51 A (»ç‡æÌ) MATHEMATICS

This Question Paper consists of 36 questions including 5 figures and 12 printed pages + Graph sheet.
§â ÂýàÙ-˜æ ×ð´ 36 ÂýàÙ ÌÍæ 5 ç¿˜æ °ß´ 12 ×éçÎýÌ ÂëcÆU + »ýæȤ àæèÅU ãñ´Ð
Roll No.
Code No.
¥Ùé·ý¤×æ´·¤
·¤æðÇU Ù´.
51/AS/3
MATHEMATICS
Set
(»ç‡æÌ)
A
(211)
Day and Date of Examination
ÂÚUèÿææ ·¤æ çÎÙ ß çÎÙæ´·¤
Signature of Invigilators
1.
çÙÚUèÿæ·¤æð´ ·ð¤ ãSÌæÿæÚU
2.
General Instructions :
1.
Candidate must write his/her Roll Number on the first page of the Question Paper.
2.
Please check the Question Paper to verify that the total pages and total number of questions
contained in the Question Paper are the same as those printed on the top of the first page.
Also check to see that the questions are in sequential order.
3.
For the objective type of questions, you have to choose any one of the four alternatives given
in the question i.e. (A), (B), (C) or (D) and indicate your correct answer in the Answer-Book
given to you.
4.
All the questions including objective type questions are to be answered within the allotted
time and no separate time limit is fixed for answering objective type questions.
5.
Making any identification mark in the Answer-Book or writing Roll Number anywhere other
than the specified places will lead to disqualification of the candidate.
6.
Write your Question Paper code No.
7.
(a)
(b)
51/AS/3-A on the Answer-Book.
The Question Paper is in English/Hindi medium only. However, if you wish, you can
answer in any one of the languages listed below :
English, Hindi, Urdu, Punjabi, Bengali, Tamil, Malayalam, Kannada, Telugu, Marathi,
Oriya, Gujarati, Konkani, Manipuri, Assamese, Nepali, Kashmiri, Sanskrit and Sindhi.
You are required to indicate the language you have chosen to answer in the box provided
in the Answer-Book.
If you choose to write the answer in the language other than Hindi and English, the
responsibility for any errors/mistakes in understanding the question will be yours only.
51/AS/3-211-A ]
1
!51/AS/3-211-A!
[ Contd...
âæ×æ‹Ø ¥ÙéÎðàæ Ñ
1.
ÂÚUèÿææÍèü ÂýàÙÂ˜æ ·ð¤ ¤ÂãÜð ÂëcÆU ÂÚU ¥ÂÙæ ¥Ùé·ý¤×æ´·¤ ¥ßàØU çܹð´Ð
2.
·ë¤ÂØæ ÂýàÙÂ˜æ ·¤æð Áæò¡¿ Üð´ ç·¤ ÂýàÙÂ˜æ ·ð¤ ·é¤Ü ÂëcÆUæð´ ÌÍæ ÂýàÙæð´ ·¤è ©ÌÙè ãè ⴁUØæ ãñ çÁÌÙè ÂýÍ× ÂëcÆ ·ð ¤âÕâð
ª¤ÂÚU ÀUÂè ãñÐ §â ÕæÌ ·¤è Áæò¡¿ Öè ·¤ÚU Üð´ ç·¤ ÂýàÙ ·ý ç×·¤ UM¤Â ×ð´ ãñ´Ð
3.
ßSÌéçÙcÆU ÂýàÙæð´ ×𴠥淤æð ¿æÚU çß·¤ËÂæð´
©žæÚU-ÂéçSUÌ·¤æ ×ð´ ¥æ âãè ©žæÚ çÜç¹°ÐU
4.
ßSÌéçÙcÆU ÂýàÙæð´ ·ð¤ âæÍ-âæÍ âÖè ÂýàÙæ𴠷𤠩žæÚ çÙÏæüçÚUÌ ¥ßçÏ ·ð ÖèÌÚU ãè ÎðÙð ãñ´Ð ßSÌéçÙcÆU ÂýàÙæð´ ·ð¤ çÜ°¤¥Ü»
âð â×Ø Ùãè´ çÎØæ Áæ°»æÐ
5.
