IoE Model Test -4

Solution ( IoE Model Test -4)
4 ………..(i) put x =2
1. 'b' 2[2f (2)-3f
3 f(2) = …………….(ii) put x =1/2
3[2f
26. 'd' 1 L of air = 210cc of O2, 22400 cc  1 mol
0.0093
Hence, 210 cc =
Adding i and ii
27. 'd' All the 5 electron in 3d orbital of Fe+++ are
unpaired
-5f(2) =
2. 'c' Hint: The graph of y = x and y= ex do not intersect
3. 'd'
24. 'b' 25. 'a'
4 is a root : 16+4p +12 = 0  7
30. 'd' 3Br2+6CO32- +3H2O  5Br - + Br O3- +6HCO3–
 Now x2+px+q = 0 has equal roots
Here O.N. of Br increase from O in Br2 to +5 in Br
O3- and decreases to -1 in Br- , therefore Br2 is
both reduced & oxidized. This is called
disproportination reaction.
 p2-4q = 0, q = p2/4= 49/4
4. 'a' Hint :
a2+b2 + 2 .
28. 'c' 29. 'd'
31. 'a' Weakest acidic nature of HF is due to the strong
H-F bonds and low value of electron affinity of
fluorine atom.
2 .
 . >0, cos > 0,  is acute
32. 'c' Approx. Atomic wt. =
5 'a' Hint: BA = B
.
.
(BA) B = BB= B2
.
 B(AB) = B
56.1, valency =
3
CONC. H2SO4
33. 'a' HCOOH
2
.
.
H2O+ (dehydration)
6. 'a' continuous function is not always differentiable
34. 'd' If number of hydrogen atom in acid is odd
number, multiply the formula of acid by 2 & water
is subtracted. HNO3 ×2 = H2N2O6–H2O = N2O5 d
7. 'c' f(x) is odd differentiable f (-x)= -f(x) 
35. 'b'
f' (-x)(-1)=-f ' (x)  f' (-x)= f '(x), f ' (-3)
36. 'b'
= f '(3) = -2
37. 'a' ZnO = Philosopher's Wool  'a'
 BA= B2  B = B2
8. 'd' in three dimensions two planes together represents
a line  x=2, y = 3 ; x=2, z=5, and y=3, z=5,
represents three lines through (2,5,4)
10.'a'
=
∆
∆
∆
∆
38.'c' i) -CH2OH
or, tan-1 [2a]=  /4  a = ½
2
9. 'b'
ZnCO3 = Calamine
.
∆
.
11. 'a' 12. 'c' 13. 'c' 14. 'b' 15. 'c' 16. 'b' 17. 'a'
18. 'd' 19. 'a' 20. 'c' 21. 'c' 22. 'a' 23. 'd'
ii) CH-CH2 CH2OH

CH3
iii) HOCH2- CH- iv) –CH3


CH3
–C–CH2-OH
39. 'c'
40. 'b' Na4[Fe (CN)6 ]+ FeCl3 Fe4 [Fe (CN)6]3
(Prussian blue)
41. 'a' mvr/mv=[ML2T-1]/[MLT-1]
42.'b'
43.'c' ET4
75.'c' y = tan-1 b+tan-1 x 
44.'c' 45.'a' 46.'c' 47.'b' 48.'b' 49.'d'
√
76. 'a'
√
=
.
50.'d' 51. 'b' 52. 'c' 53. 'd' 54. 'a' 55. 'a
=
2√
√
56. 'c' 57. 'b' 58. 'a' 59. b 60. 'b' 61 'b'
=
77. 'd' f ' (x) = 3 (x-2)2  f 'x = 0  x =2
62. 'd' 63. 'd' 64.'a' 65.'c'
 f " (2) = 0
f " (x) = 6 (x-2)
Group B
66. 'a'   +2 = -p/3 ,
+2 = -p/3
From (i)
now f ''' (x) = 6
f ''' (2) = 6 so neither
maximum nor minimum since odd order derivative
is not zero.
 . 2= 1
 3=1
 = 1, , 2 (i)
p=3
1
78. 'a' 0
0
1
=0  (1-f 2)+g (-g)=0  f 2+g2 =1
1
67. 'd' n = 3m, 1+n+2n = 1+3m+ 6m
= 1+(3)m+(3)2m
79. 'b' y = mx  a√1
= 1+1+1= 3
68. 'a'
=
√
2
1
/
valid when
<2 | |
| |
1
 √3
√
x2+y2 =
81.'d'
69.'c'  47C4+51C3+50C3+49C3+48C3+47C3
=48C4+51C3+50C3+49C3+48C3
=49C4+51C3+50C3+49C3=52C4 ( Processing similarly)
/
5 1
√
√
10
0
80. 'b' Two perpendicular tangents to the parabola
y2=4ax always meet on the directrix i.e. x = -a
.
=
70. 'd' 4
=
=
.
82. 'c' direction ratio of line = 1,2,1
Direction cosine of line
,
√
,
√
√
-1
71.'b' If non- singular then A exist then A (AB) =
A-1(AC)  IB =IC  B=C
72. 'b' Unit vectors  to
.
 xy = 16  'd'
=
-1
 x2+y2 =
and
(l,m.n) =
√
,
√
,
√
Required projection of line
= (x1-x2)l+(y2-y1)m+(z2-z2)n
 no of unit vectors perpendicular to
=
given vectors is two.
73. 'c' log162 (apply logxa . logbx = logba )
=
=
√
√
√
=
√
√
83. 'c' Area above x axis (A1) =
=

