ARITHMETIC. Centres at:

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1 entres t: ================================================================================== RITHMETI () () 3 is equl to 5. The gretest numer mong , 3 is () 3 () numer N is positive three-digit numer If is t its hundred's plce nd y is t its unit's plce, then the numer N-00-y is lwys divisile y () 8 () 9 0. If m nd n re two integers such tht m = n - n, then (m -m) is lwys divisile y () 9 () If the digit in the unit s plce of two digit numer is hlved nd the digit in the ten s plce is douled, the numer thus otined is equl to the numer otined y interchnging the digits. Which of the following is definitely true? () igits in the unit s plce nd the ten s plce re equl () Sum of the digits is two-digit numer igit in the Unit s plce is hlf of the digit in the ten s plce, igit in the Unit s plce is twice the digit in the ten s plce 6. When certin positive integer P is divided y nother positive integer, the reminder is r, when second positive integer Q is divided y the sme integer, the reminder is r, nd when (P + Q) is divided y the sme divisor, the reminders is r 3. Then the divisor my e () (r + r + r 3 ) () (r r +r 3 ) (r + r r 3 ) (r r r 3 ) 7. When 35 percent of numer is dded to nother numer, the second numer increses y 0 percent. Wht is the rtio etween the second numer nd the first numer? () : 7 () 7 : 8 : 5 t indequte 8. In set of 5 numers the sum of two of these numers is 6 more thn the sum of the remining three numers, wheres the sum of these three numers is two times one of those two numers. Wht definitely is one of those two numers? () 8 () 6 t indequte 9. In n rithmetic progression, if p th term is q nd q th term is p, then the sum of first pq terms of the rithmetic progression is equl to () ( pq ) () p q ( pq ) q p 0. ought pples nd ornges nd spend ` 0 for the pples nd ` 6 for ornges. The verge cost of pple is.75 times the cost of ornges. Find the no. of pples? () 7 () In n engineering college the verge slry of ll engineering grdutes from mechnicl trde is `.5 lkhs per nnum nd tht of the engineering grdutes from electronic trde is ` 3.56 lcs per nnum. The verge slry of ll mechnicl nd electronics grdutes is ` 3. lcs per nnum. Find the lest numer of electronic grdutes pssing out from this institute. () 55 () 67 None of these cnnot e determinded. pinter is pid ` rupees for pinting every 0 sq. metre of wll nd ` y for pinting every etr meter during one week. He pinted 0m on Mondy, 3m on Tuesdy, m on Wednesdy, m on Thursdy nd m on Fridy. Wht is his verge dily erning in rupees for the five dys of the week. () + y () + y 8y + +.6y 5 3. solution of sugr syrup hs 5% sugr. nother solution hs 5% sugr. How mny liters of the second solution must e dded to 0 liters of the first solution to mke solution of 0% sugr? () 5 litres () 0 litres 6 litres litres

2 () , 3 () 3 5 () 3 () N N 00 y () (). m n m = n - n, y 8 6 pq q p () ( pq ) () p q ( pq ) q p () 7 () (m m) () 9 () 6 8 () 55 P Q y r r P + Q r 3 (r + r + r 3 ) (r r + r 3 ) (r + r r 3 ) (r r r 3 ) () + y 8y + 5 () + y +.6y () 5 () 0 6

