COMMON CENTRAL OFFICE_MADHAPUR OFFICE_MADHAPUR_HYD _HYD
JR.IPLCO 07/07/2014 Ti! : 3:00 M#$. M#%&': 1(0
2013_P1 - MODEL MODEL
Dt:
JEE-AD"ANCED
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KEY SHEET PHY SI CS 1) 7) 13) 19)
C C A,C,D 3
2) 8) 14) 20)
A B A,B,C 5
3) B 9) D 15) B,C
4) C 10) B 16) 1
5) C 11) 11) B,C 17) 4
6) B 12) A,B 18) 6
25) D 31) A,C,D 37) 3
26) B 32) B,D 38) 6
45) B 51) B,C 57) 0
46) A 52) C,D 58) 2
CHEMI MI STRY 21) 27) 33) 39)
A B A,B,C 4
22) 28) 34) 40)
B A A,B 7
23) C 29) C 35) A,B,D
24) C 30) B 36) 4
MAT HEMAT I CS 41) 47) 53) 59)
D A A,C,D 4
42) 48) 54) 60)
B A A,C 6
43) A 49) C 55) A,C,D
44) A 50) C 56) 2
P#)!
1
N#%#*#+# ,%i C#it#+*# IIT A#!* 2013_P1 M! 5TA-6
07/07/14_JR.IPLCOA#+!
HINTS & SOLUTION PHYSICS Section-I 1.
f max = ( 0.5 ) ( 2 ) ( 10 )
= 10 N
f F1 f
a=
2.
20 − f
F L2 − h 2 WL − Fh
a = A ( 1 + cos θ )
=
3 A 2
mg
( θ = 60 ) 0
3 2
T+N
4.
=
2 4 f = 8 N f < f max f = 8 N N + F sin θ = W F cos θ = µ N
µ =
3.
−2
f
F2
1
3 A
2
2
+ mA − T = m 3 2
= MA
F cosθ = µ N F sin θ + N = mg
F =
mg cos θ + µ sin θ
For ‘F’ shou! "# minimum
P#)! N :2
N#%#*#+# ,%i C#it#+*# IIT A#!* 2013_P1 M! 5TA-6
d
( cos θ + µ sin θ ) do µ = ranθ µ mg F min = 1 + µ 2
5.
mg [ sin θ
amax
7.
]
[
+ µ cos θ = 2 mg sin θ − µ cos θ
]
= µ g
µ g = t =
=0
= 3µ = 3ranφ
ranθ ranθ
6.
07/07/14_JR.IPLCOA#+!
at
2m 2 µ mg a
(
) ( 2 ) ( 10) = 12 N f = ( 0.3) ( 4 ) ( 10 ) = 12 N = 0.6
f
2
8.
$#% fric%ion &24 $ F < f , %h# "oc's !o#s is mo(# T + 12 = 16 → T = 4 N f 2 = T = 4 N N sin 45 = µ N sin 45 + mg N cos 45 = µ N cos 45 + ma a
1 + µ = g 1 − µ
).
P#)! N :3
N#%#*#+# ,%i C#it#+*# IIT A#!* 2013_P1 M! 5TA-6
N cos60 − F =
T
+
F 2
mF 2m
= 3F
N
10.
07/07/14_JR.IPLCOA#+!
= 80
T = 80 − ( 70*) ( 0.5) = 45 N
T + F 1 = 20 = −20 N
F1
X 1 11.
= −0.5m
( f ) s1
(
= 0.4 max
(
f k
= 0.2
1
( f ) s2
) ( 2) ( 10)
) ( 2 ) ( 10 ) (
) (
) ( ) t = 1s, 2 N < 36 N t = 4s ,8 N < 36 N
a B
>
a A , %h#r# i "# com/r#ssion in %h# s/rin-
µ1
>
µ 2
1
a=
16.
+h# "oc' i%h o#r (au# a% µ i %#n! %o ha(# -r#a%#r acc##ra%ion f a A > aB , %h#r# i "# #x%#nsion in %h# s/rin-
( f )
15.
)
= 0.6 6 10 = 36 N
max
= 0.4 6 10 = 24 N
1
14.
= 4 N
(
f k
12. 13.
= 8 N
max
>
( f ) 2
max
T − µ mg
m 200 − kx = 20 a F F a= + m1 m2 T
= mg
f = µ 2 N = 3T T + mg = N µ M m= 2 3 − µ 2
17.
abox
= atrox − µ k g P#)! N :4
N#%#*#+# ,%i C#it#+*# IIT A#!* 2013_P1 M! 5TA-6
S
18.
=
1 2
aboxt 2
m A g − 4T
=
mA g
For "oc' B, + f 1).
07/07/14_JR.IPLCOA#+!
