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

Solved Question Paper

Applied mathematics-1 Dec-2018

PSBTE • DIPLOMA • Cvil Engineering • 1st-2nd • Dec-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

Solved

SECTION-A
Q1. a) Choose the correct answer.

i. If n_P4 = 20 × n_P2 then n is equal to
a) 7 b) 8 c) 2 d) 4

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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,

(a) option
Modulus of 3 – 4i is
a) 6 b) 5 c) 4 d) 3

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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b
Slope of line 3x + y – 2 = 0 is
a) 3 b) 2 c) - 3 d) -2

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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c
Mid points internally of (-a, b) and (a, -b) is
a)
b)
c) a + b

d) (0, 0)

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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d

The point (-4, -5) lies in quadrant
a) 1st b) 2nd c) 3rd d) 4th

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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c
State True or False.
vi. Sin(A + B) = SinA CosB – CosA SinB

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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False
Sum of first n natural numbers is

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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False
If a, b, c are in A.P then 2b = 2a + c.

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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False

Length of latus rectum of ellipse + = 1 is .

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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True
The equation 3x + 4y + 5 = 0 and 4x – 3y + 7 = 0 represent perpendicular lines.

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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True
Fill in the blanks.
xi. nth term of a G.P is ________

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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The eccentricity of parabola is _________

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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1

The equation x + 2y + 3 = 0 to the slope form is _________

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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Two lines are ________if their slopes are equal.

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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Parallel
Value of = ________

Very Short Answer Dec-2018 • PSBTE DIPLOMA

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-1
SECTION-B

Q2. Attempt any six questions.

a. If Show that .

Short Answer Dec-2018 • PSBTE DIPLOMA

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Given log2 = .30103, log5 = 0.69897 Solve the equations 2^x. 5^y = 1, 5^x+1. 2^y = 2.

Short Answer Dec-2018 • PSBTE DIPLOMA

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Equations

Taking log on both sides

Taking log on both sides

Equation 1 multiplying by log 5 and equation 2 by log 2, then subtracting 1 and 2, we get

, Ans
Find the term independent of x in the expansion of .

Short Answer Dec-2018 • PSBTE DIPLOMA

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Find the term independent of x in expansion of

Solution :

Let is the term independent of x.

Term independent of x if

Ans
Resolve into partial fraction  .

Short Answer Dec-2018 • PSBTE DIPLOMA

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Resolve into partial fraction

Sol:
Express the Complex number -3 + 3i in polar form.

Short Answer Dec-2018 • PSBTE DIPLOMA

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Express into in polar form.

From 1 and 2, we get

From equation 3.

Find the co-ordinates of foot of perpendicular from the point (2, 3) on the line y = 3x + 4.

Short Answer Dec-2018 • PSBTE DIPLOMA

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The slope of line perpendicular to
Prove that .

Short Answer Dec-2018 • PSBTE DIPLOMA

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Prove that

Solution :
Sum the series 0.9 + 0.09 + 0.009 + ----- to nth term.

Short Answer Dec-2018 • PSBTE DIPLOMA

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The sum of two angles is and their difference is . Find the angles in degrees and radians.

Short Answer Dec-2018 • PSBTE DIPLOMA

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SECTION-C
Q3. Attempt any three questions.

i. Find the equation of circle which passes through the points (4, 1) and (6, 5) and has its centre lies on the line 4x + y = 16.

Long Answer Dec-2018 • PSBTE DIPLOMA

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If

Long Answer Dec-2018 • PSBTE DIPLOMA

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--------1

---------2

Squaring and adding 1 and 2

2 sin

2+2

Squaring 1 and 2 and subtranction 1 from 2

                                                             Hence Proved
Find the co-ordinates of focus, vertex, the equation of directrix and axis of parabola y² - 4y – 2x – 8 = 0

Long Answer Dec-2018 • PSBTE DIPLOMA

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Equation of parabola is given by

------------1

Shift the origin to the point (-6,2) by putting   x=x1-6   and    y=y1+2

vertex is (0,0)

Focus is   (12 , 0) and directrix   is (

Vertex is (-6,2)

Focus    is   (-6+

            (

Directrix is

                       X+6=

                     X= -6-
A boy observes the angle of elevation of a mountain top to be 60⁰ and after walking directly away from it on level ground through 100 meters, the angle of elevation is 45⁰. Find the height of the mountain and the distance between the mountain and first position of the boy.

Long Answer Dec-2018 • PSBTE DIPLOMA

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In right angle triangle ABD

1=

h=x                                                                              -------1

in right angle triangle ACD

                 --------2

From eq 1 and 2               we get :

=

h (

h =

h =

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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?

This page is meant to help students find MATH-1 old question papers and related study material. Availability of PDF files may vary based on what is listed on the page.

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 Dec-2018 (DIPLOMA 1st-2nd)

Applied mathematics-1 Dec-2018

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