JEE Main 2017 Question Paper 09 Apr B.Tech

PHYSICS ÷ÊÒÁÃ∑§ ÁflôÊÊŸ

1. A physical quantity P is described by the
1. ∞∑§ ÷ÊÒÁÃ∑§ ⁄UÊÁ‡Ê P ÁŸêŸ ‚¥’¥œ mÊ⁄UÊ ¬Á⁄U÷ÊÁ·Ã ∑§Ë
relation
¡ÊÃË „Ò–
1
P = a 2 b2 c 3 d−4 1
P = a 2 b2 c 3 d−4
If the relative errors in the measurement
of a, b, c and d respectively, are 2%, 1%, ÿÁŒ a, b, c •ÊÒ⁄U d ∑§ ◊ʬŸ ◊¥ ‚ʬˇÊ òÊÈÁ≈U ∑˝§◊‡Ê—
3% and 5%, then the relative error in P 2%, 1%, 3% fl 5% „Ê ÃÊ P ◊¥ ‚ʬˇÊ òÊÈÁ≈U „ÊªË —
will be :
(1) 8%
(2) 12%
(1) 8%
(3) 32%
(2) 12%
(4) 25%
(3) 32%
(4) 25%
2. A car is standing 200 m behind a bus,
which is also at rest. The two start moving
at the same instant but with different 2. ∞∑§ ∑§Ê⁄U ∞∑§ ∆U„⁄UË „ÈÿË ’‚ ‚ 200 m ¬Ë¿U π«∏Ë „Ò–
forward accelerations. The bus has ŒÊŸÊ¥ ∞∑§ „Ë ˇÊáÊ •‹ª-•‹ª •ª˝ÁŒÁ‡Ê∑§ àfl⁄UáÊ ‚
acceleration 2 m/s 2 and the car has
acceleration 4 m/s2. The car will catch ø‹ŸÊ ‡ÊÈM§ ∑§⁄UÃ „Ò¥– ’‚ ∑§Ê àfl⁄UáÊ 2 m/s2 ÃÕÊ
up with the bus after a time of : ∑§Ê⁄U ∑§Ê àfl⁄UáÊ 4 m/s2 „Ò– Á∑§ÃŸ ‚◊ÿ ’ÊŒ ÿ„
∑§Ê⁄U ’‚ Ã∑§ ¬„È°ø ¡ÊÿªË?
(1) 110 s

(2) 120 s
(1) 110 s
(3) 10 2 s

(4) 15 s (2) 120 s

(3) 10 2 s

(4) 15 s

1 IX - PHYSICS

3. Two particles A and B of equal mass M 3. ‚◊ÊŸ Œ˝√ÿ◊ÊŸ M ∑§ ŒÊ ∑§áÊ A ÃÕÊ B ‚◊ÊŸ
are moving with the same speed v as
øÊ‹ v ‚ ÁøòÊÊŸÈ‚Ê⁄U ø‹ ⁄U„ „Ò¥– fl„ ¬ÍáʸÃÿÊ •¬˝àÿÊSÕ
shown in the figure. They collide
completely inelastically and move as a ‚¥ÉÊ^ ∑§⁄UÃ „Ò¥ ÃÕÊ ‚¥ÉÊ^ ∑§ ’ÊŒ ∞∑§ ∑§áÊ C ∑§Ë Ã⁄U„
single particle C. The angle θ that the path ø‹Ã „Ò¥– ∑§ÊáÊ θ, ¡Ê ∑§áÊ C ∑§Ê ¬Õ X-•ˇÊ ‚
of C makes with the X-axis is given by : ’ŸÊÃÊ „Ò, ∑§Ê ÁŸêŸ ‚ê’㜠‚ ÁŒÿÊ ¡ÊÿªÊ —

3+ 2 3+ 2
(1) tan θ= (1) tan θ=
1− 2 1− 2

3− 2 3− 2
(2) tan θ= (2) tan θ=
1− 2 1− 2

1− 2 1− 2
(3) tan θ= (3) tan θ=
2 (1+ 3 ) 2 (1+ 3 )

1− 3 1− 3
(4) tan θ= (4) tan θ=
1+ 2 1+ 2

2 IX - PHYSICS

4. The machine as shown has 2 rods of length 4. ÁøòÊ ◊¥ ÁŒπÊÿË ªÿË ∞∑§ ◊‡ÊËŸ ∑§Ë ŒÊ ¿U«∏Ê¥, Á¡Ÿ∑§Ë
1 m connected by a pivot at the top. The
‹ê’Ê߸ 1 m „Ò, ∑§ ™§¬⁄UË Á‚⁄UÊ¥ ∑§Ê ∞∑§ ‚ÊÕ œÈ⁄Uʪ˝SÃ
end of one rod is connected to the floor by
a stationary pivot and the end of the other Á∑§ÿÊ ªÿÊ „Ò– ∞∑§ ¿U«∏ ∑§Ê •ÊÁπ⁄UË Á‚⁄UÊ ∞∑§ ÁSÕ⁄U
rod has a roller that rolls along the floor in œÈ⁄UË mÊ⁄UÊ »§‡Ê¸ ‚ ¡Ê«∏Ê ªÿÊ „Ò ÃÕÊ ŒÍ‚⁄UË ¿U«∏ ∑§
a slot. As the roller goes back and forth, •ÊÁπ⁄UË Á‚⁄U ¬⁄U ∞∑§ ⁄UÊ‹⁄U ‹ªÊ „Ò ¡Ê Á∑§ »§‡Ê¸ ¬⁄U
a 2 kg weight moves up and down. If the
roller is moving towards right at a constant
’Ÿ πÊ°ø ◊¥ ø‹ÃÊ „Ò– ¡’ fl„ ⁄UÊ‹⁄U •Êª ¬Ë¿U
speed, the weight moves up with a : ø‹ÃÊ „Ò ÃÊ ∞∑§ 2 kg ∑§Ê ÷Ê⁄U ™§¬⁄U ŸËø ø‹ÃÊ „Ò–
ÿÁŒ ⁄UÊ‹⁄U ŒÊÁ„ŸË ÁŒ‡ÊÊ ◊¥ ∞∑§ ‚◊ÊŸ øÊ‹ ‚ ø‹ÃÊ
„Ò ÃÊ fl„ ÷Ê⁄U ø‹ªÊ, ∞∑§ —

(1) constant speed
(2) decreasing speed
(3) increasing speed (1) ‚◊ÊŸ øÊ‹ ‚
3 (2) ÉÊ≈UÃË „È߸ øÊ‹ ‚
(4) speed which is th of that of the
4 (3) ’…∏ÃË „È߸ øÊ‹ ‚
roller when the weight is 0.4 m
above the ground 3
(4) øÊ‹ ¡Ê Á∑§ ⁄UÊ‹⁄U ∑§Ë øÊ‹ ∑§Ê 4 „Ò ¡’ fl„
÷Ê⁄U »§‡Ê¸ ‚ 0.4 m ∑§Ë ™°§øÊ߸ ¬⁄U „Ò

3 IX - PHYSICS

5. A conical pendulum of length 1 m makes 5. ∞∑§ ‡ÊÊ¥∑§fl (conical) ŒÊ‹∑§, Á¡‚∑§Ë ‹ê’Ê߸ 1 m
an angle θ=458 w.r.t. Z-axis and moves
„Ò •ÊÒ⁄U ¡Ê Z-•ˇÊ ‚ θ=458 ∑§ ∑§ÊáÊ ¬⁄U „Ò¥, XY
in a circle in the XY plane. The radius of
the circle is 0.4 m and its center is vertically ‚◊Ë ◊¥ ∞∑§ ªÊ‹Ê∑§Ê⁄U ¬Õ ◊¥ ø‹ÃÊ „Ò– ªÊ‹Ê∑§Ê⁄U
below O. The speed of the pendulum, in ¬Õ ∑§Ë ÁòÊíÿÊ 0.4 m „Ò •ÊÒ⁄U ©‚∑§Ê ∑§ãŒ˝ Á’ãŒÈ O
its circular path, will be : (Take g=10 ms−2) ∑§ ∆UË∑§ ŸËø „Ò– ©‚ ŒÊ‹∑§ ∑§Ë ªÁà ªÊ‹Ê∑§Ê⁄U ¬Õ
◊¥ „ÊªË — (g=10 ms−2)

(1) 0.4 m/s
(2) 4 m/s (1) 0.4 m/s
(3) 0.2 m/s (2) 4 m/s
(4) 2 m/s (3) 0.2 m/s
(4) 2 m/s

4 IX - PHYSICS

R 6. Œ˝√ÿ◊ÊŸ M ÃÕÊ ÁòÊíÿÊ R flÊ‹ ∞∑§‚◊ÊŸ Á«US∑§ ◊¥
6. A circular hole of radius is made in a
4 R
thin uniform disc having mass M and ∞∑§ ÁòÊíÿÊ ∑§Ê ªÊ‹Ê∑§Ê⁄U ¿UŒ, ÁøòÊÊŸÈ‚Ê⁄U, Á∑§ÿÊ
4
radius R, as shown in figure. The moment
ªÿÊ „Ò– Á’¥ŒÈ O ‚ ¡ÊŸ flÊ‹ ÃÕÊ Á«US∑§ ∑§ ‚◊Ë
of inertia of the remaining portion of the
disc about an axis passing through the ∑§ ‹ê’flØ •ˇÊ ∑§ ‚ʬˇÊ, Á«US∑§ ∑§ ’ø „È∞ ÷ʪ
point O and perpendicular to the plane of ∑§Ê, ¡«∏àfl •ÊÉÊÍáʸ „ÊªÊ —
the disc is :

219 MR 2
(1)
219 MR 2 256
(1)
256
237 MR 2
(2)
237 MR 2 512
(2)
512
19 MR 2
(3)
19 MR 2 512
(3)
512
197 MR 2
(4)
197 MR 2 256
(4)
256

5 IX - PHYSICS

7. The mass density of a spherical body is 7. ∞∑§ ªÊ‹Ê∑§Ê⁄U Á¬á«U ∑§Ê Œ˝√ÿ◊ÊŸ ÉÊŸàfl „Ò
k
given by ρ (r)= for r ≤ R and k
r ρ (r)= ¡’ r ≤ R ÃÕÊ
ρ (r)=0 for r > R, r
where r is the distance from the centre. ρ (r)=0 ¡’ r > R, ¡„Ê° r ∑§ãŒ˝ ‚ ŒÍ⁄UË „Ò–
The correct graph that describes
qualitatively the acceleration, a, of a test ÁŸêŸ ◊¥ ‚ ∑§ÊÒŸ ‚Ê ª˝Ê$»§ ∞∑§ ¬⁄UˡÊáÊ ∑§áÊ ∑§ àfl⁄UáÊ
particle as a function of r is :
a ∑§Ê r ∑§ »§‹Ÿ ◊¥ ªÈáÊÊà◊∑§ M§¬ ‚ Œ‡ÊʸÃÊ „Ò?

