This document contains 16 multiple choice questions from Section B and 9 multiple choice or problem solving questions from Section C on topics of trigonometry, groups, and other mathematics. The questions are from past years exams between 2010-2015 and include worked examples to reference for solving some of the problems.

1. Miscellaneous QuestionForfirst years student
SectionB
Q1. With usual notations prove that
p
l
 page288 2011
Q2 Draw the graph of y=tanx, x ],[ 
Q3 Solve the triangle ABC if 421,1345,1735 /0/0
 b Example1P367(2012)
Q4 if Z1=2+I, Z2=3-2i, Z3=1+3i then express
2
31
Z
ZZ 
in the form of a+bi. Example2P24 2012
Q5 Resolve 3
2
)2(
1


x
xx
into partial fraction. Example1P184 2012
Q6 prove that 


tansin
sin1
sin1



, where Znn  ,
2
)12(

 Example3P310 2012
Q7 Find out real imaginary part of
3
)3( i by De-Moivre’s Theorem. Example5P27 2013
Q8 If a,b are elements of group G then solve the equations ax=b and xa=b.2013
Q9 In any triangle ABC, prove that sin
bc
csbs ))((
)
2
(



where s is semi perimeter of triangle? 2013
Q10 Define Group. Also give one example. Page70 2014
Q11 Prove that tan is a periodic function of  Page340 2014
Q12 contruct the truth table of qpqp  ])[( like ex2.4 2015
Q13 Prove that
0
00
00
56tan
11sin11cos
11sin11cos



Example 3 P323 2015
Q14 If (G,*) a group with e its identity then e is unique . Theorem P77 2015
Q15 Resolve
)4)(3(
257


xx
x
into partial Fractions.2015
Q16 Prove that 2
222
2
3
2
2
2
1
2
1111



cba
rrrr
Example 3 like ex12.8 2015
Section C
Q1. Drive the Fundamental law of trigonometry. 2010,2012
Q2 Prove that 3 is an irrational number. 2012
Q3 show that roots of equation (x-a)(x-b)+(x-b)(x-c)+(x-c)(x-a)=0 are real and will be equal only if a=b=c Example 3 P167 2012
Q4 If m and n are nearly equal show , that
n
mn
nm
m
n
nm
32
)
3
25
( 3
1





Example 7P279 2012
Q5 Solve the equation sin2
x+cosx=1. Example4P405 2012
Q6 sin4  to an expression involving only function of multiples of  raised to the first powerExample4 chapter10 2013
Q7 Cos4  to an expression involving only function of multiples of  , raised to the first power. Example4 chapter10 2014
Q8 Solve the equation sin2x=cosx Example 3P404 2015
Q9 Solve the equation sin2x+cosx=1 Example 4 p405 2015