Download OU Intermediate 2018 Core Subjects 0166 Mathematics Question Paper

Download OU (Osmania-University) Intermediate 2018 Core Subjects 0166 Mathematics Previous Question Papers

Totel No. of Questions~24 _ . _ _ ,
Tetal N0,~ ?of Printed Pages??-4 " v \Regd'.? No. I g (3 O I 7, 3 ' Z)? 3 3
?Part 111 .
TEES Papef HA)
(English Version) V
Time: 31101113] ' 1 ? ? ' '_ " ,. [Max Marks: 75
Note :?-Thi-s question paper consists of three Sections A B 21nd C.
,' SECTIONA _ '. q . ~._
I. ? 1 Very Short Answer Type Questions 2' ~ 1 f ' . _ 101622230 ,
, (i) ' Answer ALL questions. ~- ' " "
(ii) Each questiOn carries TWO marks. 4 _ - 1
1. If a b e R f: R ?> R de?ned by ?x) = ax +,,b"(a g; .01, ??nd-f-l. ~
2. Find the domain of real valued function}, ' ? B " ' '
'f(x)_= 4x?x2.?
3.- 1qu ' 7?
V "2 4 7 '
. ' ?1_ k
and A2 :11, then ?nd the value of ?1?.
4. 1 Find the Frank of the following matrix:
A ? ' ' 1 ' 11 1
1 1_ 1
1 .1 1
5. Find the vector equation of the line joining the pomts 2i + j + 3k and
?4i +3j 12., , q 4 q ' _ .
11660 "a ' ~, -' '1 . _ ; ; 13.1.0.7

[21'
6. . If a? _ 2i + 5 J +12 and bl: 4;? + mj + nk are collinear Vectors, then ?nd
.m? and ? 3
7.. Ifa =2i?3j+k and 5-1, +4J?2k then ?nd (a+b')>< X(d?E).?
8.4 V Prove that: 3 V . I V 3 3
cos 9? +' s4nl9? : Cof36?.
, ? COSQ??Slngo ' _
9e . Prove that 3: V 3
_ ,. [Sin 50?. ? sin 70?g+ si?lo? ; 0.
~10. ?3 Show 'fhat : '
3 L ? (coshx + Sinth? = ?Osh(n_x) +l .sinh(n?x),
for any n. E -R.' ? I ? I
_ 3 3 SECTION B V .
IL. _ Shoft-Answer Type'Question's :' ' 3 . 3 , ' I 5x4220
I (i)_ ' Answer ANY FIVE questions. 7 3 V. V 1
(ii) Each question carrie?. FOUR marks.
1&1. If 3 V 3' , ? 3
a1 '51 ?31
A: ?2 ' b2 ?32
a3 {)3 c3
? _Adj" A
is a non? ?singu1ar matrix, then prove that A?1 det A
12. V If - a b c are non? ?copl?nar Vectors, then prove that :
??a+4b.? 3c, 3a+2b 5c, ?3a+8b~? 50, ~3a+26+c
are Coplanar.
0166 C

13.
14.
715.
16.
A 17.
- 111. f
18.;
? 19.
' .20.
Prove that: '
Prove that :.
[3]"
For anytwo :Viectors d". and , 5,. show , that :
(1.11513?(1.+|51)?=11?agaf ?2
1 g
s1n10O (30leO
SolVe the ?q?ation :
sinx + 3 cosx-I; x/E.
Prove that :
A ' ? ' - ?1 2 2 ? 2.
cotA +? cotB + cotC : w
' , ? ? 4A
SECTIONC '
Long Answ?r Type Questions :'
(1')" AnsWe'r ANY FIVE qUestions
t(ii) Each question carries SEVEN marks
+16+5?Ei> < b.
tan?1 ~1? +ta11?1k l +tan'1' l ?23. -
, 2 . ' 5? . 8 4? ?
? 5x7=35,
Let f; A a B,1A and IB be identity functions on A ar1d B respect1ve1yf
'_ then prove that f 01A ? f? ? IB 0 f.
ShoW that 49? + 1672 ? 1 is d1v1sible by 64 for all positive 1ntegers ?n?.
Show that :9 -- '.
a by; c 2? 260 ? (1'2. 02 52
b _ C, a 2. c2 H.2ac?b? ? . a2 '=(a3+b3+c3?3abc).
c a b 52' a2 1-251?) 4? c
A 13.110.

.' 2.1.,
. 22.7
23.
24.
a) *+*+*??
my Egg:
, I '4 ?14 .
Solve the follbwing system Of 'equ'ation's- by Cramer?s rule :
L ? 2x ? y + 32 =' 8 4 I I
'?x?+ 2y + Z ?'4'
_3x'_+y_4z=0[
115: i 2j+ +312; 51:.2f+.j+?,?6={+j+2l?,then ?nd~l(3x~5)x3?
and ?5 x (?5 X5?.
?If A + B + C: 23, then prove that:
COS < S ?' A) + COS(S "- B) + COS < S ?' C) '1? C088 " 4008? COSEICOSE'
.If P , P , P. are altitudes d1?aWn from vertice?s A, B, C to the opposite .
1 2 3
sides of a. triangle respectively, then show that:
1 1 1_1
P,
1 P2 P3 7?;
. (abb)? 8A3"
8R3 , (Ibo.
0166?0.