CBSE Board Questions Paper of Previous Year of 2010

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1040123 - B1
Class - X
MATHEMATICS
Time : 3 to 3½ hours
â×Ø : 3 âð 3½ ƒæ‡ÅUð
Maximum Marks : 80
¥çÏ·¤Ì× ¥´·¤ : 80
Total No. of Pages : 13
·é¤Ü ÂëcÆUæð´ ·¤è ⴁØæ : 13
General Instructions :
1.
All questions are compulsory.
2.
The question paper consists of 34 questions divided into four sections A, B, C and D.
Section - A comprises of 10 questions of 1 mark each, Section - B comprises of 8 questions of
2 marks each, Section - C comprises of 10 questions of 3 marks each and Section - D comprises
of 6 questions of 4 marks each.
3.
Question numbers 1 to 10 in Section - A are multiple choice questions where you are to select
one correct option out of the given four.
4.
There is no overall choice. However, internal choice has been provided in 1 question of two
marks, 3 questions of three marks each and 2 questions of four marks each. You have to
attempt only one of the alternatives in all such questions.
5.
Use of calculator is not permitted.
6.
An additional 15 minutes time has been allotted to read this question paper only.
âæ×æ‹Ø çÙÎðüàæ Ñ
1.
âÖè ÂýàÙ ¥çÙßæØü ãñ´Ð
2.
§â ÂýàÙ-˜æ ×ð´ 34 ÂýàÙ ãñ´, Áæð ¿æÚU ¹‡ÇUæð´ ×ð´ ¥, Õ, â ß Î ×ð´ çßÖæçÁÌ ãñÐ ¹‡ÇU - ¥ ×ð´ 10 ÂýàÙ ãñ´ ¥æñÚU ÂýˆØð·¤
ÂýàÙ 1 ¥´·¤ ·¤æ ãñ, ¹‡ÇU - Õ ×ð´ 8 ÂýàÙ ãñ´ ¥æñÚU ÂýˆØð·¤ ÂýàÙ 2 ¥´·¤æð´ ·ð¤ ãñ´, ¹‡ÇU - â ×ð´ 10 ÂýàÙ ãñ´ ¥æñÚU ÂýˆØð·¤
ÂýàÙ 3 ¥´·¤æð´ ·¤æ ãñ, ¹‡ÇU - Î ×ð´ 6 ÂýàÙ ãñ´ ¥æñÚU ÂýˆØð·¤ ÂýàÙ 4 ¥´·¤æð´ ·¤æ ãñÐ
3.
Âýà٠ⴁØæ 1 âð 10 Õãéçß·¤ËÂèØ ÂýàÙ ãñ´Ð çΰ »° ¿æÚU çß·¤ËÂæð´ ×ð´ âð °·¤ âãè çß·¤Ë ¿éÙð´Ð
4.
§â×ð´ ·¤æð§ü Öè âßæðüÂçÚU çß·¤Ë Ùãè´ ãñ, Üðç·¤Ù ¥æ´ÌçÚU·¤ çß·¤Ë 1 ÂýàÙ 2 ¥´·¤æð´ ×ð´, 3 ÂýàÙ 3 ¥´·¤æð´ ×ð´ ¥æñÚU 2 ÂýàÙ
4 ¥´·¤æð´ ×ð´ çΰ »° ãñ´Ð ¥æ çΰ »° çß·¤ËÂæð´ ×ð´ âð °·¤ çß·¤Ë ·¤æ ¿ØÙ ·¤Úð´UÐ
5.
·ñ¤Ü·é¤ÜðÅUÚU ·¤æ ÂýØæð» ßçÁüÌ ãñÐ
6.
