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SHRI KRISHNA ACADEMY,NAMAKKAL-9965531727 1
SHRI KRISHNA ACADEMY NEET,JEE AND BOARD EXAM COACHING CENTRE
SBM SCHOOL CAMPUS,TRICHY MAIN ROAD,NAMAKKAL CELL:9965531727-9443231727
QUARTERLY EXAMINATION -2019
XI - BUSINESS MATHEMATICS TENTATIVE ANSWER KEY
ANSWER KEY
Q.No PART – I 1.
1 5
30 2 12.
2 47
5 5
a
2. c.4
3.
1.
nb A
4. d. prof.Wassily W.Leontief
5. c.2n-1
6. a.9
7. (all options wrong)correct answer is 18
8. b.20
9. 2.
hc
b
10. d.
2 22 0x ay y
11. a. Latus returm
12. c.Rene Descartes
13. 3 1.
2 2d
14. 1
.3
a
15. b.56/55
16. a.0
17. d.2
18. a.1
19. a.-1
20.
2.5 xC e
x
PART – II
21. 2
2
2
a ab ac
ab b bc
ac bc c
Tacking a,b,c common from c1, c2, c3
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SHRI KRISHNA ACADEMY,NAMAKKAL-9965531727 2
0
0
2
a a a
abc b b b
c c c
a a
abc b b
c c c
Expanding along c1
2
2 2 2
2
2
4
a aabc c
b b
abc ab ab
a b c
22. 0.8 0.2
0.9 0.7
0.2 0.2
0.9 0.3
0.12 0
B
I B
I B
I B is negative Hawkins- simon condition are not satisfied.
23. 2
1
1 11
A B
x xx
Multiplying both side by (x-1)(x+1), we get
1 1 1
11
2
11
2
A x B x
putx A
putx B
24. 2 4 1 3
1 2 0 0
3! 2! 1! 0!
6 4 0 0 1
E X A M
RANK =1
25. Let m1 and m2 be the slope of 2x-y+3=0 and x+y+2+=0
m1=2 , m2= -1
1
2 1tan 3
1 2( 1)
tan (3)
26. The given equation are
2 2 16 3 4 0x y and x y p
The condition for the tangency is c2 = a
2 (1+m
2)
a2 = 16 from the equation 3 4 0x y p
3
4 4
py x
Comparing with y =mx+c
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SHRI KRISHNA ACADEMY,NAMAKKAL-9965531727 3
2
2 2 2
2
3
4 4
(1 )4
400 20
pm c
pc a m
p p
27.
8 12 8 122cos cos
2 2
2cos10 cos 2
2cos10 cos 2
A A A A
A A
A A
28. ( )
0
0
y f x x
x if x
x if x
x -2 -1 0 1 2
y 2 1 0 1 2
Points (-2,-2),(-1,1)(0,0),(1,1),(2,2) and draw a smooth curve.
29. 3 3
3 30
3
330
0
log(1 )lim
sin
log(1 ) 1lim
sinlim
1
x
x
x
x x
x x
x
x x
x
30. Since ABCD are a quadrilateral
0 0
0 0
0 0
0
180 180
180 180
. . sin sin
sin sin 180 180
sin sin 360 ( )
sin sin
0
A c c A
B D D B
L H S A B C D
A B A B
A B A B
A B A B
PART – III
31.
1 1
1 1
1
2 1
4 2 2 1
3 1 1 0
4 2 2 11
3 1 1 02
5 311
4 22
2
5 3 5 312
4 2 4 22
A B
adjA adjB
A B
A B
AB
adjAB AB
From 1 and 2 A-1
B-1
=(AB)-1
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SHRI KRISHNA ACADEMY,NAMAKKAL-9965531727 4
32.
1
1
2 0 1 0
5 1 0 4
0 1 3 5
1 0
3 1 1
15 6 5
5 2 2
3 1 1
15 6 5
5 2 2
x
y
z
AX B
A A exists
adjA
A
33.
34.
35.
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SHRI KRISHNA ACADEMY,NAMAKKAL-9965531727 5
36. Given x+y=6 and x+2y=4 are two diameters of the circle.
Solve the two equation y = -2 , x = 8
The poin of intersection of two diameters = (8,-2) and center = C(8,-2)
Equation of the circle is (x-8)2+(y+2)
2=r
2 at passing through the point (2,6)
r2=100
Required equation of the circle x2+y
2-16x+4y-32=0.
