NSTSE Class 9 Solved Paper 2011

CLA SS : iX

MA TH EM AT IC S

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CL AS S :IX

m at M ari N. Th e AB is par all el to CD, EF int ers ect s the If lAM E= 80° , the n bis ect ors of M an d N me et at Q. j M~ .is :

B •

sta nts and if y = 1 If Y =a + ~ , wh ere "a" an d "b" nre con n a + b equ als : wh en x= -1, and y = 5; wh en x= -5, the 0D) ll (C) 1 CB)O (A) - 1 ''b"·is rev olv ed 360° A rec tan gle of len gth "a" and bre adt h ult ing cyl ind er is: abo ut its len gth . Th e vol um e of the res 2 (A ) 2n a b

•

•

(B ) na? b

(C)

1t

ab .

(D ) 2n ab

tio ns is m. If tw o Ar ith me tic me an . of ''n" ob ser va n the new me an wil l . obs erv ati ons 0 and ma re add ed, the be: m( n+ l ) mn m 2 ) (D (C) (B) (A )ni n+ n +1 n +1 53 sun :da ys in a Wh at is the pro bab ilit y tha t the re are

r '

leapye~?

1 (A ) 6

•

2 (B ) -

7

3 (C) -

8

4 9

(D ) -

2 9 div ide d by X is: Th e rem ain der ·wh en x4- 3x + 2x is (D) 0 2 (A) xS - 3x2 + 2x (B ) 2x - 3xS (C) 1

UC N/ 201 1/IX

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,

If

xy X+Y

xz

yz = b and - - = c, X+Z . y+z

= a , --

where u, h

nd

~

arc

other than zero, then x equals:

abc . 2abc 2abc (A) ab+bc+ca (B) ~b+bc+ca (C) ab+ac-bc

~be

(IJ)

hc+cu ab

X, Y, Z, U are four points in a straight line. If dlltanco from X to Y is 15, Y to Z is 5, Z to U is 8 and X to U is 2, th n the correct sequence of the points will be: (A) X- Y -Z- U (B)X-Z- Y- U (C) X-U- Z- Y (D) X- Z- U - Y

IJ If ABC is a triangle and D, E and F are respectively mid-

points of AB, BC and C.A, then the triangle ABC is: (A) Similar to LillEF but not LillBE . (B) Similar to LillEF but not 6ECF (C) Similar to the triangle DBE, ECF, ADF and DEF (D) Not similar to any of the triangles DBE, ECF, ADF and DEF

~~ ABCD is a parallelogram ofAreaS. E and Fare the middle points of the sides AD and BC resp·e ctively. H G is any point on the line EF, then the area of L\AGB is equal to:

s

(A)-

mIn

2

~B)

s

3.

. (C) S

4

(D) 38 4

the figure given below, if LAOP = 75° and LAOB =120°,

then what is LAQP? R

p

(B) 37.5°

CD) 22.5°

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IIJ If the volume of two cubes are in the ratio 27 : 1, the ratio of their edges is: (A) 3 : 1

·

(B) 27: 1

(C) 1 : 3

(D) 1 : 2'i

A man has certain number of chickens and goats. Their head count is 30. If the total number of their legs is 84, what is the ratio between the number of chickens and goats? (A) 1 : 2 (B) 2 : 3 (C) 3 : 2 (D) 3 : 4

II If (x -

2) is a common factor of x 3

-

4x2 + ax + b and

r- ax + bx + 8, then the values of a and b are respectively: 2

(A) 3 and 5

(B) 2 and -4

(C) 4 and 0

(D) 0 and 4

IIJ If a and bare positive integers such that a b = 125, then (a- b)a + h- 4 is equal to: (A) 16

(B ) 25

6

.

(C) 28

(D ) 30

Ill The sides of a triangle are 5 em, 12 em and 13 em, then its area is: (A) 0.0024 m 2

(B ) 0.0026 m 2 (C) 0.003 m 2

(D) 0.0015 m 2

In fig. LABP = LACQ, LBAC =68° measure of LABC is:

(A) 124°

(B) 560

IIJ The area of the triangle formed between lines and 2x - 3y + 6 (A) 3 Sq, units (C) 2 Sq. units

x= 0, y

=0

=0 is:

(B) 4 Sq. units (D) 5 Sq. units

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ClASS l fX $

t

Unified Council

If 37a =37b == 5661, what is the average of a and b? (A) 74.5 (B) 151 (C ) 76.5 CD) 153 The diameter of a solid metallic right circular cylinder is equal to its height. After cutting out the largest possible solid sphere S from this cylinder, the remaining material is recast to form a solid sphere 8 1 • What is the ratio of the radius of spheres to that of sphere sl? . (A) 1 : 2 113

(B) 2113 : 1

(C) 2 113 : 3 113

(D ). 3 112 : 2 112

A rectangle and a parallelogram have equal areas. The

base of the parallelog.·am is 20 em and the altitude i~ 6 em. Which one of the following cannot be the ratio of dimensions of the rectangle? (The dimensions are of integral values) (A) 6: 5

(B ) 4: 3

(C) 15 : 2

(D ) 30 : 1

Two parallel chords of a circle whose diameter is 13 em are, respectively, 5 em and 12 'em in length. If both the chords lie in a semi-circle, then the distance between the chords is: (A) 8.5 e1n

(B) 5 em

p = 5+2J6 and q

· ,(A) 49

(C) 3.5 em

(D) 3 em

1 then, p 2 + q 2 is: p

= -

(B) 98

(C)100

(D) None of these

· Straight line passing through the points (-1, 1), (0, 0) and (1, -1) has equation: (A ) y

=x

(B ) x + y

=0

(C) y

= 2x

(D ) 2 + 3y =: 7x

If the co-ordinates of the point p are (3, -5)t then the perpendicular distance of p from the y-axis with proper

'+' or '-' sign prefixed is: (A ) -5

(B) 5

(C) 3

(D)-3

UCN/2011/IX

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I

CLASS : IX

· CLASS : IX

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PHYSICS

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~~ Ranvee~ pulled a table cloth from a table without dislodging the dishes. This is due to:

(A) inertia

(B) impulse

(C) force

(D) momentum

II A crane 'P' lifts a car upto a certain height in 1 minute. Another crane 'Q' lifts the same car upto the same height in 2 minute. I. Crane 'P' consumes two times inore fuel than crane 'Q'. II. Crane 'P' supplies two times more power than crane 'Q'.

Based on the above information, identify the correct . option. (A) Statement (I) is true while statement (II) is false (B) Statement (l) is false while statement (II) is true (8)

Both statements (I) and (II) are true

(D) Both statements (I) and (II) are false

111 The graph below shows the distance travelled and the time taken by four cars?

0

I

I

I

I

1 2 3 4 5 Time (hours) Which car travelled the slowest? (A) Car 1

(B)Car2

(C)Car3

(D)Car4

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hig hes t ~~ Which of the foll owi ng sou nd wav es hav e the pitc h? Amp litud e

Am plitu de

(A) 0

Am plit ude .

Amp litud e

o

(C)

4 Tim e(s) (D )

0

Tim e(s)

forc e is zer o? ' In wh ich of the foll owi ng cas es, the net ght I. A bal l free ly fall ing fro m a cer tain hei IL A cor k floa ting on the sur fac e ofwa ter Ill. An obj ect floa ting in air ~

(A) I and II only (C) III and I only

(B) II and III only

(D) I, II and III

kg are dro ppe d A bal l of ma ss 2 kg and ano the r of ma ss 4 a fall of 30 fee t, tog eth er fro m a 60 fee t tall bui ldin g. Aft er the rati o of: the ir res pec tive kin etic ene rgie s wil l be in (A)

../2: 1

(B ) 1: 4

(C) 1: 2

(D ) 1:

.J2

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Assertion : A metal ball hits a wall and does not rebound whereas a rubber ball of the same mass on hitting the wall with the same velocity rebounds back. Re~ason : Rubber ball suffers a greater change in momentum than metal ball. (A) Both Assertion and Reason are tru e. Reason is the correct explanation of as-sertion. (8) Both Assertion and Reason are true. Reaso:Q is not the correct explanation of assertion. (C) Assertion is true and reason is false (D) Both assertion and reason are false. Consider a heavenly body which has a mass twice that of the earth and a radius thrice that of the earth. The weight of a book on this heavenly b o dyt if its weight on .the earth is 900 N will be : (B) 600 N (C) 500 N (A) 400 N (D) 200 N Figures given below represent two types of wave motion.

Oscillating or vibrating particle . . .__

i

-- ~·ave

Direction of (} -·· ··r i

(hcillatlng or vibra t.ing pardcle .• / Uirection·or lt"L~Ve

- ---\ ..)-··- ·

...

