(C) x 3 + y 3 = 2(x 2 + y 2 ) (D) x y 2 (A) (10)! (B) (11)! (C) (10)! + 1 (D) (11)! 1. n in the expansion of 2 (A) 15 (B) 45 (C) 55 (D) 56

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Download "(C) x 3 + y 3 = 2(x 2 + y 2 ) (D) x y 2 (A) (10)! (B) (11)! (C) (10)! + 1 (D) (11)! 1. n in the expansion of 2 (A) 15 (B) 45 (C) 55 (D) 56"

Philomena Hamilton
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1 Cocep rackig paper-7 (ST+BT) Q. If 60 a = ad 60 b = 5 he he value of SINGLE OPTION CORRECT a b ( b) equals (D) Time-5hrs 0mis. Q. ( + x) ( + x + x ) ( + x + x + x )... ( + x + x x 00 ) whe wrie i he ascedig power of x he he highes expoe of x is (D) oe Q. If x + y = cos4 ad x y = 4 si he x 4 + y 4 = 9 x y 6 x + y = (x + y ) (D) x y 0 Q.4 The sum k k! equals k (0)! ()! (0)! + (D) ()! Q.5 I a riagle ABC, R(b + c) = a bc where R is he circumradius of he riagle. The he riagle is Isosceles bu o righ righ bu o isosceles righ isosceles (D) equilaeral Q.6 If he coefficies of x 7 & x 8 x i he expasio of are equal, he he value of is (D) 56 Q.7 If ab = si A cosa cos si A ( )cos A A he a(a + B) equals ( )cos A si A si A ( )cos A (D) si A ( )cos A Q.8 Le 5 6 = p + f where N ad p N ad 0 < f < he he value of, f f + pf p is a aural umber a prime umber a egaive ieger (D) are irraioal umber Q.9 Cosider he riagle picured as show. If 0 < < / he he umber of iegral values of c is 5 4 (D) 5 Q.0 The geeral soluio of he equaio a + a = is give by : = = ( + ) = (6 + ) (D) = Q. The sum o ifiiy of he series is equal o : 5/ (D) oe of hese Q. Give a + a + cosec F HG ( a x) I K J = 0 he, which of he followig holds good?

2 Cocep rackig paper-7 (ST+BT) Time-5hrs 0mis. a = ; x I a = ; x I a R ; x (D) a, x are fiie bu o possible o fid x x Q. I he expasio of / / /, he erm which does o coai x is x x x x 0 C 0 0 C 7 0 C 4 (D) oe Q.4 I a acue agled riagle ABC, poi D, E ad F are he fee of he perpediculars from A, B ad C oo BC, AC ad AB respecively. H is he iersecio of AD ad BE. If si A = /5 ad BC = 9, he legh of AH is (D) 54 Q.5 A riagle has sides 6, 7, 8. The lie hrough is icere parallel o he shores side is draw o mee he oher wo sides a P ad Q. The legh of he segme PQ is (D) 9 Q.6 I he expasio of ( + x + x x 7 )( + x + x x 4 ), he coefficie of x 8 is (D) 405 Q.7 Triagle ABC has BC = ad AC =. The maximum possible value of he agle A is (D) 6 4 Q.8 If he cosa erm of he biomial expasio x is 60, he is equal o x (D) 0 Q.9 Number of pricipal soluio(s) of he equaio, si x 6si x 4 6, is (D) 4 Q.0 Triagle ABC is righ agled a A. The pois P ad Q are o he hypoeuse BC such ha BP = PQ = QC. If AP = ad AQ = 4 he he legh BC is equal o (D) 54 Q. The se of agles bwee 0 ad saisfyig he equaio 4 cos cos = 0 is RST RST 5 9,,, 5 9,, UVW UVW 7 7,,, 7 9 (D),,, Q. If ( + x x ) 45 = a 0 + a x + a x +... he a 0 a + a a +... eds wih 7 (D) 9 Q. Le ABC be a riagle righ agled a C. The value of RST log log bc bc a log a log (D) / cb cb a a UVW (b + c, c b ) equals

