Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) B.Sc (Non-Medical) 2020 March Previous Question Papers
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Sc (Non Medical) (2018 & Onwards) (Sem.?1)
SOLID GEOMETRY
Subject Code : BSNM-106-18
M.Code : 75747
Time : 3 Hrs. Max. Marks : 50
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying ONE mark
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION-A
1. a) Find the equation of plane passing through the points (2, 3, ?4) and (1, ?1, 3) and
parallel to x-axis.
b) Find the equation of the plane through the points (2, 2, 1) and (9, 3, 6) and
perpendicular to the plane x + 2y + 2z = 5.
c) Find the equation of the sphere passing through the origin and the points ( ?, 0, 0),
(0, ?, 0) and (0, 0, ?).
d) Prove that the circles x
2
+ y
2
+ z
2
? 2x + 3y + 4z ? 5 = 0, 5y + 6z + 1 = 0 and x
2
+ y
2
+
z
2
? 3x ? 4y + 5z ? 6 = 0, x + 2y ? 7z = 0 lie on the same sphere and find its equation.
e) Find the limiting point of the coaxial system of spheres determined by
x
2
+ y
2
+ z
2
+ 4x ? 2y + 2z + 6 = 0 and x
2
+ y
2
+ z
2
+ 2x ? 4y ? 2z + 6 = 0.
f) Find the equation of the cone whose vertex is the origin and which passes through the
curve of intersection of the plane lx + my + nz = p and the surface ax
2
+ by
2
+ cz
2
= 1.
g) Find the equation of the right circular cylinder of radius 2 whose axis is the line
1 2 3
2 1 2
x y z ? ? ?
? ? .
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1 | M-75747 (S105)-1949
Roll No. Total No. of Pages : 02
Total No. of Questions : 09
B.Sc (Non Medical) (2018 & Onwards) (Sem.?1)
SOLID GEOMETRY
Subject Code : BSNM-106-18
M.Code : 75747
Time : 3 Hrs. Max. Marks : 50
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying ONE mark
each.
2. SECTION-B contains FIVE questions carrying FIVE marks each and students
have to attempt any FOUR questions.
3. SECTION-C contains THREE questions carrying TEN marks each and students
have to attempt any TWO questions.
SECTION-A
1. a) Find the equation of plane passing through the points (2, 3, ?4) and (1, ?1, 3) and
parallel to x-axis.
b) Find the equation of the plane through the points (2, 2, 1) and (9, 3, 6) and
perpendicular to the plane x + 2y + 2z = 5.
c) Find the equation of the sphere passing through the origin and the points ( ?, 0, 0),
(0, ?, 0) and (0, 0, ?).
d) Prove that the circles x
2
+ y
2
+ z
2
? 2x + 3y + 4z ? 5 = 0, 5y + 6z + 1 = 0 and x
2
+ y
2
+
z
2
? 3x ? 4y + 5z ? 6 = 0, x + 2y ? 7z = 0 lie on the same sphere and find its equation.
e) Find the limiting point of the coaxial system of spheres determined by
x
2
+ y
2
+ z
2
+ 4x ? 2y + 2z + 6 = 0 and x
2
+ y
2
+ z
2
+ 2x ? 4y ? 2z + 6 = 0.
f) Find the equation of the cone whose vertex is the origin and which passes through the
curve of intersection of the plane lx + my + nz = p and the surface ax
2
+ by
2
+ cz
2
= 1.
g) Find the equation of the right circular cylinder of radius 2 whose axis is the line
1 2 3
2 1 2
x y z ? ? ?
? ? .
2 | M-75747 (S105)-1949
h) Prove that the (1, 1, 1) and (?3, 0, 1) lie on the opposite sides of the plane 3x + 4y ?
12z + 13 = 0.
i) Define rectangular cone.
j) Prove that the cones ax
2
+ by
2
+ cz
2
= 0 and
2 2 2
0
x y z
a b c
? ? ? are reciprocal.
SECTION-B
2. Find the equation the planes which bisect the angles between the two given planes.
3. Find the equation of the right circular cylinder described on the circle through the points
(1, 0, 0), (0, 1, 0) and (0, 0, 1) as the guiding curve.
4. Prove that the plane 2x ? 2y + z + 12 = 0 touches the sphere x
2
+ y
2
+ z
2
? 2x ? 4y + 2z ? 3
= 0.
5. Prove that the polar line
3 1 2
1 2 3
x y z ? ? ?
? ? with respect to the sphere x
2
+ y
2
+ z
2
= 1 is
the line
7 3 7 2
1 11 5
x y z ? ?
? ?
? ?
.
6. Find the angle between the generating lines in which a plane cuts a cone.
SECTION-C
7. Find the equation of the plane passing through the line of the intersection of the line of
intersection of the plane ax + by + cz + d = 0and a ?x + b ?y + c ?z + d ? = 0 and perpendicular
to xy ? plane.
8. Find the necessary and sufficient condition that the general equation of second degree
ax
2
+ by
2
+ cz
2
+ 2fyz + 2gzx + 2hxy + 2ux + 2vy + 2wz + d = 0 represents a cone.
9. a) Find the locus of the tangent lines drawn to the sphere and parallel to a given line.
b) If
1 2 3
x y z
? ? represents one of the three mutually perpendicular generator of the cone
5yz ? 8zx ? 3xy = 0; find the equation of other two.
NOTE : Disclosure of Identity by writing Mobile No. or Making of passing request on any
page of Answer Sheet will lead to UMC against the Student.
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This post was last modified on 02 April 2020