21-07-2024

9610XPE801084240003 TM

PHYSICS

1) If and . Find the magnitude of .

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

2) If the vectors and are perpendicular to each other, then the value of
x is:

(1) 2
(2) 3
(3) –2
(4) –3

3) If and , then the cosine of the angle θ between the two vectors is:

(1)

(2)

(3)

(4)

4) If then the angle between the vectors and is

(1) 120º
(2) 180º
(3) 45º
(4) 90º

5) What is the magnitude of resultant force, if the two forces of magnitude 6N and 8N respectively
are acting on a body and the angle between them is 90º.

(1) 100N
(2) 10N
(3)
(4) 20N

6) If is a unit vector along X-axis and , then what is the value of ?

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

7) A particle is moving with displacement under the action of force . The

work done by the force in an arbitrary unit is:

(1) 8
(2) 10
(3) 12
(4) 16

8) If and are unit vectors along x, y and z axis respectively, then choose the wrong statement:

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

9) If and are unit vectors along x, y and z axis respectively, then choose the correct statement:

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

10) If the diagonals of a parallelogram are and then area of parallelogram is :

(1) 2 sq. units

(2) 3 sq. units
(3) 8 sq. units
(4) 16 sq. units

11) Find the scalar product of the vectors:

and

(1) 12
(2) 20
(3) 18
(4) 24

12) If two vectors and are such that then vectors

(1) act at an angle 60º

(2) act at an angle 30º
(3) are perpendicular to each other
(4) are parallel to each other

13) Which of the following is not a fundamental quantity?

(1) mass
(2) time
(3) temperature
(4) density

14) The density of a substance is 0.6g/cm3. It's value in SI unit is

(1) 6000kg/m3
(2) 600kg/m3
(3) 0.06kg/m3
(4) 6kg/m3

15) Convert an acceleration of 20m/s2 in km/h2

(1) 25.92×104km/h2
(2) 2.592km/h2
(3) 0.2592×103km/h2
(4) 25.92×106km/h2

16) The dimensional formula of force is

(1) [M1L1T1]
(2) [M1L1T–2]
0
(3) [M LT–2]
0
(4) [M1L T–2]

17) 1 kg m2s–2 = ................gcm2s–2

(1) 106
(2) 107
(3) 105
(4) 103

18) The dimensional formula of momentum is

(1) [MLT–1]
(2) [M2LT–1]
(3) [ML2T–2]
(4) [MLT]

19) The dimensional formula [ML2T–3] represent the quantity:

(1) Energy
(2) Force
(3) Power
(4) Momentum

20) Evaluate : if and :

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

CHEMISTRY

1) If cathode ray experiment is performed using hydrogen, Helium and Oxygen gases in seperate

experiments. For which gas the ratio of cathode rays will be maximum.

(1) Hydrogen
(2) Helium
(3) Oxygen
(4) All have same value

2) Which of the following is not the possible path of cathode rays ejecting from the surface of
cathode?

(1)
(2)

(3)

(4)

3) Which of the following experiment is responsible for finding out the charge of electron?

(1) Millikan’s oil drop experiment

(2) Cathode rays discharge tube experiment
(3) Rutherford’s α- particle scattering experiment.
(4) None of these

4) Statement type question:

Statement-I: Thomson proposed that an atom consists of a uniform sphere of positive charge in
which the electrons are distributed more or less uniformly.
Statement-II: Thomson model is a static modal. It does not reflect the movement of electron.

(1) Statement-I is true only

(2) Statement-II is true only
(3) Both Statements are true
(4) Both Statements are false

5) Rutherford’s experiment on scattering of alpha particles showed for the first time that atom has :-

(1) Electrons
(2) Protons
(3) Nucleus
(4) Neutrons

6) Number of protons, neutrons and electrons in the element 89Y231 is :-

(1) 89, 231, 89

(2) 89, 89, 242
(3) 89, 142, 89
(4) 89, 71, 89

7) In 7N14 if mass of electron were doubled and the mass of protons were halved, the atomic mass
would become approximately :-

(1) Halved
(2) Doubled
(3) Reduced by 25%
(4) Remain same

8) Two atoms are said to be isobars if :-

(1) They have same atomic number but different mass number
(2) They have same number of electrons but different number of neutrons.
(3) They have same number of neutrons but different number of electrons.
(4) Sum of the number of protons and neutrons is same but the number of protons is different.

9) Atoms and are related to each other as :-

(1) Isotones
(2) Isoelectronic
(3) Isodiaphers
(4) Isosters

10) Two elements A and B are isotones. Their mass numbers are respectively 32 and 31 if atomic
number of A is 16, what will be the atomic number of B ?

