BOARD OF INTERMEDIATE EDUCATION A.P.: HYDERABAD
MODEL QUESTION PAPER w.e.f. 2012-13
MATHEMATICS - IA
(English Version)
Time: 3 hours
Max. Marks: 75
Note: This Question paper consists of three sections A, B and C
SECTION - A
10 x 2 = 20 Marks
I.
Very Short Answer Questions:
(i) Answer All Questions
(ii) Each Question carries Two marks.
1.
If A
2.
Find the domain of the real-valued function
3.
A certain bookshop has 10 dozen chemistry books, 8 dozen physics books, 10 dozen economics
books. Their selling prices are Rs. 80, Rs. 60 and Rs. 40 each respectively. Find the total
amount the bookshop will receive by selling all the books, using matrix algebra.
4.
If A
5.
Show that the points whose position vectors are
0,
, , ,
6 4 3 2
2
5
and f : A
4
, then find A
3
B is a surjection defined by f ( x )
cos x then find B.
1
.
log(2 x)
A and A A .
2a 3b
5c , a 2b
3c , 7a c are
collinear when a , b , c are non-coplanar vectors.
6.
Let a
2i
4j
tion of a b
5k , b
i
j k and c
j 2k . Find unit vector in the opposite direc-
c.
7.
If a i 2 j 3k and b
to each other.
8.
Prove that
9.
Find the period of the function defined by f ( x )
10.
If sinh x 3 then show that x log e (3
cos90
cos90
sin9 0
sin9 0
3i
2 j 2k then show that a b and a b are perpendicular
cot360 .
10) .
tan( x
4 x 9 x .... n 2 x ) .
SECTION - B
II.
5 x 4 = 20 Marks
Short Answer Questions.
(i)
Answer any Five questions.
(ii)
Each Question carries Four marks.
bc b c 1
ca c a 1
ab a b 1
(a b)(b c)(c a)
.
11.
Show that
12.
Let A B C D E F be regular hexagon with centre ‘O’, show that
AB AC AD AE AF 3AD 6 AO .
2 j 3k , b
j k and c
13.
If a
14.
If A is not an integral multiple of
i
2i
2
(i) tan A
cot A
2 cosec 2A
(ii) cot A
tan A
2 cot 2A
15.
Solve: 2 cos 2
16.
Prove that cos 2 tan
17.
In a ABC prove that tan
, prove that
1 0.
3 sin
1
3 j 2k find a (b c ) .
i
1
7
sin 4 tan
1
B C
2
1
.
3
b c
A
cot .
2
b c
SECTION - C
III.
5 x 7 = 35 Marks
Long Answer Questions.
(i)
Answer any Five questions.
(ii)
Each Question carries Seven marks.
18.
Let f : A
19.
By using mathematical induction show that
1
1.4
1
4.7
B, g:B
C be bijections. Then prove that ( gof )
1
......upto n terms
7.10
n N,
n
.
3n 1
1
f 1og 1 .
1
A
0
2
2 3
1 4
then find ( A ) 1 .
2 1
20.
If
21.
Solve the following equations by Gauss - Jordan method
3 x 4 y 5 z 18 , 2 x
y 8 z 13 and 5 x 2 y 7 z
20 .
22.
If A = (1, 2, 1), B = (4, 0, 3), C = (1, 2, 1) and D = (2, 4, 5), find the distance between
AB and CD .
23.
If A, B, C are angles of a triangle, then prove that
sin 2
24.
In a
A
B
C
sin 2
sin 2
2
2
2
1 2 cos
A
B
C
cos sin .
2
2
2
ABC , if a = 13, b = 14, c = 15, find R, r, r1, r2 and r3.
OOO