(SAMPLE PAPER C XI)...(A) rational and distinct (B) real and equal (C) imaginary (D) irrational and...

(SAMPLE PAPER Class XIl)

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RAT(2021)(Reliable Aptitude Test)

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1

RAT_TEST PAPER

MATHEMATICS

This section contains 20 multiple choice questions. Each question has four choices (A),(B),(C) and

(D) out of which only one is correct

1. If = -x 3 5 , then + -

x

2 3x 2 is equal to -

(A) 5 (B) 15

(C) 5 (D) 1

5

Ans. (D)

Sol. = -x 3 5

( )= - = - 22x 6 2 5 5 1 = -2x 5 1 ...(i)

3x – 2 = 7 – 3 5

2(3x – 2) = 14 – 2.3. 5 = ( )- 23 5 ( )- = -2 3x 2 3 5 ...(ii)

now ( )

=+ - + -

x 2x

2 3x 2 2 2 3x 2

-

= =-5 1 1

5 5 5

2. Minimum value of cos2q + cosq for all real values of q is-

(A) -98

(B) 0 (C) –2 (D) None

Ans. (A)

Sol. cos2q + cosq

2cos2q – 1 + cosq

é ùæ öq + - -ê úç ÷è øê úë û

21 1 1

2 cos4 2 16

é ùæ öq + -ê úç ÷è øê úë û

21 9

2 cos4 16

æ öq + -ç ÷è ø

21 9

2 cos4 8


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RAT_TEST PAPER

3. If a and b are solutions of x2 – 10x + 10 = 0 such that a b

+ =b a

b , then roots of equation

2x2 + 10x + 3b = 0 are

(A) rational and distinct (B) real and equal

(C) imaginary (D) irrational and distinct

Ans. (C)

Sol. a + b

= =ab

2 2

b 8

second equation becomes

x2 + 10x + 24 = 0

D < 0 Þ imaginary roots

4. If = - -x 2 3 and value of x4 + 8x3 + 16x2 + 4x + 3 = - -( a b) , where a, b Î N, then value of

a + b is equal to -

(A) 52 (B) 11 (C) 40 (D) 48

Ans. (A)

Sol. = - -x 2 3 Þ x2 + 4x + 1 = 0

x4 + 8x3 + 16x2 + 4x + 3 = (x2 + 4x + 1) (x2 + 4x – 1) + 4x + 4

At = - -x 2 3

LHS ( )= + - - +0 4 2 3 4 - - = - - Þ = =a b 4 48 a 4, b 48

a + b = 52

5. For p > 0 & q > 0 if p2q3 = 32, then the minimum value of 2p + 3q is-

(A) 12 (B) 36 (C) 25 (D) 10

Ans. (D)

Sol. + + + +

³ 2 3 1/5p p q q q

(p q )5

Þ (2p + 3p)min = 10

6. The value of ( )( ) æ ö+ ç ÷è ø

2

2 2 163

log log log 36 log 9 is equal to-

(A) –1 (B) 2 (C) 3 (D) 5

Ans. (C)

Sol. ( )( ) +2 2log log 4 4 ( )= +2log 2 2 = 1 + 2 = 3


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RAT_TEST PAPER

7. Complete set of values of m, for which point (m,1) lies in smaller segment formed by circle

x2 + y2 – 3x + 1 = 0 and line 2x – y = 2, is-

(A) (1,2) (B) æ öç ÷è ø

3,2

2 (C)

æ öç ÷è ø

31,

2 (D) ( ) ( )-¥ È ¥,1 2,

Ans. (C)

Sol. S1 < 0 Þ m2 – 3m + 2 < 0

Þ m Î (1, 2)

and (2m – 1 – 2)æ ö- - -


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RAT_TEST PAPER

10. If a and b are roots of x2 – 21x + 4 = 0 and ba

b a, are roots of px2 + qx + 2 = 0, then value of

of (26p + q) is

(A) 12 (B) 15 (C) 9 (D) 6

Ans. (C)

Sol. a + b = 21

ab = 4

( )a + b = a + b + ab2 2 then we get a + b = 5

\ required equation 4x2 – 95x + 2 = 0

11. The value of + °

°4 3 3 cosec70

sec 70 is-

(A) 3 (B) 3 (C) 2 (D) 2

Ans. (A)