(1) 15
(2) 30
(3) 32
(4) 31

11)

Which of the following set is not isosters?

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

12) Species which are isoelectronic to one another are

(a) CN– (b) OH– (c) (d) N2 (e) CO
Correct Ans. :-

(1) a, b, c
(2) a, c, d
(3) a, d, e
(4) b, c, d

13) Which of the following properties of Electromagnetic wave is incorrect according to

Electromagnetic wave theory?

(1) Electromagnetic wave do not require medium and can move in vacuum.
(2) Speed of the light is in vacuum.
Electric and magnetic fields are perpendicular to each other and parallel to the direction of
(3)
propagation of wave.
(4) None of the above.

14) The correct sequence of frequency of the electromagnetic radiations in electromagnetic

spectrum is

(1) X-rays > UV rays > Microwaves > Radio waves

(2) Radio waves > Microwaves > UV rays > X-ray
(3) UV ray > X-ray > Radio waves > Microwaves
(4) Radio waves > Microwaves > X-rays > UV rays

15)

Radiocity broadcasts on a frequency of 5000 kHz. What is the wavelength of electromagnetic

radiation emitted by the transmitter?

(1) 50 m
(2) 60 m
(3) 70 m
(4) 80 m

16) The wavelength of a photon having energy ‘E’ is 6000 Å. Find wavelength of a photon having
energy ‘3E’.

(1) 18000 Å
(2) 6000 Å
(3) 2000 Å
(4) 3000 Å

17) How many photons of light having a wavelength of 5000 Å necessary to provide 1 joule of energy
?

(1) 2.5 × 1010 photons

(2) 2.5 × 1018 photons
(3) 2.5 × 1015 photons
(4) 2.5 × 1011 photons

18)

Bohr's radius of H-atoms is 0.529 Å. What is the radius of second shell of He+?

(1) 0.529 Å
(2) 10.58 Å
(3) 1.058 Å
(4) 0.2645 Å

19) The velocity of electron in third excited state of Be3+ ion will be :-

(1)
(2.188 × 108) ms–1

(2)
(2.188 × 106) ms–1
(3) (2.188 × 106) Kms–1
(4) (2.188 × 103) Kms–1

20) Bohr's atomic model is not applicable to :-

(1) He+
(2) Li+2
(3) He
(4) H atom

MATHEMATICS

1) Find the range of f(x) = x2 + 4x + 4

(1) [4, ∞)
(2) (– ∞, 0]
(3) [0, ∞)
(4) [– ∞, 4)

2) Find the range of f(x) = 9 – x2

(1) [9, ∞)
(2) [0, ∞)
(3) (–∞, 0]
(4) (–∞, 9]
3) Find the signs of a, b, c in the given graph of y = ax2 + bx + c

(1) a > 0, b >0, c > 0

(2) a > 0, b < 0, c > 0
(3) a > 0, b < 0, c < 0
(4) a < 0, b < 0, c > 0

4) Find the signs of a, b, c and D in the given graph of y = ax2 + bx + c

(1) a < 0, b > 0, c < 0, D < 0

(2) a < 0, b < 0, c > 0, D < 0
(3) a < 0, b > 0, c > 0, D > 0
(4) a > 0, b > 0, c < 0, D > 0

5) If both roots of the equation x2 – (m + 1)x + (m + 4) = 0 are less than zero, then m equals -

(1) –7 < m < – 5

(2) –4 < m ≤ –3
(3) 2 < m < 5
(4) 3 ≤ m < 4

6) The real value of 'a' for which the quadratic equation 2x2 –(a2 + 8a – 1) x + a2 – 4a = 0 has one
root is greater than zero and the other is less than zero, is

(1) a > 5
(2) 0 < a < 4
(3) a > 0
(4) a > 7

7) In an A.P. if a = 28, d = – 4, n = 7, then an is :

(1) 4
(2) 5
(3) 3
(4) 7

8) Which term of the A.P. 3, 8, 13,18, ... is 78?

(1) 12th
(2) 13th
(3) 15th
(4) 16th

9) What is the common difference of an AP in which a18 – a14 = 32?

(1) 8
(2) –8
(3) –4
(4) 4

10) The next term of the sequence is (x ≠ 1)

(1) 1 +
(2) 1 –

(3)

(4)

11) The sum of all odd integers between 2 and 100 divisible by 3 is

(1) 17
(2) 867
(3) 876
(4) 786

12) If 7 times the 7th term of an A.P. is equal to 11 times its 11th term, 18th term is,

(1) 18
(2) 9
(3) 77
(4) 0

13) The 6th term of a G.P. is 32 and its 8th term is 128, then the common ratio of the G.P. is

(1) –1
(2) 2
(3) 4
(4) None of these

14) If first term of a G.P. is 20 and common ratio is 4. Find the 5th term.

