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Eustacia Ryan
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1 BITSAT MATHEMATICS PAPER III. For the followig liear programmig problem : miimize z = + y subject to the costraits + y, + y 8, y, 0, the solutio is (0, ) ad (, ) (0, ) ad ( /, ) (0, ) ad (, ) (d) (0, ) ad (, ). Sectio-wise epediture of a State Govt. is show i the give figure. The epediture icurred o trasport is % 0% % (d) %. If the covariace betwee ad y is ad the variace of ad y are ad 9 respectively, the the coefficiet of correlatio betwee ad y is (d) 0.9. The mea ad variace of a biomial distributio are ad respectively, the the probability of gettig eactly si successes i this distributio is C C C (d) C. I a etrace test there are multiple choice questios. There are four possible aswers to each questio of which oe is correct. The probability that a studet kows the aswer to a questio is 90%. If he gets the correct aswer to a questio, the the probability that he was guesg, is (d) 9. If the product of three terms of G.P. is. If 8 added to first ad added to secod term, so that umber may be i A.P., the the umbers are,, 8, 8,,, (d) Noe of these

2 7. Let a relatio R be defied by R = {(, ); (, ); (, ); (7, ); (, 7)} the R or is {(, ), (, ), (, 7), (7, ), (7, 7), (, )} {(, ), (, ), (7, 7), (, )} {(, ), (, ), (, )} (d) Noe of these 8. Let U be the uiversal set ad A B C = U. The {( A B) ( B C) ( C A) } is equal to A B C A ( B C) A B C (d) A ( B C) 9. If ( ) log ( ) the belogs to the iterval log (, ] (, ] ( c) [,+ ) (d) Noe of these. If =, the = + ( ) / (d) /. The value of p for which both the roots of the equatio 0 p + ( p + p ) are less tha, lies i ( /, ), ) ( (, / ) (d) (, ). Out of white, 9 black ad 7 red balls, the umber of ways i which selectio of oe or more balls ca be made, is (d) 89!! 7! = e e e (d) e. C. 9 C + C. 9 C + C. 9 C + C. 9 C + C. 9 C + C = 9 C + the = a) 8 b) 8 c) 8 d) 8. The values of lyig betwee ad = π/ satisfyig 0, are + + cos + cos cos = a) π 7π, b) 7π π, c) π π, π d)

3 . If A is ay square matri of order. Observe the followig list List I List II A) adj A ) A A B) adj (adj A) ) A ( ) C) )adj A) - ) A ( ) D) adj(adj A) ) A a) A ; ;B ; C ; D b) A ; B ; C ; D c) A ; B ; C ; D d) A ; B ; C ; D ) A 7. The value of c i Lagrage s mea value theorem for f() = ( a) m ( b) i [a, b] is a) mb a m + + b) ma b m + + c). A a b m + 8. If A + B + C = 70 o, the cos A + cos B + cos C + A B C = 0 (d) 9. If cos α + α + K α =, the K = 0. If ta(cos ) = cot, the = (d) + d) a + b ± ± ± (d) Noe of these. I Δ ABC, if s = a + b + c, the the value of = s ( s a) ( s b)( s c) bc bc A cos A ta A (d) Noe of these

4 . A balloo is comig dow at the rate of m/mi. ad its agle of elevatio is o from a poit o the groud which has bee reduced to 0 o after miutes. Balloo will be o the groud at a distace of how may meters from the observer 0 m 0 ( + ) m ( ) m + (d) Noe of these. The perpedicular distace from A(,, ) to BC where B = (,, ), C = (0,, ) is a) 7 b) 7 c) 7. If I is the cetre of a circle iscribed i a ΔABC, the BC IA + CA IB + AB IC = a) 0 b) IA + IB + IC c) IA + IB+ IC d) d) ( IA + IB + IC ). A straight lie passes through a fied poit ( h, k). The locus of the foot of perpedicular o it draw from the origi is + y h ky + y + h + ky c) + y + h ky (d) Noe of these. The area (i square uits) of the quadrilateral formed by the two pairs of lies lm l is l m y ( l + my ) ad m y + ( l my ) lm lm 7. The locus of the middle poits of chords of the circle + y y which passes through the origi, is (d) lm + y + + y + y + y + y + y (d) + y y 8. The locus of the cetres of the circles which touch eterally the circles + y = a ad +, will be y = a y a + 9a + y a + 9a y + a + 9a (d) + y + a + 9a 9. The equatio of the commo taget of the parabolas = 8 y ad y =, is + y = + y + + y = (d) + y +

5 0. The equatio of the taget to the ellipse = o + y makig a agle of 0 with -ais is y + 7 y 7 y ± 7 (d) Noe of these. The reciprocal of the eccetricity of rectagular hyperbola, is (d). If three mutually perpedicular lies have directio coes l, m, ),( l, m, ) ad ( l, m, ), the the lie havig directio coes l + l + l, m m + m make a agle of... with each other (d) 90 ( + ad + +. A poit moves i such a way that the sum of its distace from y-plae ad yzplae remais equal to its distace from z-plae. The locus of the poit is y + z = + y z y + z (d) y z =. If y cos + cos y = π, the y (0 ) is π 0 (d) π. The slope of a curve at ay poit is the reciprocal of twice the ordiate at the poit ad it passes though the poit (, ). The equatio of the curve is = y + y = y = + (d) = y. The differetial equatio of all circles i the first quadrat which touch the coordiate aes is of order (d) Noe of these 7. The area eclosed betwee the curve y = loge ( + e) ad the co-ordiate aes is (d) π 8. log d = 0 π log log log π (d) log 9. d + 7 = = d + 7 equals 7 (d) 0

6 0. ( ) / d is equal to / + c / + c / + + c (d) Noe of these (log ) + (log ). d is equal to e + c + (log ) + c (d) c + c + log (log ) A fuctio f from the set of atural umbers to itegers defied by., whe is odd f ( ) =, whe is eve, is Oe-oe but ot oto Oto but ot oe-oe Oe-oe ad oto both (d) Neither oe-oe or oto 0 / ( + ) e lim equals π / 0 / e (d) e / log [ ] [ ]. lim, N, ([ ] deotes greatest iteger less tha or equal to ) Has value Has value 0 Has value. Fuctio y = is ot differetiable for + (d) Does ot eist < =, > (d) Noe of these KEY: - b b c b b b a c c d -0 d c c a b c a b b b -0 b b a a a a d a b c -0 c a c b c a c a d a - b c d a b

Mathematics Extension 1

Mathematics Extension 1 016 Bored of Studies Trial Eamiatios Mathematics Etesio 1 3 rd ctober 016 Geeral Istructios Total Marks 70 Readig time 5 miutes Workig time hours Write usig black or blue pe Black pe is preferred Board-approved