Zeal Education Society’s
ZEAL POLYTECHNIC,
PUNE.
NARHE │PUNE -41 │ INDIA
FIRST YEAR (FY)
DIPLOMA ALL BRANCHES
SCHEME: I SEMESTER: I
NAME OF SUBJECT: Basic Mathematics
Subject Code: 22103
MSBTE QUESTION PAPERS & MODEL ANSWERS
1. MSBTE SUMMER-18 EXAMINATION
2. MSBTE WINTER-18 EXAMINATION
3. MSBTE SUMMER-19 EXAMINATION
4. MSBTE WINTER-19 EXAMINATION
,*22103*
22103
21718
3 Hours / 70 Marks Seat No.
Instructions : (1) All questions are compulsory.
(2) Answer each next main question on a new page.
(3) Illustrate your answers with neat sketches wherever necessary.
(4) Figures to the right indicate full marks.
(5) Use of Non-programmable Electronic Pocket Calculator is
permissible.
(6) Mobile Phone, Pager and any other Electronic Communication
devices are not permissible in Examination Hall.
Marks
1. Attempt any five of the following : 10
⎛2⎞ ⎛4⎞ ⎛8⎞
a) Find the value of log⎜ ⎟ + log⎜ ⎟ − log⎜ ⎟ .
⎝ 3⎠ ⎝ 5⎠ ⎝ 15 ⎠
b) Find the area of the triangle whose vertices are (3, 1), (–1, 3) and (–3, –2).
c) Without using calculator, find the value of sec (3660°).
d) The length of one side of the rectangle is twice the length of its adjacent side. If the
perimeter of rectangle is 60 cms, find the area of the rectangle.
e) Find the surface area of a cuboid of dimensions 26 cms ; 20 cms and 12 cms.
f) Find range and coefficient of range for the data :
120, 50, 90, 100, 180, 200, 150, 40, 80.
g) If coefficient of variation of a distribution is 75% and standard deviation is 24, find its
mean.
2. Attempt any three of the following : 12
⎡3 − 1⎤ ⎡1 2⎤
a) If A = ⎢ , B = . Find X such that 2X + 3A – 4B = I.
⎣2 4 ⎥⎦ ⎢− 3
⎣ 0⎥⎦
b) Resolve into partial fractions : x2 + 1 .
x ( x 2 − 1)
P.T.O.
,22103 [2] *22103*
Marks
c) The voltage in an electric circuit are related by following equations :
V1 + V2 + V3 = 9; V1 – V2 + V3 = 3; V1 + V2 – V3 = 1 find V1, V2 and V3 by using
Cramer’s rule.
d) Calculate the mean deviation about the mean of the following data :
3, 6, 5, 7, 10, 12, 15, 18.
3. Attempt any three of the following : 12
a) Without using calculator, find the value of
cos 570°. sin 510° + sin(–330°).cos(–390°).
sin 4θ + sin 2θ
b) Prove that = tan 2θ .
1 + cos 2θ + cos 4θ
sin 3A − sin A
c) Prove that = tan A .
cos 3A + cos A
1 2
d) Prove that tan −1 + tan −1 = cot −1 2 .
4 9
4. Attempt any three of the following : 12
a) Find x and y if
⎡2⎤
⎧ ⎡1 2 0⎤ ⎡1 3 − 1⎤ ⎫⎢ ⎥ ⎡ x ⎤
⎨4 ⋅ ⎢ ⎥ − 2⋅⎢ ⎬ 0 = .
⎩ ⎣2 −1 3⎦ ⎣2 −3 4 ⎥⎦ ⎭⎢ ⎥ ⎢⎣ y ⎥⎦
⎣⎢ − 1⎦⎥
b) Resolve into partial fractions 2x + 1 .
2
( x − 1) ⋅ ( x + 1)
1
c) Prove that cos20°.cos40°.cos60°.cos80° = .
16
θ 2
d) If tan = find the value of 2 sin θ + 3 cos θ .
2 3
5
e) If A and B are obtuse angles and sin A = and cos B = − 4 , then find sin(A + B).
13 5
, *22103* [3] 22103
Marks
5. Attempt any two of the following : 12
a) Attempt the following :
i) Find the length of the perpendicular from the point (5, 4) on the straight line 2x + y = 34.
3
ii) Find the equation of the line passing through (3, –4) and having slope .
2
b) Attempt the following :
i) Find the equation of line passing through the point (3, 4) and perpendicular to the line
2x – 4y + 5 = 0.
ii) Find the acute angle between the lines 3x – y = 4, and 2x + y = 3.
c) Attempt the following :
i) Find the capacity of a cylindrical water tank whose radius is 2.1 m and length is 5 m.
ii) External dimensions of a wooden cuboid are 30 cm × 25 cm × 20 cm. If the thickness of
wood is 2 cm all round. Find the volume of the wood contained in the cuboid formed.
6. Attempt any two of the following : 12
a) Calculate the mean, standard deviation and coefficient of variance of the following data :
Class interval 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
Frequency 03 05 08 03 01
b) Attempt the following :
i) Calculate the range and coefficient of range from the following data :
Marks 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69
No. of students 6 10 16 14 8 4
ii) The data of run scored by two batsmen A and B in five one day matches is given below :
Batsman Average run scored S.D.
A 44 5.1
B 54 6.31
State which batsman is more consistent ?
c) Solve the following equations by matrix inversion method :
x + 3y + 3z = 12; x + 4y + 4z = 15; x + 3y + 4z = 13.
––––––––––––––
ZEAL POLYTECHNIC,
PUNE.