(1) 10240
(2) 40960
(3) 5120
(4) 2560

15) Which term of GP 25, 125, 625, .... is 390625?

(1) 5
(2) 6
(3) 7
(4) 8

16) In a G.P., 5th term is 27 and 8th term is 729. Find its 11th term.

(1) 729
(2) 2187
(3) 6561
(4) 19683

17) Find the sum of the series 1 + + + ..... up to ∞ terms.

(1) 3

(2)

(3)

(4) 2

18) Find the sum of 3 + 32 + 33 + ..... + 38.

(1) 6561
(2) 6560
(3) 9840
(4) None of these

19) If three positive integers a, b, c are in G.P., then log a, log b, log c are in

(1) A.P.
(2) G.P.
(3) Both A.P. and G.P.
(4) None of these

20) If the first term is 125 and the common ratio is , what will be the 4th term of the G.P.?

(1) 8
(2) 12
(3) 6
(4) 10
 ANSWER KEYS

PHYSICS

Q. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A. 3 3 3 4 2 2 1 4 3 1 2 4 4 2 1 2 2 1 3 4

CHEMISTRY

Q. 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40
A. 4 4 1 3 3 3 3 4 3 1 3 3 3 1 2 3 2 3 4 3

MATHEMATICS

Q. 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60
A. 3 4 2 1 2 2 1 4 1 4 2 4 2 3 3 4 4 3 1 1
 SOLUTIONS

PHYSICS

1)

– =

2)

=6–8–x=0
⇒ x = –2

3)

Cosθ =

4)

Angle between and is 90º.

5)

R=
= 10N

6)

= –

7)

Work done =
=
=2+3+3=8

8)
As angle between them is 0º and sin0º = 0

9)

is a correct statement

10)

Area of parallelogram =

= (4) = 2 sq. units

11)

= (2×3)+[–3×(–6)]+[2×(–2)]
= 6 + 18 – 4 = 20

12)

If then and are parallel to each other.

13)

Density is a derived quantity

14)

× 106kg/m3 = 600kg/m3

15)

= 25.92 × 104km/h2

16)

Force = ma = [M] [LT–2] = [M1L1T–2]

17)

1kg = 1000×104 g

18)

Momentum = mv = [M][LT–1] = [MLT–1]

19)

[ML2T–3] = [MLT–2] [LT–1]

⇒ Force×Velocity = Power
 20)

CHEMISTRY

21) In cathode ray experiment, the of particle (electron) forming cathode rays
does not depend on nature of gas.

22)

Cathode rays have property that, they are emitted normal to surface of cathode.

23)

Millikan's oil drop experiment is responsible for finding out the charge on an electron.

24)

Thomson proposed that an atom consists of a uniform sphere of positive charge in which the
electrons are distributed more or less uniformly.
Second statement is the drawback of Thomson model. It says it is a static model and does not reflect
the movement of electron.

25)

Rutherford's experiment led to the discovery of nucleus.

26)

EA = 89Y231
Z

Number of protons = atomic number

= number of electrons
= 89
Number of neutrons = A – Z
= 231 – 89 = 142

27)

p n atomic mass
 Old 7 7 7+7 = 14

New 7 3.5+7 = 10.5

% Change =

=– = 25% decrease

28)

Isobars have same mass number but different number of protons.

29)

Isodiaphers n-p = 1 in both cases.

→ n = 7, p = 6 (7 – 6 = 1)
→ n = 9, p = 8 (9 – 8 = 1)

30) Neutrons same

nA = nB
(A – Z)A = (A – Z)B
32 – 16 = 31 – ZB
ZB = 15

31) Isosters : Same number of atoms and electrons.

and CNO–
e– = 7 + 2 × 8 + 1 6+7+8+1
e– = 24 e– = 22
Electrons are not same.

32)

Isoelectronic → having same no. of electrons

CN– = 6 + 7 + 1 = 14
OH– = 8 + 1 + 1 = 10
=6+3–1=8
N2 = 7 × 2 = 14
CO = 6 + 8 = 14

33)

Electric and magnetic fields are perpendicular to each other and perpendicular to the direction of
propagation of wave.

34)
 Electromagnetic waves in increasing order of their frequency :
Radio waves , micro waves, infrared waves, visible light, ultraviolet radiation, X rays, γ rays.