Sol. + 8° ° ° + °æ ö= ç ÷

° °è ø(4 sec 2 ) 4sin 20 cos20 sin 20

3 3cosec20 cos20

° + ° + °æ ö= ç ÷

°è øsin 40 sin 40 sin 20

3cos20

° + ° °æ ö= ç ÷

°è øsin 40 2sin 30 cos10

3cos20

° + °

=°

(sin 40 sin 80 )3

cos20

° °æ ö= ç ÷

°è ø2sin 60 cos20

3cos20

=3, 3 3

12. If < ++ -5 3

1x 2 x 1

, then x Î

(A) (–2,1) (B) ( ) ( )-¥ - È ¥, 2 1,

(C) R – {–2,1} (D) (1,¥)

Ans. (B)


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RAT_TEST PAPER

Sol. + -

<+ -5 3 x 1

x 2 x 1

+

<+ -5 2 x

x 2 x 1

+

Þ - <+ -5 2 x

0x 2 x 1

( )

( )( )- - +

Þ <+ -

25x 5 x 2

0x 2 x 1

( )( )- - - -

Þ <+ -

25x 5 x 4 4x0

x 2 x 1

( )( )

- + -Þ <

+ -

2x x 90

x 2 x 1

( )( )

- +Þ >

+ -

2x x 90

x 2 x 1

( )( )

Þ >+ -

10

x 2 x 1

13. The sum of series + + + +101 101101 101

3 1011 2101 101 101 101

0 1 2 100

C CC C2 3 ...... 101

C C C C equals

(A) 5050 (B) 5051 (C) 4950 (D) 5151 Ans. (D)

Sol. ( )-

= = -101

rr 101

r 1

r. CT 102 r

C

( )=

= -å101

r 1

sum 102 r = 101 + 100 + ..... + 2 + 1 = 5151

14. The distance between pair of parallel lines 9x2 – 24xy + 16y2 – 6x + 8y – 3 = 0 is -

(A) 54

(B) 45

(C) 1 (D) 32

Ans. (B) Sol. (3x – 4y + 1) (3x – 4y – 3) = 0

dist -

=+

1 2

2 2

c c

a b=

+4

9 16=

45

15. If (a,b) lies on circle x2 + y2 = 25, then minimum value of +a b2 2225 25

is -

(A) 4 (B) 8 (C) 14

(D) 16

Ans. (D) Sol. x = 5cosq & y = 5cosq min(9sec2q + cosec2q) = (3 + 1)2 = 16 min = 16


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RAT_TEST PAPER

16. Let Tr denotes the rth term of series 5 + 11 + 19 + 29 +..., then value of ®¥

= +å

n

nr 1 r

10lim

T 1 is

(A) 5 (B) 8 (C) 10 (D) 16

Ans. (A)

Sol. S = 5 + 11 + 19 + 29 +... + Tr

S = 5 + 11 + 19 + ...........+ Tr

——————————————

0 = 5 + (6 + 8 + 10 ...... (r – 1) terms) – Tr

Þ Tr = r2 + 3r + 1

Þ Tr + 1 = (r + 1)(r + 2)

Þ ®¥

=

=+å

n

nr 1 r

10lim 5

T 1

17. The coefficient of x5 in the expansion of (1 + x2)5(1 + x)2 is

(A) 10 (B) 15 (C) 20 (D) 25

Ans. (C)

Sol. Coefficient of x5 in (1 + x2)5(1 + x)2

= Coefficient of x5 in (1 + 5x2 + 10x4 + .......)(1 + 2x + x2) = 20

18. Area of the parallelogram having sides 14x – 21y + 15 = 0, 14x – 21y – 6 = 0, 2x – 6y + 9 = 0 &

2x – 6y – 3 = 0, is equal to

(A) 6 (B) 8 (C) 10 (D) 3

Ans. (A)

Sol. use formula ( )( )

( )- -

-1 2 1 2

1 2

c c d d

m m

19. The number of ways of selection of 4 letters of the word 'PERFECT " is -

(A) 15 (B) 21 (C) 25 (D) 31

Ans. (C)

2 Alike + 2 different = =5

2C 10

All 4 different = =6

4C 15

\ Total = 24

20. If the letters of the word ' AKALA' are arranged as in the dictionary then the word which appears

on the 8th position is

(A) AAKAL (B) AKALA (C) AKAAL (D) AAKLA

Ans. (B)