(1)
(1)

(2)
(2)

(3)
(3)

(4)
(4)

6 IX - PHYSICS

8. A steel rail of length 5 m and area of cross 8. 5 m ‹ê’Ê߸ ÃÕÊ 40 cm2 •ŸÈ¬˝SÕ ∑§Ê≈U ∑§ ˇÊòÊ»§‹
section 40 cm2 is prevented from expanding
∑§Ë ∞∑§ S≈UË‹ ∑§Ë ¬≈U⁄UË ∑§Ê ‹ê’Ê߸ ∑§ •ŸÈÁŒ‡Ê
along its length while the temperature rises
by 108C. If coefficient of linear expansion ÁflSÃÊ⁄UáÊ ⁄UÊ∑§Ê ¡ÊÃÊ „Ò ¡’Á∑§ ©‚∑§Ê Ãʬ◊ÊŸ 108C
and Young’s modulus of steel are ’…∏ÊÿÊ ¡ÊÃÊ „Ò– ÿÁŒ S≈UË‹ ∑§Ê ⁄UπËÿ ¬˝‚Ê⁄U ªÈáÊÊ¥∑§
1.2×10 −5 K −1 and 2×10 11 Nm −2 ÃÕÊ ÿ¥ª ¬˝àÿÊSÕÃÊ ªÈáÊÊ¥∑§ ∑˝§◊‡Ê— 1.2×10−5 K−1
respectively, the force developed in the rail
is approximately :
ÃÕÊ 2×1011 Nm−2 „Ò¥ ÃÊ ¬≈U⁄UË ◊¥ ©à¬ÛÊ ’‹ ∑§Ê
ÁŸ∑§≈UÃ◊ ◊ÊŸ „ÊªÊ —
(1) 2×107 N
(2) 1×105 N
(1) 2×107 N
(3) 2×109 N
(2) 1×105 N
(4) 3×10−5 N
(3) 2×109 N
(4) 3×10−5 N
9. Two tubes of radii r1 and r2, and lengths l1
and l2, respectively, are connected in series
and a liquid flows through each of them 9. ŒÊ ŸÁ‹ÿÊ° Á¡Ÿ∑§Ë ÁòÊíÿÊÿ¥ ∑˝§◊‡Ê— r1 ∞fl¥ r2 ÃÕÊ
in stream line conditions. P1 and P2 are ‹ê’Ê߸ÿÊ°, l1 fl l2 „Ò¥, ∑§Ê üÊáÊË ∑˝§◊ ◊¥ ¡Ê«∏Ê ªÿÊ „Ò
pressure differences across the two tubes.
•ÊÒ⁄U ©Ÿ◊¥ ∞∑§ Œ˝fl œÊ⁄UÊ ⁄UπËÿ ¬˝flÊ„ ◊¥ ’„ÃÊ „Ò–
If P2 is 4P1 and l2 is l 1 , then the radius r2 ¬„‹Ë ÃÕÊ ŒÍ‚⁄UË Ÿ‹Ë ∑§ Á‚⁄UÊ¥ ∑§ ’Ëø ∑§ ŒÊ’ÊãÃ⁄U
4
will be equal to :
∑˝§◊‡Ê— P1 ÃÕÊ P2 „Ò¥– ÿÁŒ P2 ∑§Ê ◊ÊŸ 4P1 ÃÕÊ l2
(1) r1 ∑§Ê ◊ÊŸ l 1 „Ê ÃÊ ÁòÊíÿÊ r2 ∑§Ê ◊ÊŸ „ÊªÊ —
4
(2) 2r 1
(3) 4r 1
(1) r1
r1 (2) 2r 1
(4)
2 (3) 4r 1

r1
(4)
2

7 IX - PHYSICS

10. For the P-V diagram given for an ideal gas, 10. ∞∑§ •ÊŒ‡Ê¸ ªÒ‚ ∑§Ê P-V •Ê⁄Uπ ÁŒÿ ªÿ ÁøòÊ ◊¥
Œ‡ÊʸÿÊ ªÿÊ „Ò–

out of the following which one correctly
represents the T-P diagram ? ÁŒÿ ªÿ •Ê⁄UπÊ¥ ◊¥ ‚ ∑§ÊÒŸ-‚Ê ‚„Ë T-P •Ê⁄Uπ
Œ‡ÊʸÿªÊ?

(1)
(1)

(2)
(2)

(3)
(3)

(4)
(4)

8 IX - PHYSICS

11. N moles of a diatomic gas in a cylinder are 11. ∞∑§ Ám¬⁄U◊ÊáÊÈ∑§ ªÒ‚ ∑§ N ◊Ê‹ T Ãʬ◊ÊŸ ¬⁄U ∞∑§
at a temperature T. Heat is supplied to
Á‚‹á«U⁄U ◊¥ ’¥Œ „Ò¥– Á‚‹á«U⁄U ◊¥ ™§c◊Ê ß‚ ¬˝∑§Ê⁄U
the cylinder such that the temperature
remains constant but n moles of the ¬˝flÊÁ„à ∑§Ë ¡ÊÃË „Ò Á¡‚‚ ©‚ Ám¬⁄U◊ÊáÊÈ∑§ ªÒ‚ ∑§
diatomic gas get converted into n ◊Ê‹ ∞∑§¬⁄U◊ÊáÊÈ∑§ ªÒ‚ ◊¥ Á’ŸÊ Ãʬ◊ÊŸ ’Œ‹
monoatomic gas. What is the change in ¬Á⁄UflÁøà „Ê ¡ÊÃ „Ò¥– ªÒ‚ ∑§Ë ∑ȧ‹ ªÁá ™§¡Ê¸ ◊¥
the total kinetic energy of the gas ?
Á∑§ÃŸÊ ¬Á⁄UfløŸ „ÊªÊ?
1
(1) nRT
2
1
(1) nRT
(2) 0 2
3 (2) 0
(3) nRT
2
3
(3) nRT
5 2
(4) nRT
2
5
(4) nRT
2
12. A block of mass 0.1 kg is connected to an
elastic spring of spring constant 640 Nm−1
and oscillates in a damping medium of 12. 0.1 kg Œ˝√ÿ◊ÊŸ ∑§ ∞∑§ ªÈ≈U∑§ ∑§Ê ∞∑§ ¬˝àÿÊSÕ ÁS¬˝¥ª,
damping constant 10 −2 kg s −1 . The Á¡‚∑§Ê ÁS¬˝¥ª ÁŸÿÃÊ¥∑§ 640 Nm−1 „Ò, ‚ ¡Ê«∏Ê ªÿÊ
system dissipates its energy gradually. The „Ò– ÿ„ ªÈ≈U∑§Ê ∞∑§ •fl◊㌟ ◊Êäÿ◊, Á¡‚∑§Ê
time taken for its mechanical energy of
vibration to drop to half of its initial value, •fl◊㌟ ªÈáÊÊ¥∑§ 10−2 kg s−1 „Ò, ◊¥ ŒÊ‹Ÿ ªÁÃ
is closest to : ∑§⁄UÃÊ „Ò– ÿ„ ÁŸ∑§Êÿ œË⁄U-œË⁄U •¬ŸË ™§¡Ê¸ •¬√ÿÁÃÃ
(1) 2s ∑§⁄UÃÊ „Ò– ÁŸ∑§Êÿ ∑§ ŒÊ‹Ÿ ∑§Ë ÿÊ¥ÁòÊ∑§ ™§¡Ê¸ ∑§Ê
(2) 3.5 s ©‚∑§ •Ê⁄UÁê÷∑§ ◊ÊŸ ‚ •ÊœÊ „ÊŸ ◊¥ ‹ªŸ flÊ‹
‚◊ÿ ∑§Ê ÁŸ∑§≈UÃ◊ ◊ÊŸ „ÊªÊ —
(3) 5s
(1) 2s
(4) 7s
(2) 3.5 s
(3) 5s
(4) 7s

9 IX - PHYSICS

13. A standing wave is formed by the 13. ŒÊ Ã⁄¥Uª¥, ¡Ê Áfl¬⁄UËà ÁŒ‡ÊÊ ◊¥ ø‹ ⁄U„Ë „Ò¥, ∑§ •äÿÊ⁄UÊ¬áÊ
superposition of two waves travelling in
‚ ∞∑§ •¬˝ªÊ◊Ë Ã⁄¥Uª ’ŸÃË „Ò Á¡‚∑§Ê •ŸÈ¬˝SÕ
opposite directions. The transverse
displacement is given by ÁflSÕʬŸ ÁŸêŸ ‚◊Ë∑§⁄UáÊ mÊ⁄UÊ Á‹πÊ ¡Ê ‚∑§ÃÊ „Ò

y(x , t) = 0.5 sin 
5π 
x  cos(200 πt).
y(x , t) = 0.5 sin 
 4  5π 
x  cos(200 πt).
What is the speed of the travelling wave  4 
moving in the positive x direction ? +x •ˇÊ ∑§Ë Ã⁄U»§ ø‹Ÿ flÊ‹Ë ¬˝ªÊ◊Ë Ã⁄¥Uª ∑§Ë ªÁÃ
(x and t are in meter and second, „ÊªË —
respectively.)
(ÿ„Ê° x fl t ∑˝§◊‡Ê— ◊Ë≈U⁄U fl ‚∑§á«U ◊¥ „Ò¥– )
(1) 160 m/s
(2) 90 m/s (1) 160 m/s
(3) 180 m/s (2) 90 m/s
(4) 120 m/s (3) 180 m/s
(4) 120 m/s

10 IX - PHYSICS

14. Four closed surfaces and corresponding 14. øÊ⁄U ’¥Œ ¬Îc∆U ÃÕÊ ©Ÿ∑§ •Êfl‡Ê ÁflãÿÊ‚ ∑§Ê ÁŸêŸ
charge distributions are shown below. ÁøòÊ ◊¥ Œ‡ÊʸÿÊ ªÿÊ „Ò–

Let the respective electric fluxes through ÿÁŒ ©Ÿ∑ § ¬Î c ∆U ‚ ’h flÒ l È Ã ç‹Ä‚ ∑˝ § ◊‡Ê—
the surfaces be Φ1, Φ2, Φ3 and Φ4. Then :
Φ1, Φ2, Φ3 ÃÕÊ Φ4 „Ê¥ ÃÊ —
(1) Φ1 < Φ2=Φ3 > Φ4
(1) Φ1 < Φ2=Φ3 > Φ4
(2) Φ1 > Φ2 > Φ3 > Φ4
(2) Φ1 > Φ2 > Φ3 > Φ4
(3) Φ1=Φ2=Φ3=Φ4
(3) Φ1=Φ2=Φ3=Φ4
(4) Φ1 > Φ3 ; Φ2 < Φ4
(4) Φ1 > Φ3 ; Φ2 < Φ4

11 IX - PHYSICS

15. A combination of parallel plate capacitors 15. ‚◊ÊãÃ⁄U å‹≈U ‚¥œÊÁ⁄UòÊÊ¥ ∑§ ∞∑§ ‚¥ÿÊ¡Ÿ ∑§Ê ∞∑§ ÁŸÁ‡øÃ
is maintained at a certain potential
Áfl÷flÊãÃ⁄U ¬⁄U ⁄UπÊ ªÿÊ „Ò– (ÁøòÊ ŒÁπÿ)
difference.

When a 3 mm thick slab is introduced ¡’ 3 mm ◊Ê≈U ªÈ≈U∑§ ∑§Ê ‚÷Ë ‚¥œÊÁ⁄UòÊÊ¥ ∑§Ë å‹≈UÊ¥
between all the plates, in order to maintain ∑§ ’Ëø «UÊ‹Ê ¡ÊÃÊ „Ò, ÃÊ fl„Ë Áfl÷flÊãÃ⁄U ’ŸÊÿ ⁄UπŸ
the same potential difference, the distance ∑§ Á‹∞ å‹≈UÊ¥ ∑§ ’Ëø ∑§Ë ŒÍ⁄UË ∑§Ê 2.4 mm ‚ ’…∏ÊŸÊ
between the plates is increased by 2.4 mm.
Find the dielectric constant of the slab.
¬«∏ÃÊ „Ò– ªÈ≈U∑§ ∑§Ê ¬⁄UÊflÒlÈÃÊ¥∑§ „ÊªÊ —
(1) 3
(1) 3
(2) 4
(2) 4
(3) 5
(3) 5
(4) 6
(4) 6

16. A uniform wire of length l and radius r
has a resistance of 100 Ω. It is recast into a 16. ‹ê’Ê߸ l ÃÕÊ ÁòÊíÿÊ r ∑§ ∞∑§‚◊ÊŸ ÃÊ⁄U ∑§Ê ¬˝ÁÃ⁄UÊœ
r
wire of radius
2
. The resistance of new 100 Ω „Ò– ß‚∑§Ê ÁòÊíÿÊ r ∑§ ÃÊ⁄U ◊¥ ¬ÈŸ— …UÊ‹Ê
2
wire will be : ¡ÊÃÊ „Ò– Ÿÿ ÃÊ⁄U ∑§Ê ¬˝ÁÃ⁄UÊœ „ÊªÊ —
(1) 1600 Ω
(2) 400 Ω (1) 1600 Ω
(3) 200 Ω (2) 400 Ω
(4) 100 Ω (3) 200 Ω
(4) 100 Ω

12 IX - PHYSICS

17. The figure shows three circuits I, II and III 17. ÁŒÿ ªÿ ÁøòÊ ◊¥ ÃËŸ ¬Á⁄U¬Õ, I, II ∞fl¥ III ∑§Ê ∞∑§
which are connected to a 3V battery. If
3V ’Ò≈U⁄UË ‚ ¡Ê«∏Ê ªÿÊ „Ò– ÿÁŒ ÁflãÿÊ‚ I, II ÃÕÊ III
the powers dissipated by the configurations
I, II and III are P1, P2 and P3 respectively, ∑˝§◊‡Ê— P1, P2 ÃÕÊ P3 ‡ÊÁÄà •¬√ÿÿ ∑§⁄UÃ „Ò¥ ÃÊ —
then :

(1) P1 > P2 > P3
(1) P1 > P2 > P3 (2) P1 > P3 > P2
(2) P1 > P3 > P2 (3) P2 > P1 > P3
(3) P2 > P1 > P3 (4) P3 > P2 > P1
(4) P3 > P2 > P1