3 Cocep rackig paper-7 (ST+BT) Time-5hrs 0mis. Q.4 I he expasio of q p 7 p 0 q, here is a erm similar o pq, he ha erm is equal o 0 pq 5 pq 0 pq (D) 45 pq Q.5 I a riagle ABC, agle B < agle C ad he values of B ad C saisfy he equaio a x - k ( + a x) = 0 where (0 < k < ). The he measure of agle A is : / / / (D) /4 Q.6 The coefficie of x 49 i he expasio of (x ) x x... x 49 is equal o 50 + ve coefficie of x ve coefficie of x (D) 49 Q.7 I a isosceles riagle ABC, AB = AC, BAC = 08 ad BD AD risecs BAC ad BD > DC. The raio is DC 5 (D) 5 Q.8 The sum S = 0 C + 0 C + 0 C C 0 is equal o (D) 0 Q.9 I ABC if a = 8, b = 9, c = 0, he he value of a C si B 4 is 8 (D) 5 Q.0 The umber of soluio of he equaio, cos( r x) = 0 lyig i (0, ) is : 5 r 5 (D) more ha 5 Q. If cos = cos he a co has he value equal o {where, (0, )} cos (D) Q. The umber of values of ' r ' saisfyig he equaio, 9 9 C r C = 9 C C r is (D) 4 Q. I a riagle ABC, CD is he bisecor of he agle C. If cos C has he value ad l (CD) = 6, he has he value equal o a b r r (D) oe

4 Cocep rackig paper-7 (ST+BT) Time-5hrs 0mis. Q.4 Le a, b, c be he hree sides of a riagle he he quadraic equaio b x + (b + c a )x + c = 0 has boh imagiary roos boh posiive roos boh egaive roos (D) oe posiive ad oe egaive roos. Q.5 If is divided by 49, he he remaider is 5 5 (D) 0 Q.6 If a si x + b cos x = ad a + b = (a, b > 0), he cosider he followig saemes: I si x = a II a x = a/b III a x = b oly III is false oly I is rue All of I, II, III mus be rue (D) Noe of I, II or III is correc. Q.7 The erm idepede of 'x' i he expasio of 9 x x biomial co-efficie. The '' is 8, x > 0, is imes he correspodig (D) Q.8 Wih usual oaios, i a riagle ABC, a cos(b C) + b cos(c A) + c cos(a B) is equal o abc R abc 4R 4abc R abc (D) R Q.9 Greaes erm i he biomial expasio of (a + x) 9 whe a = & x = is : Q.40 If rd & 4 h 4 h & 5 h oly 4 h (D) oly 5 h cos x cos x 7 si x = for some agle x, 0 x, he he value of si x 5 (D) for some x, is Q.4 The sum of he biomial coefficies of x x is equal o 56. The cosa erm i he expasio is (D) oe Q.4 Wih usual oaios i a riagle ABC, ( I I ) ( I I ) ( I I ) has he value equal o R r R r 4R r (D) 6R r Q.4 The geeral soluio of he rigoomeric equaio a x + a x + a x = a x a x a x is x = ± x = (D) x = where I Q.44 The se of values of x saisfyig simulaeously he iequaliies log x 8 x log x > 0 is : a ui se a empy se a ifiie se (D) a se cosisig of exacly wo elemes. 0 ad