=
( m ) ( 4a ) B
a = 0.06ms −2 1 V A = 2ms − ( to wards right ) V P 1
=
V P
=
V A
= 1ms −1 ( upwards )
2 V B = 2ms −1 ( rowards ls )
V B
a= T
1
2
2
20.
+ V P
F m+m
m M a, m = = M + ÷ 2 2
CHEMISTRY Sec!"#$I 21. 22. 24. 25. 26. 27. 28.
Conc#/%ua Conc#/%ua Conc#/%ua Conu-a%# aci!&conu-a%# a-# ! ⊕ +h# sou%ion is n#u%ra Conc#/%ua Conc#/%ua
2).
! ⊕ = "α
= 0.01 X
2
= 2 X 10−4
100 kw 1X 10−14
−4 #! e = + = −4 = 5 X 10 ! 2 X 10
31. 32. 33. 34. 35. 36. 37. 38. 3). 40.
Conc#/%ua Conc#/%ua Conc#/%ua Conc#/%ua Conc#/%ua Conc#/%ua Conc#/%ua Conc#/%ua Conc#/%ua Conc#/%ua
M%e'%!c( Sec!"#$I 41.
cos 6 x =
1 − %an 2 x 1 + %an 2 x
= cos 2 x
P#)! N :
N#%#*#+# ,%i C#it#+*# IIT A#!* 2013_P1 M! 5TA-6
⇒ x =
nπ 4
and x ≠ ( 2n + 1)
07/07/14_JR.IPLCOA#+!
π 2
5π 7π π 3π , ,π , , , 2π 4 4 4 4 =0 1 + sin θ cos θ − sin θ cos θ −1
x = 0,
42.
− sin θ ) = 0 π π , π ⇒ θ ∈ 0, ÷ or θ ∈ ÷ 2 2 cos θ ( sin θ
θ ≠
π 4
not indomain
π ∴θ ∈ , π ÷ 2
43.
( sin x + cos x ) 3 − 2 ( sin 2 x + cos 2 x − sin x cos x ) = 8
( sin x + cos x ) [1 + 2 sin x cos x ] = 8 sin x + cos x = 2
44.
6 cos3 θ
= 1 − cos 2 θ
⇒ cosθ =
45.
1
2 L.! .S ≤ 6 and $.! . S = 6
∴ %ualit&onl& hold of sin θ
= −1 ⇒ θ =
3π π , 2 2
sum = 5π 46.
k = 5 sin 2 2 x + sin 2x − 2 = 0 ⇒ sin 2 x = 1
48.
( 2sin x − cos "x ) + ( %an x − co% x ) = 0
2
⇒ sin 2 x = 4).
1 2
( co% θ + 3 )
2
2
and %an 2 x = 1
(
+ cos "θ + 2
)
2
=0
⇒ co% θ = −
50.
54.
3 cos "θ = −2 π ⇒ θ = 2nπ − , n ∈ ' 6 π sin x + cos x = sin x ⇒ sin + x ÷ 2 4 π ⇒ 2 x = nπ + ( −1) n x + ÷ 4 π 11π ⇒ x = , 4 12 & +
Bu%
1 &
≥ 2⇒
&+
sin x + cos x ≤
1 &
≥
= sin 2 x
2
2
P#)! N :8
N#%#*#+# ,%i C#it#+*# IIT A#!* 2013_P1 M! 5TA-6
1
⇒ & + = 2 an! &
sin x + cos x =
07/07/14_JR.IPLCOA#+!
2
⇒ & = 1 an! x = π 4
57.
+h#r# is no sou%ion of %h# #ua%ion
sin x + cos x = %an
2
x + co% 2 x
sin " ≤ sin x
+ cos x ≤ 2 An! %an 2 x + co% 2 x > 2 L.! .S ≤ 2, $.! .S ≥ 2 ⇒ sin θ = 1
58.
π 5π , and x = 0 2 2 π 5π , 0 ⇒ or!#r#! /airs ar# , 0÷ and ÷ 2 2
⇒ θ =
5).
cos 7 x ≤ cos2 x and sin 4 x ≤ sin 2 x
⇒ cos7 x + sin 4 x ≤ 1
60.
7 4 o, %h# -i(#n #ua%ion sa%isfi#s if an! on if cos 7 x = 0 an! sin 4 x = 1 or cos x = 1 and sin x = 0 π ⇔ x = ( 2n + 1) or x = 2mπ 2 π 3π , 2π Q 0 ≤ x ≤ 2π , so x = 0, , 2 2 +o car(#s in%#rs#c% a% 6 /oin%s
+o%a num"#r of sou%ion of
cos 2 x = sin
−π , π ÷ is 3. 2
x h#r# x ∈
P#)! N :7
