Class
2nd YEAR Federal Board 2009
Paper:Mathematic (Objective Type) Time
Allowed: Max.Marks:
Note:Use this paper
to write the answers to the objective questions.No marks will be awarded
for cutting,over-writing
or using a pencil.This paper must be tagged with the answer-book.
1. Insert correct option.
(1) If P is the perimeter of square and
A its area them A is equal to.
(2) If f(x) =e x then -1 (x).
(a) sinx (b)
cosx
(c) lnx
(d)
ex
(3) What is domain of x2-9 .(All
real numbers,[-3,3], Positive real numbers,
(-∞,
-3]U[3,∞).
(4) d (2 5x)
dx
(a) 5.2 5x
(b)
5 2 5x In2
(c) 2 5x
In2 (d) 2 5x
In2
(5) The function ƒ(x) = 3x2
has minimum value at.
(a) x = 3
(b) x = 2
(c) x = 1 (d)
x = 0
(6) ∫3 cosec 2 (3x)dx.
(a) -cot (3x)
+c (b)
-cos 3x + c
(c) cot(3x)+c
(d)
1/3 cot(3x)+c
(7) What is the distance of the point
(1,-2) from x-axis?
(a) 2 (b)
1
(c) -1 (d)
-2
(8) If (3, 5) is midpoint of (5,a) and
(b,7) then a and b are.
(9) If a line passes through points (4,3)
and (2, ) is perpendicular to line y=2x+3then
is equal to.
(a) 2 (b)
4
(c) 3 (d)
5
(10) The solution set of the inequality ax+by <
cis the
(a) Circle (b)
Half-plane
(c) Parabola
(d) Plane
(11) A point of a solution region where two of its
boundary lines intersect is called:
(a) Point of
trisection (b)
Point of bisection
(c) Corner point
(d)
None of these
(12) When the cone is cut by a plane perpendicular
to the axis of a cone the section is a:
(a) Sphere (b)
Parabola
(c) Circle (d)
Hyperbola
(13) If the circle x2
+ y2 + x+2y+c=0 passes through (-1,-1)
then c is equal to:
(a) -1 (b)
1
(c) 0 (d)
2
(14) The direction of the parabola y2 = 8x is.
(a) x + 2 =
0 (b)
x - 2 = 0
(c) y + 2 =
0 (d)
y - 2 = 0
(15) Vertices of hyperbola x2
- y2 = 1 are .
16 4
(a) +
2, 0 (b)
0, + 4
(c) 0,
+ 4 (d)
+ 4,0
(16) If 3 and 1 are x and y-components
of a vector,then its angle with x-axis is.
(a) 30
(b)
45
(c) 60
(d)
90
(17) If a vector xi - 2j + k and 2xi + xj - 4k are
perpendicular then x is equal to.
(a) 2,
-1 (b)
2, 1
(c) -2,
1 (d)
-2, 1
(18) The area of triangle whose adacent sides are
3i + 4j and - 5i + 7j is.
(a) 20
(b) 41/2
(c) 10
(d) 5
(19) in x dx.
2. Attempt any TEN parts.
(1) Determine whether f (x) = x2/3
+ 6 is even or odd
(2) Evaluate lim tan x - sin x .
x--->o sin3
x
(3) Find dy if x = y sin y.
dx
(4) Differentiate a x
by Ab-lnitio method (a >1).
(5) Show that y = In x ,has a
miximum value at x=e
x
(6) Evaluate ∫sec x dx
(7) Evaluate ∫In(x + 2
x2 +1) dx
(8) Find the area above the x- axis bounded
by curve y2 = 3 - x from x = - 1 to
x =2.
(9) Find h such that points A (-1,h)
, B(3, 2) and
c (7, 3)are collinear.
(10) Find an equation of the perpendicular bisector
joining the points
(a) (13, 5) and (b) 19,
8).
(11) Show that line 2x + 3 y - 13 = 0 is tangent
to the circle x2 + y2
+ 6x - 4y = 0.
(12) write an equation of parabola whose focus (2,
5) and directrix y =1 .
(13) Show that the vectors 2i - j + k, i - 3 j -
5k and 3i - 4j - 4k from sides of a right angle triangle.
Attempt
any FIVE questions.
3. If 0 is measure
in radians then prove lim sin 0 = 1
0--->0 0
4. The perimeter
of a triangle is 20cm. If one side is of length 8cm, what are lengths
of other two sides for
maximum area of the triangle.
5. Evaluate
∫
sin x
dx
o (1 + cos x) (2 + cos x)
6. Find the area
of region bounded by the triangle whose sides are :
7x - y - 10
= 0, 10 x + y - 41 = 0 , 3x + 2y + 3 = 0
7. Minimize z
= 2x + y subject to constraints x + y > 3 and 7 x + 5
y < 35 where x > O.
8. Find an equation
of the ellipse mwith vertices (0,+ 5) eccentricity = 3
and sketch the graph.
5
9. Prove by the
vectors that perpendicular bisectors of the sides of a triangle
are concurrent. |