§â ÂýàÙ-Â˜æ ·¤æð ÂɸÙð ·ð¤ çÜ° 15 ç×ÙÅU ·¤æ â×Ø çÎØæ »Øæ ãñÐ §â ¥ßçÏ ·ð¤ ÎæñÚUæÙ ÀUæ˜æ ·ð¤ßÜ ÂýàÙ-Â˜æ ·¤æð Âɸð´»ð
¥æñÚU ß𠩞æÚU-ÂéçSÌ·¤æ ÂÚU ·¤æð§ü ©žæÚU Ùãè´ çܹð´»ðÐ
1
P.T.O.
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SECTION - ‘A’
Question numbers 1 to 10 carry one mark each.
1.
2.
Euclid’s division lemma states that if a and b are any two 1ve integers, then there
exists unique integers q and r such that
(A)
a5bq1r, 0 < r < b
(B)
a5bq1r, 0 d r d b
(C)
a5bq1r, 0 d r < b
(D)
a5bq1r, 0 < b < r
Which of the following is not defined ?
(A)
3.
cos 0o
(B)
tan 45o
(C)
sec 90o
(D)
sin 90o
(C)
4
(D)
3
(C)
18
(D)
4
The graph of y5p (x) given below.
The number of zeroes of p(x) are :
(A)
4.
2
6
(B)
9
The mean and median of a data are 14 and 15 respectively. The value of mode is
(A)
6.
(B)
1
If sinu5 , then the value of 2 cot2u12 is :
3
(A)
5.
0
16
(B)
17
(C)
13
(D)
18
In DLMN, ‘ L5608, ‘ M5508. If DLMN DPQR , then the value of ‘ R is
(A)
408
1040123 - B1
(B)
308
(C)
708
(D)
1108
2
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7.
The value of
1
2
(A)
8.
1
(C)
1
2
(D)
2
1
(B)
21
(C)
2
(D)
22
Which of the following is not an irrational number ?
(A)
10.
(B)
If 1 is zero of the polynomial p(x)5ax223(a21) x21, then the value of ‘a’ is
(A)
9.
tan45
is :
sin30 cos30
52 3
(B)
51 3
(C)
41 2
(D)
51 9
(C)
cosecA
(D)
cosA.
(secA1tanA) (12sinA) is equal to :
(A)
secA
(B)
sinA
SECTION - ‘B’
Question numbers 11 to 18 carry 2 marks each.
11.
In figure-2 AB & DE and BD & EF.
Prove that DC2 5CF3AC.
12.
Find the zeroes of the quadratic polynomial
13.
Write any two merits and demerits of mean.
1040123 - B1
3
3 x22 8x14 3 .
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14.
In DABC, AB5AC and D is a point on side AC such that BC25AC . CD. Prove that
BD5BC.
15.
In figure-3, ABC is right triangle, D is mid point of BC.
Show that
tan M 1
tan > 2
OR
In DPQR right angled at Q, PR1QR525cm and PQ55cm. Find the value of sin P.
16.
For which values of p does the pair of equations given below has unique solution.
4x1py1850; 2x12y1250
17.
Check whether 6n can end with the digit 0 for any natural number n.
18.
The mean of the following data is 7.5. Find the value of p.
xi
3
5
7
9
11
13
fi
6
8
15
p
8
4
SECTION - ‘C’
Question numbers 19 to 28 carry 3 marks each.
19.
Prove that
secM1 secM1
52 cosecu.
secM1 secM1
OR
Prove that
1040123 - B1
1 sinA
5secA1tanA
1 sinA
4
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20.
On dividing x323x21x12 by a polynomial g(x), the quotient and remainder were
x22 and 22x14 respectively. Find g(x).
21.
An army contingent of 616 members is to march behind an army band of 32 members
in a parade. The two groups are to march in the same number of columns. What is the
maximum number of columns in which they can march ?
OR
Find the HCF and LCM of 306 and 54. Verify that HCF3 LCM5Product of the two
numbers.
22.
Evaluate :
2sin68
2cot15
3tan45 tan20 tan40 tan50 tan70
2
cos22 5tan75
5
23.
5
1
6
3
Solve for x and y x 1 y 2 52 ; x 1 y 2 51.