18. ∞∑§ ´§áÊÊà◊∑§ ¬⁄UˡÊáÊ •Êfl‡Ê, ∞∑§ ‚Ëœ ‹ê’ ÃÊ⁄U,
18. A negative test charge is moving near a Á¡‚◊¥ œÊ⁄UÊ ’„ ⁄U„Ë „Ò, ∑§ ÁŸ∑§≈U ø‹ ⁄U„Ê „Ò– ¬⁄UˡÊáÊ
long straight wire carrying a current. The
force acting on the test charge is parallel
•Êfl‡Ê ¬⁄U ‹ªŸ flÊ‹Ê ’‹ œÊ⁄UÊ ∑§Ë ÁŒ‡ÊÊ ∑§ ‚◊ÊãÃ⁄U
to the direction of the current. The motion „Ò– •Êfl‡Ê ∑§Ë ªÁà „ÊªË —
of the charge is :
(1) away from the wire (1) ÃÊ⁄U ‚ ŒÍ⁄U
(2) towards the wire (2) ÃÊ⁄U ∑§Ë •Ê⁄U
(3) parallel to the wire along the current
(3) ÃÊ⁄U ‚ ‚◊ÊãÃ⁄U ∞fl¥ œÊ⁄UÊ ∑§Ë ÁŒ‡ÊÊ ◊¥
(4) parallel to the wire opposite to the
current (4) ÃÊ⁄U ∑§ ‚◊ÊãÃ⁄U ∞fl¥ œÊ⁄UÊ ∑§Ë Áfl¬⁄UËà ÁŒ‡ÊÊ ◊¥

13 IX - PHYSICS

19. A uniform magnetic field B of 0.3 T is along 19. 0.3 T ∑§Ê ∞∑§ ‚◊ÊŸ øÈê’∑§Ëÿ ˇÊòÊ B œŸÊà◊∑§
the positive Z-direction. A rectangular
Z-•ˇÊ ∑§Ë Ã⁄U»§ ÁŒÁ‡Êà „Ò– ∞∑§ 10 cm ÃÕÊ 5 cm
loop (abcd) of sides 10 cm×5 cm carries a
current I of 12 A. Out of the following ÷È¡Ê•Ê¥ flÊ‹ •ÊÿÃÊ∑§Ê⁄U ¬Ê‡Ê (abcd) ◊¥ 12 A œÊ⁄UÊ
different orientations which one I ’„ÃË „Ò– ÁŸêŸ ◊¥ ‚ ∑§ÊÒŸ-‚Ê ÁŒª˜ÁflãÿÊ‚ ÁSÕ⁄U
corresponds to stable equilibrium ? ‚ÊêÿÊflSÕÊ ∑§Ê ¬˝ŒÁ‡Ê¸Ã ∑§⁄UÃÊ „Ò?

(1) (1)

(2) (2)

(3) (3)

(4) (4)

14 IX - PHYSICS

20. A sinusoidal voltage of peak value 283 V 20. 283 V ◊„ûÊ◊ Áfl÷fl ÃÕÊ 320 s−1 ∑§ÊáÊËÿ •ÊflÎÁûÊ
and angular frequency 320/s is applied to
flÊ‹ ∞∑§ íÿÊfl∑˝§Ëÿ Áfl÷fl ∑§Ê ∞∑§ üÊáÊË LCR ¬Á⁄U¬Õ
a series LCR circuit. Given that R=5 Ω,
L=25 mH and C=1000 µF. The total ◊¥ ‹ªÊÿÊ ªÿÊ „Ò– ÁŒÿÊ „Ò R=5 Ω, L=25 mH
impedance, and phase difference between •ÊÒ⁄U C=1000 µF– ¬Á⁄U¬Õ ∑§Ë ∑ȧ‹ ¬˝ÁÃ’ÊœÊ ÃÕÊ
the voltage across the source and the dÊà Áfl÷fl ∞fl¥ œÊ⁄UÊ ∑§ ’Ëø ∑§‹Ê¥Ã⁄U ∑˝§◊‡Ê— „ÊªÊ —
current will respectively be :

−1  5 
(1) 10 Ω and tan  
 3
−1  5 
(1) 10 Ω •ÊÒ⁄U tan  
(2) 7 Ω and 458  3

(2) 7 Ω •ÊÒ⁄U 458
10 Ω and tan−1  
8
(3)
 3
10 Ω •ÊÒ⁄U tan−1  
8
(3)
 5  3
(4) 7 Ω and tan−1  
 3
 5
(4) 7 Ω •ÊÒ⁄U tan−1  
 3
21. The electric field component of a
monochromatic radiation is given by
→ ∧
21. Á∑§‚Ë ∞∑§fláÊ˸ÿ ÁflÁ∑§⁄UáÊ ∑§ flÒlÈà ˇÊòÊ ÉÊ≈U∑§ ∑§Ê
E = 2 E0 i cos kz cos ωt ÁŸêŸ ¬˝∑§Ê⁄U ‚ √ÿÄà Á∑§ÿÊ ¡Ê ‚∑§ÃÊ „Ò
→ → ∧
Its magnetic field B is then given by : E = 2 E0 i cos kz cos ωt

2 E0 ∧ →
(1) j sin kz cos ωt ©‚∑§ øÈê’∑§Ëÿ ˇÊòÊ B ∑§Ê ◊ÊŸ „ÊªÊ —
c
2 E0 ∧
2 E0 ∧ (1) j sin kz cos ωt
(2) − j sin kz sin ωt c
c
2 E0 ∧
2 E0 ∧ (2) − j sin kz sin ωt
(3) j sin kz sin ωt c
c
2 E0 ∧
2 E0 ∧ (3) j sin kz sin ωt
(4) j cos kz cos ωt c
c
2 E0 ∧
(4) j cos kz cos ωt
c

15 IX - PHYSICS

22. In an experiment a convex lens of focal 22. ∞∑§ ¬˝ÿÊª ∑§ ŒÊÒ⁄UÊŸ, 15 cm »§Ê∑§‚ ŒÍ⁄UË ∑§ ∞∑§
length 15 cm is placed coaxially on an
©ûÊ‹ ‹¥‚ ∑§Ê ∞∑§ ¬˝∑§Ê‡Ê ’¥ø ¬⁄U ∞∑§ ©ûÊ‹ Œ¬¸áÊ
optical bench in front of a convex mirror
at a distance of 5 cm from it. It is found ∑§ ‚Ê◊Ÿ 5 cm ŒÍ⁄UË ¬⁄U ‚◊ÊˇÊËÿ ÁSÕÁà ◊¥ ⁄UπÊ ªÿÊ
that an object and its image coincide, if „Ò– ÿÁŒ flSÃÈ ∑§Ê ‹¥‚ ‚ 20 cm ∑§Ë ŒÍ⁄UË ¬⁄U ⁄UπÊ
the object is placed at a distance of 20 cm ¡Êÿ ÃÊ flSÃÈ ÃÕÊ ©‚∑§Ê ¬˝ÁÃÁ’ê’ ‚¥¬ÊÃË „Ê ¡ÊÃ „Ò¥–
from the lens. The focal length of the
convex mirror is :
©ûÊ‹ Œ¬¸áÊ ∑§Ë »§Ê∑§‚ ŒÍ⁄UË „ÊªË —
(1) 27.5 cm
(2) 20.0 cm (1) 27.5 cm
(3) 25.0 cm (2) 20.0 cm
(4) 30.5 cm (3) 25.0 cm
(4) 30.5 cm
23. A single slit of width 0.1 mm is illuminated
by a parallel beam of light of wavelength
6000 Å and diffraction bands are observed 23. 0.1 mm øÊÒ«∏Ê߸ ∑§Ë ∞∑§ Á¤Ê⁄UË 6000 Å Ã⁄¥UªŒÒÉÿ¸ ∑§
on a screen 0.5 m from the slit. The ‚◊ÊãÃ⁄U Á∑§⁄UáÊ ¬È¥¡ ‚ ¬˝∑§ÊÁ‡Êà ∑§Ë ¡ÊÃË „Ò •ÊÒ⁄U
distance of the third dark band from the ÁflfløŸ ’Òá«U ∑§Ê Á¤Ê⁄UË ‚ 0.5 m ŒÍ⁄U ÁSÕà ¬Œ¸ ¬⁄U
central bright band is :
ŒπÊ ¡ÊÃÊ „Ò– ÃÎÃËÿ •ŒËåà ’Òá«U ∑§Ë ∑§ãŒ˝Ëÿ ŒËåÃ
(1) 3 mm
’Òá«U ‚ ŒÍ⁄UË „ÊªË —
(2) 9 mm
(3) 4.5 mm (1) 3 mm
(4) 1.5 mm (2) 9 mm
(3) 4.5 mm
24. A Laser light of wavelength 660 nm is used (4) 1.5 mm
to weld Retina detachment. If a Laser
pulse of width 60 ms and power 0.5 kW is
used the approximate number of photons 24. 660 nm Ã⁄¥UªŒÒÉÿ¸ ∑§Ë ∞∑§ ‹$¡⁄U ‹Êß≈U ∑§Ê ⁄UÁ≈UŸÊ
in the pulse are :
ÁflÿÊ¡Ÿ ∑§Ê ¡Ê«∏Ÿ ∑§ Á‹∞ ¬˝ÿÊª Á∑§ÿÊ ¡ÊÃÊ „Ò–
[Take Planck’s constant h=6.62×10−34 Js]
ÿÁŒ 60 ms øÊÒ«∏Ê߸ ∞fl¥ 0.5 kW ‡ÊÁÄà ∑§ ‹$¡⁄U
(1) 10 20
S¬ãŒ (pulse) ∑§Ê ¬˝ÿÊª Á∑§ÿÊ ¡Êÿ ÃÊ ©‚ S¬ãŒ ◊¥
(2) 10 18
»§Ê≈UÊÚŸÊ¥ ∑§Ë ‚¥ÅÿÊ ‹ª÷ª „ÊªË —
(3) 10 22 [å‹Ê¥∑§ ÁŸÿÃÊ¥∑§ h=6.62×10−34 Js]
(4) 10 19 (1) 10 20
(2) 10 18
(3) 10 22
(4) 10 19

16 IX - PHYSICS

25. The acceleration of an electron in the first 25. „Êß«˛UÊ¡Ÿ ¬⁄U◊ÊáÊÈ ∑§Ë ¬˝Õ◊ ∑§ˇÊÊ (n=1) ∑§ ß‹Ä≈˛UÊÚŸ
orbit of the hydrogen atom (n=1) is :
∑§Ê àfl⁄UáÊ „ÊªÊ —
h2
(1) h2
2
π m r 2 3 (1)
π2 m 2 r 3

h2
(2) h2
8π m r2 2 3 (2)
8π2 m 2 r 3

h2
(3) h2
4π m r2 2 3 (3)
4π2 m 2 r 3

h2
(4) h2
4πm r 2 3 (4)
4πm 2 r 3

26. Imagine that a reactor converts all given
mass into energy and that it operates at a 26. ∑§À¬ŸÊ ∑§ËÁ¡∞, ∞∑§ ÷≈˜U∆UË, ¡ÊÁ∑§ ÁŒÿ ªÿ ‚¥¬Íáʸ
power level of 109 watt. The mass of the Œ˝√ÿ◊ÊŸ ∑§Ê ™§¡Ê¸ ◊¥ ’Œ‹ÃË „Ò ∞fl¥ 109 watt ∑§Ë
fuel consumed per hour in the reactor will ‡ÊÁÄà SÃ⁄U ¬⁄U ø‹ÃË „Ò– ÷≈˜∆UË ◊¥ ∞∑§ ÉÊá≈U ◊¥ π¬Ã
be : (velocity of light, c is 3×108 m/s)
„ÊŸ flÊ‹ ßZœŸ ∑§Ê Œ˝√ÿ◊ÊŸ „ÊªÊ —
(1) 0.96 gm (¬˝∑§Ê‡Ê ∑§Ê flª, c=3×108 m/s)
(2) 0.8 gm
(1) 0.96 gm
(3) 4×10−2 gm
(2) 0.8 gm
(4) 6.6×10−5 gm
(3) 4×10−2 gm
(4) 6.6×10−5 gm
27. The current gain of a common emitter
amplifier is 69. If the emitter current is
7.0 mA, collector current is : 27. ∞∑§ ©÷ÿÁŸc∆U ©à‚¡¸∑§ ¬˝flœ¸∑§ ∑§Ê œÊ⁄UÊ ‹Ê÷ 69
(1) 9.6 mA „Ò– ÿÁŒ ©à‚¡¸∑§ œÊ⁄UÊ ∑§Ê ◊ÊŸ 7.0 mA „Ê ÃÊ
(2) 6.9 mA ‚¥ª˝Ê„∑§ œÊ⁄UÊ ∑§Ê ◊ÊŸ „ÊªÊ —
(3) 0.69 mA (1) 9.6 mA
(4) 69 mA (2) 6.9 mA
(3) 0.69 mA
(4) 69 mA

