---- ---- ---- ---- ---- •-A .

,____ ____
_

PART-I : PHYSICS • .
SECTION - I
(SINGLE CORRECT ANSWER TYPE)
This section contains 20 mult iple choic
e questions. Each question has 4 optio
ns ( 1 ), (2), (3) i:1nd (4) for
its answer, out of whic h ONLY ONE optio
n can be correct.
Mark ing scheme: +4 for correct answ
er, O if not attempted and -1 if not corre
'- ~ C]S In the arran geme nt show n in figure the ends
ct.
p and Q of an un stretchable string move down
-, r with unifo1m spee d U. Pulleys A and B arc
fixed. Mass M moves upwards with a speed-
ward s

..f
B

p
·1
l
1• 1L
~ 2Uc os0 (B) Ucos e 2U u
~
(C) cos 8 (D) cos 0
A plan k havi ng mass M is placed on smooth
horizontal surface. Block of mass m is place
d on it
coefficient of friction between block and plank
is· µ 0 + kx , where k is constant and x is relat
ive
displacement between block and plank. A force
F = at is applied on block, where a = 1O; t
second. The value of to when relative motion is in
_will occur b~~e en block and plank is (g = 10
ms-2)
m F C\
""".,_ ~~.,

:\I "1
smooth
1--:-::-~ I ~~
(A) µoM + µ0M2 (B) µom + µ0M2 ~~'
m m
(C) µom + µom2 ~ µoM + µom 2
l M- t~) ).,\'I V'~ - ~{
M M M

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3. In the figure given below, the position-time graph of a particle of mass 0.1 Kg is shown.
The impulse at t = 2sec is

i{,N)
6
4
2

(A) 0.2kgmse c-1 1

_(ia -0.2kgm sec-

(C) O.lkgmsec -• ~-'-0.4 kgm sec-' .

4. A 60 kg man stands on a spring scale in the lift. At some instant he finds, scale readmg has changed
from 60kg to 50kg for a while and then comes back to the original mark. What should we conclude?
(A) The lift was in constant motion upwards
(B) The lift was in constant motion downwards
(C) The lift while in constant motion upwards, is stopped suddenly
@ The lift while in constant motion downwards, is suddenly stopped
A force F = -K(yi + xj)
(where K is a positive constant) acts on a particle moving in the .xy-plane.
Starting from the origin, the particle is taken along the positive x-axis to the point (a, 0) and then
parallel to they-axis to the point (a, a). The total work done by the force Fon the particle is
. .. "
(A) - 2Ka2 • - ~ 2Ka2 ' ~. (C) - Ka2 (D) Ka2
A particle of mass m is moving in a horizontal circle of radius r under a centripetal force equal to
- K I r2 , where K is a constant. The t~tal energy of the particle is
K
(A)-
2r C@ - ~ = t (\\ "\
K K
(C) - - -: \J (D)-
- r r
A shell in fight explodes into 'n' equal fragments, k of the fragments reach the ground earlier than the
other fragments. Then the acceleration of their centre of mass subsequently will be-
~ (B) (n-k)g -· Cl_<...1r..;:
(n-k)g (n-k)
(D) ..,__--<-g
(C) k n

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 --------

8. A l O kg block is connected to an empty I kg bucket by a cord running over a

friction less pulley. The
static friction coefficient is 0.4 and the kinetic friction between the table and
block is 0.3. Sand is
gradually added to the bucket until the system just begins to move. The mass
of sand added to the
buck.ct and the acceleration (in m/s 2) of the system respectively (g = acceleration
due to gravity)