3 entres t: ==================================================================================. /3 nd / prts of two cns of equl. The sum of first 0 terms of the series volume re filled with milk. The cns re then filled to their cpcity with wter nd 8... is - the miture of the two cns re poured in () 3 () 3 ig pot. The rtio of milk nd the wter in 8 8 the pot is () 7 : 7 () : 3 3. Two numers nd re such tht their 8 : 5 : 3 Geometric men is 0% less thn their 5. How mny terms of the series rithmetic men. Find the rtio etween mke the sum equl to 0. the numers. () : () : 9 () 0 () 9 : 3 3 :. 0 meters long trin is running with 6. Find the sum of ll integers of 3 digits speed of 60kmph. In wht time will it pss numers tht re divisile y 7. mn who is running t 6 kmph in the () () direction opposite to tht in which the trin is going? 7. Sit strted usiness investing ` 5,000 () 6 seconds () 0 seconds Neet joined her fter si months with 7 seconds 9 seconds ` 80,000 nd Rmesh joined them with `,0,000 fter one yer. Profit erned t the end of two yers fter Sit strted the usiness should e distriuted mong Sit, Neet nd Rmesh respectively in wht rtio? () 3 : : () : 7 : 5 : 3 : 3 5 : 7 : 8. Four Milkmen rented psture. grzed 5 cows for months, grzed cows for months, grzed 8 cows for 6 month nd grzed 6 cows for 5 months. If s shre of rent is `,00. Wht is s shre of rent? () ` 980 () ` 836 ` 08 ` person lent out certin sum on S.I. nd the sme sum on.i. t certin rte of interest p.. He noticed tht the rtio etween the difference of.i. nd S.I. in 3 yrs. nd yrs. is respectively 5:8. The rte of interest is - () 5% () % 6.6% 0% 0. Two equl sums of money re lent t the sme time t 8% nd 7%per nnum S.I. The former is recovered 6 months erlier thn the lter nd the mount in ech cse is ` 560. Wht is the sum? () 380 () person invested certin mount t S.I. t the rte of 6% & erns ` 900 s n interest t the end of 3 yrs. Hd the interest een compounded every yer, how much more interest (ppro.) would he hve erned on the sme mount with sme interest rte fter three yers? () ` 55 () ` 69 ` 7 ` 8 5. hishek nd hnu oth re delers of KML Scooter. The price of KML Scooter is ` 8,000. hishek gives discount of 0% on whole, while hnu gives discount of % on the first ` 0,000 nd 8% on the rest ` 8,000. Wht is the different etween their selling price? () ` 360 () ` 0 ` 50 ` shopkeeper sold cmers t profit of 0% nd 8 cmers t profit of 0%. If he hd sold ll the 0 cmers t profit of 5%, then his profit would hve een reduced y Rs. 36. Wht is the cost price of ech cmer? () ` 80 () ` 30 ` 50 ` chemist hs 0 litres of solution tht is 0 percent nitric cid y volume. He wnts to dilute the solution to percent strength y dding wter. How mny litres of wter must e dded? () 5 () In compny there re 75% skilled workers nd remining re unskilled. 80% of skilled workers nd 0% of unskilled workers re permnent. If the numer of temporry workers is 6, then wht is the numer of totl workers? () 35 () monthly return rilwy ticket costs 5 percent more thn single ticket. week s etension cn e done for the former y pying 5 percent of the monthly ticket s cost. If the money pid for the monthly ticket (with etensions) is ` 8, then the price of the single ticket is? () ` 88 () ` 30 ` 83 ` 6 3

4 () 3 () () 7 : 7 () : 3 () 0 () 9 () : () : 9 : 3 3 : () ()70366 () 6 () KML KML () 3 : : () : 7 : 5,,,, () ` 980 () ` 836 ` 050 () ` 360 () ` 0 ` 50 ` 70 () ` 80 () ` 30 ` 50 ` 50 () 5% () % () 5 () 6 8 () 380 () 0 ` () 35 () () ` 55 () ` 69 ` 7 ` 8 () ` 88 () ` 30 ` 83 ` 6