5 Cocep rackig paper-7 (ST+BT) Time-5hrs 0mis. Q.45 Give ( x + 5x 0x ) ( + x) = + a x + a x +... ad ha a = a he he value of is 6 5 (D) Q.46 The graphs of y = si x, y = cos x, y = a x ad y = cosec x are draw o he same axes from 0 o /. A verical lie is draw hrough he poi where he graphs of y = cos x ad y = a x cross, iersecig he oher wo graphs a pois A ad B. The legh of he lie segme AB is: 5 (D) 5 Q.47 A secor OABO of ceral agle is cosruced i a circle wih cere O ad of radius 6. The radius of he circle ha is circumscribed abou he riagle OAB, is 6 cos 6 sec (cos + ) (D) sec Q.48 The expasio of ( + x) has cosecuive erms wih coefficies i he raio : : ad ca be wrie i he form C k ; C k + : C k +. The sum of all possible values of ( + k) is 8 8 (D) Q.49 Number of raioal erms i he expasio of 4 00 is : (D) 8 Q.50 Le a b c be he leghs of he sides of a riagle T. If a + b < c he which oe of he followig mus be rue? All agles of T are acue. Some agle of T is obuse. Oe agle of T is a righ agle. (D) No such riagle ca exis. Q.5 The coefficie of he middle erm i he biomial expasio i powers of x of ( + x) 4 ad of ( x) 6 is he same if equals (D) 5 Q.5 60 is he raio of wo relaive prime posiive iegers m ad. The value of k k k (k ) k (m + ) is equal o (D) 7 Q.5 If C 0, C, C... deoes he combiaorial coefficies i he expasio of ( + x) 0, he he value of C0 C C C0... is equal o (D) Q.54 Le riagle ABC be a isosceles riagle wih AB = AC. Suppose ha he agle bisecor of is agle B mees he side AC a a poi D ad ha BC = BD + AD. Measure of he agle A i degrees, is (D) 0 Q.55 The remaider, whe (5 + ) is divided by 9, is (D) 8

6 Cocep rackig paper-7 (ST+BT) Time-5hrs 0mis. Q.56 As show i he figure AD is he aliude o BC ad AD produced mees he circumcircle of ABC a P where DP = x. Similarly EQ = y ad FR = z. If a, b, c respecively deoes he sides BC, CA ad AB he has he value equal o aa + ab + ac cosa + cosb + cosc Q.57 I a ABC, he value of a cos A b cos B c cos C a b c r R R r a x b y c z coa + cob + coc (D) coseca + cosecb + cosecc R r Q.58 Geeral soluio of he equaio sec x = + cos x + cos x + cos x +..., is + where is a ieger. ± ± 6 is equal o : Q.60 Wih usual oaio i a ABC, if R = k r r r r r r r r r r r r (D) r R /4 (D) 4 Q.6 If N & is eve, he (D) + 6 where k has he value equal o... =. ( )!! ( )! 5! ( 5)! ( )!!!! Q.6 The value of co x + co (60º + x) + co (0º + x) is equal o : (D) oe of hese 9a x co x a x a x (D) ax a x Q.6 The remaider, if is divided by 5 is 0 (D) Q.64 Le s, s, s... ad,,... are wo arihmeic sequeces such ha s = 0; s = ad 0 5 s = i i i i. The he value of s s 8/ / 9/8 (D) is x 5x 4 4 Q.65 I he expasio of he sum of he biomial coefficies is 64 ad he erm wih he greaes biomial coefficie exceeds he hird erm by ( ), he he value of x mus be 0 (D) Q.66 For every x R he value of he expressio y = 8 x + x cos x + cos x is ever less ha 0 (D)

7 Cocep rackig paper-7 (ST+BT) Time-5hrs 0mis. Q.67 If he icircle of he ABC ouches is sides respecively a L, M ad N ad if x, y, z be he circumradii of he riagles MIN, NIL ad LIM where I is he icere he he produc xyz is equal o : R r r R R r (D) r R Q.68 Sum of all he raioal erms i he expasio of 4 4, is (D) oe Q.69 ABC is a acue agled riagle wih circumcere 'O' orhocere H. If AO = AH he he measure of he agle A is 5 (D) 6 4 Q.70 If be a acue agle saisfyig he equaio 8 cos + 8 sec = 65, he he value of cos is equal o 8 (D) 4 Q.7 Le f (x) = cos x + cos x + cos x. Number of values of x [0, ] for which f (x) equals he smalles posiive ieger is 4 5 (D) 6 Q.7 Le L ad M be he respecive iersecios of he ieral ad exeral agle bisecors of he riagle ABC a C ad he side AB produced. If CL = CM, he he value of (a + b ) is (where a ad b have heir usual meaigs) R R 4R (D) 4 R Q.7 Oe side of a recagular piece of paper is 6 cm, he adjace sides beig loger ha 6 cms. Oe corer of he paper is folded so ha i ses o he opposie loger side. If he legh of he crease is l cms ad i makes a agle wih he log side as show, he l is si cos si cos si (D) 6 si cos Q.74,, ad are he smalles posiive agles i ascedig order of magiude which have heir sies equal o he posiive quaiy k. The value of 4 si + si + si + si is equal o : k k k (D) k Q.75 Co-efficie of i he expasio of, ( + p) m + ( + p) m ( + q) + ( + p) m ( + q) +... ( + q) m where q ad p q is : m C p q p q m m m C p q p q