(A) 5kg, g/10 (B) 3 kg,J-, @3 kg, g/1)-:, (D) 5 kg, g/2
9. A particle of mass 4m is projected from the ground at some angle with horizont
al. Its horizontal range
is R. At the highest point of its path it breaks into two pieces of masses m and
3m, respectively, such
that the smaller mass comes to rest. The larger mass finally falls at a distance
x from the point of
projection, where x is equal to
2R
(A)- (C) SR
3 (D) none of these
4
10. A ring of uniform linear mass density A and radius R is rotated about a vertical
axis
passing through its centre and perpendicular to plane of ring with constant angular
speed ' c.o '. The
tension in the ring is
(A) A.o.>2R 2 /4 (8) (11.ciR 2 )/2 (C) 11.olR2 /8 ®Ac.o2 R 2
A 10kg mass moves along x-axis. Its acceleration as a function of its position is shown
in the figure. The
total work done on the mass by the forces as the mass moves from x = 0 to x =
8 cm is

VJ J /,"
~
20
15
J- )~ ·'E
~
='
10
~ 5
Jv y,
0 2 4 6 g X (c111)
d
8x10-2 J J l 6x 10-2 J
(A)

(C) 4x I0--1 J
).
vJv
)

-t
j_
">L (8)

(D) 1.6x 10-3 J

Space for rough work

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~
vJvx 10

l'\arayana Jaipur HO: 8-28, Gopalpura Bypass Road, I0-B Scheme, Near Ridhi
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 , . .
12. Th~ slop~ ofkinctk energy displacement curve for n given particle in motion is
lA) Equal to the acceleration of the particle (D) Inversely proportional to the acceleration
(g,'Oirectly propoiiional to the acceleration (D) None of the above
~ '®) A rarticlc starts at •A' with initial speed V0 • It moves along a circular ~•th under the action of a
•I" variable force which is always directed towards 'B'. A and Bare end pomts of a diameter. When it
reaches the point •p• as shown, the speed is (Neglect the effect of gravity & take

Jtan 20 d0= -21n

• I
cos 01 ).
2
..
\

I
I:;
C
\ .

(B) 2V0 (C) 3V0 (D) 4V0

14. A body of mass 2 kg slides down a curved track which is quadrant of a circle of radius I metre. All the
swfaces are frictionless. If the body starts from rest, its speed at the bottom of the track is (g =9.8ms·2)
---lm~
---------l 1
I
,1,,.

il
0.43 m/sec (B) 2 mlsec (C) 0.5 mlsec (D) 19.6 m/sec
) 5. From a unifonn circular plate of radius 2R a circular hole of radius R cut. The centre of the circular
hole is at a distance of R/3 from the centre of the larger circular plate. Then the position of the centre
of mass of the remaining plate is
(A) Along the line joining the centers and lies at a distance 4R/9 left side, from the center of the bole "'
(B) Along the line joining the centers and lies at a distance 4R/9 right side, from the center of the hole
@Along the line joining the centers and lies at a distance R/9 left side, from the center of the bole"
(D) Along the line joining the centers and lies at a distance R/9 right side, from the center of the hole
I 6. The energy required to accelerate a car from 10 mis to 20 mis is X times the energy
required to accelerate the car from rest to 10 mis, then X value is
(A) 1 (B) 4 (C) 2 ~3
I
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~ A unifo1m rod of length / is being rotated in a horizontal plane with
a constant angular speed about an
axis passing through one of its ends. If the tension generated in the
rod due to rotation is T ( x) at a
distance x from the axis, then which of the following graphs depicts
it most closely?
T(X, T(JC )L---- -
(A)
(C) T(x) (0)

I X I I
X I X JC
18. The pctential energy between two atoms in a molecule is given by
U(x)= _!!__!!_;where a and bare
x'2 x6
positive constants and x is the distance between the atoms. The atom
is in stable equilibrium when

(A) X = 6 (B) x:~

b (C) X =0
19. A block of mass m initially at rest is dropped from a height
h on to a spring of force constant k. the
maximum compression in the spring is x then

1 2
(A) mgh = -kx RA.
~ mg(h + x) = 1 kx 2
2 2
1 1
(C) mgh = k(x +h) 2 (D) mg(h + x) = -k(x + h)2
2 2
20. An engine pump is used to pump a liquid of density P continu
ously through a pipe of
cross-sectional area A. If the speed of flow of the liquid in the pipe
is v, then the rate at which kinetic
energy is being imparted to the liquid is
1 2 1
(B) 2 Apv (C)2 Apv (D) Apv