NARHE │PUNE -41 │ INDIA
FIRST YEAR (FY)
DIPLOMA ALL BRANCHES
SCHEME: I SEMESTER: I
NAME OF SUBJECT: Basic Mathematics
Subject Code: 22103
MSBTE QUESTION PAPERS & MODEL ANSWERS
1. MSBTE SUMMER-18 EXAMINATION
2. MSBTE WINTER-18 EXAMINATION
3. MSBTE SUMMER-19 EXAMINATION
4. MSBTE WINTER-19 EXAMINATION
,*22103*
22103
21718
3 Hours / 70 Marks Seat No.
Instructions : (1) All questions are compulsory.
(2) Answer each next main question on a new page.
(3) Illustrate your answers with neat sketches wherever necessary.
(4) Figures to the right indicate full marks.
(5) Use of Non-programmable Electronic Pocket Calculator is
permissible.
(6) Mobile Phone, Pager and any other Electronic Communication
devices are not permissible in Examination Hall.
Marks
1. Attempt any five of the following : 10
⎛2⎞ ⎛4⎞ ⎛8⎞
a) Find the value of log⎜ ⎟ + log⎜ ⎟ − log⎜ ⎟ .
⎝ 3⎠ ⎝ 5⎠ ⎝ 15 ⎠
b) Find the area of the triangle whose vertices are (3, 1), (–1, 3) and (–3, –2).
c) Without using calculator, find the value of sec (3660°).
d) The length of one side of the rectangle is twice the length of its adjacent side. If the
perimeter of rectangle is 60 cms, find the area of the rectangle.
e) Find the surface area of a cuboid of dimensions 26 cms ; 20 cms and 12 cms.
f) Find range and coefficient of range for the data :
120, 50, 90, 100, 180, 200, 150, 40, 80.
g) If coefficient of variation of a distribution is 75% and standard deviation is 24, find its
mean.
2. Attempt any three of the following : 12
⎡3 − 1⎤ ⎡1 2⎤
a) If A = ⎢ , B = . Find X such that 2X + 3A – 4B = I.
⎣2 4 ⎥⎦ ⎢− 3
⎣ 0⎥⎦
b) Resolve into partial fractions : x2 + 1 .
x ( x 2 − 1)
P.T.O.
,22103 [2] *22103*
Marks
c) The voltage in an electric circuit are related by following equations :
V1 + V2 + V3 = 9; V1 – V2 + V3 = 3; V1 + V2 – V3 = 1 find V1, V2 and V3 by using
Cramer’s rule.
d) Calculate the mean deviation about the mean of the following data :
3, 6, 5, 7, 10, 12, 15, 18.
3. Attempt any three of the following : 12
a) Without using calculator, find the value of
cos 570°. sin 510° + sin(–330°).cos(–390°).
sin 4θ + sin 2θ
b) Prove that = tan 2θ .
1 + cos 2θ + cos 4θ
sin 3A − sin A
c) Prove that = tan A .
cos 3A + cos A
1 2
d) Prove that tan −1 + tan −1 = cot −1 2 .
4 9
4. Attempt any three of the following : 12
a) Find x and y if
⎡2⎤
⎧ ⎡1 2 0⎤ ⎡1 3 − 1⎤ ⎫⎢ ⎥ ⎡ x ⎤
⎨4 ⋅ ⎢ ⎥ − 2⋅⎢ ⎬ 0 = .
⎩ ⎣2 −1 3⎦ ⎣2 −3 4 ⎥⎦ ⎭⎢ ⎥ ⎢⎣ y ⎥⎦
⎣⎢ − 1⎦⎥
b) Resolve into partial fractions 2x + 1 .
2
( x − 1) ⋅ ( x + 1)
1
c) Prove that cos20°.cos40°.cos60°.cos80° = .
16
θ 2
d) If tan = find the value of 2 sin θ + 3 cos θ .
2 3
5
e) If A and B are obtuse angles and sin A = and cos B = − 4 , then find sin(A + B).
13 5
, *22103* [3] 22103
Marks
5. Attempt any two of the following : 12
a) Attempt the following :
i) Find the length of the perpendicular from the point (5, 4) on the straight line 2x + y = 34.
3
ii) Find the equation of the line passing through (3, –4) and having slope .
2
b) Attempt the following :
i) Find the equation of line passing through the point (3, 4) and perpendicular to the line
2x – 4y + 5 = 0.
ii) Find the acute angle between the lines 3x – y = 4, and 2x + y = 3.
c) Attempt the following :
i) Find the capacity of a cylindrical water tank whose radius is 2.1 m and length is 5 m.
ii) External dimensions of a wooden cuboid are 30 cm × 25 cm × 20 cm. If the thickness of
wood is 2 cm all round. Find the volume of the wood contained in the cuboid formed.
6. Attempt any two of the following : 12
a) Calculate the mean, standard deviation and coefficient of variance of the following data :
Class interval 0 – 10 10 – 20 20 – 30 30 – 40 40 – 50
Frequency 03 05 08 03 01
b) Attempt the following :
i) Calculate the range and coefficient of range from the following data :
Marks 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69
No. of students 6 10 16 14 8 4
ii) The data of run scored by two batsmen A and B in five one day matches is given below :
Batsman Average run scored S.D.
A 44 5.1
B 54 6.31
State which batsman is more consistent ?
c) Solve the following equations by matrix inversion method :
x + 3y + 3z = 12; x + 4y + 4z = 15; x + 3y + 4z = 13.
––––––––––––––