17 IX - PHYSICS

28. A signal is to be transmitted through a 28. Ã⁄¥UªŒÒÉÿ¸ λ ∑§Ë Ã⁄¥Uª mÊ⁄UÊ ∞∑§ ‚¥Œ‡Ê ∑§Ê ∞∑§ ∞∑§⁄UπËÿ
wave of wavelength λ, using a linear
∞ã≈UŸÊ ‚ ¬˝‚ÊÁ⁄Uà ∑§⁄UŸÊ „Ò– ∞ã≈UŸÊ ∑§Ë ‹ê’Ê߸ l ÃÕÊ
antenna. The length l of the antenna and
effective power radiated Peff will be given ¬˝ ÷ ÊflË ©à‚Á¡¸ à ‡ÊÁÄà P eff ∑§Ê ∑˝ § ◊‡Ê— ◊ÊŸ
respectively as : „ÊªÊ —
(K is a constant of proportionality) ( K ‚◊ÊŸÈ ¬ ÊÁÃ∑§ ÁSÕ⁄U Ê ¥ ∑ § (constant of
2 proportionality) „Ò)
λ , Peff = K  
l
(1)
λ 2
λ , Peff = K  
l
(1)
λ
, Peff = K  
λ l
(2)
8 λ
, Peff = K  
λ l
(2)
3 8 λ
, Peff = K  
λ l
(3)
16 λ 3
, Peff = K  
λ l
(3)
1 16 λ
, Peff = K  
(4)
λ l 2
5 λ 1
, Peff = K  
(4)
λ l 2
5 λ

18 IX - PHYSICS

29. In a meter bridge experiment resistances 29. Á∑§‚Ë ◊Ë≈U⁄U ‚ÃÈ ¬˝ÿÊª ∑§ ŒÊÒ⁄UÊŸ, ¬˝ÁÃ⁄UÊœÊ¥ ∑§Ê ÁøòÊÊŸÈ‚Ê⁄U
are connected as shown in the figure.
¡Ê«∏Ê ªÿÊ „Ò– ‡ÊÈM§ ◊¥ ¬˝ÁÃ⁄UÊœ P=4 Ω ÃÕÊ Ÿ‹
Initially resistance P=4 Ω and the neutral
point N is at 60 cm from A. Now an Á’ãŒÈ N, Á’ãŒÈ A ‚, 60 cm ∑§Ë ŒÍ⁄UË ¬⁄U „Ò– ∞∑§
unknown resistance R is connected in series •ôÊÊà ¬˝ÁÃ⁄UÊœ R ∑§Ê P ∑§ ‚ÊÕ üÊáÊË ∑˝§◊ ◊¥ ¡Ê«∏Ê
to P and the new position of the neutral ¡ÊÃÊ „Ò Á¡‚‚ Ÿ‹ Á’ãŒÈ ∑§Ë Ÿß¸ ÁSÕÁà Á’¥ŒÈ A ‚
point is at 80 cm from A. The value of
80 cm ŒÍ⁄U „Ê ¡ÊÃË „Ò– •ôÊÊà ¬˝ÁÃ⁄UÊœ R ∑§Ê ◊ÊŸ
unknown resistance R is :
„ÊªÊ —

33
(1) Ω 33
5 (1) Ω
5
(2) 6Ω
(2) 6Ω
(3) 7Ω
(3) 7Ω
20
(4) Ω 20
3 (4) Ω
3

19 IX - PHYSICS

30. In an experiment to determine the period 30. ∞∑§ ¬˝ÿÊª ◊¥, 1 m ‹ê’Ê߸ ∑§Ë ∞∑§ ‚⁄U‹ ŒÊ‹∑§ ∑§Ê
of a simple pendulum of length 1 m, it is
•Êflø ∑§Ê‹ ÁŸ∑§Ê‹Ÿ „ÃÈ ©‚∑§Ê r1 ÃÕÊ r2 ÁòÊíÿÊ•Ê¥
attached to different spherical bobs of radii
r1 and r2. The two spherical bobs have ∑§ •‹ª-•‹ª ªÊ‹Ê∑§Ê⁄U ‹Ê‹∑§ ‚ ¡Ê«∏Ê ¡ÊÃÊ „Ò–
uniform mass distribution. If the relative ŒÊŸÊ¥ ªÊ‹Ê∑§Ê⁄U ‹Ê‹∑§Ê¥ ∑§ Œ˝√ÿ◊ÊŸ ÁflÃ⁄UáÊ ∞∑§ ‚◊ÊŸ
difference in the periods, is found to be „Ò¥– ÿÁŒ •Êflø∑§Ê‹Ê¥ ∑§Ê ‚ʬˇÊ •¥Ã⁄U 5×10−4 s
5×10−4 s, the difference in radii, ?r1−r2?
is best given by :
¬ÊÿÊ ªÿÊ „Ê ÃÊ ©Ÿ∑§Ë ÁòÊíÿÊ•Ê ¥ ◊ ¥ •ãÃ⁄U ,
?r1−r2? ∑§Ê ÁŸ∑§≈UÃ◊ ◊ÊŸ „ÊªÊ —
(1) 1 cm
(2) 0.1 cm
(3) 0.5 cm
(1) 1 cm
(4) 0.01 cm
(2) 0.1 cm
(3) 0.5 cm
-o0o-
(4) 0.01 cm

-o0o-

20 IX - PHYSICS

CHEMISTRY ⁄U‚ÊÿŸ ‡ÊÊSòÊ

1. An ideal gas undergoes isothermal
expansion at constant pressure. During 1. ∞∑§ •ÊŒ‡Ê¸ ªÒ‚ ÁSÕ⁄U ŒÊ’ ¬⁄U ‚◊ÃʬËÿ ¬˝‚Ê⁄UáÊ
the process : ∑§⁄UÃË „Ò– ß‚ ¬˝∑˝§◊ ◊¥ —
(1) enthalpy increases but entropy
decreases. (1) ∞ãÕÒÀ¬Ë ’…∏ÃË „Ò ¬⁄UãÃÈ ∞ã≈˛UÊÚ¬Ë ÉÊ≈UÃË „Ò–
(2) enthalpy remains constant but
entropy increases.
(2) ∞ãÕÒÀ¬Ë ÁSÕ⁄U ⁄U„ÃË „Ò ¬⁄UãÃÈ ∞ã≈˛UÊÚ¬Ë ’…∏ÃË „Ò–
(3) enthalpy decreases but entropy
increases.
(4) Both enthalpy and entropy remain (3) ∞ãÕÒÀ¬Ë ÉÊ≈UÃË „Ò ¬⁄UãÃÈ ∞ã≈˛UÊÚ¬Ë ’…∏ÃUË „Ò–
constant.
(4) ∞ãÕÒÀ¬Ë ÃÕÊ ∞ã≈˛UÊÚ¬Ë ŒÊŸÊ¥ „Ë ÁSÕ⁄U ⁄U„ÃË „Ò¥–
2. 50 mL of 0.2 M ammonia solution is
treated with 25 mL of 0.2 M HCl. If pKb
of ammonia solution is 4.75, the pH of the
mixture will be : 2. 0.2 M •◊ÊÁŸÿÊ Áfl‹ÿŸ ∑§ 50 mL ∑§Ê 0.2 M
(1) 3.75 HCl ∑§ 25 mL ∑§ ‚ÊÕ •Á÷∑Χà Á∑§ÿÊ ¡ÊÃÊ „Ò–
(2) 4.75 ÿÁŒ •◊ÊÁŸÿÊ Áfl‹ÿŸ ∑§ pKb ∑§Ê ◊ÊŸ 4.75 „Ê ÃÊ
(3) 8.25 Á◊üÊáÊ ∑§Ê pH „ÊªÊ —
(4) 9.25 (1) 3.75
(2) 4.75
3. The electron in the hydrogen atom (3) 8.25
undergoes transition from higher orbitals (4) 9.25
to orbital of radius 211.6 pm. This
transition is associated with :
(1) Lyman series 3. „Êß«˛UÊ¡Ÿ ¬⁄U◊ÊáÊÈ ◊¥ ß‹Ä≈˛UÊÚŸ ©ìÊÃ⁄U •ÊÚÁ’¸≈U‹ ‚
(2) Balmer series 211.6 pm ÁòÊíÿÊ flÊ‹ •ÊÚÁ’¸≈U‹ Ã∑§ ‚¥∑˝§◊áÊ ∑§⁄UÃÊ

(3) Paschen series
„Ò– ß‚ ‚¥∑˝§◊áÊ ∑§Ê ‚ê’㜠Á¡‚‚ „Ò fl„ „Ò —
(4) Brackett series
(1) ‹Êß◊ÒŸ üÊáÊË
(2) ’Ê◊⁄U üÊáÊË
(3) ¬Ê‡ÊŸ üÊáÊË
(4) ’˝∑§≈U üÊáÊË

1 IX - CHEMISTRY

4. At 300 K, the density of a certain gaseous 4. 300 K ¬⁄U; 2 ’Ê⁄U ¬⁄U ⁄Uπ Á∑§‚Ë ªÒ‚Ëÿ •áÊÈ ∑§Ê
molecule at 2 bar is double to that of
ÉÊãÊàfl, 4 ’Ê⁄U ¬⁄U ⁄Uπ «UÊߟÊß≈˛UÊ¡Ÿ (N2) ∑§ ÉÊŸàfl
dinitrogen (N2) at 4 bar. The molar mass
of gaseous molecule is : ∑§Ê ŒÍŸÊ „Ò– ªÒ‚Ëÿ •áÊÈ ∑§Ê ◊Ê‹⁄U Œ˝√ÿ◊ÊŸ „Ò —
(1) 28 g mol−1
(1) 28 g mol−1
(2) 56 g mol−1
(2) 56 g mol−1
(3) 112 g mol−1
(3) 112 g mol−1
(4) 224 g mol−1
(4) 224 g mol−1

5. What quantity (in mL) of a 45% acid
solution of a mono-protic strong acid must 5. ∞∑§ ◊ÊŸÊ¬˝ÊÁ≈U∑§ ¬˝’‹ •ê‹ ∑§ 45% ∞Á‚«U Áfl‹ÿŸ
be mixed with a 20% solution of the same ∑§Ë Á∑§ÃŸË ◊ÊòÊÊ (mL ◊¥) ©‚Ë •ê‹ ∑§ 20%
acid to produce 800 mL of a 29.875% acid
solution ?
Áfl‹ÿŸ ∑§ ‚ÊÕ Á◊‹ÊÿË ¡ÊŸË øÊÁ„∞ Á∑§ 29.875%
∞Á‚«U Áfl‹ÿŸ ∑§Ê 800 mL ’Ÿ ¡Êÿ ?
(1) 320
(2) 325
(1) 320
(3) 316
(2) 325
(4) 330
(3) 316
(4) 330
6. To find the standard potential of M3+/M
electrode, the following cell is constituted :
Pt/M/M 3+ (0.001 mol L −1 )/Ag + (0.01 6. M3+/M ß‹ÒÄ≈˛UÊ«U ∑§ ◊ÊŸ∑§ Áfl÷fl ∑§Ê ÁŸ∑§Ê‹Ÿ
mol L−1)/Ag
∑§ Á‹∞ ÁŸêŸ ‚‹ ’ŸÊÿÊ ªÿÊ —
The emf of the cell is found to be 0.421 Pt/M/M 3+ (0.001 mol L −1 )/Ag + (0.01
volt at 298 K. The standard potential of mol L−1)/Ag
half reaction M3++3e−→ M at 298 K will
be : ‚‹ ∑§Ê ߸.∞◊.∞»§. 298 K ¬⁄,U 0.421 V ¬ÊÿÊ ªÿÊ–
298 K ¬⁄U, M3++3e−→ M, •h¸ •Á÷Á∑˝§ÿÊ
∑§Ê ◊ÊŸ∑§ Áfl÷fl „ÊªÊ —
(1) 0.38 Volt
)
(2) 0.32 Volt
(3) 1.28 Volt (1) 0.38 V