¤ ©žæÚU-ÂéçSUÌ·¤æ ×ð´ Âã¿æÙ-ç¿q ÕÙæÙð ¥Íßæ çÙçÎücÅU SÍæÙæ𴠷𤤠¥çÌçÚU€Ì ·¤ãè´ Öè ¥Ùé·ý¤×æ´·¤ çܹÙð ÂÚU ÂÚUèÿææÍèü
·¤æð ¥Øæð‚Ø ÆUãÚUæØæ ÁæØð»æÐ
(A), (B), (C)
ÌÍæ
(D)
×ð´ âð ·¤æð§ü °·¤ ©žæÚ ¿éÙÙæ ãñ ÌÍæ Îè »§ü
6.
¥ÂÙè ©žæÚU-ÂéçSUÌ·¤æ ÂÚU ÂýàÙÂ˜æ ·¤è ·¤æðÇU ⴁØæ 51/AS/3-A çܹð´Ð
7.
(·¤) ÂýàÙÂ˜æ ·ð¤ßÜ çã´Îè/¥´»ýðÁè ×ð´ ãñÐ çȤÚU Öè, ØçÎ ¥æ ¿æãð´ Ìæð Ùè¿ð Îè »§ü ç·¤âè °·¤ Öæáæ ×ð´ ©žæÚ Îð â·¤Ìð
ãñ´ Ñ
¥´»ýðÁè, çã´Îè, ©Îêü, ´ÁæÕè, Õ¡»Üæ, Ìç×Ü, ×ÜØæÜ×, ·¤‹ÙǸ, ÌðÜé»é, ×ÚUæÆUè, ©çǸØæ, »éÁÚUæÌè, ·¤æð´·¤‡æè,
×ç‡æÂéÚUè, ¥âç×Øæ, ÙðÂæÜè, ·¤à×èÚUè, â´S·ë¤Ì¤¥æñÚU çâ´ÏèÐ
·ë¤ÂØæ ©žæÚU-ÂéçSÌ·¤æ ×ð´ çΰ »° Õæò€â ×ð´ çܹð´ ç·¤ ¥æ 緤â Öæáæ ×ð´ ©žæÚU çܹ ÚUãð ãñ´Ð ¤
(¹) ØçÎ ¥æ çã´Îè °ß´ ¥´»ýðÁè ·ð¤ ¥çÌçÚU€Ì ç·¤âè ¥‹Ø Öæáæ ×ð´ ©žæÚU çܹÌð ãñ´ Ìæð ÂýàÙ ·¤æð â×ÛæÙð ×ð´ ãæðÙð ßæÜè
˜æéçÅUØæð´/»ÜçÌØæð´ ·¤è çÁ×ðUÎæÚè ·ð ßÜ ¥æ·¤è ãæð»èÐ
51/AS/3-211-A ]
2
!51/AS/3-211-A!
[ Contd...
MATHEMATICS
(»ç‡æÌ)
(211)
Time : 2½ Hours ]
[ Maximum Marks : 85
â×Ø Ñ 2½ ƒæ‡ÅðU ]
Note :
çÙÎðüàæ Ñ
[ Âê‡ææZ·¤ Ñ 85
(1)
Question Numbers (1-10) are Multiple Choice Questions. Each question carries
one mark. For each question, four alternative choices A, B, C and D are provided,
of which only one is correct. You have to select the correct alternative and indicate
it in the answer-book provided to you by writing (A), (B), (C) or (D) as the case
may be. Q. No. 11 to 15 also carry one mark each.
(2)
Question Numbers (16-25) carry 2 marks each.
(3)
Question Numbers (26-33) carry 4 marks each.
(4)
Question Numbers (34-36) carry 6 marks each.
(5)
All questions are compulsory.