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RAT_TEST PAPER

CHEMISTRY

This section contains 20 multiple choice questions. Each question has four choices (A),(B),(C) and (D) out of which only one is correct

21. In figure, A and B are two adiabatic curves for two different gases. Then A and B corresponds to :

(A) Ar and He respectively (B) He and H2 respectively

(C) O2 and H2 respectively (D) H2 and He respectively

Ans. (B)

Sol. Slope = –g dPdV

As slope of A > slope of B

\ g of A > g of B

or A ® Helium

B ® Hydrogen

22. If Z is a compressibility factor, vander Waals equation at low pressure can be written as :

(A) Z = 1 + RTPb

(B) Z = 1 – a

VRT (C) Z = 1 –

PbRT

(D) Z = 1 + PbRT

Ans. (B) Sol. In low pressure region, vanderwaal equation becomes.

Z = 1 – m

aRTV

23. The molarity of a solution obtained by mixing 750 mL of 0.5(M) HCl with 250 mL of 2(M)HCl will be :

(A) 0.875 M (B) 1.00 M (C) 1.75 M (D) 0.975 M Ans. (A)

Sol. 1 1 2 21 2

+=

+fM V M VM

V V

3 10.5 24 41

´ + ´= = 0.875 M

24. In which of the following reactions H2O2 acts as a reducing agent ?

(a) H2O2 + 2H+ + 2e¯ ¾® 2H2O

(b) H2O2 – 2e¯ ¾® O2 + 2H+

(c) H2O2 + 2e¯ ¾® 2OH¯

(d) H2O2 + 2OH¯ – 2e¯ ¾® O2 + 2H2O

(A) (a), (b) (B) (c), (d) (C) (a), (c) (D) (b), (d)


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RAT_TEST PAPER

Ans. (D) Sol. H2O2 acts as reducing agent when it releases electrons. i.e. (b) & (d)

25. An acid HA ionises as

HA H+ + A–

The pH of 1.0 M solution is 5. Its dissociation constant would be :- (A) 1 × 10–10 (B) 5 (C) 5 × 10–8 (D) 1 × 10–5

Ans. (A)

Sol. HA H+ + A–

pH = 5

\[H+] = 10–5 Q [H+] = +aK C

10–5 = ´aK 1

Ka = 10–10

26. How many moles of electron weigh one kilogram :

(A) 6.023 × 1023 (B) 1

9.108 × 1031 (C)

6.0239.108

× 1054 (D) 1

9.108 6.023´ × 108

Ans. (D)

Sol. 9.108 × 10–21 kg is the wt. of 1 e– = A

1N

moles of e–

So 1 kg is the wt. of 1 e– = 31A

1 19.108 10 N-

´´

= 31 231

9.108 10 6.023 10-´ ´ ´ =

8109.108 6.023´

.

27. Two closed bulbs of equal volume(V) containing an ideal gas initially at pressure pi and

temperature T1 are connected through a narrow tube of negligible volume as shown in the figure

below. The temperature of one of the bulbs is then raised to T2. The final pressure pf is :-

(A) 1 2i1 2

T T2pT T

æ öç ÷+è ø

(B) 1 2i1 2

T TpT T

æ öç ÷+è ø

(C) 1i1 2

T2pT T

æ öç ÷+è ø

(D) 2i1 2

T2pT T

æ öç ÷+è ø

Ans. (D)

28. Gaseous N2O4 dissociates into gaseous NO2 according to the reaction N2O4(g) 2NO2(g) at 300

K and 1 atm pressure, the degree of dissociation of N2O4 is 0.2. If one mole of N2O4 gas is

contained in a vessel, then the density of the equilibrium mixture is : (A) 3.11 g/L (B) 4.56 g/L (C) 1.56 g/L (D) 6.22 g/L Ans. (A)

T1p ,Vi p ,Vi

T1 T1p ,Vf p ,Vf

T2Þ


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RAT_TEST PAPER

29. The quantum number of four electrons are given below -

I. n = 4, l = 2, ml = –2, ms = – ½

II. n = 3, l = 2, ml = 1, ms = + ½

III. n = 4, l = 1, ml = 0, ms = + ½

IV. n = 3, l = 1, ml = 1, ms = – ½

The correct order of their increasing energies will be -

(A) IV < III < II < I (B) IV < II < III < I (C) I < II < III < IV (D) I < III < II < IV

Ans. (B)

30. The correct order of electron affinity is :-

(A) Cl > F > O (B) F > O > Cl (C) F > Cl > O (D) O > F > Cl

Ans. (A)

31. In which of the following processes, the bond order has increased and paramagnetic character has

changed to diamagnetic ?