(4) 0.66 Volt (2) 0.32 V
(3) 1.28 V
(4) 0.66 V

2 IX - CHEMISTRY

7. A gas undergoes change from state A to 7. ∞∑§ ªÒ‚ •flSÕÊ A ‚ •flSÕÊ B ∑§Ê ¡ÊÃË „Ò– ß‚
state B. In this process, the heat absorbed
¬˝∑˝§◊ ◊¥, ªÒ‚ mÊ⁄UÊ ‡ÊÊÁ·Ã ™§c◊Ê ÃÕÊ Á∑§ÿÊ ªÿÊ ∑§Êÿ¸
and work done by the gas is 5 J and 8 J,
respectively. Now gas is brought back to ∑˝§◊‡Ê— 5 J ÃÕÊ 8 J „Ò¥– •’ ªÒ‚ ∑§Ê ŒÍ‚⁄U ¬˝∑˝§◊
A by another process during which 3 J of mÊ⁄UÊ ¬ÈŸ— A •flSÕÊ ◊¥ ‹ÊÃ „Ò¥ ß‚◊¥ 3 J ™§c◊Ê
heat is evolved. In this reverse process of ÁŸ∑§‹ÃË „Ò– B ‚ A ∑§ ß‚ ©À≈U ¬˝∑˝§◊ ◊¥ —
B to A :
(1) 10 J of the work will be done by the
gas.
(2) 6 J of the work will be done by the (1) ªÒ‚ mÊ⁄UÊ 10 J ∑§Êÿ¸ Á∑§ÿÊ ¡ÊÿªÊ–
gas.
(3) 10 J of the work will be done by the (2) ªÒ‚ mÊ⁄UÊ 6 J ∑§Êÿ¸ Á∑§ÿÊ ¡ÊÿªÊ–
surrounding on gas.
(4) 6 J of the work will be done by the (3) ªÒ‚ ¬⁄U ¬Á⁄Ufl‡Ê mÊ⁄UÊ Á∑§ÿÊ ªÿÊ ∑§Êÿ¸ 10 J
surrounding on gas.
„ÊªÊ–
(4) ªÒ‚ ¬⁄U ¬Á⁄Ufl‡Ê mÊ⁄UÊ Á∑§ÿÊ ªÿÊ ∑§Êÿ¸ 6 J „ÊªÊ–
8. Adsorption of a gas on a surface follows
Freundlich adsorption isotherm. Plot of
x
log versus log p gives a straight line
m 8. Á∑§‚Ë ¬Îc∆U ¬⁄U ∞∑§ ªÒ‚ ∑§Ê •Áœ‡ÊÊ·áÊ, »˝§ÊÚÿã«UÁ‹∑§
with slope equal to 0.5, then : •Áœ‡ÊÊ·áÊ ‚◊Ãʬ ∑§Ê •ŸÈ∑§⁄UáÊ ∑§⁄UÃÊ „Ò– log p
x x
( is the mass of the gas adsorbed per ∑§ ÁflL§h log m ∑§Ê å‹Ê≈U ∞∑§ ‚⁄U‹ ⁄UπÊ ŒÃÊ „Ò–
m
gram of adsorbent)
Á¡‚∑§Ê S‹Ê¬ 0.5 ∑§ ’⁄UÊ’⁄U ¬ÊÿÊ ªÿÊ, Ã’ —
(1) Adsorption is independent of x
pressure.
( m , ¬˝Áà ª˝Ê◊ •Áœ‡ÊÊ·∑§ mÊ⁄UÊ •Áœ‡ÊÊÁ·Ã ªÒ‚ ∑§Ê
(2) Adsorption is proportional to the Œ˝√ÿ◊ÊŸ „Ò)
pressure.
(1) •Áœ‡ÊÊ·áÊ, ŒÊ’ ¬⁄U •ÊÁüÊà Ÿ„Ë¥ „Ò–
(3) Adsorption is proportional to the
square root of pressure.
(2) •Áœ‡ÊÊ·áÊ, ŒÊ’ ∑§ ‚◊ʟȬÊÃË „Ò–
(4) Adsorption is proportional to the
square of pressure.
(3) •Áœ‡ÊÊ·áÊ, ŒÊ’ ∑§ flª¸◊Í‹ ∑§ ‚◊ʟȬÊÃË „Ò–

(4) •Áœ‡ÊÊ·áÊ, ŒÊ’ ∑§ flª¸ ∑§ ‚◊ʟȬÊÃË „Ò–

3 IX - CHEMISTRY

9. The rate of a reaction quadruples when 9. Ãʬ 300 ‚ 310 K ¬Á⁄UflÁøà „ÊŸ ◊¥ •Á÷Á∑˝§ÿÊ ∑§Ë
the temperature changes from 300 to
Œ⁄U øÊ⁄U ªÈŸÊ „Ê ¡ÊÃË „Ò– ß‚ •Á÷Á∑˝§ÿÊ ∑§Ë ‚Á∑˝§ÿáÊ
310 K. The activation energy of this
reaction is : ™§¡Ê¸ „Ò :
(Assume activation energy and pre- (ÿ„ ◊ÊŸ ∑§⁄U øÁ‹ÿ Á∑§ ‚Á∑˝§ÿáÊ ™§¡Ê¸ ÃÕÊ
exponential factor are independent of ¬˝Ë∞Ä‚¬ÊŸÁã‡Êÿ‹ »Ò§Ä≈U⁄U Ãʬ ¬⁄U ÁŸ÷¸⁄U Ÿ„Ë¥ „Ò;
temperature; ln 2=0.693; R=8.314 J
ln 2=0.693; R=8.314 J mol−1 K−1)
mol−1 K−1)
(1) 107.2 kJ mol−1
(2) 53.6 kJ mol−1
(1) 107.2 kJ mol−1
(3) 26.8 kJ mol−1
(2) 53.6 kJ mol−1
(4) 214.4 kJ mol−1
(3) 26.8 kJ mol−1
(4) 214.4 kJ mol−1
10. A solution is prepared by mixing 8.5 g of
CH2Cl2 and 11.95 g of CHCl3. If vapour
pressure of CH2Cl2 and CHCl3 at 298 K 10. 8.5 g CH2Cl2 ÃÕÊ 11.95 g CHCl3 ∑§Ê Á◊‹Ê∑§⁄U
are 415 and 200 mmHg respectively, the ∞∑§ Áfl‹ÿŸ ÃÒÿÊ⁄U Á∑§ÿÊ ¡ÊÃÊ „Ò– ÿÁŒ 298 K ¬⁄U
mole fraction of CHCl3 in vapour form is :
(Molar mass of Cl=35.5 g mol−1) CH2Cl2 ÃÕÊ CHCl3 ∑§ flÊc¬ ŒÊ’ ∑˝§◊‡Ê— 415
ÃÕÊ 200 mmHg „Ê ÃÊ flÊc¬ M§¬ ◊¥ ©¬ÁSÕÃ
(1) 0.162 CHCl3 ∑§Ê ◊Ê‹ •¥‡Ê „Ò —

(2) 0.675 (Cl ∑§Ê ◊Ê‹⁄U Œ˝√ÿ◊ÊŸ=35.5 g mol−1)
(3) 0.325
(1) 0.162
(4) 0.486
(2) 0.675
(3) 0.325
11. The electronic configuration with the
highest ionization enthalpy is : (4) 0.486
(1) [Ne] 3s2 3p1
(2) [Ne] 3s2 3p2 11. ©ëøÃ◊ •ÊÿŸŸ ∞ãÕÒÀ¬Ë flÊ‹Ê ß‹Ä≈˛UÊÁŸ∑§ ÁflãÿÊ‚
(3) [Ne] 3s2 3p3 „Ò —
(4) [Ar] 3d10 4s2 4p3 (1) [Ne] 3s2 3p1
(2) [Ne] 3s2 3p2
(3) [Ne] 3s2 3p3
(4) [Ar] 3d10 4s2 4p3

4 IX - CHEMISTRY

12. The following reaction occurs in the Blast 12. flÊàÿÊ÷^Ë (é‹ÊS≈U »§⁄UŸ‡Ê) ◊¥ ÁŸêŸ •Á÷Á∑˝§ÿÊ „ÊÃË
Furnace where iron ore is reduced to iron
„Ò Á¡‚◊¥ •Êÿ⁄UŸ •ÿS∑§ •¬øÁÿà „Ê∑§⁄U •Êÿ⁄UŸ
metal :
œÊÃÈ ’ŸÃÊ „Ò;
Fe2O3(s)+3 CO(g) ⇌ 2 Fe(l)+3 CO2(g)
Fe2O3(s)+3 CO(g) ⇌ 2 Fe(l)+3 CO2(g)
Using the Le Chatelier’s principle, predict
which one of the following will not disturb ‹-‡ÊÊÃÒÁ‹∞ Á‚hÊãà ∑§Ê ¬˝ÿÊª ∑§⁄U∑§ ¬˝ÊªÈÁÄà ∑§ËÁ¡∞
the equilibrium ? Á∑§ ÁŸêŸ ◊¥ ‚ ∑§ÊÒŸ ‚Ê ∞∑§ ‚Êêÿ ∑§Ê ¬˝÷ÊÁflà Ÿ„Ë¥
(1) Removal of CO ∑§⁄UªÊ?
(2) Removal of CO2 (1) CO ∑§Ê ÁŸ∑§Ê‹ ∑§⁄U „≈UÊ ŒŸÊ
(3) Addition of CO2
(2) CO2 ∑§Ê ÁŸ∑§Ê‹ ∑§⁄U „≈UÊ ŒŸÊ
(4) Addition of Fe2O3
(3) CO2 ∑§Ê Á◊‹Ê ŒŸÊ

13. Which one of the following is an oxide ? (4) Fe2O3 ∑§Ê Á◊‹Ê ŒŸÊ
(1) KO2
(2) BaO 2 13. ÁŸêŸ ◊¥ ‚ ∑§ÊÒŸ ‚Ê ∞∑§, •ÊÚÄ‚Êß«U „Ò?
(3) SiO2 (1) KO2
(4) CsO2 (2) BaO 2
(3) SiO2
14. Which of the following is a set of green (4) CsO2
house gases ?
(1) CH4, O3, N2, SO2
14. ÁŸêŸ ◊¥ ‚ ∑§ÊÒŸ‚Ê ª˝ËŸ „Ê©‚ ªÒ‚Ê¥ ∑§Ê ‚◊ÈìÊÿ „Ò?
(2) O3, N2, CO2, NO2
(3) O3, NO2, SO2, Cl2
(1) CH4, O3, N2, SO2
(4) CO2, CH4, N2O, O3
(2) O3, N2, CO2, NO2
(3) O3, NO2, SO2, Cl2
(4) CO2, CH4, N2O, O3

5 IX - CHEMISTRY

15. The group having triangular planar 15. fl„ ª˝È¬ Á¡‚◊¥ ÁòÊ∑§ÊáÊ ‚◊ËËÿ ‚¥⁄UøŸÊflÊ‹ „Ò¥, „Ò —
structures is :
2−
(1) BF3, NF3, CO 3 2−
(1) BF3, NF3, CO 3
(2) CO 23− , NO−
3 , SO3 (2) CO 23− , NO−
3 , SO3
(3) NH3, SO3, CO 23−
(3) NH3, SO3, CO 23−
(4) NCl3, BCl3, SO3
(4) NCl3, BCl3, SO3

16. XeF 6 on partial hydrolysis with water
produces a compound ‘X’. The same 16. XeF6, ¡‹ ∑§ ‚ÊÕ •Ê¥Á‡Ê∑§ ¡‹-•¬ÉÊ≈UŸ ∑§⁄UŸ
compound ‘X’ is formed when XeF6 reacts ¬⁄U, ∞∑§ ÿÊÒÁª∑§ ‘X’ ŒÃÊ „Ò– ÿ„Ë ÿÊÒÁª∑§ ‘X’ Ã’
with silica. The compound ‘X’ is : ’ŸÃÊ „Ò ¡’ XeF6 Á‚Á‹∑§Ê ∑§ ‚ÊÕ •Á÷Á∑˝§ÿÊ ∑§⁄UÃÊ
(1) XeF2 „Ò– ÿÊÒÁª∑§ ‘X’ „Ò —
(2) XeF4 (1) XeF2
(3) XeOF4 (2) XeF4
(4) XeO3 (3) XeOF4
(4) XeO3
17. The number of P−OH bonds and the
oxidation state of phosphorus atom in
pyrophosphoric acid (H 4 P 2 O 7 ) 17. ¬Êÿ⁄UÊ»§ÊS»§ÊÁ⁄U∑§ ∞Á‚«U (H4P2O7) ◊¥ P−OH
respectively are : •Ê’ãœÊ¥ ∑§Ë ‚¥ÅÿÊ ÃÕÊ »§ÊS»§Ê⁄U‚ ¬⁄U◊ÊáÊÈ ∑§Ë
(1) four and four •ÊÚÄ‚Ë∑§⁄UáÊ •flSÕÊ ∑˝§◊‡Ê— „Ò¥ —
(2) five and four
(3) five and five (1) øÊ⁄U ÃÕÊ øÊ⁄U
(4) four and five (2) ¬Ê°ø ÃÕÊ øÊ⁄U
(3) ¬Ê°ø ÃÕÊ ¬Ê°ø
(4) øÊ⁄U ÃÕÊ ¬Ê°ø

6 IX - CHEMISTRY

18. Which of the following ions does not 18. ÁŸêŸ •ÊÿŸÊ¥ ◊¥ ‚ ∑§ÊÒŸ ‚Ê ÃŸÈ •ê‹Ê¥ ‚ •Á÷Á∑˝§ÿÊ
liberate hydrogen gas on reaction with ∑§⁄UŸ ¬⁄U „Êß«˛UÊ¡Ÿ ªÒ‚ Ÿ„Ë¥ ÁŸ∑§Ê‹ÃÊ ?
dilute acids ?
(1) Ti2+
(1) Ti2+
(2) V2+
(2) V2+
(3) Cr2+
(3) Cr2+
(4) Mn2+
(4) Mn2+