(1)
Âýà٠ⴁØæ (1-10) Ì·¤ Õãéçß·¤ËÂè ÂýàÙ (Multiple Choice Questions) ãñ´Ð ÂýˆØð·¤ ÂýàÙ °·¤
¥´·¤ ·¤æ ãñÐ ÂýˆØð·¤ ÂýàÙ ×ð´ ¿æÚU çß·¤Ë A, B, C ÌÍæ D çÎØð »Øð ãñ´, çÁÙ×ð´ âð ·ð¤ßÜ °·¤ âãè ãñÐ
¥æ·¤æð âãè çß·¤Ë ¿éÙÙæ ãñ ÌÍæ ÂýˆØð·¤ ÂýàÙ ·ð¤ ©žæÚU ¥ÂÙè ©žæÚU ÂéçSÌ·¤æ ×ð´ (A), (B), (C) ¥Íßæ (D)
Áñâè Öè çSÍçÌ ãæð, çܹ·¤ÚU ÎàææüÙæ ãñÐ Âýà٠ⴁØæ 11 âð 15 Öè °·¤ ¥´·¤ ·¤æ ãñÐ
(2)
Âýà٠ⴁØæ
(16-25) Ì·¤
ÂýˆØð·¤ ÂýàÙ ·ð¤ 2 ¥´·¤ ãñ´Ð
(3)
Âýà٠ⴁØæ
(26-33) Ì·¤
ÂýˆØð·¤ ÂýàÙ ·ð¤ 4 ¥´·¤ ãñ´Ð
(4)
Âýà٠ⴁØæ
(34-36) Ì·¤
ÂýˆØð·¤ ÂýàÙ ·ð¤ 6 ¥´·¤ ãñ´Ð
(5)
âÖè ÂýàÙ ¥çÙßæØü ãñ´Ð
51/AS/3-211-A ]
3
!51/AS/3-211-A!
[ Contd...
1.
60% of the students in a school are girls. If the number of boys in the school is 320, the
total number of students in the school is :
ç·¤âè çßlæÜØ ×ð´ 60% çßlæÍèü ÜǸ緤Øæ¡ ãñ´Ð ØçÎ çßlæÜØ ×ð´ ÜǸ·¤æð´ ·¤è ⴁØæ
·é¤Ü çßlæçÍüØæð´ ·¤è ⴁØæ ãæð»è Ñ
(A)
2.
400
(B)
450
(C)
320 ãæð,
600
1
Ìæð çßlæÜØ ×ð´
(D)
800
An article is sold for ` 2,000 cash or for ` 600 as cash down payment followed by
` 1680 after one year. The rate of interest charged under instalment plan is :
1
ç·¤âè ßSÌé ·¤æð ` 2,000 ·ð¤ Ù·¤Î Öé»ÌæÙ ÂÚU ¥Íßæ ` 600 ·ð¤ ÌéÚ´UÌ Öé»ÌæÙ ÌÍæ ©â·ð¤ °·¤ ßáü Âà¿æÌ÷
` 1680 ·ð¤ Öé»ÌæÙ ÂÚU Õð¿æ ÁæÌæ ãñÐ ç·¤SÌ ØæðÁÙæ ·ð¤ ¥‹Ì»üÌ Ü»æ° ÁæÙð ßæÜð ŽØæÁ ·¤è ÎÚU ãñ Ñ
(A)
3.
16%
(B)
(C)
28%
(D)
40%
1
In the figure, given here, ÐACD1ÐCBF1ÐBAE is equal to :
Øãæ¡ Îè »Øè ¥æ·ë¤çÌ ×ð´
(A)
4.
20%
ÐACD1ÐCBF1ÐBAE ÕÚUæÕÚU
1808
(B)
ãñ Ñ
3608
(C)
4508
(D)
5408
The length of the arc of a sector of a circle of radius r and central angle u is equal to :
1
ç˜æ’Øæ r ÌÍæ ·ð¤‹ÎýèØ ·¤æð‡æ u ßæÜð ç·¤âè ßëžæ ·ð¤ °·¤ ç˜æ’Ø ¹´ÇU ·ð¤ ¿æ ·¤è ܐÕæ§ü ãæðÌè ãñ Ñ
5.
(A)
pu 

2r  1 1

7208 

(B)
pu 

2r  1 1

3608 

(C)
p ru
3608
(D)
pr u
1808
sin2 6081cos2 458 is equal to :
sin2
6081cos2 458
(A)
31 2
2
(C)
1
ÕÚUæÕÚU ãñ Ñ
3
4
51/AS/3-211-A ]
4
(B)
5
4
(D)
1
4
!51/AS/3-211-A!
[ Contd...
6.
9.09 in the form
9.09 ,
(A)
7.