8 Cocep rackig paper-7 (ST+BT) m C p q p q (D) m m m C p q p q Time-5hrs 0mis. Q.76 Le a, N is a A.P. wih commo differece 'd' ad all whose erms are o-zero. If approaches ifiiy, he he sum... will approach a a a a a a a d a d a d (D) a d Q.77 If () 7 + () 7 whe divided by 6 leaves he remaider 0 (D) 4 Q.78 I which oe of he followig iervals he iequaliy, si x < cos x < a x < co x ca hold good? 0,, 4 4 5, 4 Q.79 I a ABC if b + c = a he co B co C has he value equal o : 4 (D) 7 (D), 4 Q.80 The las wo digis of he umber 400 are : (D) 0 Q.8 Le f, g, h be he leghs of he perpediculars from he circumcere of he ABC o he sides a, b ad c respecively. If a b f c g h = a b c he he value of is : f g h /4 / (D) Q.8 If ( + x + x²) 5 = a 0 + a x + a x² a 50. x 50 he a 0 + a + a a 50 is : eve odd & of he form odd & of he form ( ) (D) odd & of he form ( + ) Q.8 For a, b, c o-zero, real disic, he equaio, (a + b ) x b (a + c) x + b + c = 0 has o-zero real roos. Oe of hese roos is also he roo of he equaio : a x a (b c) x + b c = 0 a x + a (c b) x b c = 0 (b + c ) x a (b + c) x + a = 0 (D) (b c )x + a (b c) x a = 0 Q.84 If f (x) = a si x + c, where a ad c are real umbers ad a > 0, he f (x) < 0 x R c < a c > a a < c < a (D) c < a Q.85 The larges real value for x such ha 4 k0 4k k 5 x (4 k)! k! (D) 5 8 is Q.86 Le f (x) = 4 cosec x cosec x. The sum of all he soluios of f (x) = 0 i si x cos x cosec x(cosec x si x) co x si x

9 Cocep rackig paper-7 (ST+BT) [0, 00] is (D) 5050 Time-5hrs 0mis. Q.87 I a ABC if b = a ad C = 0 0 he he measure of he agle A is (D) 05 0 Q.88 5 p 4p I a ABC, a = a =, b = a, c = a such ha a p+ = a p a p p p 5 where p =, he r = r r = r r = r (D) r = r Q.89 ( + ) ( + ) ( + 5)... (4 ) is equal o : ( 4)!. ( )! ( )! ( 4)!!. ( )! ( )! p ( 4)!! ( )! ( )! (D) ( 4 )!!! ( )! Q.90 If a x + a y = 5 ad co x + co y = 0, he he value of a(x + y) is (D) 00 x 007 Q.9 Number of iegral values of x he iequaliy log 0 0 holds rue, is x (D) 008 Q.9 The sum of he roos (real or complex) of he equaio 00 x 00 + x = 0 is (D) 500 Q.9 For each aural umber k, le C k deoes he circle wih radius k ceimeers ad cere a he origi. O he circle C k, a paricle moves k ceimeers i he couer- clockwise direcio. Afer compleig is moio o C k, he paricle moves o C k+ i he radial direcio. The moio of he paricle coiues i his maer.the paricle sars a (, 0).If he paricle crosses he posiive direcio of he x- axis for he firs ime o he circle C he equal o (D) 9 Q.94 If O is he circumcere of he ABC ad R, R ad R are he radii of he circumcircles of riagles OBC, OCA ad OAB respecively he a b c R R a b c a R b c has he value equal o: R R 4 R (D) 4R Q.95 I a righ agled riagle he hypoeuse is imes he perpedicular draw from he opposie verex. The he oher acue agles of he riagle are ad 6 Q.96 The expressio 8 ad 8 4x 4x 4 ad (D) 5 ad 0 4x is a polyomial i x of degree (D)

