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Linette Summers
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1 BITSAT MATHEMATICS PAPER. If log 0.0( ) log 0.( ) the elogs to the itervl (, ] () (, ] [,+ ). The poit of itersectio of the lie joiig the poits i j k d i+ j+ k with the ple through the poits i+ j k, i j+ k d i + k is ) i+ j+ k ) i+ j+ k c) i j+ k d) Noe. If z d z re two o-zero comple umers such tht z + z = z + z, the rg ( z ) rg ( z ) is equl to π () π π (d) 0. If, re two o zero vectors d c is o zero sclr, d. r = c, r = the r = c ) ) c) c d) c ( ). The poits z, z, z, z i the comple ple re the vertices of prllelogrm tke i order, if d ol if z + z = z + z () z + z = z + z z + z = z + z 6. I college of 00 studets, ever studet reds ewspper d ever ewspper is red 60 studets. The o. of ewspper is At lest 0 () At most 0 Ectl 7. Let R d S e two o-void reltios o set A. Which of the followig sttemets is flse R d S re trsitive R S is trsitive ()R d S re trsitive R S is trsitive R d S re smmetric R S is smmetric (d)r d S re refleive R S is refleive

2 8. Let α d β e the roots of the equtio + + = 0 The equtio 7 whose roots re α 9, β is = 0 () + = 0 + = 0 (d) + + = 0 9. If root of the equtios + p + q = 0 d + α + β = 0 is commo, the its vlue will e (where p α d β q β α p () pβ αq q β q α p 0. ( + ) is divisile (where N () q ) β or ) pβ αq q β (d) All of these. The coefficiet of i the epsio of ( ) is 8 () 8 8 (d) 0. The sum of the series is!! 6 e () 6 e e (d) e +. The equtio + + z =, Uique solutio Icosistet! 7! 6! + + z =, + + 9z = hve () Ifiitel m solutios + α. The vlue of otied from the equtio γ + β α = 0 will e 0 d ( α + β + γ ) () 0 d ( α + β + γ ) d ( α β γ ) (d) 0 d ( α + β + γ ). I electio there re 8 cdidtes, out of which re to e choose. If voter m vote for umer of cdidtes ut ot greter th the umer to e choose, the i how m ws c voter vote 6 () 8 6. A vrile lie psses through fied poit P. The lgeric sum of the perpediculr drw from (,0), (0, ) d (, ) o the lie is zero, the the coordites of the P re α β β γ + γ (, ) ()(, ) (, ) (d)(, )

3 7. A stright lie through origi isect the lie pssig through the give poits ( cosα, siα) d ( cos β, si β), the the lies re Perpediculr () Prllel π Agle etwee them is 8. If the sum of slopes of the pir of lies represeted + h 7 = 0 is equl to the product of the slopes, the the vlue of h is 6 () (d) 9. If lie + = 0 touches = 0 d is orml to the circle + + = 0, the vlue of (,) will e (, ) ()(, ) (, ) (d) (, ) 0. A circle with rdius lies i the first qudrt d touches oth the es, other circle hs its cetre t (8,9) d rdius 7. Which of the followig sttemets is true Circles touch ech other iterll () Circles touch ech other eterll Circles itersect t two distict poits. If the orml to = t (, 6) meets the prol gi i (7, 8) d the circle o the orml chord s dimeter is = 0 () = = 0 (d) = 0. I the ellipse =, the equtio of dimeter cojugte to the dimeter =, is + = () = =. The equtio [( ) + ( ) ] = ( + ) represets Prol () Ellipse Hperol. If f e the gretest iteger fuctio d g e the modulus fuctio, the ( gof ) ( fog) = () (d)

4 t t. lim 6. If 0 ( cos ) is () ( ) = + k k +, for < 0 f, is cotiuous t = 0, the k =, for 0 (d) () (d) 7. If f is rel- vlued differetile fuctio stisfig f( ) f( ) ( ),, R d f ( 0) = 0, the f () equl () (d) 0 8. d si d + cot equls () (d) 9. A prticle moves so tht S = 6 + 8t t. The directio of motio reverses fter movig distce of 6 () 0 (d) If the curve = d = itersect t gle α the, t α = + log + log log log () log log + log log. The miimum vlue of is 0 () (d) 6 +. If f( ) = k is mootoicll icresig i ech itervl, the k < () k k >. The fuctio f ( ) = ( ) stisfies ll the coditios of me vlue theorem i [, ]. A poit o = ( ), where the tget is prllel to the chord joiig (, 0) d (, ) is 7 7, () (, ) (d) (, ), (d)

5 . Let = j + k, = i + j d let d e compoet vectors of prllel d perpediculr to. If i + j =, the = i j + k i + j + () i + j + k (d)noe of these. The distce of the poit of itersectio of the lie d the ple + + z = 7 from the poit (,, ) is give () / 6. If si(cot ( + ) = cos(t ), the = () 0 (d) 9 z = = 7. If the sides of trigle re i rtio : 7 : 8, the R : r is equl to : 7 () 7 : : 7 (d) 7 : 8. At poit o the groud the gle of elevtio of tower is such tht its cotget is /. O wlkig meters towrds the tower the cotget of the gle of elevtio is /. The height of the tower is 60 m () 0 m 6 m + 9. d = [si + ] + c () [si + ] + c si + + c (d) si + + c 0. If f ( ) f =, the ( ) d is equl to l f () ( + l ) l. The re eclosed the prols = d = is / () / / (d) 8/

6 . The solutio of the differetil equtio d d = φ + φ φ = k () φ = k φ = k (d) φ = k is. The equtio of fmil of curves for which the legth of the orml is equl to the rdius vector is ± = k () ± = k = k. If A d B re two evets such tht B A the P = () 0 P ( A) =, ( B) = P d P ( A B) =,. If positive itegers re tke t rdom d multiplied together, the proilit tht the lst digit of the product is,, 6 or 8, is + () KEY: -0 C B D B B C A D C B -0 C B A A C B A B C A -0 D A C A C C D B C B -0 D C B B A A B A A B - D A A A C

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[Q. Booklet Number] 6 [Q. Booklet Numer] KOLKATA WB- B-J J E E - 9 MATHEMATICS QUESTIONS & ANSWERS. If C is the reflecto of A (, ) i -is d B is the reflectio of C i y-is, the AB is As : Hits : A (,); C (, ) ; B (, ) y A (,