5 entres t: ================================================================================== 30. The rtio of numer of students ppering 36. tnk is filled in 5 hrs y 3 pipes, nd. for emintion in 998 in the sttes,, The pipe is twice s fst s nd is nd ws 3 : 5 : 6. Net yer if the no. of twice s fst s. How much time will pipe students in these sttes increses y 0%, lone tke to fill the tnk? 0% nd 0% respectively, the rtio in () 05 hrs () 70 hrs sttes nd would e :. Find the no. of 35 hrs 0 hrs students who ppered for em in the stte in 998. () 3 () 5 t indequte 3. Free noteooks were distriuted eqully mong children of clss. The no. of note ooks ech child got ws 8 th of the no. of children. Hd the no. of children een hlved, ech child would hve got 6 note ooks. How mny note ooks were distriuted? () 56 () 5 8 None of these 3. retiler ought 3850 linc pens nd 88 cello pens t the sme price. He sells linc pens in such wy tht he cn uy 650 linc pens with the sle price of 8 linc pens. gin he cn uy only 08 cello pens with the sle price of 65 pens. Wht is the ov erll per cent ge pr of it of the retiler? () 0 () None of these 33. mnufcturer undertkes to supply 000 pieces of prticulr component t ` 5 per piece. ccording to his estimtes, even if 5% fil to pss the qulity tests, he will mke profit of 5%. However s it turned out, 50% of the components were rejected. Wht is the loss of the mnufcturer? () ` 3000 () ` 500 ` 5000 ` men nd 5 women cn finish work in 6 dys. mn cn finish the work in 00 dys. In how mny dys will womn finish the work? () 50 () child cn do piece of work, 5 hours slower thn womn. The child works for 8 hours on the jo nd the womn tkes chnges for 6 hours. In this mnner, 5 3 of the work cn e completed. To complete the jo now, how much time will the womn tke? () 0 hrs () hrs 36 hrs hrs 37. ot hs to trvel upstrem 0km distnce from point X of river to point Y. The totl time tken y the ot in trvelling from point X to Y nd Y to X is minutes & 0 seconds. Wht is the speed of the ot? () 0km/hr () 7.5 km/hr None of these t indequte 38. Si pipes re fitted to wter tnk. Some of these re filling pipes, others re emptying pipes. Ech filling pipes cn fill the tnk in 9 hrs nd ech wste pipe cn empty the tnk in 6 hrs. On opening ll the pipes in the empty tnk is filled in 9 hrs. Find the no. of filling pipes? () () trin cn trvel 0% fster thn cr. oth strt from the point t the sme time nd rech point 75 km wy from t the sme time. On the wy, however, the trin lost out.5 minutes while stopping t the sttions. The speed of the cr is- () 6 km/hr () 56 km/hr 5 km/hr 60 km/hr 0. mn, womn or oy cn do jo in 0 dys, 30 dys or, 60 dys respectively. How mny oys must ssist men nd 8 women to do the work in dys? () 0 oys () 6 oys 8 oys 8 oys. Profit of usiness re distriuted mong three prtner, nd such wy tht times the mount received y is equl to 6 times the mount received y nd times the mount received y. The rtio in which, & received the mount respectively is () 33 : : () 65 : 5 : 8 9 : 7 : 58 3 : :. In milk shop there re three vriety of milk., nd. Milk hs 00% concentrtions of milk. The rtio of milk is to wter in is :5 nd in the it is 3:8 respectively. Sonli purchsed litres of milk nd litres of milk nd mied them. I f she wnted to mke the concentrtion of milk in the miture of purchsed milk to 50%. How mny litres of pure milk she hs needed? () ()

6 , () 3 (), () 05 () X Y X Y Y X 5 8 () () () 56 () 5 8 () () 5 3 () 0 () () 6 () () ` 3000 () ` 500 ` 5000 ` 750 () 50 () () 0 () 36 () 0 () 6 8 8,, () 33 : : () 65 : 5 : 8 9 : 7 : 58 3 : :, () ()

7 entres t: ================================================================================== 3. Gold is 9 times s hevy s wter nd copper 9 times s hevy s wter. The rtio 9. Find QRS in the given figure elow - in which these two metls e mied so tht the miture is 5 times s hevy s wter is : () : 3 () 3 : : : 3. From Jnury, 005 to Jnury, 006, the numer of people enrolled in Medicl Insurnce incresed y 5 percent. If the totl numer of people who hd medicl () 50º () 65º insurnce ws 5 million in Jnury, 70º 75º 006. How mny people to the nerest in 50. is such trepezium, in which million h d helth insurnce on = nd. lso = 5 cm nd Jnury, 005? = 9 cm, if the re of is 35 cm () 7 () 3 then wht will e the length of? Shtdi Epress hs cpcity of 500 sets of which 0% re in the eecutive clss nd the rest eing generl clss. uring Journey the trin ws ooked to 85% of its cpcity. If eecutive clss ws ooked to 96% of its cpcity, then how () 9 cm () 5 cm mny generl clss sets were empty 6 cm cm during tht Journey? 5. In the given figure 'O' is the centre of the () 73 () circle. If E = cm, E = cm, lso E = F nd =, then F =? 6. In given figure = = = E = EF = FG = G, then the vlue of E is () 5º () 0º 30º 5º 7. In the given figure, is rectngle where E = EF = F, then the rtio of the res of EF nd the rectngle will e () cm () cm cm 6 cm 5. Two points X nd Y re on the sides nd of the prllogrm. The r(x) is () of r( Y) () equl to Y 3 of r(y) () : () : 6 : 5 : 3 8. In the given figure OG = OF, the the re of the figure will e - Twice the r(y) 53. The re of the equilterl tringle mde inside the squre of side '' will e () () 3 6 () 6 m () 6 m 60 m 58 m

