Advance Talent exam

7/23/2019 Advance Talent exam

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Single Choice (Only one correct)

1. In figure, if PN is the internal bisector of ∠ P. If QN = 4 cm. NR = 3 cm. and PQ = 6 cm.

Find PR.

(!4." cm (#!"." cm

($!3." cm (%!6." cm

2. &he bisector of e'terior meets #$ roduced in %. If # = )* cm. $ = 4 cm. and #$ =

6 cm. Find #%

(!+ cm (#!)* cm

($!+." cm (%!)*." cm

3. If 6th arch, -**" is onda, /hat /as the da of the /ee0 on 6th arch, -**41

(a! 2unda (b! 2aturda (c! &uesda (d! ednesda

4. &he radius and ertical height of a cone are in the ratio, 354. Its slant height is " cm. Find its

cured area.

(!4 cm- (#!46 cm-

($!46.)-) cm- (%!4.)-) cm-

5. n aluminum /ire /hen bent into the form of a s7uare encloses an area of 44) cm-. If the

same /ire is bent into the form of an e7uailateral triangle, find the area of the triangle.

(!-

)+6 3cm (#! -

)+4 -cm

($! -

)+6 -cm (%!-

)+4 3cm



6. &/o oles of height )*m 8 )9m. Find the height of oint of intersection of the lines :oining

the to of each ole to the foot of the oosite ole.

(a!

46

(b!

44

(c!

4"

(d!

49

7. If a number on diision b )3 leaes remainder 4. &hen the remainder /hen the cube of that

number added to s7uare of itself is diided b )3 is(!- (#!"

($!+ (%!))

8. In the game of chess, the ;night can ma0e an of the moes dislaed in the diagram to the

right. If a ;night is the onl iece on the board, /hat is the greatest number of saces from

/hich not all 9 moes are ossible1

(a! 9 (b! -4 (c! 39 (d! 49

9. Find the length &P in the follo/ing figure. <ien that PQ = 9, radius of circle is " and &P 8

&Q are tangents from oint & to the gien circle.

T

Q

P

C

(!" (#!9

($!

-*

3 (%!

4*

3



10. No of real alues of '> /hich satisf the e7uation, ' ) ) '= − − .

(!) (#!-

($!3 (%!4

11. If- - - -

) ) ) )....

) - 3 4

+ + + +

(uto ∞! = '. &hen- - -

) ) )...

- 4 6

+ + +

(uto ∞! is(!'?3 (#!'?-

($!'?4 (%!None of these

12. If a'4 @ b'3 @ c'- @ d' @ - is e'actl diisible b ' - A ) then the alue of b @ d is

(!* (#!)

($!A) (%!can>t be determined

13. &he olnomial ')* A '+ @ '9 A ' @ '6 A '" @ '4 A '3 @ '- A ' @ ) is ositie

(!onl for ' ≥ ) (#!onl for ' ≤ *

($!onl for * ≤ ' ≤ ) (%!al/as

14. Bast digit of (-)3!- × ("6!9) is

(! (#!3

($!" (%!6

15. In the figure sho/n PQR2& is a star. hat is the alue of ∠P @∠Q @ ∠R @ ∠2 @ ∠&.

Q

P

T

SR

(!)-*C (#!)9*C

($!-4*C (%!cannot be determents



16. <ien

)' 3

'− =

D then the alue of

4

4

)'

'+

is

(!)*) (#!))

($!))+ (%!)-3

17. &he roduct of ( '- @ 3' @ "! and ( '- E) ! is

(a! '4 @ 3'3 A 4'- A 3' A " (b! '4 @ '3 @ ' @ "

(c! '4 @ 3'3 @ 4'- @ 3' A " (d! '4 @ 3'3 @ 4'- A 3' A "

18. )- eole sa the follo/ing statements one after another5 )5 &here are no honest eole in

this roomD -5 &here is at most one honest erson in this roomD 35 &here are at most t/o

honest eole in this room . . . . . . . . . . )-5 &here are no more than )) honest eole in this

room. &otal number of honest eole in the room is

(a! 4 (b! 6 (c! )- (d! None

19. $o/ and a #uffalo /ere bought for Rs. 9***?E each. &here /as a lost of 4 on the buffalo