OR
For what values of a and b does the following pairs of linear equations have an infinite
number of solutions.
2x13y57; a(x1y)2b(x2y)53a1b22.
24.
The perpendicular AD on the base BC of DABC intersects BC in D such that BD53CD.
Prove that 2AB252AC21BC2.
25.
The given distribution shows the number of runs scored by some top batsmen of the
world in one - day international cricket matches. Find the mode of the data.
Runs Scored
No. of batsmen
Runs Scored
No.of batsmen
1040123 - B1
3000-4000
4000-5000
5000-6000
6000-7000
4
18
9
7
7000-8000
8000-9000
9000-10000
10000-11000
6
3
1
1
5
P.T.O.
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26.
In the figure-4 ABC is a right angled triangle, right angled at C. DE A AB. Prove that
DABC DADE and hence find the lengths of AE and DE.
27.
During the medical check up of 35 students of a class, their weights were recorded as
follows. Draw a less than type ogive for the given data. Hence obtain Median weight
from the graph.
28.
Weight (in kg)
No. of students
less than 38
less than 40
less than 42
less than 44
less than 46
less than 48
less than 50
less than 52
0
3
5
9
14
28
32
35
Prove that
2 3
is irrational.
5
SECTION - ‘D’
Question numbers 29 to 34 carry 4 marks each.
29.
Solve the system of equations graphically.
x12y55 ; 2x23y524. Also find the points where the lines meet the x - axis.
30.
Prove that :
1040123 - B1
tanM
cotM
1 secM.cosecM
1 cotM
1 tanM
6
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31.
32.
If the median of the distribution given below is 28.5, find the values of x and y.
Class Intervals
0-10
10-20
20-30
30-40
40-50
50-60
Total
Frequency
5
x
20
15
y
5
60
Prove that :
1
1
1
1
cosecA cotA
sinA
sinA
cosecA cotA
OR
Prove that : sec2u2
sin 2 M 2sin 4 M
2cos 4 M cosM 2
51.
33.
If the polynomial x426x3116x2225x110 is divided by another polynomial x222x1k,
the remainder comes out to be x1a, find the values of k and a.
34.
Prove that the ratio of the areas of two similar triangles is equal to the ratio of the
squares of their corresponding sides.
OR
Prove that in a triangle, if the square of one side is equal to the sum of the squares of the
other two sides, then the angle opposite to the first side is a right angle.
-o0o-
1040123 - B1
7
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¹‡ÇU-¥
Âýà٠ⴁØæ 1 âð 10 Ì·¤ ÂýˆØð·¤ ÂýàÙ 1 ¥´·¤ ·¤æ ãñÐ
1.
2.
Øêç€ÜÇU çßÖæÁÙ Âý×ðçØ·¤æ âð ØçÎ a ÌÍæ b Îæð ÏÙæˆ×·¤ Âê‡ææZ·¤ ãñ´, Ìæð q ÌÍæ r §â Âý·¤æÚU °·¤Ü Âê‡ææZ·¤ âð ÁéÇðU
ãñ´ ç·¤ Ñ
(A)
a5bq1r, 0 < r < b
(B)
a5bq1r, 0 d r d b
(C)
a5bq1r, 0 d r < b
(D)
a5bq1r, 0 < b < r
çِ٠×ð´ âð ·¤æñÙ âæ ÂçÚUÖæçáÌ Ùãè´ ãñ?
(A)
3.
(C)
sec 90o
(D)
sin 90o
0
(B)
2
(C)
4
(D)
3
(C)
18
(D)
4
1
6
(B)
9
·é¤ÀU, ¥æ¡·¤Ç¸æð´ ·¤æ ׊Ø×æÙ ÌÍæ ×æçŠØ·¤æ ·ý¤×àæÑ 14 ÌÍæ 15 ãñÐ §â×ð´ ÕãéÜ·¤ ·¤æ ×æÙ ãæð»æ Ñ
(A)
6.
tan 45o
ØçÎ sinu5 3 Ìæð 2 cot2u12 ·¤æ ×æÙ ãæð»æ Ñ
(A)
5.
