Karnatak University 2009 P.U.C Physics, Chemistry, Maths & Biology Mathematics - Question Paper
Thursday, 24 January 2013 09:20Web
MODEL PAPER 2009
First PUC-Mathematics
Time : three hours Max. Marks : 100
Instructions: 1. The ques. paper has five parts A, B, C, D and E
2. ans all parts
3. Write ques. number properly as indicated in the ques. paper.
PART - A
ans ALL the ques.. 10X1=10
1. obtain x if log10(x-9)=2
2. If sum of 2 roots of x3 -5x2 -16x+80=0 is zero , obtain the 3rd root.
3. Write the inverse of the proposition " If 'a' is a divisor of 'b' then "b' is a multiple of "a'
4. Expand ?3-2
x ?4
5. If the midpoint of (3,K) and (9, -3) is (6,5) obtain K
6. If A={x ? N/1
5?
36 in degrees
8. Draw a two regular graph with three vertices
9. obtain the formula of the straight line with slope -3 and passing through the point (-1, -3)
10. obtain the area of the triangle ABC if a=12, b=15 c=13
PART -B
ans any TEN ques. 10X2=20
11. Resolve into partial fractions :
2x?5
x2?5x-6
12. obtain by synthetic division, the quotient and the reminder when the polynomial x3 +5x2 +6 is
divided by x+1.
13. obtain the term independent of x in the expansion of (x2 -
1
x )8 .
14. If a certain compound proposition (p? q)?(rV ~ s) is known to be false. obtain the truth values
of p, q, r and s
15. Simplify:
sin ????? cos ?2?-??
tan??
2 ???cot ??
2 -??
16. If a cosA = b cosB in a triangle ABC, then Prove that triangle is isosceles or right angled
17. obtain the value of sin 150 using sin(A-B) formula
18. obtain the formula of a line through (4,5) and perpendicular to 4x-3y+7=0.
19. obtain k if the lines 2x-3y+k=0, 3x-4y-13=0 and 8x-11y-33=0 are concurrent.
20. obtain the acute angle ranging from the pair of lines represented by 3x2 -48xy+23y2 =0
21. Derive slope intercept form of formula of straight line
22. describe a complete graph. provide an example
PART-C
ans any 8 ques. 8X5=40
23. a)If the function f:R?R and g:R?R are described by f(x)=x2 and g(x)=x+3. obtain fog(x) and gof(x). Are
they equal? 3
b)If f:Q?Q described by f(x)=2x-5 obtain f-1 ?23
? 2
24. State the 4 laws of Logarithms (any four). If x1/3 +y1/3 +z1/3 =0,
show that loge ?x?y?z
3 ? =
13
log (xyz) 5
25. Prove that ~(p ?q) is logically equivalent to (p? ~q)V (q?~p) 5
26. Resolve into partial fractions :
x3?7x2?17x?11
x2?5x?6
5
27. Prove by mathematical Induction : 1.2+3.4+5.6+.......... to n terms=
n?n?1??4n-1?
3 5
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28. a)Prove that
cosec A
cosec A-1 +
cosec A
cosec A-1 =2sec2 A 3
b)Prove that cot(-4050 ) tan 1350 + cot 1350 =0 2
29. In a triangle prove that sin2 A + sin2 B + sin2 C = 2+2 cosA cosB cosC
30. Prove geometrically sin (A+B) = SinA . Cos B + CosA. Sin B
31. a)Solve the triangle ABC if a=2 ; b= ?3 -1 and C=1200 3
b)Prove the sine rule
a
sin A =2R in an acute angled traingle 2
32. Derive the formula for the area of the triangle whose vertices are (x1 , y1 ) , (x2 , y2 )
and (x3 , y3 ) 5
33. obtain the orthocentre of the triangle whose vertices are (-5,6) , (13, 2) and (-5, -7) 5
34. obtain the formula of the bisector of the acute angle ranging from the lines 2x=y+4 and 2y=x+10
5
PART-D
ans any 2 ques. 2X10=20
35. a)Find the value of k if the formula 4x2 +xy-3y2 -9x+5y+k=0 represents a pair of lines and hence obtain
the separate equations and their point of intersection. 6
b) sum the series: 1.3+3.5+5.7+........ n terms 4
36. a)From the top of a house 50 meters high, the angle of elevation of the top of a tower is 450 and the
angle of depression of the foot of the tower is 300 . obtain the height of the tower and ists distance from
the house. 6
b)Solve x3 -9x2 +23x -15=0 provided that the roots are in AP 4
37. a)Prove that lim
??0
tan ?
?
=l where ? is in radians and evaluate lim
x?0
1-cosx
x2 6
b)sum the series
1
1.3? 1
3.5? 1
5.7?...........upto n terms 4
38. a)State and prove binomial theorem for a + ve integral index 6
b)Examine the continuity of f(x) at x=0 where f(x) =
cosax-cos bx
x2 x#0
= b2-a2
2
for x=0 4
PART -E
ans any 1 ques. 1X10=10
39. a)Find the locus of a point which moves so that its distances from the points A(2,1) and B(1,-2) are in
the ratio 2:1 4
b)If p is the perimeter 'A' is the area of a sector of a circle of radius r, then show that 2r2 -pr+2A=0 4
c)write the switching circuit for the boolean expression: (pVq') ? (p'? q) 2
40. a)In any triangle ABC Show that
cos2A
a2 -cos2B
b2 =
1
a2- 1
b2 4
b)Evaluate lim
x?0
6x-3x-2x?1
x2 4
c)Find the 7th root of 0.00003587 by using log tables 2
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