Space for ro11gh work

\

Narayana Jaipur HO: 8-28, Gopalpura Bypass Road, I 0-B Scheme,

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 SECTION-II
(NUMERICAL VALUE ANSWER TYPE)
in
each question Is a Numerical value. If the Answer
This section contains 10 questions. The answer to 10 quest ions and
to Answer any 5 only out of
the decimals, Mark nearest Integer only. Have
ding to the follow ing marki ng scheme:
question will be evaluated accor
d answe r, -1 in all other cases.
Marking scheme: +4 for corre
J
A piece of wire is bent in the shape of a parabola y = /cx 2
( y- axis vertical) with a bead of mass N
·m' on it. The bead can slide on the wire without frictio
n. It stays at the lowest point of the parabola
I
paraJlel to the x - axis with a constant
when the wire is at rest. The wire is now accelerated
n of the bead, where the bead can stay ar
accele ration 'a'. The distance of the new equilibrium positio
a . .\-,.-.- e ) ?.,, f.. ') <.,
'n'
rest with respect to the wire, from the y - axis is - - . Find
2ngk
connected by a massless spring as shown in
Two blocks of masses IO kg and 20 kg respectively are
t shown, tht: 10 kg block has acceleration
figure. A force of 200 N acts on the 20 kg block. At the instan 1\-j
12 m I sec in the direction of applied force.
Then the acceleration of 20 kg block is -
I
2

/2 t 4~•'8foiN7 0

in the figure. The cube is moving with a

I
A solid sphere of mass 2 kg is resting inside a cube as shown I
surfaces ar~ smooth. The sphere is at rest
velocity v = (Sti + 211)n Is . Here t is the time in second. All
sphere on the cube is (Take g = 10 m/~J
with respec t to the cube. Then the total force exerted by the
y

D
D s

C
(side ,iew)

0 X

figure. The Minim um

24. 2-.! block of mass I 5 kg is resting on a rough inclined plane as shown in the coeffic ient of friction
ard slipping, the
--- horizontal force F of 50N is required to prevent downw
' 2
Om/ s )
between the surfaces of contact is _!_, then x value ( g = I
X

Sp11ct for r i,gh ~rk

)
l~)

V1 1i , ) -+ ,, , "- -
) l)
FtZ J7-.-'1 2 -1 1ii'
=- ¾
e, Near Ridhi Sidhi Circle, Jaipur, Rajasthan 302018
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 lnitial velocity of the block v =45 i F=25 (-f). Jt coefficient of static
while external force on it is
and kinetic friction arc 0.3 and 0.2 respectively then distance travelled by the block in 12 sec. (g = JO
m/s2) is:

u =-4S m/sec
m= 10 kg

~v 26. ~ woode1~ block is cut into two pieces, one with three times the mass of the other. A small depressio_n
J
1
3 1s made m both faces of the cut so that a light fire cracker can be placed in it and the block ts
--~ 1,, "><.. reassembled. The reassembled block is set on rough surface and the fuse is lit. When the fire cracker
explodes, the two blocks separate. Then the ratio of distances travelled by lighter to heavier blocks is

27. A bomb of mass 3m kg explodes into two pieces of mass m kg and 2m kg. If the velocity of m kg mass
is 16 mis, if the total kinetic energy relea.sed in the explosion is mX J, the value of X is

28. The displacement x of a particle moving in one dimension under the action of a constant force is
0 related to the time t by the equation t = J; + 3 , where x is in meters and t is in seconds. The work done
by the force in the first 6 seconds is

~29. The distance of centre of mass fyom end A of a one dimensional rod (AB) having mass density

,l = Ao (I - ; ) kglm and length L ( in meter) is 3: m. The value of a is _ _ _. (where xis the

distance from end A)

30. The ratio of power of two motors is t , that are capable of raising 300 kg water in 5 minutes and
L6 x+l
50 kg water in 2 minutes respectively from a well of 100 m deep. The value ofx will be-

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j
 . PART-II : CHEMISTRY .
SECTION- I
(SINGLE CORRECT ANSWER TYPE)
( 1), (2), (3) and (4) for
This section contains 20 multiple choice questions. Each question hos 4 options
fts answer, out of which ONLY ONE option can be correct.
Marking scheme: +4 for corred answer, 0 if not attempte d and -1 if not correct.

