spectra, Bohrs atomic model (Excluding Derivations), Expression for
energy, Radius, Velocity, Orbital Frequency, Time Period, Practice
problems, Dual behaviour of matter - Debroglies hypothesis,
Practice problems.
TOPICS
MATHS
PRESENT WEEK 50%:
Mutiple & Sub-Multiple Angles: Introductory Formulae ON 2A, 3A
ETC., FORMULAE ON A/2 ,A/3, ETC., T RATIOS OF SPECIFIC
ANGLES LIKE 18,36,54,72 DEGREES, 7½,22½, DEGREES ETC.,
RELATED PROBLEMS.
PREVIOUS WEEK 50%:
Compound Angles: Introductory Formulae On (A±B), (A±B±C). T
Ratios Of Specific Angles Like 15 Degrees, 75 Degrees Etc.
Problems On Compound Angles
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SECTION-I(1-20)
(Single Answer Type)
This section contains 20 multiple choice questions. Each question has 4 options
(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 in all other cases.
01. If C A B= + then
1) C is always greater than A
2) C is always equal to A+B
3) C is never equal to A+B
4) It is possible to have C A and C B
02. If a unit vector is represented by ˆ ˆ ˆ0.5i 0.8j ck+ + , then the value
of c is
1) 1 2) 0.11 3) 0.01 4) 0.39
03. Two vectors having equal magnitudes A make an angle ( ) with
each other. The magnitude of the resultant is
1) 2 sin2
A
2) 2 cos2
A
3) 22
A tan
4) All of these
04. Two forces whose magnitude are in the ratio 3:5 give a resultant of
28 N. If the angle of their inclination is 60º, find the magnitude of
each force.
1) 10 N, 12 N 2) 12 N, 15 N
3) 12 N, 20 N 4) 10 N, 20 N
05. At what angle should the two forces 2P and 2P act so that the
resultant force is P 10
1) 45º 2) 60º 3) 90º 4) 120º
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06. If A 2= and B 4= and angle between them is 60º, then A B−
1) 13 2) 3 3 3) 3 4) 2 3
07. The expression 1 1ˆ ˆi j2 2
+
is a
1) unit vector 2) null vector
3) vector of magnitude 2 4) scalar
08. Six vectors have magnitude and direction as indicated in the figure.
Which of the following statement is true?
1) b+e=f 2) b+c=f 3) d+c=f 4) d+e=f
09. If ( )( )3 2 2 1y x x= + − then dy
dx is
1) ( ) ( )3 2 2 3x x+ − 2) 12 1x +
3) 12 1x − 4) 6 2x +
10. If 23 2y x x= + then dy
dx is
1) 6 2x + 2) 6x 3) 3 2x + 4) 26 2x +
11. If 23 5y t t= − then dy
dt
at 1t = is
1) 2 2) 4 3) 1 4) 0
12. If 4y at= , 3x bt= then
dy
dx
is
1) 3
4
b
at 2)
4
3
at
b 3)
4
3
a
b 4)
3
4
b
a
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13. If 2cosy x= then dy
dx is
1) cos2x 2) 2cos x
3) sin2x 4) sin2x−
14. If 2 1y x
x= − then integral of y w.r.t. x is
1)
3
log3
e
xx c− + 2)
3 2
3 2
x xc− +
3)
2
log2
e
xx c− + 4)
3
log3
e
xx c+ +
15.
2
2
cos .x dx−
= ____
1) 1 2) 2 3) 0 4) 1−
16. 2
RGMm
E dxx
= , (where , ,G M m are constants ) equal to
1) 2
GMm
R− 2)
2
GMm
R+ 3)
GMm
R− 4)
GMm
R+
17. ( )3
2
0
ax bx c dx+ − = _____
1) 9
9 32
ba c+ − 2)
99 3
2
ba c+ +
3) 9
9 32
ba c− − 4)
99 3
2
ab c+ +
18. 2
1
. _______
x
x
F dx = where F kx= , and k is constant
1) ( )2 22 1
2
kx x− 2) ( )2 1
2
kx x−
3) 2 21 2
2
kx x − 4) 1 2
2
kx x−
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19. sin . _________ax dx =
1) cosax
ca
− + 2) sinax
ca
+
3) cosax
ca
+ 4) sinax
ca
− +
20. . __________xe dx =
1) e + constant 2) xe + constant
3)
1
1
xe
x
+
+ + constant 4) constant
SECTION-II(21-25)
(Numerical Value Answer Type)
This section contains 5 questions. The answer to each question is a Numerical
values comprising of positive or negative decimal numbers (place value ranging from Thousands Place to Hundredths Place). Eg: 1234.56, 123.45, -
123.45, -1234.56, -0.12, 0.12 etc. Marking scheme: +4 for correct answer, 0 in all other cases.