35) =
= 60 m

36)

⇒ Å

37)

E=

n=

n= = 2.5 × 1018

38) radius = 0.529 × Å (n = 2, z = 2)

Å = 1.058Å

39)

V = 2.18 × 106 × m/s

V = 2.18 × 106 ×
= 2.18 × 106 m/s
= 2.18 × 103 km/s

40)

Bohr's model is applicable for single electron species only.

MATHEMATICS
 41) f(x) = x2 + 4x + 4 = (x + 2)2
Minimum value of (x + 2)2 is 0.
Hence, f(x) ∈ [0, ∞)

42)

f(x) = 9 – x2

=9
f(x) ∈ (–∞, 9]

43)

a > 0, b < 0, c > 0

44)

a < 0, b > 0, c < 0, D < 0

45)

Method (i)
x2 – (m + 1) x + (m + 4) = 0
Both roots are negative,
sum of roots < 0
⇒m+1<0
⇒ m < –1 ....(i)
and products of roots > 0 ⇒ m + 4 > 0
⇒ m > –4 ....(ii)
Also, D ≥ 0 ⇒ (m +1)2 –4(m + 4) ≥ 0
⇒ m2 + 2m + 1 – 4m – 16 ≥ 0
⇒ m2 – 2m – 15 ≥ 0
⇒ (m – 5) (m + 3) ≥ 0
⇒ m ∈ (–∞, – 3] ∪ [5, ∞] .....(iii)
Taking intersection of (i), (ii) and (iii)

⇒ m ∈ (–4, –3]
Method (ii)
Since leading coefficient is positive
(1) D ≥ 0
(2) af(d) > 0

(3)
Now solving
(1) D ≥ 0
⇒ (m +1)2 –4(m + 4) ≥ 0
⇒ m2 + 2m + 1 – 4m – 16 ≥ 0
⇒ m2 – 2m – 15 ≥ 0
⇒ (m – 5) (m + 3) ≥ 0
⇒ m ∈ (–∞, – 3] ∪ [5, ∞] .......(i)
(2) af(d) > 0 ⇒ f(0) > 0
⇒m+4>0
⇒ m > –4
m∈(–4, ∞) ....... (ii)

(3) ⇒
⇒m+1<0
⇒ m < –1
m∈ (–∞, –1) ......... (iii)
Taking intersection of (i), (ii) and (iii)

⇒ m ∈ (–4, –3]

46)

2x2 – (a2 + 8a –1)x + a2 – 4a = 0

f(0) < 0 ⇒ a2 – 4a < 0
⇒ a (a – 4) < 0 ⇒ a ∈ (0, 4)

47) an = a7 = a + 6d = 28 + 6 (– 4)
= 28 – 24 = 4

48)

a = 3, d = 5
an = 78
78 = a + (n – 1)d
78 = 3 + (n – 1)5
75 = (n – 1)5
⇒ n – 1 = 15
⇒ n = 16

49)

a18 – a14 = 32 ⇒ (a + 17d) – (a + 13d)= 32

⇒ 17d – 13d= 32 ⇒ 4d = 32
⇒d=8

50)

are terms of AP, d =

Next term =
 51)

Sn = 3 + 9 + 15 + .... + 99
⇒ 99 = 3 + (n – 1)6 ⇒ n = 17

⇒ Sn = [3 + 99] = (102)
⇒ Sn = 17 × 51 = 867

52)

7(a + 6d) = 11 (a + 10d)

⇒ 7a + 42d = 11a + 110 d
⇒ 4a + 68d = 0
⇒ 4(a + 17d) = 0
⇒ a18 = 0

53)

ar5 = 32 and ar7 = 128

⇒ r2 = 4 ⇒ r = 2

54)

a = 20, r = 4
⇒ T5 = ar4 = 20 × 44 = 5120

55)

a = 25, r = 5
⇒ an = arn–1
⇒ 390625 = 25 × 5n–1
⇒ 15625 = 5n–1
⇒ 56 = 5n–1
⇒n=7

56)

⇒ ar4 = 27
and, ar7 = 729

⇒ r3 = 27 ⇒ r = 3

⇒ a(34) = 27 ⇒ a =

⇒ a11 = ar10 = × 310 = 39 = 19683

57)
1+ + + .....

S∞ = =2.

58)

a = 3, r = 3

⇒ s8 = = 9840

59)

b2 = ac
log a + log c = 2 log b
⇒ ac = b2
Hence, log a, log b and log c are in A.P.

60)

a = 125, r =

a4 = ar3 = 125 × =8