(A)
1
1
(B)
a5 512 6
ãæð, Ìæð
4 6
101
11
(C)
100
11
(D)
10
1
1
is equal to :
a
a2
1
a
(B)
1
ÕÚUæÕÚU ãæð»æ Ñ
(C)
24 6
10
(D)
210
1
A triangle ABC is necessarily congruent to another triangle PQR if :
·¤æð§ü ç˜æÖéÁ
9.
·ð¤ L¤Â ×ð´ ÕÚUæÕÚU ãñ Ñ
If a5 512 6 , then a 2
ØçÎ
8.
p
q
1
p
is equal to :
q
ABC °·¤
¥‹Ø ç˜æÖéÁ PQR ·ð¤ ¥ßàØ×ðß âßæZ»â× ãæð»è ØçÎ Ñ
(A)
ÐA5ÐP, ÐB5ÐQ, ÐC5ÐR
(B)
ÐA5ÐP, ÐB5ÐQ, AB5QR
(C)
AB5PQ, BC5QR, ÐC5ÐQ
(D)
ÐB5ÐQ, ÐC5ÐR, BC5QR
In the plane of a triangle, the point equidistant from the vertices of the triangle is its :
(A)
centroid
(B)
incentre
(C)
circumcentre
(D)
1
orthocentre
ç·¤âè ç˜æÖéÁ ·ð¤ â×ÌÜ ×ð´ ç˜æÖéÁ ·ð¤ àæèáü çՋÎé¥æð´ âð â×æÙ ÎêÚUè ÂÚU çSÍÌ çՋÎé ©â ç˜æÖéÁ ·¤æ ãæðÌæ ãñ Ñ
(A)
·ð¤‹Îý·¤
51/AS/3-211-A ]
(B)
¥‹ÌÑ·ð¤‹Îý
5
(C)
ÂçÚU·ð¤‹Îý
(D)
ËæÕ ·ð¤‹Îý
!51/AS/3-211-A!
[ Contd...
10.
Which of the following is not true ?
1
(A)
A trapezium is also a parallelogram.
(B)
A rhombus is also a parallelogram.
(C)
A rectangle is also a parallelogram.
(D)
A square is also a parallelogram.
ç‹æÙçÜç¹Ì ×ð´ âð ·¤æñÙ âæ ·¤ÍÙ âˆØ Ùãè´ ãñ?
11.
(A)
°·¤ â×Ü´Õ °·¤ â×æ‹ÌÚU ¿ÌéÖéüÁ Öè ãæðÌæ ãñÐ
(B)
°·¤ â׿ÌéÖéüÁ °·¤ â×æ‹ÌÚU ¿ÌéÖéüÁ Öè ãæðÌæ ãñÐ
(C)
°·¤ ¥æØÌ °·¤ â×æ‹ÌÚU ¿ÌéÖüéÁ Öè ãæðÌæ ãñÐ
(D)
°·¤ ß»ü °·¤ â×æ‹ÌÚU ¿ÌéÖéüÁ Öè ãæðÌæ ãñÐ
In the figure, given here, O is the centre of the circle and OP^AB. If AB58 cm and
OP53 cm, find the diameter of the circle.
1
Øãæ¡ Îè »Øè ¥æ·ë¤çÌ ×ð´ O ßëžæ ·¤æ ·ð¤‹Îý ãñ ÌÍæ OP^AB ãñÐ ØçÎ AB58 âð.×è. ÌÍæ OP53 âð.×è. ãæð, Ìæð
ßëžæ ·¤æ ÃØæ⠙ææÌ ·¤èçÁ°Ð
12.
Find the volume of a right circular cone whose area of the base is 36p cm2 and slant
height is 10 cm.
1
©â ÜÕ ßëžæèØ àæ´·é¤ ·¤æ ¥æØÌÙ ™ææÌ ·¤èçÁ° çÁâ·ð¤ ¥æÏæÚU ·¤æ ÿæð˜æÈ¤Ü 36p âð.×è2. ãñ ÌÍæ çÁâ·¤è çÌUØü·÷¤
ª¡¤¿æ§ü 10 âð.×è. ãñÐ
13.
In a DABC, ÐB5908, AB55 cm and BC57 cm. Find the value of tan A2cot C.