19. The correct sequence of decreasing number
of π-bonds in the structures of H 2SO 3, 19. H2SO3, H2SO4 ÃÕÊ H2S2O7 ∑§Ë ‚¥⁄UøŸÊ ◊¥
H2SO4 and H2S2O7 is : π- •Ê’ãœÊ¥ ∑§Ë ÉÊ≈UÃË ‚¥ÅÿÊ ∑§Ê ‚„Ë ∑˝§◊ „Ò —
(1) H2SO3 > H2SO4 > H2S2O7
(2) H2SO4 > H2S2O7 > H2SO3 (1) H2SO3 > H2SO4 > H2S2O7
(3) H2S2O7 > H2SO4> H2SO3 (2) H2SO4 > H2S2O7 > H2SO3
(4) H2S2O7 > H2SO3 > H2SO4 (3) H2S2O7 > H2SO4> H2SO3
(4) H2S2O7 > H2SO3 > H2SO4
20. [Co2(CO)8] displays :
(1) one Co−Co bond, six terminal CO 20. [Co2(CO)8] •Á÷√ÿÄà ∑§⁄UÃÊ „Ò —
and two bridging CO
(2) one Co−Co bond, four terminal CO (1) ∞∑§ Co−Co •Ê’ãœ, ¿U— ≈U⁄UÁ◊Ÿ‹ CO
and four bridging CO ÃÕÊ ŒÊ ‚ÃÈ’¥œŸ CO
(3) no Co−Co bond, six terminal CO (2) ∞∑§ Co−Co •Ê’ãœ, øÊ⁄U ≈U⁄UÁ◊Ÿ‹ CO
and two bridging CO
ÃÕÊ øÊ⁄U ‚ÃÈ’¥œŸ CO
(4) no Co−Co bond, four terminal CO
and four bridging CO (3) Co−Co •Ê’㜠Ÿ„Ë¥, ¿U— ≈U⁄UÁ◊Ÿ‹ CO
ÃÕÊ ŒÊ ‚ÃÈ’¥œŸ CO
(4) Co−Co •Ê’㜠Ÿ„Ë¥, øÊ⁄U ≈U⁄UÁ◊Ÿ‹ CO
ÃÕÊ øÊ⁄U ‚ÃÈ’¥œŸ CO

7 IX - CHEMISTRY

21. A compound of molecular formula 21. ∞∑§ ÿÊÒÁª∑§ Á¡‚∑§Ê •áÊÈ‚òÍ Ê C8H8O2 „Ò, ∞Á‚≈UÊ»§ŸÊŸ
C8H8O2 reacts with acetophenone to form
‚ ∞∑§ ˇÊÊ⁄U∑§ ∑§Ë ©¬ÁSÕÁà ◊¥ •Á÷Á∑˝§ÿÊ ∑§⁄U∑§ ∞∑§
a single cross-aldol product in the presence
of base. The same compound on reaction „Ë ∑˝§Ê‚-∞À«UÊ‹ ©à¬ÊŒ ’ŸÊÃÊ „Ò– fl„Ë ÿÊÒÁª∑§ ‚ÊãŒ˝
with conc. NaOH forms benzyl alcohol as NaOH ∑§ ‚ÊÕ •Á÷Á∑˝§ÿÊ ∑§⁄U∑§ ’¥Á¡‹ ∞À∑§Ê„ÊÚ‹,
one of the products. The structure of the ¡Ê ’ŸŸflÊ‹ ©à¬ÊŒÊ¥ ◊¥ ‚ ∞∑§ „Ò, ’ŸÊÃÊ „Ò– ÿÊÒÁª∑§
compound is :
∑§Ë ‚¥⁄UøŸÊ „Ò —

(1)

(1)

(2)

(2)

(3)

(3)

(4)

(4)

8 IX - CHEMISTRY

22. Which of the following compounds is most 22. ÁŸêŸ ◊¥ ‚ ∑§ÊÒŸ ‚Ê ÿÊÒÁª∑§, ‚ÊÁ«Uÿ◊ ∑§Ê’Ê¸Ÿ≈U ∑§
reactive to an aqueous solution of sodium
¡‹Ëÿ Áfl‹ÿŸ ∑§ ¬˝ÁÃ, ‚flʸÁœ∑§ •Á÷Á∑˝§ÿʇÊË‹
carbonate ?
„Ò?

(1)
(1)

(2)
(2)

(3)
(3)

(4)
(4)

23. In the following structure, the double
bonds are marked as I, II, III and IV 23. ÁŸêŸ ‚¥⁄UøŸÊ ◊¥, Ám •Ê’ãœÊ¥ ∑§Ê I, II, III ÃÕÊ IV ‚
ÁøÁqà Á∑§ÿÊ ªÿÊ „Ò–

Geometrical isomerism is not possible at
site (s) :
íÿÊÁ◊ÃËÿ ‚◊ÊflÿflÃÊ ß‚ SÕÊŸ/ߟ SÕÊŸÊ¥ ◊¥ ‚¥÷fl
(1) III Ÿ„Ë¥ „Ò —
(2) I
(1) III
(3) I and III
(2) I
(4) III and IV
(3) I ÃÕÊ III

(4) III ÃÕÊ IV

9 IX - CHEMISTRY

24. The major product of the following 24. ÁŸêŸ •Á÷Á∑˝§ÿÊ ∑§Ê ◊ÈÅÿ ©à¬ÊŒ „Ò —
reaction is :

(1)
(1)

(2)
(2)

(3)
(3)

(4)
(4)

10 IX - CHEMISTRY

25. The incorrect statement among the 25. ÁŸêŸ ◊¥ ‚ ª‹Ã ∑§ÕŸ „Ò —
following is :
(1) α-D-glucose and β-D-glucose are
(1) α-D-Ç‹Í∑§Ê¡ ÃÕÊ β-D-Ç‹Í∑§Ê¡ ∞ŸÊ◊⁄U „Ò¥–
anomers.
(2) α-D-glucose and β-D-glucose are
enantiomers. (2) α-D-Ç‹Í∑§Ê¡ ÃÕÊ β-D-Ç‹Í∑§Ê¡ ¬˝ÁÃÁ’ê’M§¬
(3) Cellulose is a straight chain „Ò–¥
polysaccharide made up of only
β-D-glucose units.
(3) ‚‹Í‹Ê¡ ∞∑§ ´§¡È oÎ¥π‹Ê ¬Ê‹Ë‚Ò∑§⁄UÊß«U „Ò
¡Ê ∑§fl‹ β-D-Ç‹Í∑§Ê¡ ∞∑§∑§Ê¥ ‚ ’ŸÊ „Ò–
(4) The penta acetate of glucose does not
react with hydroxyl amine.
(4) Ç‹Í∑§Ê¡ ∑§Ê ¬ã≈UÊ ∞‚Ë≈U≈U, „Êß«˛UÊÁÄ‚‹ ∞◊ËŸ
26. Which of the following is a biodegradable ∑§ ‚ÊÕ •Á÷Á∑˝§ÿÊ Ÿ„Ë¥ ∑§⁄UÃÊ „Ò
polymer ?

26. ÁŸêŸ ◊¥ ‚ ∑§ÊÒŸ ‚Ê ¡ÒflÁŸêŸŸËÿ ’„È‹∑§ „Ò?
(1)

(2) (1)

(2)
(3)

(4) (3)

(4)

11 IX - CHEMISTRY

27. The increasing order of the boiling points 27. ÁŸêŸ ÿÊÒÁª∑§Ê¥ ∑§ ÄflÕŸÊ¥∑§Ê¥ ∑§Ê ’…∏ÃÊ „È•Ê ∑˝§◊ „Ò —
for the following compounds is :
C 2 H5 OH C 2 H5Cl C 2 H5CH3
C 2 H5 OH C 2 H5Cl C 2 H5CH3 (I) (II) (III)
(I) (II) (III)
C 2 H5OCH3
C 2 H5OCH3 (IV)
(IV)
(1) (III) < (IV) < (II) < (I)
(1) (III) < (IV) < (II) < (I)
(2) (IV) < (III) < (I) < (II)
(2) (IV) < (III) < (I) < (II)
(3) (II) < (III) < (IV) < (I)
(3) (II) < (III) < (IV) < (I)
(4) (III) < (II) < (I) < (IV)
(4) (III) < (II) < (I) < (IV)

28. Which of the following compounds will
28. ÁŸêŸ ÿÊÒÁª∑§Ê¥ ◊¥ ‚ Á∑§‚∑§Ê Ámœ˝Èfl •ÊÉÊÍáʸ ‚flʸÁœ∑§
show highest dipole moment ? „ÊªÊ?

(I) (II) (I) (II)

(III) (IV) (III) (IV)

(1) (I) (1) (I)
(2) (II) (2) (II)
(3) (III) (3) (III)
(4) (IV) (4) (IV)

12 IX - CHEMISTRY

29. In the following reaction sequence : 29. ÁŸêŸ •Á÷Á∑˝§ÿÊ ∑˝§◊ ◊¥ —

The compound I is :
ÿÊÒÁª∑§ I „Ò —
(1)
(1)

(2)
(2)

(3)
(3)

(4)
(4)

30. Among the following compounds, the
increasing order of their basic strength is : 30. ÁŸêŸ ÿÊÒÁª∑§Ê¥ ∑§ ˇÊÊ⁄UËÿ ‚Ê◊âÿ¸ ∑§Ê ’…∏ÃÊ „È•Ê ∑˝§◊
„Ò —
(I) (II)
(I) (II)

(III) (IV)
(III) (IV)
(1) (I) < (II) < (IV) < (III)
(2) (I) < (II) < (III) < (IV) (1) (I) < (II) < (IV) < (III)

(3) (II) < (I) < (IV) < (III) (2) (I) < (II) < (III) < (IV)

(4) (II) < (I) < (III) < (IV) (3) (II) < (I) < (IV) < (III)
(4) (II) < (I) < (III) < (IV)

13 IX - CHEMISTRY

MATHEMATICS ªÁáÊÃ

1. The function f : N → N defined by
x
»§‹Ÿ f : N → N, f (x ) = x − 5  5  mÊ⁄UÊ
f ( x ) = x − 5   , where N is the set of
x 1.
5
¬Á⁄U÷ÊÁ·Ã „Ò, ¡„Ê° N, ¬˝Ê∑Χà ‚¥ÅÿÊ•Ê¥ ∑§Ê ‚◊ÈìÊÿ „Ò
natural numbers and [x] denotes the
greatest integer less than or equal to x, is : ÃÕÊ [x], x ‚ ∑§◊ ÿÊ ©‚∑§ ‚◊ÊŸ ◊„ûÊ◊ ¬ÍáÊÊZ∑§ „Ò,
(1) one-one and onto.
¡Ê —
(2) one-one but not onto. (1) ∞∑Ò§∑§Ë ÃÕÊ •Êë¿UÊŒ∑§ „Ò–
(3) onto but not one-one. (2) ∞∑Ò§∑§Ë „Ò ¬⁄UãÃÈ •Êë¿UÊŒ∑§ Ÿ„Ë¥ „Ò–
(4) neither one-one nor onto. (3) •Êë¿UÊŒ∑§ „Ò ¬⁄UãÃÈ ∞∑Ò§∑§Ë Ÿ„Ë¥ „Ò–
(4) Ÿ ÃÊ ∞∑Ò§∑§Ë „Ò •ÊÒ⁄U Ÿ „Ë •Êë¿UÊŒ∑§ „Ò–
2. The sum of all the real values of x satisfying
2
the equation 2(x−1)(x +5x−50)=1 is :
(1) 16 2. ‚◊Ë∑§⁄UáÊ 2(x−1)(x2+5x−50)=1 ∑§Ê ‚¥ÃÈc≈U ∑§⁄UŸ
(2) 14 flÊ‹ x ∑§ ‚÷Ë flÊSÃÁfl∑§ ◊ÊŸÊ¥ ∑§Ê ÿÊª „Ò —
(3) −4 (1) 16
(4) −5 (2) 14
(3) −4
3. The equation (4) −5

Im 
iz − 2 
 + 1 = 0, z  C , z ≠ i
 z −i  3. ‚◊Ë∑§⁄UáÊ
represents a part of a circle having radius
Im 
equal to : iz − 2 
 + 1 = 0, z  C , z ≠ i
 z −i 
(1) 2
©‚ flÎûÊ ∑§ ∞∑§ ÷ʪ ∑§Ê ÁŸM§Á¬Ã ∑§⁄UÃË „Ò, Á¡‚∑§Ë
(2) 1
ÁòÊíÿÊ „Ò —
3 (1) 2
(3)
4
(2) 1
1
(4) 3
2 (3)
4

