is:-Multan Board 2016
INTERMEDIATE PART-II (12th CLASS)
MATHEMATICS
TIME ALLOWED: 30 Minutes
MAXIMUM MARKS: 20
OBJECTIVE
Note: You have four choices for each objective type question as A, B, C and D. The choice which you think is correct; fill that circle in front of that question number. Use marker or pen to fill the circles. Cutting or filling two or more circles will result in zero mark in that question. Attempt as many questions as given in objective type question paper and leave others blank. No credit will be awarded in case BUBBLES are not filled. Do not salve question on this sheet of OBJECTIVE PAPER.
Q.No.1
is:-(A)
(B)
(C)
(D)
is:-(A) x2 - y2 = r2
(B) x2 + y2 = r2
(C) y2 - x2 = r2
(D)+
(A)
(B)
(C)
(D)
- 3
+ 
is:- (A)
(B)
(C)
(D)
along 
is:- (A)
,
(B)
(C)
(D),
( x ) = x2/3 + 6 then 
( 0 ) = (A) 1
(B) 4
(C) 6
(D) 8
=(A)
(B)
(C)
(D)
(
2)=(A)
2
(B)2
(C)2
2
(D)2
2
(
)= (A)
(B)
(C)
(D)
x)=(A) 2x
(B)x
(C) 1/2x
(D)
-1
=(A)
(B)
(C)
(D)
-1
= (A)
(B)
(C)
(D)
(A)
(B)x
-1
(C)xCosee-1
(D)x
-1
(A)
(B)
(C)
(D)
(A)
(B)
(A)
(A)
= (A) 0
(B) 4
(C) 8
(D) 16
= (A)
(B)
(C)
(D)
(A)
(B)
(C)
(D)
=1 is:(A) Slope intercept form
(B) Two intercept form
(C) Symmetric form
(D) Normal form
is:- (A)
(B)
(C)
(D)
Time: 2:30 Hours (Subjective Part)
Marks: 80
SECTION-I
GROUP-I
NOTE: - Write same question number and its part number on answer book as given in the question paper.
2. Attempt any eight parts.
2 
if 
; find 
3 
2
2
-2x
then find 
for 
2= 2 
4 
3 
2
when 
- 
3. Attempt any eight parts.
if 
= 
2 and 
changes from 3 to 3.02.
(
+1) 
- axis and the curve 
2
from
to 
= 0
4. Attempt any nine parts.
such that 
are vertices of a right triangle
into normal form.
3
) and radius 2
to circle 5x2 + 
2 
directrix 
2 + 
2
if 
= 
given that 
—
= 21— j + k and 
= — 
+
and 
are coplanar.
SECTION-II
NOTE: - Attempt any three questions.
5.(a) 
(b) 
(
(
prove that 
2 
+
6.(a) Evaluate 
(b) The vertices of a triangle are 
and 
Find coordinates of orthocentre.
7. (a) Solve the differential equation (
2 — 
2 ) 
2 — 
2= 0
(b) Maximize 
subject to the constraints 
, 
,
0, y
0
8. (a) Write an equation of circle which passes through the points 
(b) Find the vector from the point 
to the origin when 
and 
is the point 
9.(a) Find equation of parabola with given elements, focus 
and directrix 
(b) In any triangle
, prove that by vector method
=
=
Multan Board 2016
INTERMEDIATE PART-II (12th CLASS)
MATHEMATICS PAPER-II
TIME ALLOWED: 30 Minutes
MAXIMUM MARKS: 20
OBJECTIVE
Note: You have four choices for each objective type question as A, B, C and D. The choice which you think is correct; fill that circle in front of that question number. Use marker or pen to fill the circles. Cutting or filling two or more circles will result in zero mark in that question. Attempt as many questions as given in objective type question paper and leave others blank. No credit will be awarded in case BUBBLES are not filled. Do not salve question on this sheet of OBJECTIVE PAPER.
Q.No.1
3
) (A)
2
(B)2
(C)
(D)
2has minimum value at: -(A)
(B)
(C)
(D)
(A)
(B)
(C) -
(D)
= (A)
(B)
(C)
(D)
3 
(A)
(B)
(C)
(D)
(A)
(B)
(C)
(D)
(A)
(B)
(C)
(D)
1, 
1 ) and 
2,
2 ). Then its slope is:-(A)
(B)
(C)
(D) -
having slope 2 is:-(A)
(B)
(C)
(D)
to line
is:-(A)
(B)
(C)
(D)
is solution of:- (A)
(B)
(C)
(D)
and radius is 3. Then equation of circle is:-(A)
2
2
(B)2 +
2
(C)2
2
(D)2
2
at point 
(x1, y1 ) is:-(A)
(B)
(C)1 –
1 =0
(D)1+
1 =0
and 
is:-(A)
(B)
(C)
(D)
and 
are perpendicular if:(A)
=0
(B)=0
(C)
(D)
is: (A) (
)
(B) [-1,
(C) [0,
(D) [-1,1]
= (A)
(B) 2
(C) 3
(D)
(A)
(B)
(C)
(D)
(A)
2
(B)2
(C)
(D)2
10 
(A)
(B)
(C)
(D)
Time: 2:30 Hours (Subjective Part)
Marks: 80
SECTION-I
GROUP-II
NOTE: - Write same question number and its part number on answer book as given in the question paper.
2. Attempt any eight parts.
2/x 
by definition. 
,then find 
2 
2 
, then find 
1
when 
= 
3 
1/2 
-1 (
), find 
2 when 
(x - 9 )
2.
3 3. Attempt any eight parts.
and 
when 
= 
2 -1and 
changes from 3 to 3.02.
, 
, 
4. Attempt any nine parts.
so that the line joining 
and the line joining
are parallel.
and 
and perpendicular to a line having slope 
2 
2
lies above or below the line 
2
2
lies outside, on or inside the circle
2 
2 
2 = 
2 
-
find 
-
+
and 
= -
+ 
=
, 
+ 3
+ 
and 
= 2
- 
+2
Find a unit vector perpendicular to both 
and 
. SECTION-II
NOTE: - Attempt any three questions.
5.(a) 
(b)
, 
then prove that 
6.(a) Evaluate 
(b) Show that distance of the point 
(x1, y1) from the line 
is 
7. (a) Evaluate 
(b) Minimize 
subject to constraints 
15
8. (a) Show that the circles 
2 
2 
and 
2 
2 
touch externally.
(b) Prove that the line segments joining the mid points of the sides of a quadrilateral taken in order form a parallelogram using Vector Method.
9.(a) Find the focus, vertex and directrix of the parabola 
2
(b) Find the moment about 
of each of the concurrent forces 
- 2
, 3
+2
-
,5
+2
where 
is their point of concurrency.
