Question Paper

Applied mathematics-1 May-2018

PSBTE • DIPLOMA • Information Technology • 1st-2nd • May-2018

MATH-1 for Punjab State Board of Technical Education Diploma in Engineering students is a useful subject page for finding subject-wise previous year question papers and old exam papers for the 1st-2nd semester. Students can use these papers to revise key topics, understand the exam pattern, and practice the kinds of questions that are asked again and again in Applied Mathematics-1. This page is meant to help you search for semester-wise question papers, exam pattern questions, and important questions for revision before the test. BRpaper is not the official website of the university or board, so the papers shown here should be used as a study aid for preparation and practice.

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Solved Questions

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SECTION-A

Q1. Choose the correct answer.

(i) The modulus of 1 + Ý…√3 is a) √2 b) -1 c) 2 d) 0

Very Short Answer 5x1=5 Marks May-2018 • PSBTE DIPLOMA

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z = 1 +

|z| =

Option C
The value of 3π/12 radians in degree is

a) 60° b) 45° c) 90° d) 120°

Very Short Answer May-2018 • PSBTE DIPLOMA

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π radian = 180⁰

Option B
Characteristic of log 0.07426 is

a) 1 b) 2 c) 0 d) 1

Very Short Answer May-2018 • PSBTE DIPLOMA

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log0.07426 = -2.6001 (Find with the help of log table)

option B
If Sin (A-B) = ½ and Cos (A+B) = ½ then value of A and B will be

a) A=15° , B=45° b) A=45°, B=15° c) A=45°, B=45° d) A=30°, B=60°

Very Short Answer May-2018 • PSBTE DIPLOMA

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We know that

Option B

The centroid of a triangle with two vertices (3,4) (-1,-9) is (2, -4) then third vertex is a) (-4 , -7) b) (4, -7) c) (4,7) d) (-4,7)

Very Short Answer May-2018 • PSBTE DIPLOMA

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Vertices of triangle are (3,4),(-1,-9) and let third vertices is (x,y).

Its centroid is (2,-4)

Formula of centroid

=

Option B
State True or False.

a. The series of the R.H.S of the expansion (1 + x)ⁿ extends to infinity

Very Short Answer 5x1=5 Marks May-2018 • PSBTE DIPLOMA

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False
If k, k+1, k+3 are in G.P, then k=2

Very Short Answer May-2018 • PSBTE DIPLOMA

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k, k+1,k+3, ------

k = 2

2,3,5,….. is not in G.P.

False
Value of tan 120° is √3

Very Short Answer May-2018 • PSBTE DIPLOMA

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False

Sec(270 ÌŠ + θ) = Cosecθ

Very Short Answer May-2018 • PSBTE DIPLOMA

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True
The point (3,4); (7,7); (x,4) are collinear, if x=3

Very Short Answer May-2018 • PSBTE DIPLOMA

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(3,4),(7,7) and (x,4) are collinear if x=3

A (3,4), B (7,7), C(3,4)

By distance formula

True
Fill in the blanks.

i. Radius is a -------- angle.

Very Short Answer 5x1=5 Marks May-2018 • PSBTE DIPLOMA

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constant
The revolving line is always ---------

Very Short Answer May-2018 • PSBTE DIPLOMA

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rotate about fixed point.

If CosA = ½ then Cos3A =

Very Short Answer May-2018 • PSBTE DIPLOMA

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cos3A = -1
The conic is parabola if ---------

Very Short Answer May-2018 • PSBTE DIPLOMA

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e = 1
Equation of line perpendicular to line ax+by+c=0 is -------

Very Short Answer May-2018 • PSBTE DIPLOMA

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-bx+ay+c = 0
SECTION-B

Q4. Attempt any six questions.

a. In how many ways, 3 boys and 3 girls are seated at round table, so that no two girls sit together.

Long Answer 6x5=30 Marks May-2018 • PSBTE DIPLOMA

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3 boys can be seated at a round table in i.e. Ways

When 3 boys have occupied their seats in any one of these Ways, then 3 girls can occupy any 3 out of 3 seats between boys so that no two girls are sitting together. This can be done in ways

Hence required number of ways

= 12 Ans

Find the co-ordinates of the incentre of the triangle whose vertices are (-36,7), (20,7) and (0,-8)

Long Answer May-2018 • PSBTE DIPLOMA

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Formula of the center of the triangle is

, where a,b,c are the length of the sides of triangle.

To find a,b and c by distance formula

e

Put all values in formula
Resolve ((3x+7) over (x+3)(x^2 + 1)) into partial fractions

Long Answer May-2018 • PSBTE DIPLOMA

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Resolve     into partial fractions.

=

=

Comparing coefficients of x, x² and constant terms

        ----- 1

           ----- 2

          ----- 3

From 2

This is put in 1

    ------ 4

Subtract 4 from 3

As

From 3

= Ans
A (10, 4); B (-4, 9); C (-2,-1) are the vertices of a triangle ABC, find the equation of the median through A.

Long Answer May-2018 • PSBTE DIPLOMA

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D is mid point of BC

To find the co-ordinate of D is

We write the equation of line AB by using Two-point form,
Prove that Cos α + Cos(α+2π/3) + Cos(α+4π/3) = 0

Long Answer May-2018 • PSBTE DIPLOMA

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Prove that

L.H.S.

If l({log x over y-z} = {logy over z-x} = {log z over x-y} ) then show that x²y²z² = 1

Long Answer May-2018 • PSBTE DIPLOMA

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If then Show that

Sol :

And

Take

Taking log on both sides

Using 1 and 2

Hence it is proved that
Prove that (sinA Sin3A Sin5A Sin7Aover CosA Cos 3A Cos 5A cos 7A) = tan4A

Long Answer May-2018 • PSBTE DIPLOMA

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Prove that

Sol. L.H.S.

By using C,D formulae from trignomentary
Prove that ( { cot heta + Coses heta - 1over cot heta + Coses heta + 1} = {1+Cos heta over sin heta})

Long Answer May-2018 • PSBTE DIPLOMA

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Prove that

Sol:

L.H.S.
How many terms of the series 3+8+13+18+ ------ must be taken so that their sum is 1010?

Long Answer May-2018 • PSBTE DIPLOMA

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3+8+13+18+ ……………

This is A.P

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01 Where can I find MATH-1 previous year question papers for PSBTE Diploma?

You can use this page to look for subject-wise MATH-1 previous year question papers for the Punjab State Board of Technical Education Diploma in Engineering 1st-2nd semester.

02 Can I download the MATH-1 question paper PDF from this page?

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03 Are solved question papers available for Applied Mathematics-1?

Some students search for solved question papers, but this page should be treated mainly as a source for previous year papers and exam practice material, not as a guarantee of solved answers.

04 How do MATH-1 PYQ papers help with preparation?

MATH-1 PYQ papers help you understand the exam pattern, spot repeated questions, and revise important topics from Applied Mathematics-1 before the exam.

05 Is BRpaper the official website for PSBTE?

No. BRpaper is not the official website of Punjab State Board of Technical Education. It only helps students find previous year papers and study resources.

Solved question paper for MATH-1 May-2018 (DIPLOMA 1st-2nd)

Applied mathematics-1 May-2018

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