ç·¤âè ç˜æÖéÁ
·¤èçÁ°Ð
ABC
51/AS/3-211-A ]
×ð´,
ÐB5908, AB55
6
âð.×è. ÌÍæ
BC57
âð.×è. ãñÐ
tan A2cot C
1
·¤æ ×æÙ ™ææÌ
!51/AS/3-211-A!
[ Contd...
14.
A bag contains 15 red balls and some white balls. If the probability of drawing a white
ball from the bag is
1
, find the number of white balls in the bag.
6
ç·¤âè ÍñÜð ×ð´ 15 ÜæÜ ÌÍæ ·é¤ÀU âÈð¤Î »ð´Î ãñÐ ØçÎ ÍñÜð ×ð´ âð °·¤ âÈð¤Î »ð´Î çÙ·¤æÜð ÁæÙð ·¤è ÂýýæçØ·¤Ìæ
Ìæð ÍñÜð ×ð´ âÈð¤Î »ð´Îæð´ ·¤è ⴁØæ ™ææÌ ·¤èçÁ°Ð
15.
1
1
ãæð,
6
The mean of 8 observations was found to be 30. Later it was detected that one observation
64 was mistakenly read as 24. Find the correct mean.
1
8 Âýðÿæ‡ææð´
·¤æ ×æŠØ 30 çÙ·¤æÜæ »ØæÐ ÕæÎ ×ð´ ÂÌæ ¿Üæ ç·¤ °·¤ Âýðÿæ‡æ 64 ·¤æð »ÜÌè âð 24 Âɸ çÜØæ »Øæ ÍæÐ
âãè ×æŠØ ™ææÌ ·¤èçÁ°Ð
16.
Evaluate the polynomial 2x323x228x112 for x522 and state whether this value of
x is a zero of the given polynomial or not.
2
x522 ·ð¤
çÜ° ÕãéÂÎ 2x323x228x112 ·¤æ ×æÙ ™ææÌ ·¤èçÁ° ÌÍæ ÕÌ槰 ç·¤ x ·¤æ Øã ×æÙ çÎØð »°
ÕãéÂÎ ·¤æ °·¤ àæê‹Ø·¤ ãñ ¥Íßæ Ùãè´Ð
17.
Find the distance between the points (26, 21) and (26, 11).
çՋÎé¥æð´
18.
(26, 21) ÌÍæ (26, 11) ·ð¤
2
Õè¿ ·¤è ÎêÚUè ™ææÌ ·¤èçÁ°Ð
Find the coordinates of the point which divides the line-segment joining the points
(21, 4) and (0, 23) in the ratio 1 : 4 internally.
2
©â çՋÎé ·ð¤ çÙÎðüàææ´·¤ ™ææÌ ·¤èçÁ° Áæð çՋÎé¥æð´ (21, 4) ÌÍæ (0, 23) ·¤æð ç×ÜæÙð ßæÜð ÚðU¹æ-¹´ÇU ·¤æð 1 : 4
·ð¤ ¥æ‹ÌçÚU·¤ ¥ÙéÂæÌ ×ð´ çßÖ€Ì ·¤ÚUÌæ ãñÐ
19.
An integer is chosen between 0 and 20. Find the probability that the chosen integer is
a prime number.
2
0 ÌÍæ 20 ·ð¤
Õè¿ °·¤ Âê‡ææZ·¤ ·¤æ ¿ØÙ ç·¤Øæ ÁæÌæ ãñÐ ¿éÙð »° Âê‡ææZ·¤ ·¤æ °·¤ ¥Öæ’Ø ⴁØæ ãæðÙð ·¤è
ÂýæçØ·¤Ìæ ™ææÌ ·¤èçÁ°Ð
51/AS/3-211-A ]
7
!51/AS/3-211-A!
[ Contd...
20.
The perimeter of a rectangular plot of land is 32 m. If the length is increased by 2 m
and the breadth decreased by 1 m, the area of the plot remains the same. Find the
length and breadth of the plot.
