2
Higher Math 1
st
Paper Chapter-1
5| A = (1 –2 3) [h‡kvi †evW©- Õ23]
X = (x y z), B =
1
1
4
– 2
5
– 2
3
0
1
C =
(m + n)
2
m
2
n
2
l
2
(n + l)
2
n
2
l
2
m
2
(l + m)
2
(K) 3
1
2
– 1
4
+ E = I
2
n‡j E g¨vwUª·wU wbY©q Ki|
(L) †µgv‡ii wbq‡g BX
T
= A
T
mgxKiY †RvU mgvavb
Ki|
(M) †`LvI †h, |C| = 2lmn(l + m + n)
3
.
DËi:
(K)
– 2
– 6
3
– 11
; (L) (x, y, z) =
32
59
–
30
59
–
1
59
6| A =
2
1
1
– 1
1
– 1
3
1
2
, B =
x
y
z
, C =
2
5
4
[Kzwgjøv †evW©- Õ23]
(K) Kx k‡Z© `yBwU g¨vwUª‡·i †hvM I ¸Y Kiv m¤¢e?
(L) AB = C n‡j †µgv‡ii wbq‡g mgxKiY †RvUwUi
mgvavb Ki|
(M) A
–1
wbY©q Ki|
DËi:
(L) (x, y, z) = (– 15, 7 13) ; (M)
3
– 1
– 2
– 1
1
1
– 4
1
3
7| M =
a – 5
2
2
a – 2
, N =
– 1
2
4
2
1
– 2
– 3
0
5
P =
– 2
– 2
a + b – c
a + b
b + c
c
2
– c
– a
ab
[Kzwgjøv †evW©- Õ23]
(K) a Gi gvb KZ n‡j M GKwU e¨wZµgx g¨vwUª· n‡e?
(L) N
2
– 5N + 4I wbY©q Ki|
(M) †`LvI †h, |P| = (c – a) (a
2
+ b
2
+ c
2
)
DËi:
(K) a = 1, 6 ; (L)
2
– 10
– 8
– 4
4
6
3
– 6
– 8
8| 2x – y – z = 6, x + 3y + 2z = 1 Ges 3x – y – 5z = 1
[PÆMÖvg †evW©- Õ23]
(K) we¯Ívi bv K‡i
a
b
c
1
1
1
b + c
c + a
a + b
Gi gvb wbY©q Ki|
(L) x, y I z Gi mnM¸‡jv wb‡q MwVZ g¨vwUª· A n‡j A
–1
wbY©q Ki|
(M) †µgv‡ii wbq‡g mgxKiY †RvU mgvavb Ki|
DËi:
(K) 0 ; (L)
1
27
13
– 11
10
4
7
1
– 1
5
– 7
(M) (x, y, z) = (3, – 2, 2)
9| Q =
3 + x
4
2
4
2 + x
3
2
3
4 + x
[PÆMÖvg †evW©- Õ23]
(K)
1
– 1
2
– k
g¨vwUª·wU e¨wZµgx g¨vwUª· n‡j k Gi gvb
wbY©q Ki|
(L) hw` x = 7 nq, Q
2
– 5Q + 3I
3
Gi gvb wbY©q Ki
†hLv‡b I
3
GKK g¨vwUª·|
(M) |Q| = 0 n‡j, mgvavb †mU wbY©q Ki|
DËi:
(K) k = 2 ; (L)
73
62
44
62
64
53
44
53
82
;
(M) { }– 9 – 3 3
10| A =
p
p + 1
p + 1
p + 1
p
p + 1
p + 1
p + 1
p
[wm‡jU †evW©- Õ23]
(K) we¯Ívi bv K‡i
1
4
6
2
5
7
3
6
8
Gi gvb wbY©q Ki|
(L) DÏxc‡Ki Av‡jv‡K A
2
– 7A – 8I
3
wbY©q Ki ; hLb
p = 2
(M) AX = B n‡j wbY©vq‡Ki mvnv‡h¨ ‘X’ wbY©q Ki ;
†hLv‡b p = 1, B =
11
10
9
DËi:
(K) 0 ; (L)
0
0
0
0
0
0
0
0
0
; (M) X =
x
y
z
=
1
2
3
11| px + qy + rz = 1 [wm‡jU †evW©- Õ23]
p
2
x + q
2
y + r
2
z = a
(p
3
– 1)x + (q
3
– 1)y + (r
3
– 1)z = a
2
(K) cÖgvY Ki †h,
4
– 4
3
– 3
GKwU mgNvZx g¨vwUª·|
(L) DÏxc‡Ki mgxKiY¸‡jv‡K AX = B AvKv‡i cÖKvk
K‡i †`LvI †h, pqr = 1, hLb Det(A) = 0 Ges
p q r
(M) l = 1, m = 2, n = – 1 n‡j, A
–1
wbY©q Ki|
DËi:
(M)
1
– 18
15
– 2
– 7
3
2
7
– 6
2
– 2
12| mgxKiY †RvU: tx + uy + vz = 5 [ewikvj †evW©- Õ23]
t
2
x + u
2
y + v
2
z = 5
(t
3
– 1)x + (u
3
– 1)y + (v
3
– 1)z = – 5
(K) M =
2
9
– 3
, N = [– 3 5 6] n‡j, [MN]
T
wbY©q Ki|
(L) t = 1, u = 2, v = 3 n‡j †µgv‡ii wbq‡g mgxKiY
†Rv‡Ui mgvavb Ki|
(M) x, y, z Gi mnM¸wj Øviv MwVZ wbY©vqK D n‡j cÖgvY
Ki, D = (tuv – 1) (t – u) (u – v) (v – t)
DËi:
(K)
– 6
10
12
– 27
45
54
9
– 15
– 18
; (L) (x, y, z) = (2, 3, – 1)