2
Decreasing order of ionic radii of Se
2
-, 1-, Br-, 0 - and p- is

~5e2- 1- B - 0 2- p- (B) 1- Se 2- 0 2- Br- p-

~ ' , r, ' ' ' ' '
2 2
(q Se -, 1-, Br-) p-, 0 - (D) 1-,Se ,Br-, 0
2- 2-, p-
-
For an atom X, measured values of different radii are 100pm, l 12pm and 90pm.These
values
r~tive1 y are
(A)Crystal, van der Waal's and covalent
(8) crystal, covalent and van der Waal 's
€)coval ent, Van der Waal's and cry~tal_,
(D) Van der Waal's, covalent and crystal
group. This
33. The first element of a group in many ways differs from the other heavier members of the
due to •-
..
.
• ·• F ..~ •

(A) The small size . l

' I• • ,,

(B) The high electro ne~tivity and hlgh ionizati~n p~tenti~i

(C) The unavailability of d-orbitals .·-
@An of the above •• ;.. . , •• '

34. With respect to oxygen, maximum valency is shown by

~ Halogen family (B) Oxygen family
(C) Nitrogen family (D) Boron family
35. Select the correct statement(s)
(A) Along a period from left to right, acidic nature of oxides incr~ases
(B) Along a group from top to bottom, basic nature of oxides increases
(C)Ox ideofh ydrog enis~ ~ J-
~AU of the above are correct statements '

Spt1ce for rough work

u
fl'J_ '""' - - 'r\' .._.. ""- <:) \-\ -
.._,
-
~ 2.5:J ~~ °'~~~',\,..ae~,~

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• .
 -- ----- ----- ~--- -~--

36. Given,
Bond energy ofll-H bond-104.2kcal mot'
Bond energy of F-F bond=36.6kcal mot'
Bond energy ofH-F bond=l34.6kc&l mor•
Electro negativity of Hon Pauling's scalc=2.05
Thus, electro negativity of fluorine is
0.60 ([3) 5.65 (C) 1.55 (D) -3.60
37. The general electronic configuration of the outermost and penultimate shell for a d-block element is
6
given by (n-l)s2p d.rm-" .For a divalent cation of an element with n=4,x=6 and y=2, number of
protons is
(A) 24 (B) 25 ~6 (D) 27
38. The oxidation numbers of Pin Ba(H2PO2)1,Ba(H 2POJ2 and Ba(H2PO,J1 are respectively
(A)+l,+2,+3 (8)+3,+2,+I @+l,+3,+5 (D)+2inall
Oxidatiorw-3-~~efined as the terms
I. Gain of electron and hydrogen ~Gain of oxygen and loss of electron
Ill. Increase in oxidation number ~ecrease in oxidation number
Select the correct terms
(@ I and II (B) II and III (C) I and III (D) I and IV

40. PCl:xF's-:x Shows non-polar behaviour when x is e) J)

®o, 3, 5 (B) 0,2,5 (C) 2, 1, 4 (D) 0, 4, 1

41. Which of the following species does not show disproportionation reaction?
(A) C/0- (B) C/O2- (C) C/O3-

42. Which of the following can disproportionate ?

(A) HNQ3 (@) NH3
43. Oxidation number of P in HJPO" is
(A)-3 __<B) +3 @+s (D)-5
44. Number of electrons lost by each molecule of H2C2O• in the given reaction is-
•J '1
MnO4+H 2C2O4 +H2SO4 ➔ MnSO 4 +CO 2 +H 2O
(A) 3 (B) 4 (C) 1 ~2

Space for ro11g/r work

)

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•.