10 Cocep rackig paper-7 (ST+BT) Time-5hrs 0mis. Q.97 The sum 4 is equal o 4 /4 / /8 (D) / Q.98 Le X be he se of all soluios o he equaio cos x si x = 0. Number of real umbers x coaied by X i he ierval (0 < x < ), is 0 (D) more ha Q.99 The medias of a ABC are 9 cm, cm ad 5 cm respecively. The he area of he riagle is 96 sq cm 84 sq cm 7 sq cm (D) 60 sq cm a / Q.00 If he secod erm of he expasio a is 4a 5/ he he value of a 4 (D) 6 Q.0 If r, r, r be he radii of excircles of he riagle ABC, he A co A B co co A r r r C C is equal o : A a (D) a Q.0 The value of (4 C + 4 C + 4 C ) is (D) 5 Q.0 The sum of he coefficies of all he eve powers of x i he expasio of (x x + ) is (D) oe is 00 Q.04 The sum k k 4 k k is equal o (D) oe Q.05 If x, y ad z are he disaces of icere from he verices of he riagle ABC respecively he a b c x y z is equal o A A A A a co a (D) si Q.06 Las hree digis of he umber N = are (D) 000 Q.07 A circle of radius r is iscribed i a square. The mid pois of sides of he square have bee coeced by lie segme ad a ew square resuled. The sides of he resulig square were also coeced by segmes so ha a ew square was obaied ad so o, he he radius of he circle iscribed i he h square is

11 Cocep rackig paper-7 (ST+BT) Time-5hrs 0mis. r r 5 r (D) r Q.08 If i a ABC, cosa cosb + sia sib sic = he, he saeme which is icorrec, is ABC is isosceles bu o righ agled ABC is acue agled ABC is righ agled (D) leas agle of he riagle is 4 Q.09 The produc of he arihmeic mea of he leghs of he sides of a riagle ad harmoic mea of he leghs of he aliudes of he riagle is equal o : (D) 4 [ where is he area of he riagle ABC ] Q.0 If si x + 7 cos px = 9 has aleas oe soluio he p mus be a odd ieger a eve ieger a raioal umber (D) a irraioal umber Q. I a riagle ABC, ABC = 0, AB = ad BC = 4. If perpedicular cosruced o he side AB a A ad o he side BC a C mees a D he CD is equal o (D) Q. If abcd = where a, b, c, d are posiive reals he he miimum value of a + b + c + d + ab + ac + ad + bc + bd + cd is 6 0 (D) 0 Q. A riagle has base 0 cm log ad he base agles of 50 ad 70. If he perimeer of he riagle is x + y cos z where z (0, 90) he he value of x + y + z equals (D) 40 Q.4 The posiive value of 'a' so ha he coefficie of x 5 is equal o ha of x 5 i he expasio of 0 a x x is (D) Q.5 A sequece of equilaeral riagles is draw. The aliude of each is imes he aliude of he precedig riagle, he differece bewee he area of he firs riagle ad he sixh riagle is 968 The perimeer of he firs riagle is 0 6 (D) 8 square ui. Q.6 Le ABC be a riagle wih BAC = ad AB = x such ha (AB)(AC) =. If x varies he he loges possible legh of he agle bisecor AD equals / / / (D) / Q.7 If a, b ad c are hree cosecuive posiive erms of a G.P. he he graph of y = ax + bx + c is a curve ha iersecs he x-axis a wo disic pois. eirely below he x-axis. eirely above he x-axis. (D) age o he x-axis. Q.8 Se of value of r for which, 8 C r +. 8 C r + 8 C r 0 C coais :