-···--·-··--···-

...

What can you infer about the types of wave motion? (A) The direct ion of wave motion is always perpendicular to th e

direction of a vibrating particle. (B) The dir ection of wave motion is always parallel to t he direction pf a vibrating particle. (C) The direction of vibration of a particle and the propagation of a wave results in different kinds of"Yave motion. (D) The direction of wave in positive X-axis always results in wave motion. U C N/2 0 11 /IX ·

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E!J A spring balance is graduated on 'sea level.

A body of mass 1 kg is weighed at consecutiv ely increasing heights from the earth's surface, then what would be the weight indicated by the balance?

(A) Weight will go on increasing continuous ly (B) Weight will go on decreasing continuous ly (C) Weight will remain same (D) Weight will first increase and then decreases

While testing the safety of a car, a durnmy driver is used and the car is propelled at different speeds to hit a dgid wall. In one such test, the dummy driver had a mass of 70 kg and the speed of the car just before impact was 40 m s-J.. If the time interval between the collision and the car coming to rest was 0.2 s, then find the decelerati on of the dun1my ddver due to impact? (A) 200m s-2

(B) 80 m s- 2

(C) 110m s-2

(D) 280m s-2

The distance of a particle versus time is shown below. 100'

9oi

i

80

(l}

70

u

60

.3 so40

.~

"tj

30

20 10 0

1

2 3 4 5 Time

--+

·What does the graph indicate? (A) The particle starts with certain velocity with retarded motion and finally comes to rest. (B) The velocity of the particle is constant throughout . (C) The acceleratio n of the particle is constant throughout . (D) The particle starts with a certain velocity and finally becomes uniform after certain time. U C N/ 2 0 1 1 /IX

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· Assertion : The kinetic energy, with any reference, must be positive. Reason : In the expression for kinetic energy, the -relocity appears with power 2. (A) Both Assertion and Reason are. true. Reason is the cor.rect explanation of assertion. (B) Both Assertion and Reason are true. Reason is not the correct explanation of assertion. (C) Assertion is true and reason is false (D)

Both assertion and reason are false.

~~ The given figure shows two shoulder bags, one with a thin strap, and the other with a wide strap.

If both bags are equally heavy, the sling bag with the wide strap will be more comf~rtable to carry because:

(AJ the thin strap has a greater inertia per unit length. (B) the thin strap causes greater momentum to be exerted. (C) the wide strap allows friction to be s'p read over a bigger area, thus reducing the force between the shoulder and the strap. (D) the wide strap enables the weight of the bag to be spread over a bigger area, thus redu~ing the pressure on the shoulder.

~~ When the force retards the motion of a body, the work done by the force during retardation is: (A) zero (B) negative (C) positive (D) positive or negative depending upon the magnitude of force and displacement UCN/2011/IX

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l)nifl~d

Council

II In a 100 m race between Ramesh and Suresh, Ramesh wins the race. Assuming they run with uniform acceleration. Which of the following is correct? (A) Acceleration of Suresh is more than Ramesh (B) Acceleration of Ramesh is more than Suresh (C) Both Suresh and Ramesh have equal acceleration (D) Both Suresh and Ramesh have equal average velocities

IIJ The acceleration of a particle 'X' remains constant in magnitude but not in direction, which of the following paths does particle 'X' can have? (A) Straight line

(B) Circular path

(C) Elliptical path

(D) Parabolic path

Ill A microphone is connected to an oscilloscope.. Th~­ diagram shows the trace on the screen when the microphone receives a pure note. I

Which trace can be obtained when a musical instrument produces a note of the same pitch but of a different quality? . (A)

(C)

AJ"

(B)f\J\

f\j\}\;

II Rahul takes 1 minute to raise a box to a height of 1 metre and Rohan takes 1/2 ~inute to do so. Comment on the energy by the two. (A) Energy spent by the Rahul is more (B) Energy spent by both Rahul and Rohan is same (C) Energy spent by the Rohan is more (D) Cannot be said UCN/2011/IX

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I

Unified Council

The two ends of a train moving with uniform acceleration passes a certain point with velocities 6 kmph and 8 kmph respectively. What is the velocity with which thf middle point of the train passes the s~e point? (A) 14kmph

