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Guess Paper – 2009
CLASS – XI
MATHEMATICS
Time allowed – 3 Hrs
Maximum Marks – 100
General instructions –
(i)
(ii)
All questions are compulsory.
The question paper consists of 29 questions divided in to three sections A, B and C. Section A comprises of 10
questions of 1 mark each, Section B comprises of 12 questions of 4 marks each and Section C comprises of 7
questions of 6 marks each.
All questions in Section A are to be answered in one word, one sentence or as per the exact requirement of the
question.
There is no over all choice. However, internal choice has been provided in 4 questions of four marks each and 2
questions of six marks each. You have to attempt only one of the alternatives in all such questions.
Use of calculators is not permitted
(iii)
(iv)
(v)
SECTION – A
1. If Cr @ C3  C2 , find r A
2. If set A has n elements then find the number of elements in set P(A).
8
7
7
3. The minute hand of a watch is 1.5 cm long. How far does its tip move in 40 minutes?
4. Find the value of cos(-1710 ).
5. Let P(n) be the statement “n2 + n is an even integer”. Show that if P(m) is true then P(m + 1) is also true.
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6. Solve p 2 x 2  x  p 2  0
7. Find the modulus and argument of complex number
1ffffffffffffff
i
.
1 @i
5ffffffffffffffffffff
@2x xffff
 @5 and represent the solution on number line.
3
6
1fff
fffff
9. If the angle between two lines is
and slope of one of the lines is
, find the slope of the other line.
4
2
8. Solve
10. Given 5 flags of different colours, how many different signals can be generated if each signal requires the
use of two flags, one below the other?
SECTION B
11. Show that the area of the triangle formed by the lines y  m1 x  c1 , y  m2 x  c2
and x  0 is
`
a2
c1 @c2
ffffffffffffffffffffffffffffffffffffffff
2 |m1 @m2 |
OR
If p is the length of perpendicular from the origin to the line whose intercepts on the axes are a
and b, then show that
1
ffffffff
p
2

1
fffffff
a
2

1
fffffff
b
2
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12. Find the sum of
0.7 + 0.77 + 0.777 + ------- to n terms.
13. If p, q, r are in G.P. and the equations, px2 + 2qx + r = 0 and dx2 + 2ex + f = 0 have a common root, then
dfffff effff ffffff
are in A.P.
, ,
p q r
show that
14. The sums of n terms of two arithmetic progressions are in the ratio 5n + 4 : 9n + 6. Find the ratio of their
18th terms.
15. The coefficients of the (r – 1)th , rth and (r + 1)th terms in the expansions of (x +1)n are in the ratio
1 : 3 : 5. Find n and r.
`
a
1ffffffffffffffffffffffffffffffffffffffffffffffffffffff
A3 A5  2n @1 n n
16. Show that the middle term in the expansion of (1 + x) is
2 x , where n is a positive
n!
2n
integer.
17. Find the number of words with or without meaning which can be made using all the letters of the word
AGAIN. If these words are written as in dictionary, what will be the 50th word?
18. In how many ways can the letters of the word PERMUTATIONS be arranged if the
(i)
words start with P and end with S,
(ii)
vowels are all together,
(iii)
there are always 4 letters between P and S.
19. Solve the following system of inequalities graphically
4x  3y  60,
y  2x,
x  3, x  0,
y0
OR
A solution of 8% boric acid is to be diluted by adding a 2% boric acid solution to it. The resulting
mixture is to be more than 4% but less than 6% boric acid. If we have 640 litres of the 8%
solution, how many litres of the 2% solution will have to be added?
20. Prove that sin 18  =
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pfffffffffffffffffffffff
5 @1
4
OR
Prove that sin 10° sin 50° sin 60° sin 70° =
21. Prove that :
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pfffffffffff
3
16
sin A  sin 3A  sin 5A  sin 7A
fffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffffff
cos A  cos 3A  cos 5A  cos 7A
 tan 4A
b
c
`
a
22. Using properties of sets show that for any sets A and B, A  A T B S A @B and
`
a b
c
A S B @A  A S B
OR
In a survey it was found that 21 people liked product A, 26 liked product B and 29 liked product
C. If 14 people liked products A and B, 12 people liked products C and A, 14 people liked
products B and C and 8 liked all the three products. Find how many liked product C only.
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SECTION C
23. dProve
that
the productd of the
lengths
of the perpendiculars drawn from the points
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w e
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w e
q a 2 @b 2 , 0 and @q a 2 @b 2 , 0 to the line xffffcos  yfffffsin  1 is b 2
a
b
24. Find the sum to n terms of the series 1 + 5 + 12 + 22 + 35 + - - OR
150 workers were engaged to finish a job in a certain number of days. 4 workers dropped out on second
day, 4 more workers dropped out on the third day and so on. It took 8 more days to finish the work. Find
the number of days in which the work was completed.
25. If the coefficients of a r @1 , a r and a r  1 in the expansion of the (1 + a)n are in arithmetic progression,
prove that n2 - n(4r +1) + 4 r2 – 2 = 0.
26. Find the square roots of – 15 – 8i.
OR
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If x  @5  2 p @4 , find the value of x4 + 9x3 + 35x2 – x + 4.
L
M
L
M
L fffffffffffffffffffffffffff
M

@
ffffff M.
27. If α and β are different complex numbers with | β | = 1, then find L
L
M
L 1 @  M
b
c
7
n1
fffffff
28. Prove 7  77  777  AAA 7777 
n @digits
induction.
29. Prove that
81
10
@9n @10 by principle of mathematical
cos
5x  cos 4x
ffffffffffffffffffffffffffffffffffffffffffffffff
 @cos 2x @cos x
1 @2 cos 3x
.
Paper Submitted by:
Karmendra Varshney
Email:- [email protected]
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