(A) N2 ® N2+ (B) NO ® NO+ (C) O2 ® O22– (D) O2 ® O2+

Ans. (B)

32. The correct statement for the molecule, CsI3, is :

(A) it is a covalent molecule. (B) it contains Cs+ and –3I

(C) it contains Cs3+ and I¯ ions. (D) it contains Cs+, I¯ and lattice I2 molecule.

Ans. (B)

Sol. It is a simple & popular fact.

33. The set representing the correct order of first ionization potential is :

(A) K > Na > Li (B) Be > Mg > Ca (C) B > C > N (D) Ge > Si > C

Ans. (B)

Sol. Down the group the effective nuclear charge remains almost constant. But down the group with

increasing atomic number the number of atomic orbits increases and there by atomic size

increases. As a result, the distance of valence shell electron from nucleus increases and attraction

between them decreases and therefore ionization energy decreases.

34. The number of isomers of dibromobiphenyl (Biphenyl = C6H5-C6H5) is

(A) 8 (B) 10 (C) 12 (D) 4

Ans. (C)


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RAT_TEST PAPER

Sol. + + + + +

+ + + +

+

Overall 12 isomers.

35. The IUPAC name of the following compound is

CONH2

(A) 3-Aminocarbonylpent-1-en-4-yne

(B) 2-Ethenylbut-3-yn-1-amide

(C) 2-Ethynylbut-3-en-1-amide

(D) 3-Aminocarbonylpent-4-en-1-yne

Ans. (C)

36. The order of basicity among the following compounds is

(A) II > I > IV > III (B) IV > II > III > I

(C) I > IV > III > II (D) IV > I > II > III

Ans. (D)

NH

NH2H3CI II III IV

N NH HN N

NH2

NHH2N


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RAT_TEST PAPER

37. Among the following compound that is not aromatic?

(A) (B) (C) (D)

Ans. (D)

Sol. (D)

It is non aromatic since in tub shape it is non-planar

38. Inductive effect is a polarisation of a

(A) sigma bond (B) p -bond (C) co-ordinate bond (D) conjugated system.

Ans. (A)

39. The IUPAC name of the following compound is :

(A) 3,5-dimethyl-4-propylhept-6-en-1-yne

(B) 3-methyl-4-(3-methylprop-1-enyl)-1-heptyne

(C) 3-methyl-4-(1-methylprop-2-ynyl)-1-heptene

(D) 3,5-dimethyl-4-propylhept-1-en-6-yne

Ans. (A)

40. Identify the alkene which will not provide the following alcohol upon oxymercuration

demercuration.

(A) (B) (C) (D)

Ans. (D)

O

CHH C3CH3

CH3CH2


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RAT_TEST PAPER

PHYSICS

This section contains 20 multiple choice questions. Each question has four choices (A),(B),(C) and (D) out of which only one is correct

41. Fleming’s left hand rule is used to find : (A) The direction of induced current (B) Force acting on current carrying conductor placed in magnetic field. (C) Force acting on a charged particle moving in electric field. (D) None of these Ans. (B) 42. Analyse the given statements and choose the correct option. Statement-I : The energy of charged particle moving in a uniform magnetic field does not

change. Statement-II : Work done by the magnetic field on the charge is zero. (A) Both statement-I and statement-II are correct and statement-II is the correct explanation of

statement-I. (B) Both statement-I and statement-II are true but statement-II is not the correct explanation of

statement-I. (C) Statement-I is true but statement-II is false. (D) Statement-I is false but statement-II is true. Ans. (A) 43. Two trucks 'A' and 'B', one loaded and the other unloaded are moving and have same kinetic

energy. The mass of 'A' is double that of B brakes (providing same retarding force) are applied to both and are brought to rest. If the distance covered by 'A' before coming to rest is S1 and that of B is S2, then