37.
38. Given tanA – tanB = x and cotB – cotA = y
1 1 1 1
tan tan cot cot
1 1
1 1tan tan
tan tan
1 tan tan
tan tan tan tan
1 tan tan
tan tan
1
tan
cot
x y A B B A
A B
B A
A B
A B A B
A B
A B
A B
A B
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SHRI KRISHNA ACADEMY,NAMAKKAL-9965531727 6
39.
40. f(x) is continuous at x=1
Lf(x)=Rf(x)=1
1 1
1
1
lim lim ( ) 15
lim ( ) 15
2 5 1
lim ( ) 15
2 15 2
x x
x
x
f x
f x
a b
f x
a b
From 1 & 2 a = 5 and b = -5
PART – IV
41.(a) 4 11 5
35 35 351 3 71 6 25
4 2 335 35 35
1 2 16 1 10
35 35 35
35 0 01
0 35 035
0 0 35
1 0 0
0 1 0
0 0 1
,ly
AB
I
lll BA I
AB BA I
A and B are inverce of each other.
(b) 0.4 0.7
0.1 0.7
0.6 0.7
0.1 0.3
0.11
B
I B
I B
The system is viable.
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SHRI KRISHNA ACADEMY,NAMAKKAL-9965531727 7
1
1
0.3 0.71
0.1 0.60.11
0.3 0.7 6.81
0.1 0.6 10.20.11
83.45
61.82
I B
X I B D
A
B
Out put A=83.45 tonnes & B=61.82 tonnes.
42.(a)
(b)
11 415 15 1365C C
10 414 14 1001C C
11 314 14 364C C
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SHRI KRISHNA ACADEMY,NAMAKKAL-9965531727 8
43.(a) Let y represent the costand x represent the no.of TV sets.
1 1
2 1 2 1
220000 80
287500 220000 125 80
220000 80
67500 45
1500 100000
y y x x
y y x x
y x
y x
y x
The cost of 100 TV set.
=1500(100)+100000
=RS.250000.
(b)
44.(a)
1 1
1
2 21 1
2 2
. . tan tan
tan
1
tan tan (1)4
m m nL H S
n m n
m m n
n m n
m m n
n m n
m n
m n
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SHRI KRISHNA ACADEMY,NAMAKKAL-9965531727 9
(b)
2
2
2 2
2 2
cos 4 cos 2(2 )
1 2sin (2 )
1 2(2sin cos )
1 2(4)sin cos
1 8sin cos . .
x x
x
x x
x x
x x R H S
45.(a)
1
3 2
2
3 4
5 6 3 2
x xY
x x x
Tacking log on both sides
3 21log log 3 log 4 log 5 6 3 log 2
2y x x x x x
2
3 2
3 2
3 22
1 1 1 3 10 6 1
2 3 4 5 6 3 2
3 41 1 3 10 6 1
2 3 4 5 6 3 25 6 3 2
dy x x
y dx x x x x x
x xdy x x
dx x x x x xx x x
(b)
Given
21m
y x x
Differentiating both sides,with respect to x,
112 2 2
2
12
2
1
11 1 1 2
2
1
1
1
m
m
dym x x x x
dx
m x xy
x
y x my
Differentiating both sides,with respect to x
2 2 2
1 1 2 12 1 2 2xy x y y m yy
Dived each term by 2y1
2 2
11 0x xy m y
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SHRI KRISHNA ACADEMY,NAMAKKAL-9965531727 10
46.(a)
(b)
47.(a)
2
2
2
2
2
6 4 21 0
6 4 21
6 9 9 4 21
3 4 3
4
x x y
x x y
x x y
x y
X aY
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SHRI KRISHNA ACADEMY,NAMAKKAL-9965531727 11
3
3
14 1
4
X x
Y y
a a
Axis: x = -3
Vertex: V( -3 , 3)
Focus: F( -3 , 4)
Directrix: y=2
Length of latus rectum: 4(1)=4
(b)
22
2
3 5
1 11 1
3 5 1 1
x A Bx C
x xx x
x A x Bx C x
Sub 1x
4A
Equating coefficient of x2
A + B = 0
B = -4
Equating coefficient of x -B + C = 3
C= -1
22
3 5 4 4 1
1 11 1
x x
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