~S. A (''-·m,pound is fonn~d with three ckmcnts A, ll and C

Elt-me11t Oxidation number
A +2
B +S
C -2
Thus. possible fonnula of the compound is
(A) A~tB<;)l ~3(B C.. )2 (D) ABC2
46. Covalent nature of NaF, Na O and Na N in the increasing order is
2 1

(A) Na3 N < Na2O < NaF ~NaF < Na2O < Na1 N
(C) Na20 < NaF < Na N (D) Na 2O < Na1 N < NaF
3
\
\\'hich pair is not in the correct order of lattice energy? _
4' .-t<
(A) KO< Mg0 (B) AIN > MgO
©)Be C03 > MgCq (D) Na2 SO.. < K 2SO..
Consider following types of bonds.
1. ionic bond II. Covalent CT -bond
Ill. Coordinate bond TV. Covalent tr -bond
All these bonds are presen t"'-
(A) NaOH • ~ NaN03 (D) NaN3
49. Xe/; is isostructural with
_. __ (A) Tef; @) /C/ 2- (C) SbC/3 (D) BaC/2 ~
~~ - • I: B atom is s/'2--hybridised in B,H, Sf,~
Statemr o• II: Tbcre is no Jone pair or unpaired electron in B H
2 6 v
(A) Both statement I and statement II are correct and statement II is the correct
explanation of
mtemen tl
(B) Boch statement I and statement Il are correct and statement II is not the
correct explanat ion of
staaane ntl
(C) Stasanen• I is correct but statement II is incorrect
eState meot II is CC>rTeCt but statement I is incorrect

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 SECTION-II
(NUMERICAL VALUE ANSWER TYPE) /
This section contains l O questions. The answer to each
question Is a Numerical value. II the' Answer in
5 only out of 10 questions and
the decimals, Mark neares t Integer only. Have to Answe r any
~uestion will be evalua ted according to the following
marking schemes
cases.
Marking scheme: +4 for correct answe r, -1 in all other

51. Number of nodal planes in 1/ 2 px orbitals arc t

52.2-H ow many of the following molecule are polar? z_

•
0_Jfl, ~, NO, so2
~,C ~/2 ,o/s ,9)2
- ~3. Mno.- Oxidises H 20 2 to 0 2 in acidic medium

x.MnO4- + yH 2 0 2 + zH+ ➔ Mn + + 0 2 + H 2O
2

The Sum of Coefficient x, y and z is

le ofF2.
54. 6 How many lone pair of electrons are present in one molecu
volume at 0°C and I atm. pressure is-
55. I The numbe r of moles ofHe(g ) that occupies 22.4 litre of
56. <poAt what temperature (in K) most probable speed of 2
0 molecules have the same value of root mean

square speed of 0 2 molecules at 300K?

4ezcx .,Con sider the follo~ ng ~olecules

XeF2, If3, SF,., BrFs, SF6, IF,
Let, A= Number of non-po lar and planar molecules
'•

B = Number of polar and non-planar molecules

Find 100 x IA-Bl =?
ature are filled with 44g of H 2 in
~8. The closed containers of the same capacity and at the same temper
. .
, second container is I atm. That of
one and 44g of CO2 in the other. If the pressure of CO2 in the
hydrogen in the first container would be (in atm)
59. 2 The unit of R, the universal gas constant is J mol-.r K->'. Find x + y.
60. Swn of bond order of CO and NO+ is
Z-+