8 a rofit of 9 on the $o/. Find the gain or loss ercent, on the /hole transaction

(! Boss of 4 (#! <ain of 4 ($! Boss of - (%! <ain of -

20. In a room there are "* electric bulbs numbered from ) to "*. Gach bulb has a s/itch

corresonding to it. &here are also "* men standing in room /ith numbers ) to "*. Initiall

all bulbs are s/itched off. First man no/ /al0s to s/itchboard and reerses the s/itch

osition of the bulb>s /hich are diisible b his number. &hen the second man goes and



reerses the s/itch osition of all the bulbs /hich are diisible b his number and so on this

rocess is continued till "*th man. Ho/ man bulbs are s/itched onJ finall.

(! 6 (#! ($! 9 (%! +

21. man /al0s a distance of 49km in a gien time. If he /al0s - 0m?hr faster, he /ill

comlete the :ourne 4 hours before. His normal rate of /al0ing is

(! 6km hr (#! 4km hr ($! 9km hr (%! )-km hr

22. hat is the erimeter of ∆ #F 1

A

1

B

F

CD

3 00

4 50

4 50

E( f g u r e i s d r a w n t o t h e s c a l e )

(! 2 + 2 3 (#! 1 + 2 + 3

($! 2 + 2 2 + 3 (%! 2 2 + 2 3

23. farmer o/ns seeral dair co/s, some blac0 and some bro/n. He finds that 4 blac0 co/s

and 3 bro/n co/s gie the same amount of mil0 in " das as 3 blac0 co/s and " bro/n

co/s gie in 4 das. hich gies more mil0 in a da, a blac0 co/ or a bro/n co/.

(! #lac0 (#! #ro/n ($! #oth gie e7ual mil0 (%! %ata insufficient

24. If- - - - -

= ', then ' =

(! 3- (#! -3- ($!

)

3-- (%!

3)

3--



25. %etermine( ) x

from the figure

6 3

x x

(!

3

" (#!

3

- ($! - -." (%! 3 -."

26. train traelling at -" 0m?hr, leaes %elhi at + a.m. and another leaes %elhi at 3" 0m ?hr at

- .m. in the same direction. Ho/ man 0m from %elhi do the meet1

(a! 43." 0m (b! -** 0m (c! 6-" 0m (d! 3"* 0m

27. If 3* men /or0ing hours er da can do a /or0 in )9 das, then in ho/ man das /ill -)

men /or0ing 9 hours a da do the same /or01

(a! -* (b! --." (c! -4 (d! -"."

28. 4 ies can fill a tan0 in )", -*, 3*, 6* hours resectiel. &he first /as oened at 6 a.m.D

second at a.m. third at 9 a.m. and fourth at + a.m. /hen /ill the tan0 be full

(a! )) a.m. (b! ) .m. (c! 4 .m. (d! )* a.m.

A B

C

29. &he shaded region reresents

(a! ( ) A B C ∪ ∩(b! ( ) A B C ∩ ∩

(c! ( ) A B C ∪ ∪(d! ( ) A B C ∩ ∪

30. If log)* Klog)* ( log)* '! = * , then

(a! ' = )*3 (b! ' = )* )* (c! ' = )* )*** (d! ' = )



340 450

300

K = ?

31.

(a! )*+* (b! )* (c! 4"* (d! )3"*

32. -" metre long ladder is laced against a ertical to/er such that the foot of the ladder is

metres from the foot of the to/er. If the to of the ladder slides 4 metres do/n/ards then

the foot of the ladder /ill slide b

(a! - metres (b! 4 metres (c! 9 metres (d! )6 metres

33. hat is the ma'imum number of 3'3 s7uares that can be formed from the s7uares in the 6'6

chec0er board to the right1

(a! 6 (b! )- (c! )6 (d! -4

34. In a fourEda eriodLonda through &hursdaLeach of the follo/ing temorar office

/or0ers /or0ed onl one da, each a different da. s. Mohnson /as scheduled to /or0 on

onda, but she traded /ith r. $arter, /ho /as originall scheduled to /or0 on

ednesda. s. Fal0 traded /ith r. ;ir0, /ho /as originall scheduled to /or0 on

&hursda. fter all the s/itching /as done, /ho /or0ed on &uesda1(a!r. $arter (b!s. Fal0 (c!s. Mohnson (d!r. ;ir0



35. If the radius of the shere is reduced b "*, then its olume is reduced b5

(a! "* (b!