12 Cocep rackig paper-7 (ST+BT) Time-5hrs 0mis. 4 elemes 5 elemes 7 elemes (D) 0 elemes Q.9 For which posiive iegers is he raio, k k k k a ieger? odd oly eve oly = + 6k oly, where k 0 ad k I (D) = + k, ieger k 0 [COMPREHENSION TYPE] Paragraph for Quesio Nos. 4 o 4 A aliude BD ad a bisecor BE are draw i he riagle ABC from he verex B. I is kow ha he legh of side AC =, ad he magiudes of he agles BEC, ABD, ABE, BAC form a arihmeic progressio. Q.0 The area of circle circumscribig ABC is 8 4 (D) Q. Le 'O' be he circumcere of ABC, he radius of circle iscribed i BOC is 8 4 (D) Q. Le B' be he image of poi B wih respec o side AC of ABC, he he legh BB' is equal o 4 4 Paragraph for Quesio Nos. 44 o 46 Cosider he biomial expasio R = ( + x) = I + f, where I is he iegral par of R ad 'f' is he fracioal par of R, N. Also he sum of he coefficies of R is 656. Q. The value of ( + R Rf) for x = equals (D) 0 (D) Q.4 If i h erms is he greaes erm for x =, he ' i ' equals (D) 7 Q.5 If k h erms is havig greaes coefficie he sum of all possible value(s) of k is 6 7 (D) Paragraph for Quesio Nos. 47 o 49 Le a m (m =,,...,p) be he possible iegral values of a for which he graphs of f (x) = ax + bx + b ad g (x) = 5x bx a mees a some poi for all real values of b. Le p r = ( r a m ) ad S = r, N. m Q.6 The miimum possible value of a is r

13 Cocep rackig paper-7 (ST+BT) Time-5hrs 0mis (D) 4 Q.7 The sum of values of for which S vaishes is (D) 5 Q.8 The value of is equal o r5 r 6 5 (D) 8 Paragraph for quesio os. 50 o 5 Cosider a riagle ABC wih b =. Aliude from he verex B mees he opposie side i D, which divides AC ierally i he raio :. A circle of radius passes hrough he poi A ad D ad ouches he circumcircle of he riagle BCD a D. Q.9 If E is he cere of he circle wih radius he agle EDA equals si 5 4 si 4 si 4 5 (D) si 6 Q.0 If F is he circumcere of he riagle BDC he which oe of he followig does o hold good? 5 FCD = si 4 riagle DFC is a isosceles riagle Q. If R is he circumradius of he ABC, he R equal FDC = cos 4 (D) Area of ADE = (/4) h of he area of DBC [REASONING TYPE] Q. Le ABC be a acue riagle whose orhocere is a H. Aliude from A is produced o mee he circumcircle of he riagle ABC a D. Saeme-: The disace HD = 4R cos B cos C where R is he circumradius of he riagle ABC. because Saeme-: Image of orhocere H i ay side of a acue riagle lies o is circumcircle. Saeme- is rue, saeme- is rue ad saeme- is correc explaaio for saeme-. Saeme- is rue, saeme- is rue ad saeme- is NOT he correc explaaio for saeme-. Saeme- is rue, saeme- is false. (D) Saeme- is false, saeme- is rue. Saeme- is rue, saeme- is false. (D) Saeme- is false, saeme- is rue. Q. Le ABC be a acue agle riagle ad D, E, F are he fee of he perpedicular from A, B, C o he sides BC, CA ad AB respecively. Saeme- : Orhocere of riagle ABC is he Icere of riagle DEF. because Saeme- : Triagle DEF is he exceral riagle of riagle ABC.