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(12)
 PART-Ill: MATHEMATICS
SECTION- I
(SINGLE CORRECT ANSWER TYPE)
This section contains 20 multiple choice questions. Each question has 4 optio~s ( 1}, (2), (3) and (4) for
its answer, out of which ONLY ONE option can be correct.
Marking scheme: +4 for correct answer, 0 if not attempted and -1 if not corred.
~ 61. If the orthoccntre of the triangle, whose vertices are {l,2),{2,3)and {3,{l) _is {a,p), then the

quadratic equation Whose roots are a+ 4P and 4a + P, is

s 1)
;\
~ )
(A) x2-19x+90=0 (B) x2-20x+99=0
2
(q x -18x+80=0 (D) x 2 -22x+l20=0
~62. Let A.~ 0 be a real number. let a, p be the roots of the equation l 4x2 -3 lx + 32 = 0 and a, y be

therootsoftheequation 35x2 -53x+4A=0. Then a and

3 4
a aretherootsoftheequation
P r
2
(A) 7x +245x-250=0
(B) 49x2 + 245x+ 250 =0
(q 49x2 - 245x + 250 =0
(D) 7x2-245x+250=0

63. If a,p,y,8 are the roots of the equation x 4 +x 3 + x 2 + x+ 1 = O, then

a 2021 + p2021 + y202l + ~2021 .
u is equal to
(A) -4 (8) -1 (C) I · (D) 4
64. The number ofreaJ solution of the equation (¾or =-3 + x-x 2 is

, (A) 2 (8) 0 (C) I . (D) 3

2
65. If ax2 +bx+c =0 and bx +cx+a =0 have a common root and a,b,c are non-zero, then '
aJ +bJ +cJ
6abc

(A)_!. (8) _!.

2 (C) 1
4 (D) 3

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 66. The quadratic equation whose roots arc the x and y imcrccpts of the line passing through {J, I) and

~ing a triangle of area A with the a~cs, may be

2 2
~ x +Ax+2A=0 (B) x -2Ax+2A=0
2
(C) x - Ax+ 2A = 0 (D) x 2 - 2Ax- 2A = 0
~67. A square of side a lies above the x-axis and ha~ one vertices at the origin. The side passing through
the origin makes an angle a(O <a<![ I 4) with the positive direction of the x-axis. The equation
of its diagonal not passing through the origin is
(A) y( cosa+sina )+x(sina-cosa) = a (B) y( cosa+sina)+x(sina+cm:a )= a
~) y( cosa +sin a )+x(cos a-sin a)= a y(cosa-sina)-x(sina-cosa) = a
(D)

.lf'6s. One diagonal of a square is along the line 8x-15y=Oand one of its vertex is (1,2). Then the

equations of the sides of the square passing through this vertex are
'
(A) 7x-8y+9=0,8x+7y-22=0 (B) 9x-8y+7=0,8x+9y-26=0
(C) 23x-7y-9;:::: 0, 7x+ 23y-53 = 0 (D) None of these

~69. The line x + 3y - 2 = 0 bisects the angle between a pair straight lines of which one has equation
x- 7 y + 5 = 0. The equation of the other line is
(A) 3x+3y-l =0 (B) x-3y+2=0

(C) 5x+5y-3=0 . . of..these

(D) None ,

i 70. The area of the triangle fonned by the lines y = ax,'~+ y...,: i= 0, and the ·y-axis is equal to
a2
(C) _!_ ~
1 a2

(A) 2ll+al (B) II+al . 2 l+a <D> 211+al

~71. Consider the points A ( 3, 4) and B ( 7, 13). If P is a point on the line y = x such that PA+ PB is

minimum, then the coordinates of P are

(A) (12/7,12/ 7) (B) (-24/5,17 /5) (C) (31 /7,31 /7) (D) (0,0)

72. The value of cos (72K) cos (4K)

+ (6K).
7 cos 7 + 1s equal to

(A) -1 @-.!.2 • (C) --

1
3
(D) - -
I
4

• Space for rough work

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 .'
73. 1·hc value of cot ( 1t I 24) is

~./2.+ ✓3+2-./6 (8) .fi.- ✓3-2+ ✓6

(C) 3✓2-~-./6 ✓2+ ✓3+2+ ✓6
74. -
(D)

The set of nll possible values of 0in the interval ( 0, ,r) for which the points (1,2) and