a
0
ydx
a
74. 'b'
lim
x
θ
= cos + sin
(using the L-Hospital rule)
=
√
=

a
0
4ax dx  2 a
0

a
0
 3
x2 
x dx = 2 a  
 3 
 2  0
84. 'c'
We have,
1
1
1
a
b
c apply C2 : C2 – C1. C3 : C3 –C1
a3
b3
c3
1
= a
a3
3
a
ba
b3  a 3
ca
c3  a 3
99.'a' =v/c
1
a
100. 'b' 1/=r.d./a.d. or ¾= r.d./30
0
0
1
b  ab  a 2
1
c  ac  a 2
2
2
1
a3
101.'b'




/
/

.2
102.'c' q=Ne = 5 x 10 17 x 1.6 x - 19
Apply C3 : C3 – C2 we get
= (b–a) (c–a) a
/
98. 'd' Fbeat=f-f100
1
3
2
96.'c' =3
97. 'a'
= (b–a) (c–a) a
2
95.'a' max v=wr and
0
0
1
b 2  ab  a 2
1
c 2  b 2  ac  ab
103. 'b' two wheatstone bridge.
104.'b' I = P/V and N/t= I/e
105.'a'
2
2
= (b-a) (c-a) (c – b +ac –ab)
106.'b' W=LI2/2 and
= (b-a) (c-a) (c-b) (a+b+c)
85. 'd'
x+
(

>0
x–
x)(
–

2
2
x<
also 

2
x)>0
109.'b'
0
0

2

,
x<
110.'b' Energy = 6.02 x 23 x 200 MeV/235
x<


4
,
4
1

√
86. 'a'
87. 'a'
88. 'd'
89. 'd'
90. 'b'
91. 'b'
√
92. 'b' F=vm/t and P=Fv
93. 'a' g’=g(1-2h/R)
94. 'd' y= F/A.strain
and
107. 'b' sp .charge of electron/sp.charge of hydrogen ion
= e/m/e/1840m
108.'c' En = -13.6/ n2 eV

/
111. 'd' 2HCl+Na2CO3  2NaCl+CO2+H2O
No. of milimoles = V in ml ×molarity
= 10×0.2 = 2 mmole
1 mole of Na2CO3 = 2mol of HCl
2
"
" 2×2 = 4 milimole
112. 'a' If m is atomic mass of the metal M, then 16 y g
of oxygen combine with x mg of the metal
 8g m oxygen will combine with metal
=
8

′ ′
113.'c' Ksp = [Ag+] [Cl-] = [10-5] [10-5]=10-10
In 0.1 M NaCl sol. = 10-10 or [Ag+]= 10-9 M
114. 'd'
115. 'b' H2C = CH-C  CH
No of  bonds = 3 (c-c) +(c-h) = 7
No of  bonds = 3 (c-c) =3  b
116. 'b' 117. 'd' 118. 'a' 119. 'b' 120. 'a'

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