(B)
ÕãéÂÎ y5p (x) ·¤æð »ýæȤ mæÚUæ ¥æ·ë¤çÌ (1) ×ð´ çιæØæ »Øæ ãñÐ §â×ð´ àæê‹Øæ´·¤ ·¤è ⴁØæ ãæð»è Ñ
(A)
4.
cos 0o
16
(B)
ç˜æÖéÁ LMN ×ð´
‘ L5608, ‘ M5508.
(A)
408
1040123 - B1
(B)
17
(C)
ØçÎ
13
DLMN DPQR, ÌÕ ‘ R
308
(C)
708
(D)
18
·¤æ ×æÙ ãæð»æ Ñ
(D)
1108
8
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7.
tan45
sin30 cos30
1
2
(A)
8.
1
(C)
1
2
(D)
2
1
(B)
21
(C)
2
(D)
22
(C)
41 2
(D)
51 9
(C)
cosecA
(D)
cosA.
çِ٠×ð´ âð ·¤æñÙ âæ ¥ÂçÚU×ðØ â´Øæ Ùãè´ ãñ?
(A)
10.
(B)
ØçÎ p(x)5ax223(a21) x21 ·¤æ àæê‹Øæ´·¤ 1 ãæð Ìæð a ·¤æ ×æÙ ãæð»æ Ñ
(A)
9.
·¤æ ×æÙ ãñ Ñ
52 3
(B)
(secA1tanA) (12sinA)
(A)
secA
51 3
ÕÚUæÕÚU ãñ Ñ
(B)
sinA
¹‡ÇU-Õ
Âýà٠ⴁØæ 11 âð 18 Ì·¤ ÂýˆØð·¤ ÂýàÙ 2 ¥´·¤ ·¤æ ãñÐ
11.
¥æ·ë¤çÌ
(2) ×ð´ AB & DE ÌÍæ BD & EF Ìæð
çâh ·¤èçÁØð ç·¤ Ñ
DC2 5CF3AC.
1040123 - B1
9
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12.
3 x22 8x14 3
çmƒææÌ ÕãéÂÎ ·ð¤ àæê‹Øæ´·¤ ™ææÌ ·¤ÚUæðÐ
13.
׊Ø×æÙ ·ð¤ ·¤æð§ü Îæð ©ÂØéQ¤Ìæ ÌÍæ ¥ÙéÂØéQ¤Ìæ çÜç¹ØðÐ
14.
ç˜æÖéÁ ABC ×ð´, AB5AC °ß´ D çՋÎé, ÖéÁæ AC ÂÚU §â Âý·¤æÚU çSÍÌ ãñ ç·¤,
·¤Úð´U ç·¤ BD5BC.
15.
¥æ·ë¤çÌ - 3 ×ð´ DABC °·¤ â×·¤æð‡æ ç˜æÖéÁ ãñ ÌÍæ D, BC ·¤æ ×ŠØ çՋÎé ãñÐ
Ìæð Îàææü§Øð
BC25AC. CD,
Ìæð çâh
tan M 1
tan > 2
Øæ
â×·¤æð‡æ DPQR ·¤æ
·¤èçÁ°Ð
16.
p ·ð¤
‘ Q â×·¤æð‡æ
ãñÐ
PR1QR525 âð.×è.
ÌÍæ PQ55 âð.×è, Ìæð
sin P ·¤æ
×æÙ ™ææÌ
ç·¤â ×æÙ ·ð¤ çÜØð çِ٠ÚñUç¹·¤ â×è·¤ÚU‡æ Øé‚× ·¤æ ãÜ °·¤Ü ãæð»æ?
4x1py1850; 2x12y1250
17.