2
ç·¤âè ¥æØÌæ·¤æÚU Öê¹´ÇU ·¤æ ÂçÚU×æ 32 ×è ãñÐ ØçΠܐÕæ§ü ×ð´ 2 ×è ·¤è ßëçh ÌÍæ ¿æñǸæ§ü ×ð´ 1 ×è ·¤è ·¤×è
·¤è Áæ°, Ìæð Öè Öê¹´ÇU ·¤æ ÿæð˜æÈ¤Ü ÂãÜð ·ð¤ â×æÙ ãè ÚUãÌæ ãñÐ Öê¹´ÇU ·¤è ܐÕæ§ü ÌÍæ ¿æñǸæ§ü ™ææÌ ·¤èçÁ°Ð
21.
At what rate of interest per annum will simple interest be half of the principal in
5 years ?
2
ŽØæÁ ·¤è ç·¤â ßæçáü·¤ ÎÚU âð 5 ßáü ×ð´ âæÏæÚU‡æ ŽØæÁ ×êÜÏÙ ·ð¤ ¥æÏð ·ð¤ ÕÚUæÕÚU ãæð»æ?
22.
2
Show that a cyclic parallelogram is a rectangle.
çι槰 ç·¤ °·¤ ¿·ý¤èØ â×æ‹ÌÚU ¿ÌéÖüéÁ °·¤ ¥æØÌ ãæðÌæ ãñÐ
23.
In the figure, given here, O is the centre of the circle and PQ and PR are the
tangent - segments of the circle. Find ÐRPO.
Øãæ¡ Îè »Øè ¥æ·ë¤çÌ ×ð´ O ßëžæ ·¤æ ·ð¤‹Îý ãñ ÌÍæ PQ ÌÍæ PR ßëžæ ·ð¤ SÂàæü-ÚðU¹æ¹´ÇU ãñ´Ð
·¤èçÁ°Ð
24.
The volume of a solid hemisphere is 718
ç·¤âè ÆUæðâ ¥hü-»æðÜð ·¤æ ¥æØÌÙ
[p5
718
2
3
ÐRPO ·¤è
2
×栙ææÌ
2
22
cm3. Find its total surface area. [use p 5
]
3
7
2
âð.×è.3 ãñÐ §â·¤æ âÂê‡ææü ÂëcÆèØ ÿæð˜æÈ¤Ü ™ææÌ ·¤èçÁ°Ð
22
ÜèçÁ°Ð]
7
51/AS/3-211-A ]
8
!51/AS/3-211-A!
[ Contd...
25.
Standing on the top of a tower, 100 m high, Swati observes two cars parked on the
opposite sides of the tower. If their angles of depression are 458 and 308, find the
distance between the cars.
2
°·¤ 100 ×è ª¡¤¿è ×èÙæÚU ·ð¤ çàæ¹ÚU ÂÚU ¹Ç¸è ãæð·¤ÚU SßæçÌ ×èÙæÚU ·¤è çßÂÚUèÌ çÎàææ¥æð´ ×ð´ ¹Ç¸è ·¤è »Øè Îæð ·¤æÚUæð´
·¤æ ¥ßÜæð·¤Ù ·¤ÚUÌè ãñÐ ØçÎ ©Ù·ð¤ ¥ßÙØÙ ·¤æð‡æ 458 ÌÍæ 308 ãñ´, Ìæð ·¤æÚUæð´ ·ð¤ Õè¿ ·¤è ÎêÚUè ™ææÌ ·¤èçÁ°Ð
26.
At what rate percent per annum will a sum of ` 15,625 become ` 17,576 in 3 years on
compound interest when the interest is compounded annually ?
4
ØçÎ ŽØæÁ ßæçáü·¤ L¤Â ×ð´ â´ØæðçÁÌ ãæð, Ìæð ` 15,625 ·¤è ÏÙÚUæçàæ ç·¤â ßæçáü·¤ ÎÚU ÂýçÌàæÌ âð ¿·ý¤ßëçh ŽØæÁ
ÂÚU 3 ßáZ ×ð´ ` 17,576 ãæð»è?
27.
In the figure, given here, AD is the bisector of ÐBAC. If AB59 cm, AC512 cm and
BC57 cm, find the measures of BD and DC.
4
Øãæ¡ Îè »Øè ¥æ·ë¤çÌ ×ð´, AD ·¤æð‡æ ÐBAC ·¤æ â×çmÖæÁ·¤ ãñÐ ØçÎ AB59 âð.×è., AC512 âð.×è. ÌÍæ
BC57 âð.×è. ãæð´, Ìæð BD ÌÍæ DC ·¤è ×栙ææÌ ·¤èçÁ°Ð
28.