1
(4)
2

1 IX - MATHEMATICS

4. For two 3×3 matrices A and B, let 4. ŒÊ 3×3 •Ê√ÿÍ „ Ê ¥ A ÃÕÊ B ∑ § Á‹∞ ◊ÊŸÊ
A+B=2B9 and 3A+2B=I3, where B9 is
A+B=2B9 ÃÕÊ 3A+2B=I3 „Ò, ¡„Ê° B9 •Ê√ÿÍ„
the transpose of B and I3 is 3×3 identity
matrix. Then : B ∑§Ê ¬Á⁄Uflø „Ò ÃÕÊ I3 ∞∑§ 3×3 Ãà‚◊∑§ •Ê√ÿÍ„

(1) 5A+10B=2I3
„Ò, ÃÊ —
(2) 10A+5B=3I3 (1) 5A+10B=2I3

(3) B+2A=I3 (2) 10A+5B=3I3

(4) 3A+6B=2I3 (3) B+2A=I3
(4) 3A+6B=2I3

5. If x=a, y=b, z=c is a solution of the
system of linear equations 5. ÿÁŒ x=a, y=b, z=c ⁄ÒUÁπ∑§ ‚◊Ë∑§⁄UáÊ ÁŸ∑§Êÿ
x+8y+7z=0 x+8y+7z=0
9x+2y+3z=0 9x+2y+3z=0
x+y+z=0 x+y+z=0
such that the point (a, b, c) lies on the plane ∑§Ê ∞∑§ ∞‚Ê „‹ „Ò Á∑§ Á’¥ŒÈ (a, b, c) ‚◊Ë
x+2y+z=6, then 2a+b+c equals : x+2y+z=6 ¬⁄U ÁSÕà „Ò, ÃÊ 2a+b+c ’⁄UÊ’⁄U
„Ò —
(1) −1
(1) −1
(2) 0
(2) 0
(3) 1
(3) 1
(4) 2
(4) 2

6. The number of ways in which 5 boys and
3 girls can be seated on a round table if a 6. 5 ‹«∏∑§Ê¥ ÃÕÊ 3 ‹«∏Á∑§ÿÊ¥ ∑§Ê ∞∑§ ªÊ‹ ◊$¡ ∑§ øÊ⁄UÊ¥
particular boy B1 and a particular girl G1 •Ê⁄U ß‚ ¬˝∑§Ê⁄U Á’∆UÊŸ, Á∑§ ∞∑§ ÁflÁ‡Êc≈U ‹«∏∑§Ê B1
never sit adjacent to each other, is :
ÃÕÊ ∞∑§ ÁflÁ‡Êc≈U ‹«∏∑§Ë G1 ∑§÷Ë ÷Ë ∞∑§ ‚ÊÕ Ÿ
(1) 5×6! ’Ò∆U ‚∑¥§, ∑§ Ã⁄UË∑§Ê¥ ∑§Ë ‚¥ÅÿÊ „Ò —
(2) 6×6!
(1) 5×6!
(3) 7!
(2) 6×6!
(4) 5×7!
(3) 7!
(4) 5×7!

2 IX - MATHEMATICS

7. The coefficient of x −5 in the binomial
 x +1 x − 1 10
 x +1 x −1  10 7.  2 1
− 1  , ¡„Ê° x ≠ 0, 1,
expansion of  2 1
− 1  ,  x3 −x3 +1 x −x2 
 x3 −x3 +1 x −x2  ∑§ Ám¬Œ ÁflSÃÊ⁄U ◊¥ x−5 ∑§Ê ªÈáÊÊ¥∑§ „Ò —
where x ≠ 0, 1, is :
(1) 1
(1) 1
(2) 4
(2) 4
(3) −4
(3) −4
(4) −1
(4) −1

8. If three positive numbers a, b and c are in
A.P. such that abc=8, then the minimum 8. ÿÁŒ ÃËŸ œŸÊà◊∑§ ‚¥ÅÿÊ∞° a, b ÃÕÊ c ‚◊Ê¥Ã⁄U üÊ…Ë
possible value of b is : ◊¥ „Ò¥ Á¡Ÿ∑§ Á‹∞ abc=8 „Ò, ÃÊ b ∑§Ê ãÿÍŸÃ◊ ‚¥÷fl
(1) 2 ◊ÊŸ „Ò —
1 (1) 2
(2) 43
1
(2) 43
2
(3) 43
2
(4) 4 (3) 43
(4) 4
9. Let
1 1+2
Sn = 3 + 3 +
1+2+3
+ 9. ◊ÊŸÊ
1 1 + 23 13 + 2 3 + 33 1 1+2 1+2+3
Sn = 3 + 3 3
+ 3 +
....... + 3
1 + 2 + ....... + n
. If 100 Sn=n, 1 1 +2 1 + 2 3 + 33
1 + 2 3 + ....... + n 3 1 + 2 + ....... + n
then n is equal to : ....... + 3 . ÿÁŒ
1 + 2 3 + ....... + n 3
(1) 199 100 Sn=n „Ò, ÃÊ n ’⁄UÊ’⁄U „Ò —
(2) 99
(1) 199
(3) 200
(2) 99
(4) 19
(3) 200
(4) 19

3 IX - MATHEMATICS

10. The value of k for which the function 10. k ∑§Ê fl„ ◊ÊŸ Á¡‚∑§ Á‹∞ »§‹Ÿ
 4 tan 4x
 4 tan 4x

   tan 5x
, 0<x<
π   tan 5x π
 5    , 0<x<
2 
f (x) =  f ( x ) =  5  2
 2 π  2 π
 k+ , x= k+ , x=
 5 2 
 5 2
π
is continuous at x = , is : x=
π
¬⁄U ‚ÃØ „Ò, „Ò —
2 2
17 17
(1) (1)
20 20
2 2
(2) (2)
5 5
3 3
(3) (3)
5 5
2 2
(4) − (4) −
5 5

1 − 15 1 1
11. If 2 x = y 5 + y and 11. ÿÁŒ 2 x = y 5 + y− 5 ÃÕÊ
d2 y dy d2 y dy
( x 2 − 1) 2
+ λx + ky = 0, then λ+k ( x 2 − 1) + λx + ky = 0 „Ò, ÃÊ λ+k
dx dx dx 2 dx
is equal to :
’⁄UÊ’⁄U „Ò —
(1) −23
(1) −23
(2) −24
(2) −24
(3) 26
(3) 26
(4) −26
(4) −26

4 IX - MATHEMATICS

12. The function f defined by 12. f (x)=x3−3x2+5x+7 mÊ⁄UÊ ¬Á⁄U÷ÊÁ·Ã »§‹Ÿ f —
f (x)=x3−3x2+5x+7, is :
(1) increasing in R. (1) R ◊¥ flœ¸◊ÊŸ „Ò–
(2) decreasing in R.
(2) R ◊¥ OÊ‚◊ÊŸ „Ò–
(3) decreasing in (0, ∞) and increasing
in (−∞, 0). (3) (0, ∞) ◊¥ OÊ‚◊ÊŸ ÃÕÊ (−∞, 0) ◊¥ flœ¸◊ÊŸ
(4) increasing in (0, ∞) and decreasing „Ò–
in (−∞, 0). (4) (0, ∞) ◊¥ flœ¸◊ÊŸ ÃÕÊ (−∞, 0) ◊¥ OÊ‚◊ÊŸ
„Ò–
13. Let f be a polynomial function such that
f (3x)=f 9(x) ⋅ f 99(x), for all x e R. Then :
(1) f (2)+f 9(2)=28
13. ◊ÊŸÊ ∞∑§ ’„ȬŒ »§‹Ÿ f ∞‚Ê „Ò Á∑§ ‚÷Ë x e R ∑§
Á‹∞ f (3x)=f 9(x) ⋅ f 99(x) „Ò, ÃÊ —
(2) f 99 (2)−f 9(2)=0
(1) f (2)+f 9(2)=28
(3) f 99(2)−f (2)=4
(2) f 99 (2)−f 9(2)=0
(4) f (2)−f 9(2)+f 99(2)=10
(3) f 99(2)−f (2)=4
(4) f (2)−f 9(2)+f 99(2)=10
f 
3x − 4  4
14. If  = x + 2, x ≠ − , and
 3x + 4  3
f 
3x − 4  4
∫ f (x) dx = A log 1 − x + Bx + C, then 14. ÿÁŒ  = x + 2, x ≠ −
 3x + 4  3
ÃÕÊ
the ordered pair (A, B) is equal to :
(where C is a constant of integration) ∫ f (x) dx = A log 1 − x + Bx + C „Ò , ÃÊ
∑˝§Á◊à ÿÈÇ◊ (A, B) ’⁄UÊ’⁄U „Ò —
8 2
(1)  ,  (¡„Ê° C ∞∑§ ‚◊Ê∑§‹Ÿ •ø⁄U „Ò)
3 3

 8 2 8 2
(2) − , 
(1)  , 
 3 3 3 3

 8 2  8 2
(3) − , −  (2) − , 
 3 3  3 3

8 2 (3)  8 2
(4)  ,−  − , − 
3 3  3 3

8 2
(4)  ,− 
3 3

5 IX - MATHEMATICS

2 2

∫ ( x − 2x + 4 ∫ ( x − 2x + 4)
dx k dx k
15. If 3
= , then k is 15. ÿÁŒ 3
= „Ò, ÃÊ k ’⁄UÊ’⁄U
2 ) 2 k + 5 2 2 k+5
1 1
equal to : „Ò —
(1) 1 (1) 1
(2) 2 (2) 2
(3) 3 (3) 3
(4) 4 (4) 4

16. If
16. Á∑§‚Ë œŸÊà◊∑§ flÊSÃÁfl∑§ ‚¥ÅÿÊ a ∑§ Á‹∞ ÿÁŒ
a a a
lim 1 + 2 + ........ + n 1
n →∞ a−1
= lim 1a + 2 a + ........ + n a 1
(n+1) [(na+1)+(na+2)+..... +(na+n)] 60 n →∞ a−1
=
(n+1) [(na+1)+(na+2)+..... +(na+n)] 60
for some positive real number a, then a is
equal to : „Ò, ÃÊ a ’⁄UÊ’⁄U „Ò —
(1) 7
(2) 8 (1) 7
(2) 8
15
(3)
2 15
(3)
2
17
(4)
2 17
(4)
2

6 IX - MATHEMATICS

17. A tangent to the curve, y=f (x) at P(x, y) 17. fl∑˝§ y=f (x) ∑§ Á’¥ŒÈ P(x, y) ¬⁄U S¬‡Ê¸⁄UπÊ x-•ˇÊ
meets x-axis at A and y-axis at B. If
∑§Ê A ¬⁄U ÃÕÊ y-•ˇÊ ∑§Ê B ¬⁄U ∑§Ê≈UÃË „Ò– ÿÁŒ
AP : BP=1 : 3 and f (1)=1, then the curve
also passes through the point : AP : BP=1 : 3 ÃÕÊ f (1)=1 „Ò, ÃÊ fl∑˝§ ÁŸêŸ Á’¥ŒÈ
‚ ÷Ë „Ê ∑§⁄U ¡ÊÃÊ „Ò —
1 
(1)  , 24 
3  1 
(1)  , 24 
3 
1 
(2)  , 4
2  1 
(2)  , 4
2 
(3)  1
 2, 
 8 (3)  1
 2, 
 8
(4)  1 
 3, 
 28  (4)  1 
 3, 
 28 

18. A square, of each side 2, lies above the
x-axis and has one vertex at the origin. If 18. ∞∑§ flª¸, Á¡‚∑§Ë ¬˝àÿ∑§ ÷È¡Ê 2 „Ò, x-•ˇÊ ‚ ™§¬⁄U
one of the sides passing through the origin
makes an angle 308 with the positive
ÁSÕà „Ò ÃÕÊ Á¡‚∑§Ê ∞∑§ ‡ÊË·¸ ◊Í‹ Á’¥ŒÈ ¬⁄U „Ò– ÿÁŒ
direction of the x-axis, then the sum of the ß‚∑§Ë ◊Í‹ Á’¥ŒÈ ‚ „Ê∑§⁄U ¡ÊÃË „È߸ ∞∑§ ÷È¡Ê, x-•ˇÊ
x-coordinates of the vertices of the square ∑§Ë œŸÊà◊∑§ ÁŒ‡ÊÊ ‚ 308 ∑§Ê ∑§ÊáÊ ’ŸÊÃË „Ò, ÃÊ flª¸
is : ∑§ ‡ÊË·¸ Á’¥ŒÈ•Ê¥ ∑§ x-ÁŸŒ¸‡ÊÊ¥∑§Ê¥ ∑§Ê ÿÊª „Ò —
(1) 2 3 −1

