. Th maimum valu of Ë Ë c /. Th contraositiv of th convrs of th statmnt If a rim numbr thn odd If not a rim numbr thn not an odd If a rim numbr thn it not odd. If not an odd numbr thn not a rim numbr. If not a rim numbr thn odd Ans:. Th simlifid form of n n+ n+ n+ i + i + i + i i - 0. Th cofficint of variation of two dtributions ar 0 and 0. th standard dviation ar and rsctivl, thn thir man.. Ans: (, ). Th slo of th tangnt to th curv =t - KCET 0 TEST PAPER WITH ANSWER KEY (HELD ON WEDNESDAY th MAY, 0) + - = - - t, t t at th oint (, -) Ans:. Suos a+ b+ c= 0,a =,b=,c=, thn th angl btwn a&b / / / MATHEMATICS. Lt * b a binar oration dfind on R b a * b = a + b " a,b Œ R thn th oration * Nithr Associativ nor commutativ Associativ but not commutativ Commutativ but not Associativ Commutativ and Associativ Ans: m n. if ( ) m n = + + thn d qual to d 0 Ans: + - - sc 9. If sin ( t -) Ë t - = &= thn d qual to d - - Ans: 0. If + sinq+ sin q+... uto = +, thn q = / / / /. Th ordr and dgr of th diffrntial quation / È d d ˆ ˆ d sin + + = d d Í Ë Ë Î d ordr = dgr not dfind = ordr dg r = ordr dg r == ordr = dg r = Ans: = /
. Th valu of sin - cos ˆ Ë - 0-0 Ans:. If a =, b =, c = ach on of a,b&c rndicular to th sum of th rmaining thn a+ b + c qual to. Th ral art of ( -cosq+ in q ) - cot q + cosq tan q. Ara ling btwn th curvs sq.units sq.units sq.units sq.units = and =. If th straight lins + - = 0 and + k+ = 0 ar rndicular, thn th valu of k -/ -/ / / È - -ˆ È - -ˆ sin ( ) tan -cos ( ) tan Ë Ë A =,B=. If - - - ˆ ˆ - sin cot ( ) sin -tan ( ) Í Ë Í Ë Î Î thn A - B qual to I I 0 I Ans:. Th st A has lmnts and th st B has lmnts thn th numbr of injctiv maings that can b dfind from A to B 0 0 Ans: 9. Intgrating factor of - log d d - = - È 0. If A = Í Î- thn A - A qual to -I I -I I Ans:. Two cards ar drawn at random from a ack of cards. Th robabilit of ths two bing Acs Ans:. Th valu of / 0 0 Ú sin.cos d -/ 0 ˆ Ë Ans: 0 ( ) 0 / /
. lim Æ0 -sin qual to 0. If = + cos q and = - sin q rrsnt a circl thn th cntr and radius (-,- ), (,, ) (, ), (, ),9 Ans:. If sin + sin =, thn qual to - - - 0 -. Th valu of th 0 0 0 sin + sin +... + sin9 qual to 0-0. Th th trm in th ansion of + Ë 00 00 Ans: i 999. If A a matri of ordr m n and B a matri such that AB and B A ar both dfind, th ordr of th matri B m n n m n n m m Ans: 9. Th diffrntial cofficint of log0 to log 0 00 ( ) Ans: - log 0 ( log ) 0 0. Th two curvs - + = 0 and - = Cut at an angl / Cut at an angl / Cut ach othr at right angl Touch ach othr Ans: -. If tan ( ) with rsct + =a thn d qual to d - -. Th rat of chang of ara of a circl with rsct to its radius at r = cms Ans:. / 000 sin d Ú qual to 000 000 sin + cos 0 000 Ans:. Th valu fo tan qual to - + / +
. Th solution for th diffrntial quation d + d = 0 + =c = c log. log = c + = c. Find th co-ordinats of th foot of th rndicular drawn from th origin to th lan + = 0 Ans: 0, -,0 Ë 0,,0 Ë. Th simlifid from of qual to tan Ans:,0,0 Ë 0, -, Ë ˆ ˆ - -tan Ë Ë + - - 0 Ècosq -sinq. If A = Í Î sin q cos q and A + A T = I Whr I si th unit matri of & A T th transos of A, thn th valu of q qual to / / / 9. Th valu of Ans: Ú log log - - log log 0 d qual to 0. If - - tan + cot = thn qual to / - 0 Ans:. Th valu of qual to - tan - ( ) - - ( + + ) tan tan d Ú + - c + c tan ( ) + c tan + c - tan + c. Th valu of if ( ˆi Jˆ kˆ) ± ± ± + + a unit vctor. If cos a,cos b,cos g ar th dirction cosins of a vctor a, thn cosa+ cosb+ cosg qual to ± 0 -. If A an squar matri of ordr thn A qual to 9A A A A. If z ar not qual and 0, th valu of log log log z log log logz log log logz qual to log( + + z) 0 log( z ) log( z) /
. Th function f( ) = [ ] whr [] th gratst intgr function continuous at -.. If a.b= a.b thn th angl btwn a&b 0 90 0 0 Ans:. Th lngth of latus rctum of th arabola + + + = 0 / / Ans: 9. If P( A «B) = /0 ( ) P B = / 0, whr P stands for robabilit thn P( A B ) qual to / / /0 / 0. If z ar all diffrnt and not qual to zro and + + = 0 + z - - - + + z qual to thn th valu of - ---z Ans: - - - z z. Th valu of cot( ) tan(.) Ans: ( + ) d Ú cos. qual to ( ) + c tan( ) + c + c - cot( ) + c. Two dic ar thrown simultanousl, th robabilit of obtaining a total scor of 9. If a and b ar unit vctors thn what th angl btwn a and b for a - b to b unit vctor? 90 0 0. Th gnral solution of cot q+ tan q= n q= + - / q= n+ (-) n / ( ) n n / q= n + - / + ( - ) n ( ) n Ans:. Th vctor quation of th lan which at a dtanc of / from th origin and th normal from th origin i ˆ- j ˆ+ kˆ r. i+ k = ( ˆ ˆ) r. i+ j+ k = 9 ( ˆ ˆ ˆ). Th valu of r. i+ j = ( ˆ ˆ) r. i- j+ k = ( ˆ ˆ ˆ) 0- Ú d + 0-0 0 Ans:. Th sum of st n trms of th sr + + + + + +... + + + n( n- ) n( n- ) / n( n+ ) Ans: n+
. If = - thn d d qual to log - - ( + log ) log - log( - ) 9. Lt f : R Æ R b dfind b f( ) = + which - a bijctiv maing thn f ( ) givn b + - + - 0. Th quation of th normal to th curv ( ) + = - whr th tangnt crosss - a + + 0= 0 ++0=0 -- 0= 0 --0=0 /