Áæ¡¿ ·¤èçÁ° ç·¤ 6n ·¤æ ¥‹Ì àæê‹Ø ×ð´ ãæð â·¤Ìæ ãñ, Áãæ¡ n ·¤æð§ü Âýæ·ë¤Ì ⴁØæ ãæðÐ
18.
çِ٠¥æ¡·¤Ç¸æð´ ·¤æ ×æŠØ 7.5 ãñÐ
×æÙ ™ææÌ ·¤èçÁ°Ð
ŒÍˆž‹®Ÿ×
3
5
7
9
11
13
¼ÍÁ›<¼ÍÁ<³Í
6
8
15
p
8
4
xi
fi
p ·¤æ
1040123 - B1
10
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¹‡ÇU-â
Âýà٠ⴁØæ 19 âð 28 Ì·¤ ÂýˆØð·¤ ÂýàÙ 3 ¥´·¤ ·¤æ ãñÐ
19.
secM1
secM1
52 cosecu.
secM1
secM1
çâh ·¤ÚUæð
Øæ
1 sinA
5secA1tanA
1 sinA
çâh ·¤ÚUæð
20.
·¤æð ÕãéÂÎ g(x) âð Öæ» ÎðÙð ÂÚU ·ý¤×àæÑ Öæ»È¤Ü ÌÍæ àæðáÈ¤Ü x22 ß 22x14 ãñ Ìæð
ÕãéÂÎ g(x) ™ææÌ ·¤èçÁ°Ð
21.
ç·¤âè ÂÚðUÇU ×ð´ 616 âÎSØæð´ ßæÜè °·¤ âðÙæ (¥æ×èü) ·¤è ÅéU·¤Ç¸è ·¤æð 32 âÎSØæð´ ßæÜð °·¤ ¥æ×èü Õñ‹ÇU ·ð¤ ÂèÀðU
×æ¿ü ·¤ÚUÙæ ãñÐ ÎæðÙæð´ â×êãæð´ ·¤æð â×æ٠ⴁØæ ßæÜð SÌ´Öæð´ ×ð´ ×æ¿ü ·¤ÚUÙæ ãñÐ ©Ù SÌ´Öæð´ ·¤è ¥çÏ·¤žæ× â´Øæ €Øæ
ãñ çÁâ×ð´ ßð ×æ¿ü ·¤ÚU â·¤Ìð ãñ´Ð
x323x21x12
Øæ
(×.â.Â) ÌÍæ LCM (Ü.â.Â) ™ææÌ ·¤èçÁ° ÌÍæ âˆØæçÂÌ ·¤èçÁ° ç·¤
HCF3 LCM5ÎæðÙæð´ ⴁØæ¥æð´ ·¤æ »é‡æÙȤÜ
306
22.
ÌÍæ
54
·¤æ
HCF
×æÙ ™ææÌ ·¤èçÁ°Ð
2sin68
2cot15
3tan45 tan20 tan40 tan50 tan70
2
cos22 5tan75
5
23.
x ÌÍæ y ·ð¤
çÜØð ãÜ ·¤Úð´U Ñ
5
1
6
3
52
;
x 1
y 2
x 1
y 2 51.
Øæ
a ÌÍæ b ·ð¤
ç·¤â ×æÙ ·ð¤ çÜØð Ùè¿ð çܹð Øé‚× ÚñUç¹·¤ â×è·¤ÚU‡æ ·¤æ ¥Ù‹Ì ãÜ ãñ?
2x13y57; a(x1y)2b(x2y)53a1b22.
24.
DABC ×ð´
¥æÏæÚU
çâh ·¤èçÁ°
1040123 - B1
BC ÂÚU AD
ÜÕ ãñ ÌÍæ çՋÎé D §â Âý·¤æÚU çSÍÌ ãñ ç·¤ BD53CD
2AB252AC21BC2.
11
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25.
