Maths Question Paper
Group
A (2x 15 = 30)
1. a. Rewrite in absolute sign. -1<x>-4
c. Prove that 2 Tan-1x=cos-1
2. a. Prove that
=
b. If H be the
harmonic mean between numbers a and b2 prove that
+
=
+
c. If A =
show that A2-2A-5I=0, where 0is the 2X2 null matrix.
3. a. Construct the truth table from ((
p)V(
.
b. If x-iy =
. Prove that x2 +y2=1.
c. If one root of
equation
-px+q=0 twice the other show that 2p2=q
4. a. If p is the length of perpendicular dropped from the
origin on the line
+
=
1 prove that
+
=
b. Find the angle
between the pair of lines.
c. Find
if
y= sec -1
5. a. Find the area of curve y=4
on x-axis bounded by the ordinate x=2 and
x=4.
b. Integrate:
x
dx
c. Evaluate:
Group
B (4X10=40)
6. a. State and prove D-Morgan’s law of set theory.
b. Sketch the curve =
-
+
4x – 3
7. a. Prove by the method of induction that 1.2+2.4+3.5+……….+
n(n+2)=
b. Prove that 4(cot-13
+ cosec-1
=
Solve: Secx.Tanx=
8. a. If
+
+
prove that C=600
Given a
,b=2,c=
-1 solve triangle.
9. a. State De-Moivre’s Theorem. Use it to find the cube root of
unity.
b. If the pair of line
-2pxy-y2=6 and x2-2pxy-y2
be such that each pair bisects the angle between
Other pair. Prove
that pq =-1
10. a. A function f(x) is defined as
f(x)=
for
x
3
for x=3
Find the value of K if f(x) or continuous at x=3.
OR
Evaluate:
b. Integrate
Find area of
circle
y2=25
Group
c (6X5=30)
11. Find the sum of n terms: 1+
+
+
+…
… … …
12. Prove that circles
+y2+2ax+c2=0 and x2+y2+2by+
c2=0 touch if
+
=
13. Find the derivative of
by
first principle.
14. If roots of equation a(b-c)
+
b(c-a)x + c(a-b) = 0 are equal, prove that
+
=
15. State and prove cosine law. Also prove that
=
=
+
2R, where R is radius of circum circle.
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