(A) S1 = S2 (B) S1 = 2S2 (C) 2S1 = S2 (D) S1 = 4S2 Ans. (A) 44 Geothermal energy is energy : (A) Of sea waves (B) Of tides (C) Harnessed from the heat of the earth (D) None Ans. (C) 45. Two equal bar magnets are kept as shown in the figure. The direction if resultant magnetic field

indicated by the arrow head at the point P is (approximately) :-

(A) (B) (C) (D) Ans. (C)

N

S

PNS


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RAT_TEST PAPER

46. No force acts on the charge fired through a magnetic field, when the angle between its velocity

and magnetic field is :

(A) p (B) 34p

(C) 2p

(D) 4p

Ans. (A)

47. The V-I graph for two conductors A and B is as shown in the figure. Which conductor will

consume more power when connected across 220V supply :

(A) B (B) A

(C) Both will consume same power (D) None of these

Ans. (A)

48. The strength and direction of magnetic field due to a current carrying conductor depends upon

(A) magnitude of current in conductor (B) distance from conductor

(C) direction of flow of current (D) all of these

Ans. (D)

49. In moving from equator to pole, acceleration due to gravity

(A) decreases (B) increases

(C) first decreases then increases (D) cannot say

Ans. (B)

50. A 220 V and 100 W lamp is connected to 220 V power supply. What is the power consumed?

(A) 100 W (B) 200 W (C) Less than 100 W (D) None of these

Ans. (A)

51. A strong magnetic field is applied on a stationary electron, then–

(A) The electron moves in the direction of the field

(B) The electron moves in an opposite direction

(C) The electron remains stationary

(D) The electron starts spinning

Ans. (C)

52. Two electric bulbs rated 60W, 220V and 100 W, 220 V are connected in series across 220 V

supply. The net power of the comination is–

(A) 160 W (B) 37.5 W (C) 40 W (D) 100 W

Ans. (B)

I

V

A

B


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RAT_TEST PAPER

53. Figure (i), (ii), (iii) and (iv) respectively correspond to :

(i) (ii)

(iii) (iv)

(A) The short-sighted eye, the correction of long-sight, the long-sighted eye and the correction of

short-sight

(B) The short-sighted eye, the correction of short-sight, the long-sighted eye and the correction

of long-sight

(C) The long-sighted eye, correction of short-sight, the short-sighted eye and the correction of

long-sight

(D) None of these

Ans. (B)

54. Three equal resistors connected in series across a source of emf together dissipate 10W of power.

If the same resistors are connected in parallel across the same source of emf, the power dissipated

will be :

(A) 30 W (B) 60 W (C) 90 W (D) 120 W

Ans. (C)

55. When a bar magnet is broken into two pieces :

(A) We will have a single pole an each piece

(B) Each piece will have two like poles

(C) Each piece will have two unlike poles

(D) None of these

Ans. (C)

56. Two bulbs consume same power when operated at 200 V and 300 V respectively. When these

bulbs are connected in series across a D.C. source of 500 V, then :-

(A) Ratio of potential difference across them is 3/2

(B) Ratio of potential difference across them is 9/4

(C) Ratio of power consumed across them is 4/9

(D) Ratio of power consumed across them is 2/3

Ans. (C)

57. Explosion of crackers is example of :

(A) Nuclear fission (B) Nuclear fusion

(C) Chemical reaction (D) None of these

Ans. (C)

I


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RAT_TEST PAPER

58. When objects at different distances are seen by the eye, which of the following remains constant?

(A) the focal length of eye lens (B) the object distance from eye lens

(C) the radii of curvature of eye lens (D) the image distance from eye lens

Ans. (D)

59. If there are two bulbs B1 (150 W, 220 V) and B2 (60W, 220 V) then choose the correct statement :

(A) Resistance of B2 is more than B1 (B) Resistance of B1 is more than B2

(C) Resistance of Both B1 and B2 is same (D) Can’t say

Ans. (A)

60. A magnet (M) is in motion near a circular conducting ring (C). Then direction of Induced current

in coil (C) as seen from the side of magnet is :

(A) Clock-wise (B) Anti Clock-wise

(C) There will be no induced current (D) Either clock-wise or anti-clockwise

Ans. (A)

C

MSN

(SAMPLE PAPER C XI)...(A) rational and distinct (B) real and equal (C) imaginary (D) irrational and...

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