Jrinter Maths1a Model Paper 6 em PDF
Jrinter Maths1a Model Paper 6 em PDF
Jrinter Maths1a Model Paper 6 em PDF
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BOARD OF INTERMEDIATE EDUCATION
JUNIOR INTER MATHEMATICS PAPER - I (A)
MODEL PAPER (ENGLISH VERSION)
e t
TIME: 3 HOURS
. n
MAX.MARKS: 75
a t
ii) Answer ALL questions.
iii) Each question carries TWO marks.
p r 10 2 = 20
1.
d u
If the function f: {1, 1} {0, 2} defined by f(x) = ax + b is a surjection, then find a and b.
2.
n a x
Find the domain and range of f(x) =
2 3x
3.
e
If A =
. e [ 2 4
1 K ]
, A2 = 0, then find K.
4.
w w
( ) 0 4 2
If A = 4 0 8 is a skew-symmetric matrix, then find the value of x.
e t
5. w
2 8 x
.
If 2 i + 5 j + k and 4 i + m j + n k are collinear vectors, then find m and n. n
6.
h a
Find the vector equation of the plane passing through the points (1, 2, 5), (0, 5, 1), (3, 5, 0).
If a = (1, 1, 1), b = (2, 3, 1) find the orthogonal projection of b on a and also its magnitude.
7.
8. Expand cos (A B C).
i b
9. Find the value of sin 34 cos 4 + cos 64.
Find the domain and range of sec h1x. a t
10.
p r
SECTION - B
II. i) Short answer type questions.
d u
n
ii) Answer any FIVE questions.
a
.e e
iii) Each question carries FOUR marks.
1 2
5 4 = 20
11.
(
w )
If A = 0 1
w 2 2
3
4 then find (A')1.
1
12.
13.
w The point E divides the line segment PQ internally in the ratio 1 : 2 and R is any point not on the line
PQ. If F is a point on QR such that QF : FR = 2 : 1, then show that EF is parallel to PR.
If a , b, c are the position vectors of the points A, B, C respectively, then prove that the vector
(a b + b c + c a ) is perpendicular to the plane of ABC.
R-1-2-16
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1 sec 8 tan 8
14. Prove: = .
1 sec 4 tan 2
15. Solve: 1 + sin 2x = (sin 3x cos 3x)2.
16.
( )
1
( )
1
Solve: tan1 + tan1 = tan1
2x + 1 4x + 1
2
x2 ()
e t
17.
a
b+c b+c
2 bc A
If sin = , then show that cos = . cos .
2
. n
SECTION - C
h a
III. i) Long answer type questions.
i b
ii) Answer any FIVE questions.
a t 5 7 = 35
18.
iii) Each question carries SEVEN marks.
p r
Solve the equation (gof) (x) = (fog) (x) where f(x) = x2 and g(x) = 2x.
19.
d u
Prove, for n N, by using Induction principle:
n(5n 1)
n a
2 + 7 + 12 + ..... + (5n 3) = .
2
e
a + b + 2c a b
20.
w.e
Prove: c
c
b + c + 2a
a
b = 2 (a + b + c)3.
c + a + 2b
t
21.
w
Solve by using Gauss - Jordan Method.
w
x + y + z = 9; 2x + y z = 0; 2x + 5y + 7z = 52.
n e
22.
and r = (4, 0, 1) + t(3, 2, 2).
a .
Find the shortest distance between the skew-symmetric lines represented by r = (6, 2, 2) + s(1, 2, 2)
23.
b h
sA sB C
If A + B + C = 2s prove that, 1 + cos(s A) + cos(s B) + cos C = 4cos cos cos
2 2 2
24.
r1 r2 r3 1 1
Prove: + + = .
t i
bc ca ab r 2R
r a
u p
a d
e n
.e
w ww
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