HIGHER SECONDARY FIRST YEAR MATHEMATICS. ALGEBRA Creative Questions Time : 1.15 Hrs Marks : 45 Part - I Choose the correct answer 10 1 = 10.

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1 HIGHER SEONDARY FIRST YEAR MATHEMATIS ALGEBRA eative Questios Time :. Hs Maks : Pat - I hoose the coect aswe =. The co-efficiet of middle tem i the epasio of is a) b)...( )! c).6,...( ) d) Noe of these. The umbe of ways i which 6 me ad wome ca die at a oud table if o two wome ae to sit togethe is give by a) 6!! b) c)!! d) 7!!. Si idetical cois ae aaged i a ow. The total umbe of ways i which the umbe of heads is equal to the umbe of tails, is a) 9 b) c) d). I a eamiatio thee ae thee multiple choice questios ad each questio has choices of aswes i which oly oe is coect. The total umbe of ways i which a eamiee ca fail to get all aswes coect is a) b) c) 7 d) 6. A fathe with 8 childe takes at a time to the zoological Gades, as ofte as he ca without takig the same childe togethe moe tha oce. The umbe of times he will go to the gade is a) 6 b) c) 6 d) 6. If the lettes of the wod SAHIN ae aaged i all possible ways ad these wods ae witte out as i dictioay, the the wod SAHIN appeas at seial umbe a) 6 b) 6 c) 6 d) 6 7. The total umbe of tems i the epasio of ( a) ( a) afte simplificatio, a) b) c) d) 8. If the seveth tems fom the begiig ad the ed i the epasio of ae equal the equals ae a) 9 b) c) d) 8

2 9. Assetio : The umbe of ways of distibutig idetical balls i distict boes such that o bo is empty is Reaso : The umbe of ways of choosig ay places fom 9 diffeet places is 9 A. If both Assetio & Reaso ae Tue & the Reaso is a coect eplaatio of the Assetio. B. If both Assetio & Reaso ae Tue but Reaso is ot a coect eplaatio of the Assetio.. If Assetio is Tue but the Reaso is False. D. If both Assetio & Reaso ae False. a) A b) B c) d) D 7 7. Assetio : Fo each atual umbe, ( ) is divisible by 7 Reaso : Fo each atual umbe, 7 A. If both Assetio & Reaso ae Tue & the Reaso is a coect eplaatio of the Assetio. B. If both Assetio & Reaso ae Tue but Reaso is ot a coect eplaatio of the Assetio.. If Assetio is Tue but the Reaso is False. D. If both Assetio & Reaso ae False. a) A b) B c) d) D Pat - II Aswe ay thee of the followig questios = 6. How may ways i which 7 pesos ca be seated at a oud table if two paticula pesos ae ot to sit togethe. Detemie the maimum umbe of poits of itesectio of 8 cicles. Fid a if the 7 th ad 8 th tems of the epasio ( a) ae equal. If fid. 8! 9!!. Fid the sum of the seies... Pat - III Aswe ay thee of the followig questios = 9 6. Fid the umbe of ectagles ecludig squaes fom a ectagle of size. 7. If the sum of the biomial coefficiets i the epasio of Idepedet tem is 6, the fid the

3 8. Fid the lagest tem i the epasio of ( ) whee = 9. Fid if P 6 P. If all pemutatios of the lettes of the wod AGAIN ae aaged as i dictioay, the fid the th wod. Pat - IV Aswe ay fou of the followig questios =. If, ad the fid. If the thee successive coefficiets i the Biomial epasio of ( ) ae 8, 6 ad 7 espectively, the fid. Fid the umbe of itegal tems i the epasio of 6 8. I a eamiatio, a questio pape cosists of questios divided ito two pats i.e., Pat I ad Pat II, cotaiig ad 7 questios, espectively. Astudet is equied to attempt 8 questios i all, selectig at least fom each pat. I how may ways ca a studet select the questios?. Pove that..., N by mathematical iductio method ***** T. Ayyaa, M.Sc., B.Ed., D.P.Tech Istucto (Mathematics) SBGGHSS, Puduchey 6 akathik@gmail.com ell: 78976,

4 Q.No Optios b a b d c 6 d HIGHER SEONDARY FIRST YEAR MATHEMATIS ALGEBRA eative Questios Aswes ad Solutios Pat - I 7 b 8 b 9 a a Pat II. Total o of ways 7 pesos seated at a oud table = ( 7 )! No of ways fo two pesos sit togethe = ( 6 )! =! = = 6! = 7 No of ways fo two paticulas pesos ot sit togethe = 7. No of itesectio poits = No of tiagles No of tiagles = 8 = 6 = 8. T a 6 6 a

5 T a 7 7 a T7 T 8 a a 7 6 a ! 9 8! 9 8! 9 9. ( ) =... put = = = 9 = Pat III p 6. No of ectagles = ( p )( ) p =, = (sice ) No of ectagles = 6 = 66 No of squaes = ( p )( ) = 66 No of ectagles ecludig squaes = = 9

6 7. Sum of biomial coefficiets = T 6 Idepedet tem Idepedet tem is 6 = 6 = 6 T ( ) 8. T ( ) ( = ) (6 ) () = The lagest tem = th tem 9. P P 6! (6 )! ( )!! 6 8 o 6 6. I a dictioay a wod stat with A - A(AGIN) No of ways =! = A wod stat with G - G(AAIN)! No of ways = =! A wod stat with I - I(AAGN)

7 No of ways = =! Total ways = ++ =8 9th wod stat with N is NAAGI th wod is NAAIG Pat IV.! ( )!( )!! ( )!! ( ) 9 9 ( )! ( )!!! 8 ( )!( )! ( ) 8 8( ) ( ) Solve ad =, = 8. Let the thee success tems be,,! ( )!( )!! ( )!! 6 8

8 ( ) ( ) 7 6! ( )!( )!! ( )!( )! ( ) ( ) ( ) ( ) 9 Solve ad = 8, = T T The above tems will be atioal if epoet of ad ae iteges 6 It meas ad must be iteges 8 The possible values of is,8,6,...6= tems. Pat I Pat II 7 ombiatios Total Selectios Total.

9 Let P() deote the statemet..., N put = P() is tue Assume that P(k) is tue P( k) k... k To pove: P(k+) is tue... k ( k ) ( k ( k k 6k ) ( k ) ( k ) k ( k ) k P(k+) is tue By the piciple of Mathematical iductio, P() is tue fo all N..., N ) T. Ayyaa, M.Sc., B.Ed., D.P.Tech Istucto (Mathematics) SBGGHSS, Puduchey 6 akathik@gmail.com ell: 78976,