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SI LVERBELLSSCHOOL UNI TTEST 202122 MATHEMATI CS CLASS XI I Max.Mar ks-50 Gener alI nst r uct i ons: 1.Al l quest i onsar ecompul sor y . 2.Thequest i onpaperconsi st sof20quest i onsdi v i dedi nt of oursect i onsA, B, CandD.Sect i on A compr i sesof6quest i onof1mar keach.Sect i on Bcompr i sesof3quest i onsof2mar kseach. Sect i on Ccompr i sesof6quest i onsof3mar kseachandSect i on Dcompr i sesof4quest i ons of4mar kseach. 3.Pl easecheckt hatt hi squest i onpapercont ai ns2pr i nt edpages. 4.Useofcal cul at ori snotper mi t t ed. Sect i onA Q. 1 I fA= t hent hedet er mi nantofA2 2Ai s ( a)5 Q. 2 Q. 3 Q. 4 Q. 5 ( c)5 ( b)1 ( c)abc ( d)25 = ( a)0 I f ( d)a+b+c =kxy z, t henk= ( a)1 ( b)3 ( c)4 ( d)2 I fA=[ aij]i sasquar emat r i xofor dern nandki sascal ar , t hen| kA| = ( a)kn| A| ( b)k| A| ( c)kn 1| A| ( d)none I fA= andAB=It henB= ( a) Q. 6 ( b)25 ( b) ( c) ( d) 1 sec2( Tan 12)+cosec2( Cot 3)i sequal t o ( a)1 ( b)5 ( c)10 Sect i onB ( d)15 Q. 7 I f t henf i ndt hev al uesof sat i sf y i ngt heequat i on . Q. 8 Q. 9 Fi ndt hev al ueofxi ft hear eaof i s35squar ecmswi t hv er t i ces( x, 4) , ( 2, 6)and( 5, 4) . Ev al uat e: Sect i onC Q. 10 Fi ndt hemat r i xXf orwhi ch . Q. 11 Pr ov et hat : . Q. 12 Pr ov et hat Q. 13 , Pr ov et hat: . Q. 14 I f , Thenpr ov et hat . Q. 15 Pr ov et hat: . Sect i onD Q. 16 Fort hemat r i x , showt hat hence, f i nd Q. 17 St at et hecondi t i onunderwhi cht hef ol l owi ngsy st em ofequat i onshav eauni quesol ut i ons. I fA= , f i nd andhencesol v et hef ol l owi ngsy st em ofequat i ons: 9x+7y+3z=6;5x y+4z=1; 6x+8y+2z=4. Q. 18 Showt hat . Q. 19 Usi ngpr oper t i esofdet er mi nant spr ov et hat : . Q. 20 I f and ar et wosquar emat r i ces,f i ndABandhence sol v et hesy st em ofl i nearequat i on: x+y+2z=1; 2x+y+3z=2; 3x+2y+z=7.
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