8 QRS () : 3 () 3 : : : 3 () 7 () º 65º 70º 75º = = 5 = 9 () 73 () = = = E = EF = FG = G, E 9 O E = E = E = F = F = 5º 0º 30º 5º E = EF = F EF X Y X Y Y OG = OF Y Y

9 entres t: ================================================================================== 5. The se '' of the verticl tower is on 6. In the given figure, is prlleogrm the plne. is the midpoint of. The ngle whose sides = units, = units of from point P is. If P = n., then nd E : E = :, EFG is rectngle tn is whose side EF = 3E. Wht will e the rtio n n of the re? () () n n n n n n 55. Two circles touch ech other interlly. The rdii of these circles re cm nd 3 cm respectively. Find the length of the lrgest chord of the outer circle which touches the internl circle t point. () cm () cm 3 cm None of these 56. If cosec sin = m nd sec cos = n 3 then m n mn 3? () () If sec + cosec + c = 0, nd p sec + q tn + r = 0, then (r qc) (pc r) =? () (q p) () (p q) (q p) 3 cos sin 58. If, then the vlue of cos sin cos sin is cos sin () () The epression cos8 is equl to wht? () sin sin () cos cos 60. If cos, then cos will e equl to () () 6. If sin, cos, nd c cosec then the vlue of c 3 is () 3 () 3 0 () : () : : : If then the ngle etween the lines cos ysin p nd ds cos ysin p' is () 6. If is () sin( y), then the vlue of sin( y) () () tn tny If then wht will e the vlue 8 3 of 3? () 3 () 0 y If ;, y 0 then ( y )? y () 0 () 67. If ( ) c; ( ) c nd c( c ) c, then the vlue of is c () () 0 9

10 P P = n. tn n n n n = = E : E = : EFG EF = 3E n n n n 3 cosec sin = m m n 3 mn 3 sec cos = n sec + cosec + c = 0 p sec + q tn + r = 0 (r qc) (pc r) = (q p) (p q) (q p) 3 8 cos sin cos sin 0 cos8 sin cos sin cos cos sin cos sin cos cos sin, cos, c c cosec : : : : 5 cos ysin p' sin( y) sin( y) c( c cos ysin p tn tny y y ;, y 0 3 ( 3 3 y )? ( ) c; ( ) c ) c c 0

11 entres t: ================================================================================== y y z 68. If ( y z), ( y z) nd 75. If the rdii of the two ends of ucket in the form of frusturm of height 5 cm is z ( z y z) then wht will e the vlue 8 cm nd 7 cm, then the volume of the of y z( 0, given)? () 0 () 3 ucket (in cm 3 ) is Tke 7 () 850 () ? The se of right tringulr prism is () 0 () trpezium. Length of the prllel sides re 8 cm nd cm, lso the distnce etween p q r 70. If, then p q r? prllel sides is 8 cm. If the volume of the c c prism is 056cm () 0 (), then its height is None of these () cm () 6.5 cm 7. If pqr =, then the vlue of cm 0.56 cm 77. Ech interior ngle of regulr polygon is twice of its eterior ngle, then the numer will e p q q r r p of sides in the polygon is () () pq () 8 () The se of pyrmid is in the form of squre whose side is 6 cm. If its height is cm, then wht will e its volume (in cm 3 )? () 000 () qr pq 7. The height of uilding t distnce of 00 m from tower is 0 m. The top nd the ottom of the tower sustend right ngle t the top of the uilding, then find the height of the to tower? () 80 m () 90 m 90 m 60 m 73. n oject is oserved from the three points, &. These three points lie on stright line tht psses through just elow the oject. The ngle of elevtion of the oject t is twice tht of t nd t is thrice tht of t. If = nd = units, then the height of the oject will e. () ( )(3 ) 3 () ( )(3 ) ( )(3 ) None of these 7. person oserves two ojects in stright line towrds the west. When he covers distnce of 'c' towrds the North, he finds the two ojects mking n ngle of ' ' in his eyes nd when he moves nother distnce of 'c' units, the two ojects mke n ngle ' ' in his eyes. The distnce etween the two ojects is () () 3 units cot cot 3c units cot cot 3c units cot cot 3 units cot cot 79. In, is the isector of tht intersects in. If = 8 cm nd = cm, then find :. () : 3 () 3 : : 3 3 : 80. If the point (, 3) is the centroid of tringle nd (, y), ( 3, 7), (9, 7) re its vertices, then find the re of the tringle? () 66 () 55 ) If + + c = 5 nd + c + c = 0 then the vlue of c 3 3 is () 8 () Find the re of the tringle formed y the grph of + y = c (Where, re positive rel numer) nd the co-ordinte es c () cue es () cue es c c cue es cue es c