14 Cocep rackig paper-7 (ST+BT) Time-5hrs 0mis. Saeme- is rue, saeme- is rue ad saeme- is correc explaaio for saeme-. Saeme- is rue, saeme- is rue ad saeme- is NOT he correc explaaio for saeme-. Saeme- is rue, saeme- is false. (D) Saeme- is false, saeme- is rue. Q.4 Saeme-: Circumradius ad iradius of a riagle ca o be ad 8 respecively. because Saeme-: Circumradius (iradius) Saeme- is rue, saeme- is rue ad saeme- is correc explaaio for saeme-. Saeme- is rue, saeme- is rue ad saeme- is NOT he correc explaaio for saeme-. Saeme- is rue, saeme- is false. (D) Saeme- is false, saeme- is rue. Q.5 I he expasio of x [MULTIPLE OBJECTIVE TYPE] log. here appears a erm wih he power x here does o appear a erm wih he power x here appears a erm wih he power x (D) he raio of he co-efficie of x o ha of x is / x : cos x cos x cos x cos 4x cos 5x cos 6x cos 7x Q.6 Le y = he which of he followig hold si x si x si x si 4x si 5x si 6x si 7x good? The value of y whe x = /8 is o defied. The value of y whe x = /6 is. The value of y whe x = / is. (D) The value of y whe x = /48 is. Q.7 Give ha si = si, he which of he followig agles will be equal o cos? cos cos cos (D) cos Q.8 If y = log 7 a (x + x + a + ) is defied x R, he possible iegral value(s) of a is/are 4 (D) 5 Q.9 If i is kow ha he hird erm of he biomial expasio x / 00 (D) 5 Q.40 If si(x y), si x ad si (x + y) are i H.P., he si x. sec y = x x log 0 is 0 6 he x is equal o (D) Q.4 Le si x + cos y = ad si y + cos x = 4 he x + y = (4 + )/, I x + y = ( + )/, I x ad y ca be he wo o righ agles of a -4-5 riagle wih x > y. (D) x ad y ca be he wo o righ agles of a -4-5 riagle wih y > x. Q.4 If si = si cos he cos has he value equal o :

15 Cocep rackig paper-7 (ST+BT) Time-5hrs 0mis. + si si 4 si (D) cos 4 Q.4 The equaio cosec x + sec x = has o soluio i 0, a soluio i 4, 4 o soluio i, (D) a soluio i 4, 4 Q.44 I a ABC, followig relaios hold good. I which case(s) he riagle is a righ agled riagle? (Assume all symbols have heir usual meaig) r + r = r r a + b + c = 8 R If he diameer of a excircle be equal o he perimeer of he riagle. (D) R = r r Q.45 Le ( + x ) ( + x) = A 0 + A x + A x +... If A 0, A, A are i A.P. he he value of is : 5 (D) 7 Q.46 Two parallel chords are draw o he same side of he cere of a circle of radius R. I is foud ha hey subed a agle of ad a he cere of he circle. The perpedicular disace bewee he chords is R si si cos cos R cos cos R (D) R si si 4 4 Q.47 The equaio si = a( ) + cos a holds rue if = + = + = ad R (D) = ad R ( is a ieger) Q.48 Cosider he biomial expasio of x 4 x, N. where he erms of he expasio are wrie i decreasig powers of x. If he coefficies of he firs hree erms form a arihmeic progressio he he saeme(s) which hold good is/are oal umber of erms i he expasio of he biomial is 8 umber of erms i he expasio wih iegral power of x is here is o erm i he expasio which is idepede of x (D) fourh ad fifh are he middle erms of he expasio Q.49 I a ABC, a semicircle is iscribed, whose diameer lies o he side c. If x is he legh of he agle bisecor hrough agle C he he radius of he semicircle is abc 4R (si A si B) x

16 Cocep rackig paper-7 (ST+BT) Time-5hrs 0mis. C s(s a)(s b)(s c) x si (D) s Where is he area of he riagle ABC ad 's' is semiperimeer. a cos A bcos B c cos C Q.49 A riagle ABC has he feaure, = he he correc saeme(s) is/are : a b c riagle is righ agled R = r a = b = c Q.50 If 9 80 I is a odd ieger si A (D) = si A = + f where I, are iegers ad 0 < f <, he I is a eve ieger (I + f) ( f) = (D) f = 9 80 Q.5 x, x are he roos of he equaio x x + A = 0; x, x 4 are roos of he equaio x x + B = 0, such ha x, x, x, x 4 form a icreasig G.P., he A = B = x + x = 5 (D) x + x 4 = 0

S n. = n. Sum of first n terms of an A. P is

S n. = n. Sum of first n terms of an A. P is PROGREION I his secio we discuss hree impora series amely ) Arihmeic Progressio (A.P), ) Geomeric Progressio (G.P), ad 3) Harmoic Progressio (H.P) Which are very widely used i biological scieces ad humaiies.