WINTER 2017 EXAMINATION
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1 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer ject Code: Important Instructons to Eamners: ) The answers should be eamned by key words and not as word-to-word as gven n the model answer scheme. ) The model answer and the answer wrtten by canddate may vary but the eamner may try to assess the understandng level of the canddate. ) The language errors such as grammatcal, spellng errors should not be gven more mportance (Not applcable for subject Englsh and Communcaton Sklls). 4) Whle assessng fgures, eamner may gve credt for prncpal components ndcated n the fgure. The fgures drawn by canddate and model answer may vary. The eamner may gve credt for any equvalent fgure drawn. ) Credts may be gven step wse for numercal problems. In some cases, the assumed constant values may vary and there may be some dfference n the canddate s answer and model answer. 6) In case of some questons credt may be gven by judgement on part of eamner of relevant answer based on canddate s understandng. 7) For programmng language papers, credt may be gven to any other program based on equvalent concept. 0 Q. wer Markng. Attempt any fve of the followng: 0 a) Evaluate log 8 log 8 log 4 4log OR b) log 8 log8 log 4 log log 4 4log log Show that the ponts 8,, 4 and, are collnear usng determnant. y Consder y y 0 Page 0/
2 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng. b) c) d) e) Ponts are collnear Wthout usng calculator fnd the value of sn 0 sn 0 0 sn sn 60 cos 4 cos60 sn OR Fnd area of rhombus whose dagonals are of length 0 cm and 8. cm Area of rhombus d d sq. cm If the volume of a sphere s cm.fnd ts surface area 4 Volume of sphere r 4 4 r r r Surface area of sphere 4 r 4 4 OR.6 cm Page 0/
3 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng. f) g) Fnd the range and coeffcent of range of the data: 0, 90, 0, 40, 80, 00, 80. Range L S L S Coeffcent of range L S = = OR If the coeffcent of varaton of certan data s and mean s 60.Fnd the standard devaton. SD.. Coeffcent of varaton 00 Mean SD SD.. 00 SD Attempt any three of the followng: a) If A, whether s sngular or non-sngular matr? 0 B AB AB 0 4 AB AB 9 6 AB AB 0 AB s non-sngular matr b) Resolve nto partal fractons : Page 0/
4 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng. b) c) A B C A B C Put 4 A 6 4 A A Put B 4 8B B 4 Put C 6 4 4C C Usng Cramers rule solve y z ; y 4z 4 ; y 6z D = 4 6 = D = = D 8 D 8 Page /
5 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng. c) d) D y = Dy 6 y D 8 D = 4 z = D 8 z Dz 8 z D Compute the standard devaton for,, 7,, 9,, 4, 9. d d d 0 Mean n Page 0/
6 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng. d) 8 Mean 6 8 Standard devaton OR n d Mean n Standard devaton N Page 06/
7 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng. Attempt any three of the followng: a) b) If tan y and tan y 8.Prove that tan Consder y y y tan y y y tan tan y y tan = tan tan 8 = = 6 tan 77 6 OR Let y A y B 8 tan A, tan B 4 A B y y tan tan A B tan A tan B = tan A tan B 8 = = 6 tan If A 0, verfy that ) sna sn Acos A tan )cos A tan A A Page 07/
8 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng. b) c) ) L. H. S. sn A 0 sn (0 ) sn 60 R. H. S. sn Acos A sn 0 cos sn A sn A cos A ) L. H. S. cos A cos 0 cos 60 tan A R. H. S. tan A tan 0 tan tan A cos A tan A Prove that cos 0cos 40cos60cos80 6 L. H. S. cos 0cos 40cos60cos80 cos 0cos 40 cos80 cos 0cos 40 cos80 4 Page 08/
9 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng. c) L.H.S. cos 60 cos 0 cos80 4 cos 0 cos80 4 cos80 cos 0cos80 4 cos80 cos 0cos80 8 cos80 cos00 cos60 8 cos80 cos00 8 cos80 cos 80 8 cos80 cos R. H. S. d) Prove that cos cos cos 6 Put cos 4 4 cos A sn A cos 6 Put cos B cos B sn B cos A A B Page 09/
10 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng. d) sn B Consder, cos( A B) cos A.cos B sn A.sn B 4 cos( A B) cos( A B) 6 A B cos 6 4 cos cos cos 6 OR Let cos A 4 cos A 4 tan A 4 A tan 4 cos 4 tan 4 Let cos B cos B tan B B tan cos tan 4 L. H. S. cos cos Page 0/
11 [[ Q. (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng. d) L.H.S. tan tan 4 tan tan 6 Let tan C 6 tan C cos C 6 C cos tan cos R. H. S C 4. a) Attempt any three of the followng: 6 6 If A, B 0 4.Verfy that 0 AB B A AB AB AB 0 8 T 4 0 AB T T 6 0 B A T T T Page /