ç·ý¤·ð¤ÅU ×ñ¿ ×ð´ çِÙçÜç¹Ì ÕæÚ´UÕæÚUÌæ Õ´ÅUÙ â´âæÚU ·ð¤ Âýçâh ÕËÜðÕæÁæð´ mæÚUæ ÚUÙæð´ ·¤è ⴁØæ ÎàææüÌè ãñÐ çِÙ
¥æ¡·¤Ç¸æð´ ·¤æ ÕãéÜ·¤ ™ææÌ ·¤ÚUæðÐ
Á<ÀÍכž‹Ïɛh¿Í
¼²Ã׼ͨÍכž‹Ïɛh¿Í
Á<ÀÍכž‹Ïɛh¿Í
¼²Ã׼ͨÍכž‹Ïɛh¿Í
3000-4000
4000-5000
5000-6000
6000-7000
4
18
9
7
7000-8000
8000-9000
9000-10000
10000-11000
6
3
1
1
26.
¥æ·ë¤çÌ - 4 ×ð´
27.
·¤ÿææ ·ð¤ 35 Փææð´ ·ð¤ SßæS‰Ø Áæ¡¿ ·ð¤ â×Ø ©Ù·ð¤ ÖæÚU ·¤æ çßßÚU‡æ çِ٠Âý·¤æÚU çÎØæ »Øæ ãñÐ °·¤ ÌæðÚU‡æ Ò·¤×
Âý·¤æÚU ·¤æÓ ¹è´ç¿Øð´ ÌÍæ ׊Ø×æÙ ·¤æ ×æÙ »ýæȤ mæÚUæ ×æÜê× ·¤èçÁ°Ð
28.
°·¤ â×·¤æð‡æ ç˜æÖéÁ ãñ çÁâ·¤æ ‘ C â×·¤æð‡æ ãñÐ ØçÎ DE A AB Ìæð çâh ·¤èçÁ°
DABC DADE ÌÍæ ÖéÁæ AE ÌÍæ DE ·¤è ܐÕæ§ü Öè ™ææÌ ·¤ÚUæðÐ
ABC
¸È¼7ə†ßȹҖ
ÉÁNÈɯ޺ÈҖ ™†ÊĖcºÈ
38 Éמ‹¾
0
40 Éמ‹¾
3
42 Éמ‹¾
5
44 Éמ‹¾
9
46 Éמ‹¾
14
48 Éמ‹¾
28
50 Éמ‹¾
32
52 Éמ‹¾
35
çâh ·¤èçÁØð
1040123 - B1
2 3
5
°·¤ ¥ÂçÚU×ðØ â´Øæ ãñÐ
12
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¹‡ÇU-Î
Âýà٠ⴁØæ 29 âð 34 Ì·¤ ÂýˆØð·¤ ÂýàÙ 4 ¥´·¤ ·¤æ ãñÐ
29.
â×è·¤ÚU‡æ x12y55 ; ÌÍæ 2x23y524 ·¤æð »ýæȤ mæÚUæ ãÜ ·¤ÚUæð, ÌÍæ ßã çՋÎé ×æÜê× ·¤ÚUæð Áãæ¡ ÚðU¹æØð´ x
- ¥ÿæ âð ç×ÜÌè ãñÐ
30.
çâh ·¤èçÁ°
31.
ØçÎ çِ٠մÅUÙ ·¤è ×æçŠØ·¤æ
32.
tanM
cotM
1 secM cosecM .
1 cotM
1 tanM
28.5 ãæð
Ìæð x ÌÍæ y ·¤æ ×æÙ ™ææÌ ·¤èçÁ°Ð
ÁÞ‡m®¼7Ⱦ
0-10
10-20
20-30
30-40
40-50
50-60
¿Í×¢
·È¼–7·È¼7®È
5
x
20
15
y
5
60
çâh ·¤èçÁ°
1
1
1
1
cosecA cotA
sinA
sinA
cosecA cotA
Øæ
çâh ·¤èçÁ°
sec2u2
sin 2 M 2sin 4 M
2cos 4 M cosM 2
51
33.
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