(2) 2 3 −2
(1) 2 3 −1
(3) 3 −2
(2) 2 3 −2
(4) 3 −1
(3) 3 −2

(4) 3 −1

7 IX - MATHEMATICS

19. A line drawn through the point P(4, 7) cuts 19. ÿÁŒ Á’¥ŒÈ P(4, 7) ‚ πË¥øË ªß¸ ∞∑§ ⁄UπÊ, flÎûÊ
the circle x2+y2=9 at the points A and B.
x2+y2=9 ∑§Ê Á’¥ŒÈ•Ê¥ A ÃÕÊ B ¬⁄U ∑§Ê≈UÃË „Ò, ÃÊ
Then PA⋅PB is equal to :
PA⋅PB ’⁄UÊ’⁄U „Ò —
(1) 53
(1) 53
(2) 56
(2) 56
(3) 74
(3) 74
(4) 65
(4) 65

20. The eccentricity of an ellipse having centre
at the origin, axes along the co-ordinate 20. ∞∑§ ŒËÉʸflÎûÊ Á¡‚∑§Ê ∑§ãŒ˝ ◊Í‹ Á’¥ŒÈ „Ò, •ˇÊ ÁŸŒ¸‡ÊÊ¥∑§
axes and passing through the points •ˇÊ „Ò¥ ÃÕÊ ¡Ê Á’¥ŒÈ•Ê¥ (4, −1) ÃÕÊ (−2, 2) ‚
(4, −1) and (−2, 2) is :
„Ê∑§⁄U ¡ÊÃÊ „Ò, ∑§Ë ©à∑¥§Œ˝ÃÊ (eccentricity) „Ò —
1
(1)
2
1
(1)
2 2
(2)
5
2
(2)
3 5
(3)
2
3
(3)
3 2
(4)
4
3
(4)
21. If y=mx+c is the normal at a point on 4
the parabola y2=8x whose focal distance
is 8 units, then ?c? is equal to : 21. ÿÁŒ y=mx+c ¬⁄Ufl‹ÿ y2=8x ∑§ ©‚ Á’¥ŒÈ ¬⁄U
(1) 2 3
•Á÷‹¥’ „Ò Á¡‚∑§Ë ŸÊÁ÷ ‚ ŒÍ⁄UË 8 ß∑§Ê߸ „Ò, ÃÊ ?c?
’⁄UÊ’⁄U „Ò —
(2) 8 3
(1) 2 3
(3) 10 3
(2) 8 3
(4) 16 3
(3) 10 3

(4) 16 3

8 IX - MATHEMATICS

22. If a variable plane, at a distance of 3 units 22. ∞∑§ ø⁄U ‚◊Ë, Á¡‚∑§Ë ◊Í‹ Á’¥ŒÈ ‚ ŒÍ⁄UË 3 ß∑§Ê߸ „Ò,
from the origin, intersects the coordinate
ÁŸŒ¸‡ÊÊ¥∑§ •ˇÊÊ¥ ∑§Ê A, B ÃÕÊ C ¬⁄U ∑§Ê≈UÃÊ „Ò, ÃÊ
axes at A, B and C, then the locus of the
centroid of ∆ABC is : ∆ABC ∑§ ∑¥§Œ˝∑§ ∑§Ê Á’¥ŒÈ¬Õ „Ò —

1
1 1
(1) + 2 + 2 =1
2
x y z 11 1
(1) + 2 + 2 =1
2
x y z
1
1 1
(2) + 2 + 2 =3
2
x y z 11 1
(2) + 2 + 2 =3
2
x y z
1
1 1 1
(3) + 2 + 2 =
2
x y z 9 11 1 1
(3) + 2 + 2 =
2
x y z 9
1
1 1
(4) + 2 + 2 =9
2
x y z 11 1
(4) + 2 + 2 =9
2
x y z

x −3 y +2 z +λ
23. If the line, = = lies in
y +2
1 −1 −2 23. ÿÁŒ ⁄ U π Ê, x − 3 = =
z +λ
, ‚◊Ë
the plane, 2x−4y+3z=2, then the 1 −1 −2
shortest distance between this line and the 2x−4y+3z=2 ◊¥ ÁSÕà „Ò, ÃÊ ß‚ ⁄UπÊ ÃÕÊ ⁄UπÊ
x −1 y z x −1
line, = = is : y z
= = ∑§ ’Ëø ∑§Ë ãÿÍŸÃ◊ ŒÍ⁄UË „Ò —
12 9 4 12 9 4
(1) 2
(2) 1 (1) 2
(3) 0 (2) 1
(4) 3 (3) 0
(4) 3

9 IX - MATHEMATICS

→ ∧ ∧ → ∧ ∧
24. If the vector b = 3 j + 4 k is written as the 24. ÿÁŒ ‚ÁŒ‡Ê b =3 j +4k ∑§Ê ‚ÁŒ‡Ê
→ → ∧ ∧ → ∧ ∧ → →
sum of a vector b1 , parallel to a = i + j a = i + j ∑§ ‚◊Ê¥Ã⁄U ‚ÁŒ‡Ê b1 ÃÕÊ ‚ÁŒ‡Ê a
→ → →
and a vector b2 , perpendicular to a , then ∑§ ‹¥’flà ‚ÁŒ‡Ê b2 ∑§ ÿÊª ∑§ M§¬ ◊¥ Á‹πÊ ¡Ê∞,
→ → → →
b1 × b 2 is equal to : ÃÊ b1 × b2 ’⁄UÊ’⁄U „Ò —
∧ ∧ ∧ ∧ ∧ ∧
(1) −3 i + 3 j − 9 k (1) −3 i + 3 j − 9 k

∧ ∧ 9∧ ∧ ∧ 9∧
(2) 6i − 6 j + k (2) 6i − 6 j + k
2 2

∧ ∧ 9∧ ∧ ∧ 9∧
(3) −6 i + 6 j − k (3) −6 i + 6 j − k
2 2
∧ ∧ ∧ ∧ ∧ ∧
(4) 3 i − 3 j + 9k (4) 3 i − 3 j + 9k

25. From a group of 10 men and 5 women, 25. 10 ¬ÈL§· ÃÕÊ 5 ◊Á„‹Ê•Ê¥ ∑§ ∞∑§ ‚◊Í„ ◊¥ ‚ øÊ⁄U
four member committees are to be formed
each of which must contain at least one
‚ŒSÿÊ¥ ∑§Ë ∞‚Ë ∑§◊Á≈UÿÊ¥ ’ŸÊŸË „Ò¥ Á¡Ÿ◊¥ ¬˝àÿ∑§ ◊¥
woman. Then the probability for these ∑§◊ ‚ ∑§◊ ∞∑§ ◊Á„‹Ê •fl‡ÿ „Ê– ߟ ∑§◊Á≈UÿÊ¥ ◊¥
committees to have more women than ◊Á„‹Ê•Ê¥ ∑§Ë ‚¥ÅÿÊ ¬ÈL§·Ê¥ ∑§Ë ‚¥ÅÿÊ ‚ •Áœ∑§ „ÊŸ
men, is : ∑§Ë ¬˝ÊÁÿ∑§ÃÊ „Ò —
21
(1)
220
21
(1)
3 220
(2)
11
3
(2)
1 11
(3)
11
1
(3)
2 11
(4)
23
2
(4)
23

10 IX - MATHEMATICS

26. Let E and F be two independent events. 26. ◊ÊŸÊ E ÃÕÊ F ŒÊ SflÃ¥òÊ ÉÊ≈UŸÊ∞° „Ò¥– E ÃÕÊ F ŒÊŸÊ¥ ∑§
The probability that both E and F happen
1 ÉÊ≈UŸ ∑§Ë ¬˝ÊÁÿ∑§ÃÊ 1 „Ò ÃÕÊ Ÿ E •ÊÒ⁄U Ÿ „Ë F ∑§
is and the probability that neither E 12
12
1 P(E)
1 P(E) ÉÊ≈UŸ ∑§Ë ¬˝ÊÁÿ∑§ÃÊ „Ò, ÃÊ ∑§Ê ∞∑§ ◊ÊŸ „Ò —
nor F happens is , then a value of 2 P(F)
2 P(F)
is :

4
(1) 4
3 (1)
3
3
(2) 3
2 (2)
2
1
(3) 1
3 (3)
3
5
(4) 5
12 (4)
12

27. The sum of 100 observations and the sum
of their squares are 400 and 2475, 27. 100 ¬˝ˇÊáÊÊ¥ ∑§Ê ÿÊª ÃÕÊ ©Ÿ∑§ flªÊZ ∑§Ê ÿÊª ∑˝§◊‡Ê—
respectively. Later on, three observations, 400 ÃÕÊ 2475 „Ò– ’ÊŒ ◊¥ ÃËŸ ¬˝ˇÊáÊ 3, 4 ÃÕÊ 5
3, 4 and 5, were found to be incorrect. If ª‹Ã ¬Ê∞ ª∞– ÿÁŒ ª‹Ã ¬˝ˇÊáÊÊ¥ ∑§Ê „≈UÊ ÁŒÿÊ ¡Ê∞
the incorrect observations are omitted, then
the variance of the remaining observations
ÃÊ ‡Ê· ¬˝ˇÊáÊÊ¥ ∑§Ê ¬˝‚⁄UáÊ „Ò —
is :
(1) 8.25
(2) 8.50
(3) 8.00 (1) 8.25

(4) 9.00 (2) 8.50
(3) 8.00
(4) 9.00

11 IX - MATHEMATICS

28. A value of x satisfying the equation 28. ‚◊Ë∑§⁄UáÊ sin[cot−1(1+x)]=cos[tan−1x] ∑§Ê
sin[cot−1(1+x)]=cos[tan−1x], is :
‚¥ÃÈc≈U ∑§⁄UŸ flÊ‹Ê x ∑§Ê ∞∑§ ◊ÊŸ „Ò —
1
(1) − 1
2 (1) −
2
(2) −1
(2) −1
(3) 0
(3) 0
1
(4) 1
2 (4)
2

29. The two adjacent sides of a cyclic
quadrilateral are 2 and 5 and the angle 29. ∞∑§ ø∑˝§Ëÿ-øÃÈ÷ȸ¡ ∑§Ë ŒÊ ‚¥‹ÇŸ ÷È¡Ê∞° 2 ÃÕÊ 5 „Ò¥
between them is 608. If the area of the ÃÕÊ ©Ÿ∑§ ’Ëø ∑§Ê ∑§ÊáÊ 608 „Ò– ÿÁŒ ß‚ øÃÈ÷ȸ¡
quadrilateral is 4 3 , then the perimeter ∑§Ê ˇÊòÊ»§‹ 4 3 „Ò, ÃÊ ß‚∑§Ê ¬Á⁄U◊ʬ „Ò —
of the quadrilateral is :
(1) 12.5
(2) 13.2 (1) 12.5
(3) 12 (2) 13.2
(4) 13 (3) 12
(4) 13

12 IX - MATHEMATICS

30. Contrapositive of the statement 30. ∑§ÕŸ
‘If two numbers are not equal, then their
“ÿÁŒ ŒÊ ‚¥ÅÿÊ∞° ‚◊ÊŸ Ÿ„Ë¥ „Ò¥, ÃÊ ©Ÿ∑§ flª¸ ‚◊ÊŸ
squares are not equal’, is :
Ÿ„Ë¥ „Ò¥”

(1) If the squares of two numbers are
∑§Ê ¬˝ÁÃœŸÊà◊∑§ (Contrapositive) „Ò —
equal, then the numbers are equal. (1) ÿÁŒ ŒÊ ‚¥ÅÿÊ•Ê¥ ∑§ flª¸ ‚◊ÊŸ „Ò¥, ÃÊ ‚¥ÅÿÊ∞°
(2) If the squares of two numbers are ‚◊ÊŸ „Ò¥–
equal, then the numbers are not
equal. (2) ÿÁŒ ŒÊ ‚¥ÅÿÊ•Ê¥ ∑§ flª¸ ‚◊ÊŸ „Ò¥, ÃÊ ‚¥ÅÿÊ∞°
(3) If the squares of two numbers are not ‚◊ÊŸ Ÿ„Ë¥ „Ò¥–
equal, then the numbers are not
equal.
(3) ÿÁŒ ŒÊ ‚¥ÅÿÊ•Ê¥ ∑§ flª¸ ‚◊ÊŸ Ÿ„Ë¥ „Ò¥, ÃÊ
(4) If the squares of two numbers are not
equal, then the numbers are equal.
‚¥ÅÿÊ∞° ‚◊ÊŸ Ÿ„Ë¥ „Ò–

-o0o- (4) ÿÁŒ ŒÊ ‚¥ÅÿÊ•Ê¥ ∑§ flª¸ ‚◊ÊŸ Ÿ„Ë¥ „Ò¥, ÃÊ
‚¥ÅÿÊ∞° ‚◊ÊŸ „Ò–

-o0o-

13 IX - MATHEMATICS