21. Two equal vectors have a resultant equal to either of the two. The
angle between them_____________ degree.
22. If P Q P Q+ = − , the angle between P and Q___________degree.
23. The resultant of two forces 2N and 3N is 19N . The angle between
the forces is _____________ degree.
24. The magnitude of null vector is
25. The magnitude of unit vector is
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SECTION-I(26-45)
(Single Answer Type)
This section contains 20 multiple choice questions. Each question has 4 options (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 in all other cases.
26. Which of the folloing relates a photon, both a s a wave and as a
stream of particles?
1) 2E mc= 2) Photoelectric effect
3) Diffraction 4) E hv=
27. When electron jumps from 5th energy level to 1st energy level, to
which series the spectral line belongs?
1) Blamer 2) Lyman
3) Paschen 4) Pfund
28. According to Bohr's model of atom
1) The radius of nth orbit 2n
2) The angular momentum of electron is integral multiples of 2
h
3) The magnitude of potential energy of an electron in an orbit
greater than kinetic energy
4) All of these
29. For below transitions in hydrogen like atoms, select the incorrect
relations.
1) 3 1 2v v v= + 2) 1 23
1 2
v vv
v v=
+
3) 3 1 2 = + 4) Both (2) and (3)
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30. If the electron of the hydrogen atom is replaced by another particle
of same charge but of the double mass, then:
1) radii of different shells will increase
2) speed of new particle in a shell will be lesser than the speed of
electron in the same shell
3) ionization energy of the atom will be double
4) Both (2) and (3)
31. Let r, u and E are the radius of the orbit, speed of the electron and
the total energy of the electron respectively. Which of the following
quantities are proportional to the quantum number 'n' ?
1) u
E 2) ur
3) Both (1) and (2) 4) r
E
32. Select the correct statement(s):
1) An electron near the nucleus is attracted by the nucleus and
has a low potential energy
2) Bohr's model was the first atomic model based on quantisatron
of energy
3) Bohr’s model could not explain the spectra of multielectron
atoms
4) All of these
33. What are the values of 1n and 2n respectively for H line in the
Lyman series of hydrogen atomic spectrum?
1) 3 and 5 2) 2 and 3 3) 1 and 3 4) 2 and 4
34. The fourth line of the Balmer series corresponds to the electronic
transition between two orbits of the H atom, Identify the orbits.
1) 3 and 1 2) 5 and 1
3) 5 and 2 4) 6 and 2
35. Total number of spectral lines when electron jumps from 8th orbit
to 2nd orbit
1) 6 2) 36 3) 21 4) 38
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36. The azimuthal quantum number indicates __________of the orbital.
1) Size 2) Shape 3) Orientation 4) Spin
37. Which of the following is indicated by the magnetic quantum
number?
1) Size 2) Shape
3) Spatial orientation 4) Spin
38. The spin quantum number has a value of
1) 1
2 2)
1
2+
3) 1
2− 4) either
1
2+ or
1
2−
39. Which one of the following expressions represents the electron
probability function
1) 24 r dr 2) 4 r dr 3) 2 24 r dr 4) 4 r dr
40. Radial part of the wave function depends on quantum numbers
1) n and s 2) l and m 3) l and s 4) n and l
41. Which of the following is correct with respect to 'p' orbitals?
1) Spherical 2) Strong directional character
3) Five fold degenerate 4) No directional character
42. The maximum number of electrons accommodated in 5f orbitals
1) 5 2) 10 3) 14 4) 18
43. Number of nodal spaces in 4s orbital is
1) 3 2) 1 3) 0 4) 4
44. No two electrons in an orbital can have parallel Spin. This
statement emerges from
1) Hund's rule 2) Aufbau principle
3) Pauli's exclusion principle 4) ( )1n + rule
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45. Electrons never pair, if there are empty orbitals in a given sub-shell.
This is
l) Hund's rule of maximum multiplicity
2) Pauli's exclusion principle
3) Aufbau principle
4) Heisenberg'suncertainty principle
SECTION-II(46-50)
(Numerical Value Answer Type)
This section contains 5 questions. The answer to each question is a Numerical
values comprising of positive or negative decimal numbers (place value ranging from Thousands Place to Hundredths Place). Eg: 1234.56, 123.45, -
123.45, -1234.56, -0.12, 0.12 etc. Marking scheme: +4 for correct answer, 0 in all other cases.
46. The wavelength of a certain line in Balmer Series is observed to be
04329A . To what Value of ' 'n does this correspond?