(B) 5 kmph

(C) 5~ kmph (D),lO kmph

If the earth shrinks half in radius its ~ass remaining the same, then by what percentage will the weight of an object on earth change? (A) Decreases by 50% (B) Increases by 50% (C) De'creases by25%

(D) Increases by 300%

A boy stands between the two walls and ·c laps his hands as shown below: xm

60m

If 'x~ is less than 60 m and the time between the first and the second echo is 0.25 s, then calculate the distance 'x'. (Velocity of sound in air is 344m s-1) ' (A) 36m

(B) 34m

(C) 40 m

(D)

17m

The gravitational force of attraction between two bodies at a certain distance is 70 N. If the distance of separation between them is doubled, then find the percentage change in force of attraction? (A ) Decreases by 25%

(B) Decreases by 75%

(C) Increases by 50%

(D) Increases by 75%

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m

Look at the figure showing an experime ntal setup. 4

3 2

1 Q

At the start of the experiment, the spring device is compressed to setting number 1 and released to propel the trolley P forward. When trolley P collides with trolley Q, both trolleys move together for certain distance. Identify the physical quantities that vary for both trolleys be~ore and afte r the collison. (A) Mass, velocity

(B) Mass, momentum

(C) Mass, time

ffi) Velocity, momentum

IJ Someone's car will not start, so a friend helps him by ·

pushingit.

By pushing as hard as he can for 10 seconds he makes the car reach a speed of2 m s-1 • Calculate the acceleration he gives to the car. (A ) 20m s-2

(B ) 0.2 m s-2

(C) 5 m s-2

(D ) 10 m s- 2

UCN / 2011/IX

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1

CLA SS : IX

-

-

CHE MIST RY

-

II Bromine has a melting point of -2 °C and a boilin.g p~int 59 °C. Ident ify at what temp eratu re will brom ine has a defin ite volum e but no defin ite shape ?

(A) 65 °C

(B) 36 °C

· (C) -26 °C

(D) 0 K

E!J Which of th~ following contains the same number of oxyg en atom s? L

(A) I and II only

"

1 gofO atom s II. 1 gof02 Til. lg of Ozon e 0~

(B) II and III only

(C) III and I only

(D) I, II and III

ID An isotope of helium is represented by the symbol ~ He. How many proto ns, neutr ons and elect rons are there in an atom of the isoto pe? Proto ns

~

Neut rons

Elect rons

(A)

1

2

1

(B)

1

3

2

(C) (D)

2

1

2

2

3

J2

A liquid 'X' is found to scatt er a beam of light but leave s no resid ue when passe d throu gh the filter pape r. Ident ify the categ ory to whic h liquid 'X' can be classi fied.

(A) A suspe nsion

(B) Colloidal sol

(C) True soluti on

(D) Oil

m

A salt of binar y acid H 2S is M S • Find the valen cy of 2 3 meta l 'M'? (A) 1

(B) 2

(C)3

(D)4

UCN / 2011/ IX

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Unified Coun(U

II What happens when a solid mel~s? (A) Its molecules move farther apart (B) Its molecules move closer

(C) The movement of its molecules decreases (D) The temperature decreases although heat is supplied

Ell Which of the following obey the law of constant proportions in their formatiQn? (A) Mixtures ·(B) Compounds (C) Elements

(D) Colloids

IJ A beam of alpha·particles are fired at a piece of gold foil as shown in the figure below. Beam of alphaparticles

Gold foil

\

/

s

\~ a

~_..7-k-p 1 R

After striking the gold foil in which direction does most of the alpha-particles travel? (D)S (C)R (A)P CB) Q

Em Which one of the following statements about the evaporation of water is not true? (A) Water can evaporate only at a temperature of 100 °C (B) Water vapour rises to the sky and to form clouds.

(C) When water on our skin evaporates, heat is lost from our bo~y. (D) During evaporation, water changes from a liquid state to a

vapour state.

IJ Identify a heterogeneous mixture from the following. (A) Brine solution

(B) Gallium

(C) Sulphur in carbon disulphide

(D) Gun powder

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IJI According to J.J. Thomson's atomic model, where a~e -negative charges of an atom embedded in? (A) A lump of positive charge (B) A lump of small atoms (C) A lump of neutrons

(D) The nucleus

~~~ Identify the correct increasing order of molecular weights. (A) H 2 0 >NO> C02 > S02

(B) H 20 < 802 >NO> C02

(C) 802 < C02