12 z y ( y z), ( y z) ( z y z) y z( 0 y z 3? 0 p q r c c 0 pqr = p q q r r p pq qr pq p q r? ,, = = ( )(3 ) 3 ( )(3 ) ( )(3 ), = 8 = : ( (, y), ( 3, 7), (9, 7) c 3 cot cot 3c cot cot 3c cot cot c + + c = 5 + c + c = c y = c, c c 3 cot cot c c

13 entres t: ================================================================================== 83. How mny three-digits numers re there which re completely divisile y 6? () 30 () The sum of 6th nd 5th terms of n rithmetic progression is equl to the sum of 7th, 0th nd th term of the sme rithmetic progression, then which term of this rithmetic progression is zero? () 6 () If '' is the geometric men of nd c, then irections (9-00): Study the grph crefully to nswer the questions tht follow: rekup of totl numer of 3600 employees working in different deprtments Employees working in different deprtment = 3600 ( c ) wht will e the vlue of c? () () 6 8 rekup of the numer of 00 mle employees working in different deprtments 86. The co-ordintes of the points P, Q nd S re (t, t);, nd (, o) t t respectively. Then? SP SQ () () 87. When polynomil f () = is divided y ( ), then wht will e reminder? () () If the grphs of the equtions y = nd y = + 3 re drwn, then they will e... to one nother () prellel perpendiculr () coincident None of these 89. If the grphs of the equtions 3y = 6 nd 3 + 5y = 38 intersect t point, then the co-ordintes of the point will e 90. If () (3, 3) () (, 3) (, 5) (5, ) , then the vlue of nd re () =, = 0 () = 0, = =, = =, = rekup of totl numer of 00 employees who recently got promoted in ech deprtment 9. If hlf of the numer of employees who got promoted from the IT deprtment were mles, wht ws the pproimte percentge of mles who got promoted from the IT deprtment? () 6 () Wht is the totl numer of femles working in the Production nd Mrketing deprtment together? () 68 () How mny femles work in the ccount deprtment? () () The totl numer of employees who got promoted from ll the deprtment together ws ppro wht percent of the totl numer of employees working in ll the deprtment together? () 56 ()

14 c ( c ) c 6 8 P, Q S (t, t);, (, o)? t t SP SQ f () = ( ) y = y = + 3 3y = y = =, = 0 = 0, = =, = =, =

15 entres t: ================================================================================== 95. The numer of employees who got promoted from the HR deprtment ws wht percent of the totl numer of employees working in tht deprtment? (rounded off to two digits deciml) () 36.8 () irections (96-00): Study the grph crefully to nswer the questions tht follow: Percent profit mde y two compnies over the yers IncomeEpenditure Percent Pr ofit 00 Ependiture 96. If in the yer 00 the ependitures incurred y ompny nd were the sme, wht ws the rtio of the income of ompny to tht of compny in tht yer? () 7:8 () :3 3:9 nnot e determined 97. If the mount of profit erned y ompny in the yer 007 ws Rs.5 lkhs, wht ws its ependiture in tht yer? () `.96 lkhs () `.6 lkhs `.7 lkh ` 3.75khs 98. Wht is the verge per cent profit erned y ompny over ll the yers together? () 9 () If in the yer 008, the incomes of oth the compnies nd were the sme, wht ws the rtio of the ependiture of ompny to the ependiture of ompny in tht yer? () :5 () 7:9 3:5 nnot e determined 00. Wht is the rtio of the mount of profit erned y ompny to tht y compny in the yer 009? () :3 () :7 :5 nnot e determined 5

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