Cadet College
|
Class-IX
Subject- Higher
Mathematics
Time: 2-30 hrs.
Marks: 75
Algebra- 28
Answer any seven of the following questions. 4x 7 = 28
1. Demonstrate
with the help of Venn diagrams that ( AUB)(BUA) = (AUB) \ AÇB).
2. If A = { 1, 2 } and B = { 2, 5 }, then show that
P(A) Ç
P (B) = P ( A ÇB).
3. Resolve into
factors: a( b - c)3 + b ( c - a )3
+ c ( a - b)3.
4. If 
+ 
+ 
= 
, then show that bc+ ca + ab =0 or a = b = c .
+ + = , then show that bc+ ca + ab =0 or a = b = c .
5. Simplify : 
+ 
+ 
+
+ + +
6. Resolve into
partial fractions: 
7. If S = { x: x ÎR and x2 +1 =0
}, then find S2 = R/S. What can you say about S ?
8. If 
¹ 0,
then show that ( a+b+c )( x + y + z) = ax + by + cz.
¹ 0,
then show that ( a+b+c )( x + y + z) = ax + by + cz.
Geometry- 30
Answer any five of the following questions: 6x5
=30
9. The diagonals
of the rectangle ABCD intersect at 0. It p is any point inside the rectangle,
then prove that PA2 + PB2
+PC2 +PD2 = AC2 + 4PO2
10. In the
triangle ABC, AB = AC and AC is produced to D such that AC = AD, prove that
BD2
= 2BC2+AC2.
11. The madians
of a DABC
meet at G. Prove that AB2 + BC2 +CA2 = 3 ( GA2+GB2+
GC2).
12. To construct
a triangle having given the base, the vertical angle and the difference of the
other two
two side. [
Description and tracing are required.]
13. To divide a
given straight line internally such that the rectangle contained by the whole
and the one part may be equal to
the square on the other part. [ Tracing and description are required]
14. To construct
a circle which touches a given, straight line at a given point in it and passes
through another given point outside that
line. [ Tracing and description are required.]
Trigonometry - 12
15. Define
radian. Prove that radian is a constant
anlge.
16. An angle is
denoted by D0 and Rc in the sexagesimal and circular
systems respectively. Prove that
17. The angles of
a triangle are in the ratio 2:5:3: find
the circular and sexagesimal measure of the largest angle.
18. A wheel
revolues 20 times to travel a distance of 88 km, what is the radius of the
wheel?