))-

- (c!

)9 F

- (d! -"

36. &he circumference of a circle is --* cm. &hen the side of a s7uare inscribed in the circle is

B

( 5 - x)

C

A

6

5

x

0

(a! 4" (b! 3" (c! 3" - (d! 4* -

37. In a circle of radius " cm, # and $ are - chords such that # = $ = 6cm. &he distance

of the chord #$ from the centre is

(a! ).4 cm (b! 3.6 cm (c! -.4 cm (d! 4.6 cm

38. e hae - candles of the same length. &he thic0 one burns for 6 hrs and the thin one for -

hrs. less. If both are lighted at the same time and the length of the thic0 candle is t/ice that

of the thin candle after some time. For /hat time hae the been burnt 1

(a! - hrs (b! hrs (c! " hrs (d! 3 hrs

39. For the oening game of the IPB season, the umbai Indians offered the follo/ing

incenties to its fans5

Ger "th fan /ho entered the stadium got a couon for free sand/ich.

Ger 3*th fan /ho entered the stadium got a couon for free ca0e.

Ger "*th fan /ho entered the stadium got a couon for free ocorn.

&he stadium holds 4*** fans and /as comletel full for this game. Ho/ man fans /ere

luc0 enough to receie all three free items 1

(a! 3- (b! -4 (c! 3* (d! -6

40. In a &riangle #$, % 8 G are t/o oints on the base #$ such that % = #% 8 G = G$.

lso if sum of the base angles is **, Find ∠ %G

(a! ))** (b! 4** (c! ** (d! )3**



41. Four concentric (haing the same center! circles /ith radii, ', -', 3' and 4' are dra/n to

form t/o rings and # as sho/n in the figure.

Ratio of the area of inner ring to the area of outer ring # is

(a! ) 5 - (b! ) 5 4 (c! 3 5 " (d!6 5 )4

42. In a mar0et rice of an diamond is directl roortional to s7uare of olume of diamond. If

diamond is diided in 3 arts /hich hae ratio of olume - 5 35 " /hat /ill be ercentage

loss in total rice of diamond1

(a! 39 (b! 6- (c! 4- (d! "9

43. In ce of PaceJ aer, there are "* distinct 7uestions each carring "> mar0s for correct

ans/er,

E)> for /rong ans/er and *> for an unEattemted 7uestion. &he number of /as a student

can secure -3) mar0s is

(a! " (b! 6 (c! 9 (d! None of the aboe

44. &/o secant P# and P$% are dra/n to a circle from e'ternal oint P if P = 9, # = 3, P$ =4 /hat /ill be length $%1

P

$

%

#

(a! )) (b! -- (c! )9 (d! 6



45. hen simlified the trigonometric e'ression

- -

- -

) sin sec

) cos cos ec

+ θ θ

+ θ θ reduces to

(! sin θ (#! tan θ ($! cot θ (%!-

tan θ

46. If ' and are ositie /ith ' A = - and ' = -4 then

) )

' .+

is e7ual to

(!

)

)- (#!

"

)- ($!

)

6 (%!

-"

6

PASSAG! (47!48)

&here are si' friends 2achin, ina, Prati0, Rai, 0sha and Prashant. 2achin is shorter

than ina but taller than Rai. Prati0 is tallest /hile Prashant is taller than 0sha and shorter

than Rai.

4. ho is the shortest1

(a! 2achin (b! Rai (c! Prashant (d! 0sha

49. If the seenth friend Ra:an /as to stand in the middle in order of their heights, then he /ill

stand in bet/een5

(a! 2achin and ina (b! Rai and 0sha

(c! 2achin and Rai (d! %ata inade7uate

49. Number of solutions of( ) ( )

- -' '

- 3 - 3 4− + + = are

(! ) (#! - ($! 3 (%! *

50. erson is standing at a distance of ' m from a light ole. If the height of the ole is "*

m, if the angle of eleation e'erienced b an obserer standing at a distance of -' is 4" o, if

θ is the angle of eleation obsered b . then tan θ = 1

(! ) (#! - ($!

3

- (%!

)

3

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