Mymensingh Girls' Cadet College
Progress
Test examination-2009
Class-X
Subject : General Mathematics
Time : 3 hrs. Marks:
100
1. If A = { a,
b, c } , B = { p, q }, then find A´B and B´A. 4
Or, Determine the
following sets in Roster method: { xÎN : x2 >15 and x3 < 225}.
2. Find
the solution sets :
=3, x
¹ -5. 4
3. Answer any
three: 5x3
=15
a) If 2x -
= 3, then prove
that 8 (
) = 63.
b) Resolve into factors : a3 - 9b3 + (a + b)3
c) Find the H. C. F. and L.C.M of
x2
- x ( a -c ) - ac ; x2 - x ( a +c) + ac and ax3 - a3 x.
d) Salary of Matin is x% higher than that
of Jalil. As a result Jalils salary is y% less than that of Matin. Express y in terms of x.
e) Resolve into factors: 2a3 - 3a2 + 3a - 1.
4. Simplify : 7 log
+ 5 log
+ 3 log
. 5
Or, Log
+ log
+ log
- 3log b
2c.
5. If
, then prove that, a, b, c are in continued proportion. 5
Or, If the length
of each side of a square is increased by
10%, then what is the percentage of increase in the area enclosed by the square?
6. Solve :
4
Or, The digits in
tens place of a number consisting of two digits is twice the digits in the ones
place. Show that the number is seven times the sure of the digits.
7. If f(y) =
, then prove that f (
) = f (y
2 ). 4
Or, If x ay and
y aZ,
then show that x2
+ y2
+z2 a yz +
zx + xy.
8. By the
method of cross multiplication find the solution ( x, y) and verify:
x - y
+ 2y = 10
Or, Find the
solution ( if there by any) by grafical method of 5x -
3y =10
10x
- 6y = 1
9. If in a
geometric series 1st and 2nd terms are respectively 125 and 25, find the 5th
and the 6th term. 5
Or, If the sum of
n -terms of the series 9+7+5+ ............ is -144, then find the value of n.
Answer any two of the following : 6x2=12
10. a) If the square on one side of a triangle
is 1 to the sum of the squares on the other two sides, the angle continued by these two sides
is a right angle. Prove it.
b) The locus of a point equidistant from
two intersecting straight lines is the bisectors of the terminal angles between the two given
straight lines. Prove with your hypothesis.
c) The sum of the two opposite angles of a
quadrilateral inscribed in a circle is two right angles. Prove
with the help of diagram.
11. Answer any
two : 4x2=
8
a) DABC is a right angled
isoceles triangle . P is a point on BC, its hypotenuse, prove that
PB2 + PC2 = 2PA2.
b) Prove that, three bisectors of the
angles of a triangle are concurrent.
c) Two circles touches internally at the
point P. The chord AB of the greater circle touches the smaller circle at C. show that, the line PC bisects ÐAPB.
12. To construct
a trapezium when two parallel sides of trapezium and the angles adjacent to the
greater side are given. [ sign
of diagram and description is must.] 5
Or, To draw
circle inscribed in a triangle [ sign of the diagram and explanation is
essential.]
13. Construct an
equilateral triangle whose perimeter are given. 5
Or, Draw a
tangent to a circle which is parallel to a given straight line.
14. Prove that
:
=
= SecA - tan A. 4
Or, If Sin A +
cosA = a and secA + cosesA = b, then prove that b(a2-1) = 2a.
15. Solve : 2cos
2q + 2
sin
q = 3.
Or, If q = 300, then show that
Cos 3q
= 4 cos3q - 3
cosq.
16. A man standing at a place or the bank of a river of a river
observes that the angle of elevation of a tower exactly opposite to him on the
other bank is 600.
On moving 25 metres. in the backward direction he observed that the angle of
elevation of the tower is 300. Find the height of the tower and the width of the
river. 4
Or, The shadow of a tower on the ground is increased by 44 metres,
when the anlge of elevation of the sun is changed from 600 to 450.
What is the height of the tower?
17. The area, of a rectangular region is 160 sq.m. The region
becomes a square if its length is reduced by 6 metres. Find the length and
breadth of the rectangular region. 4
Or, The length of the base of an isosceles triangles is 60 cm. If
its area is 1200 sq. cm. Find the length of the equal sides.
18. The outer measurements a rectangular box are 8 cm, 6 cm and 4
cm respectively and the area of the whale inner surface is 88 sq.cm. Find the
thickness of the wood.
Or, The height of a right circular cylinder and a cone is x and
they stand on the same base. If the areas of their curved surfaces are in the
ratio 4:3, show that the radius of the base is
.