( )( )1109678 1HR cm Z−= =
47. The ratio of wave number of the limiting line of Lyman series to the
limiting line of Balmar series in Hydrogen spectrums is
48. The number of waves made by a Bohr's electron in one complete
revolution in its 3rd orbit of H-atom is
49. The number of nodes possible in radial probability distribution
curve of 3d orbital is
50. The probability of finding an electron in yp orbital along the x-axis
is
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SECTION-I (51-70)
(Single Answer Type)
This section contains 20 multiple choice questions. Each question has 4 options (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 in all other cases.
51. If 02
and 0 02sin 3cos10 sin10 , = + then is equal to
1) 070 2) 050 3) 060 4) 040
52. 0 0 0
0 0
tan 225 cot81 .cot 69
cot 261 tan 21
−=
+
1) 1 2) 1
2 3) 3 4)
1
3
53. If tan tan 3,4 4
+ + − =
then 2 2tan tan
4 4
+ + − =
1) 6 2) 4 3) 7 4) 5
54. If ( )( )1 tan 1 tan 4 2,+ + = 0, ,16
then =
1) 20
2)
30
3)
40
4)
60
55. If 12
cos ,13
− =
24cot
7 = , 0 090 180 and 0 0180 270 , then the
quadrant in which ( )+ lies in
1) I 2) II 3) III 4) IV
56. If ,2
A B C
+ + = then ( )cos
cos .cos
B C
B C
+=
1) 1 2) 2 3) 3 4) – 2
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57. If 3
,4
− = then ( )( )1 tan 1 tan− + =
1) 0 2) 1 3) – 1 4) 2
58. ( ) ( )2 2sin cos 2sin sin cos+ + + + =
1) 2sin 2) 2sin 3) 2cos 4) 2cos
59. 0 0
2 21 1cos 112 sin 52
2 2− =
1) 3 1
4 2
+ 2)
3 1
2 2
+−
3) 3 1
4 2
+−
4) 3 1
4 2
−−
60. 0 0 0cos 20 cos100 cos140+ + =
1) 0 2) –1 3) 1 4) 2
61. 0 0cos36 cos72− =
1) 1 2) 1
2 3)
1
4 4)
1
8
62. If 0 0180 270 and 4
cot ,3
= then sin2
=
1) 3
10
− 2)
2
5
− 3)
1
5
− 4)
3
10
63. If tan ,a
b = then cos2 sin2b a+ =
1) a 2) b 3) a
b 4)
b
a
64. A quadratic equation whose roots are 0
1tan 22
2 and
01
cot 222
is
1) 2 2 2 1 0x x− + = 2) 22 2 1 0x x− + =
3) 2 2 2 1 0x x+ − = 4) 2 2 2 1 0x x− − =
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65. cos cos3 sin sin 3
cos sin
A A A A
A A
− ++ =
1) 1 2) 2 3) 3 4) 4
66. 1 cos sin
1 cos sin
− + =
+ +
1) cot2
2) tan
2
3) tan 4) cot
67. 2 0 2 0cos 72 sin 54− =
1) 5
4 2)
4
5
− 3)
5
4
− 4)
4
5
68. If 3
sin ,5
A = where 0 00 90 .A then the value of tan 2A=
1) 24
7− 2)
7
24 3)
24
7 4)
23
7
69. The roots of the equation 24 2 1 0x x− − = are
1) 0 0sin 72 ,cos36 2) 0 0sin18 ,cos72
3) 0 0sin198 ,cos36 4) 0 0sin 54 ,cos18
70. If 0 0180 270 and 3
sin ,5
= − then cos2
=
1) 1
10− 2)
1
10 3)
1
10 4) 10
SECTION-II(71-75)
(Numerical Value Answer Type)
This section contains 5 questions. The answer to each question is a Numerical values comprising of positive or negative decimal numbers (place value
ranging from Thousands Place to Hundredths Place). Eg: 1234.56, 123.45, -123.45, -1234.56, -0.12, 0.12 etc. Marking scheme: +4 for correct answer, 0 in all other cases.
71. If 2
++ = and cot ,cot ,cot are in A.P, then cot .cot is equal
to
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72. In a ,ABC if A is obtuse and 3 5
sin ,sin5 13
A B= = then 65sinC is equal
to
73. If A lies in the third quadrant and 3tan 4 0,A− = then
5sin2 3sin 4cosA A A+ + is equal to
74. If
0
0
2
12 tan 7
2cot1
1 tan 72
=
−
and sin 3 ,k = then 216k is equal to
75. If 0 0 0 0cos 40 cos80 cos160 cos 240 ,p+ + + = then 2 5p + is equal to
" When you can't control what is happening, challenge yourself to control
the way you respond to what is happening. That is where you will find