(sin0, cos0) lie on the same side of the line x+ y =I is

(D) (o, :)
'
13 1
~5. The value of L (,r ( k -1) ,r
). is equal to
l•l
sm
. ( ,r +k,r)
sm -
-+~----!...- - .
4 6 4 6
(A) 3- ✓3 (D) 2( 2+ ..fi)
~- If tan A and tan B are the roots of the quadratic equation. 3x2 -1 Ox-
25 = 0, then the value of
3sin2 ( A+B) -1O sin(A +B)co s(A +B)-2 5cos 2 (A+B ) is
(A) 10 (B) -10 (C) 25 (D) -25
4-,7. The number of solutions of sin 7 x + cos7 x =1, x E [ 0, 4,r] is equal to ".
(A) 9 (B) 5 (C) 11
(D) 7
;!ps. If Os; x < 2,r, then the number of real • values of x, which
satisfy the equation
cosx+ cos2x +cos3 x+cos 4x = 0, is
(A) 3 (B) 5 (C) 7 (D) 9
~- The number of elements in the set S ={o e [O,2,r]: 3cos 4
0-5co s 2 0-2si n6 0+ 2 = o} is
(A) 10 (B) 8 (C) 9 (D) 12
80. If tan I 5° +
tan750
1
+
1
tanl05 0
+ tan 195° = 2a , then the value of (a+.!.) a
is
---

(A)4 (C) 4-2✓3 co) s-I ✓3

2

Space for rough work .

"':t:... + j - ( --- u
.,"- -t (~e , I ""> o
s:~ le--\ ~/q); )
<5,, " X ~ \J-t
-
Narayan• Jaipur HO: 8·28, Gopalpura Bypass Road, IO•B Scheme, Near Ridhi
Sidhi Circle. Jaipur, Rajutban 302018
(1S)
 SECTION-II
(NUMERICAL VALUE ANSWER TYPE)
in
This section contains l O questions. The answer to each question Is a Numerical value. If the Answer
and
the decimals, Mark nearest Integer only. Have to Answer any 5 only out of 10 questions
question will be
evaluated according to the following marking scheme:
Marking scheme: +4 for correct answer, -1 in all other cases.

2
If a, P are roots of the equation x + 5 ( .fi.) x + 1O= O, a > p and P,, = a" - P" for each positive
.mteger n, then the value of ( P.17 P.20 + 5✓2P. 17 P.19 ) .
,-;; 1s equal to
P.sP.9+5v2Pi; ----
ii. 3- The number of distinct real roots of the equation x' - 7 x - 2 = 0 is~ then k + l is equal to 2-

83. If a, p are roots of 6x -2.x + 1 = 0 and Sn =an+ pn then nLt

2
➔oc r=I
Lsr = _ __
2
I +x x x
x J+x x 2 =0 has roots a.,a2 ,a3 ,a4 then a 1a 2a 3a4 = _ _ __
~4.
.,
x- X 1+
J
For all real values of a and b lines (2a+b)x+ (a+3b)y+ (b-3a)=O and mx+2y+ 6=0 are
~5.
concurrenL Then -m is equal to _ __
If 5a + 5b + 20c = t , then the value of t for which the line ax+ by+ c-1 = 0 always passes through
a fixed point is _ _ __

t 87. • The value of 36{ 4cos 2 9°

,r 2,r 4,r 8.;r 16.1r .
-t){4cos
•
2 2 2
27° -t){4cos 81° -1 ){ 4cos 243° -1) is _ __

88. 96cos- cos-co s-cos-c os- 1s equal to _ _ __

33 33 33 33 33

S =' { XE ( , : ~- ,:
1
- 1[ 1[) 9J-tan T+9tan
2
:.1-J _X ~ 2 (X) ,then
=10} and P= ~tan • equal
} ( P-14 )2 1s
is9. Let
22 3 6

to _ _
90. ~ The number of distinct solutions of the equation log 112 lsin xi = 2 - log 112 !cos xj in the interval

[0, 2,r], is _j_.___

Space/or rough work

. Narayana Jaipur HO: B-28, Gopalpura Bypass Road, to-B Scheme, Near Ridhi Sidhi Circle, Jaipur, Rajasthan 302018
(16)