12 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng 4. a) b) c) T T B A T T B A AB T T T B A Resolve nto partal fracton A B C A B C Put A A Put 0 AC C Put A B C B B A B A B A B A Bsn A B sn Acos B cos Asn Bsn Acos B cos Asn B Prove that : sn sn sn sn sn sn Acos B cos Asn B sn A sn B sn A sn B sn A sn Asn B sn B sn Asn B sn Asn B Page /
13 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng 4. d) If sn A = fnd the value of sna. sn A sn A 4sn A = 4 = e) sn 4A sn A sn 6A Prove that tan A cos 4A cosa cos 6A sn 4A sn A sn 6A L. H. S. cos 4A cosa cos 6A sn 4A sn 6A sn A cos 4A cos 6A cosa 4A 6A 4A 6A sn cos sn A 4A 6A 4A 6A cos cos cos A sn A cosa sn A cosacos A cosa sn A cos A cosa cos A tan A R. H. S.. a) () Attempt any two of the followng: Fnd the equaton of straght lne passes through the ponts, and 4,6. Equaton of lne s y y y y y 6 4 y y0 0 () Fnd the dstance between the parallel lnes y 7 0 and y 6 0 For y7 0 0 Page /
14 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng. a) () a, b, c 7 For y6 0 a, b, c 6 dstance between two parallel lnes s c a c b 6 7 ( ) OR.846 b) () () Fnd the acute angle between the lnes y 0 and y 4 0 For y 0 a slope m b For y 4 0, slope m m m tan mm a b tan OR Fnd the equaton of the lne through the pont of ntersecton of lnes, 4 y 8 ; an d y and parallel to the lne 7y 4y 8 y y 8 4 4y 4 Page 4/
15 [ Q. (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng. b) () c) () 4 y 4 y 4 Pont of ntersecton, 4 Slope of the lne 7 y s, a m b 7 7 Slope of the requred lne s, m 7 equaton requred lne s, y y m y y The area of a rectangular courtyard s 000 sq.m. Its sdes are n the rato 6:.Fnd the permeter of courtyard. Area of rectangular courtyard s length breadth Gven l: b 6 : l 6 e.. b 6 l b A l b bb 000 b 6 00 b b l b 0 l 60 Permeter of rectangular courtyard s l b m. 0 Page /
16 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng. c) () OR Sdes are n the rato 6 : Let be the common multple Sdes are 6 and A Sdes are 6 60 l and 0 b Permeter of rectangular courtyard s l b m. c) () A crcus tent s cylndrcal to heght m and concal above t. If ts dameter s 0 m and slant heght of cone s m,calculate the area of total canvas requred. 0 Gven h m, d 0 m r.m, l m curved surface area of cylnder rh curved surface area of cone rl sq. m sq. m. Area of total canvas requred sq. m Attempt any two: a) Usng matr nverson method, solve y z ; y z 4 ; 4y 9z 6 06 Let A 4 9 A 4 9 A Page 6/
17 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng 6. a) A 0 A ests Matr of mnors Matr of cofactors 8 OR c 6, c c 4 9 6,, 9 4 c, c 8, c, c, c, c, 6 6 Matr of cofactors 8 6 AdjA A Adj. A 6 8 A X A B 6 y z 6 Page 7/
18 [ Q. (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng 6. a) b) y = 8 z y = z 0 y = z 0, y, z Fnd mean, standard devaton and coeffcent of varance of the followng: Class: Frequency: 8 06 C.I. f f f N=0 f 440 f 900 f 440 Mean, N 0 S. D. f N 900 SD.. 0 SD Page 8/
19 (ISO/IEC Certfed) 6. b) SD.. Coeffcent of varance 00 Mean WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng OR % Class f d fd d fd N=0-6 4 fd 6 Mean, A h 0 N 0 fd fd S. D. h N N SD.. Coeffcent of varance 00 Mean OR % C.I. f f f f 0 f 440 f 0 Page 9/
20 [ Q. (ISO/IEC Certfed) 6. b) f 440 Mean, N 0 SD.. 0 SD.. 0 SD f f SD.. Coeffcent of varance 00 Mean WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng c) () % Calculate the range and coeffcent of range for the followng data: Class: Frequency: C.I f c) () Range L S L S Coeffcent of range L S = = OR The two sets of observatons are gven below. Whch of them s more consstent? Set I Set II Page 0/
21 (ISO/IEC Certfed) WINTER 07 EXAMINATION Model wer wer ject Code: 0 Markng 6. c) () Set-I SD.. Coeffcent of varaton V 00 Mean Set-II 7. V V SD.. Coeffcent of varaton V 00 Mean 8. V V 7.8 V V Set I s more consstent Important Note In the soluton of the queston paper, wherever possble all the possble alternatve methods of soluton are gven for the sake of convenence. Stll student may follow a method other than the gven heren. In such case, frst see whether the method falls wthn the scope of the currculum, and then only gve approprate marks n accordance wth the scheme of markng Page /
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