Find the mean of the following data by step-deviation method :
4
Classes
:
10 - 20
20 - 30
30 - 40
40 - 50
50 - 60
Frequencies
:
2
3
5
7
5
60 - 70
3
ÂÎ çß¿ÜÙ çßçÏ âð çِÙçÜç¹Ì ¥æ¡·¤Ç¸æð´ ·¤æ ×æŠØ ™ææÌ ·¤èçÁ° Ñ
29.
ᯁ
:
10 - 20
20 - 30
30 - 40
40 - 50
50 - 60
ÕæÚ´UÕæÚUÌæ°¡
:
2
3
5
7
5
60 - 70
3
Find the values of m for which the equation 3x216x1m50 has two distinct real roots.
m ·ð¤
ãæðд
©Ù ×æÙæð´ ·¤æð ™ææÌ ·¤èçÁ° çÁÙ·ð¤ çÜ° â×è·¤ÚU‡æ
51/AS/3-211-A ]
9
3x216x1m50 ·ð¤
4
Îæð ç֋٠ßæSÌçß·¤ ×êÜ ÂýæŒÌ
!51/AS/3-211-A!
[ Contd...
30.
Find the circumradius of equilateral triangle of side 6 cm.
6 âð.×è. ÖéÁæ ßæÜðð â×Õæãé ç˜æÖéÁ ·¤è ÂçÚUç˜æ’Øæ ™ææÌ ·¤èçÁ°Ð
4
31.
Simplify :
(5x13y)313(5x13y) 2(5x23y)13(5x13y)(5x23y)21(5x23y)3
4
âÚUÜ ·¤èçÁ° Ñ
(5x13y)313(5x13y) 2(5x23y)13(5x13y)(5x23y)21(5x23y)3
32.
Construct a right triangle ABC, right - angled at B in which BC53 cm and AC56 cm.
°·¤ °ðâð â×·¤æð‡æ ç˜æÖéÁ ABC ·¤è ÚU¿Ùæ ·¤èçÁ° çÁâ·¤æ ·¤æð‡æ B â×·¤æð‡æ, ÖéÁæ BC53 âð.×è. ÌÍæ
AC56 âð.×è.
ãæðÐ
4
OR(¥Íßæ)
For visually impaired learners only
(·ð¤ßÜ ÎëçcÅU çß·¤Üæ´» çßlæçÍüØæð´ ·ð¤ çÜ°)
Write the steps of construction of a tangent to a circle at a given point on it using the
centre of the circle.
ßëžæ ·ð¤ ·ð¤‹Îý ·¤æ ©ÂØæð» ·¤ÚU·ð¤, ßëžæ ÂÚU çSÍÌ °·¤ çՋÎé ÂÚU ßëžæ ·¤è SÂàæü ÚðU¹æ ·¤è ÚU¿Ùæ ·ð¤ ¿ÚU‡æ çÜç¹°Ð
33.
A survey of 200 students of a school was done to find which activity they prefer to do
in their free time and the information, thus collected is recorded in the following
table :
4
Preferred Activity
Number of Students
Playing
60
Reading story books
45
Watching TV
40
Listening to music
25
Painting
30
Draw a bar graph for this data.
ç·¤âè çßlæÜØ ·ð¤ 200 çßlæçÍüØæð´ ÂÚU °·¤ âßðüÿæ‡æ Øã ÁæÙÙð
·ð¤ çÜ° ç·¤Øæ »Øæ ç·¤ ßð ¥ÂÙð ¹æÜè â×Ø ×ð´
€Øæ ·¤ÚUÙæ Ââ´Î ·¤ÚUÌð ãñ´, ÌÍæ ÂýæŒÌ âê¿Ùæ ·¤æð Ùè¿ð Îè »Øè âæÚU‡æè ·ð¤ M¤Â ×ð´ çÚU·¤æÇüU ç·¤Øæ »Øæ Ñ
¼¾ §Ç™³ Ìœâ ½Ë œ‰Á˧
ÌÄlË̲á½Ëՙ œ‰Í Ǚ€½Ë
60
žÕÁ¾Ë
45
œ‰ÈË¾Í œ‰Í §ÎS±œ™Õ‰ §®¾Ë
40
ªÍ.ÄÍ. ³Õž¾Ë
25
Ǚ ͱ Çξ¾Ë
30
§Õ™ÌªU™U §Ù ¥æ¡·¤Ç¸æð´ ·ð¤ çÜ° °·¤ δÇUæÜð¹ ·¤è ÚU¿Ùæ ·¤èçÁ°Ð
OR(¥Íßæ)
51/AS/3-211-A ]
10
!51/AS/3-211-A!
[ Contd...
For visually impaired learners only
(·ð¤ßÜ ÎëçcÅU çß·¤Üæ´» çßlæçÍüØæð´ ·ð¤ çÜ°)
The following table gives the distribution of employees of different income groups residing
in a locality.
Monthly income (in C )
20,000 - 25,000
25,000 - 30,000
30,000 - 35,000
35,000 - 40,000
40,000 - 45,000
45,000 - 50,000
Number of employees
35
75
150
155
70
15
Form a cumulative frequency table for the data and answer the following questions :
(a)
How many employees earn less than or equal to ` 30,000 per month ?
(b)
How many employees earn more than ` 30,000 per months ?
Ùè¿ð Îè »Øè âæÚU‡æè °·¤ ÕSÌè ×ð´ ÚUãÙð ßæÜð çßç֋٠¥æØ-â×êãæ𴠷𤠷¤×ü¿æçÚUØæð´ ·¤æ Õ´ÅUÙ ÂýÎçàæüÌ ·¤ÚUÌè ãñÐ
×æçâ·¤ ¥æØ (` ×ð´)
·¤×ü¿æçÚUØæð´ ·¤è ⴁØæ
20,000 - 25,000
35
25,000 - 30,000
75
30,000 - 35,000
150
35,000 - 40,000
155
40,000 - 45,000
70
45,000 - 50,000
15
§Ù ¥æ¡·¤Ç¸æð´ ·ð¤ çÜ° °·¤ â´¿Øè ÕæÚ´UÕæÚUÌæ âæÚU‡æè ÕÙ槰 ÌÍæ çِÙçÜç¹Ì ÂýàÙæ𴠷𤠩žæÚU ÎèçÁ° Ñ
34.
(a)
ç·¤ÌÙð ·¤×ü¿æçÚUØæð´ ·¤è ×æçâ·¤ ¥æØ
` 30,000
âð ·¤× ¥Íßæ ÕÚUæÕÚU ãñ?
(b)
ç·¤ÌÙð ·¤×ü¿æçÚUØæð´ ·¤è ×æçâ·¤ ¥æØ
` 30,000
âð ¥çÏ·¤ ãñ?
If p th , q th and r th terms of an A.P. are x, y, z respectively.
x(q2r)1y(r2p)1z(p2q)50.
Prove that
6
ØçÎ ç·¤âè â.Ÿæð.·ð¤ pßð´, qßð´ ÌÍæ rßð´ ÂÎ ·ý¤×àæÑ x, y, z ãæð´ Ìæð çâh ·¤èçÁ° ç·¤ Ñ
x(q2r)1y(r2p)1z(p2q)50.
51/AS/3-211-A ]
11
!51/AS/3-211-A!
[ Contd...
35.
In the figure, given here, OAQB is a quadrant of a circle with centre O and radius 7 cm
and APB is a semi circle. Find the area of the shaded region.
6
Øãæ¡ Îè »Øè ¥æ·ë¤çÌ ×ð´ OAQB, O ·ð¤‹Îý ÌÍæ 7 âð.×è. ç˜æ’Øæ ßæÜð ßëžæ ·¤æ ¿ÌéÍæZàæ ç˜æ’Ø ¹´ÇU ãñ ÌÍæ APB
°·¤ ¥hüßëžæ ãñÐ ÀUæØæ´ç·¤Ì Öæ» ·¤æ ÿæð˜æÈ¤Ü ™ææÌ ·¤èçÁ°Ð
36.
If sec u1tan u5p, show that :
sin u 5
6
p 221
p 211
ØçÎ sec u1tan u5p ãæð, Ìæð çι槰 ç·¤ Ñ
sin u 5
p 221
p 211
-oOo-
51/AS/3-211-A ]
12
!51/AS/3-211-A!
[ Contd...