AMU-2013 - Career Point

SERIES-A(CODE-05) 

AMU-2013 EXAMINATION 

CAREER POINT 

Part A - PHYSICS 

A 2 

Q.1 The electric field in a region is given by : E r = î + By ĵ + Cz 

3 

x 

kˆ . The SI units of A, B and C are, 

respectively- 

3 

N − m 2 N 

2 N 

(a) , V / m , 

(b) V − m ,V / m, 

C 

2 

2 

m − C 

m − C 

Ans. 

(c) 

[a] 

V / m 

2 

N − C 

,V / m, 

2 

m 

(d) 

N 

V / m, 

− m 

C 

3 

N − C 

, 

m 

Q.2 Find the component of vector A r = 2 î + 3ĵ 

along the direction ( î − ĵ) 

- 

1 

1 

1 

1 

(a) − (î − ĵ) 

(b) − (î + ĵ) 

(c) (î − ĵ) 

(d) (î + ĵ) 

2 

2 

2 

2 

Ans. [a] 

Q.3 Angular momentum L is given by L = p.r. The variation of log L and log p is shown by- 

log L 

log L 

(a) 

(b) 

log L 

log p 

log L 

log p 

(c) 

(d) 

Ans. 

[d] 

log p 

log p 

Q.4 By what velocity a ball be projected vertically upwards so that the distance covered in 5th second is twice of 

that covered in 6th second ? 

(a) 19.6 m/s (b) 58.8 m/s (c) 49 m/s (d) 65 m/s 

Ans. [d] 

Q.5 A ball is dropped vertically from a height h above the ground. After touching the ground, it bounces up to a 

height h/2. Neglecting the air resistance, its velocity v varies with the height above the ground as- 

CAREER POINT, CP Tower, Road No.1, IPIA, Kota (Raj.) Ph.: 0744-3040000 

Website : www.careerpointgroup.com, Email: info@careerpointgroup.com 

1 / 25


v 


v 

CAREER POINT 

(i) 

h 

height 

(ii) 

h 

height 

v 

v 

(iii) 

h 

height 

(iv) 

h 

height 

Ans. 

(a) (i) (b) (ii) (c) (iii) (d) (iv) 

[a] 

Q.6 A uniform rope of mass 0.1 kg and length 2.45 m hangs from a ceiling. The time taken by a transverse wave 

to travel the full length of the rope is- 

(a) 1.2 s (b) 1.0 s (c) 2.2 s (d) 3.1 s 

Ans. [b] 

Q.7 The magnitudes of gravitational field at distances r 1 and r 2 from the centre of a uniform sphere of radius R 

and mass M are I 1 and I 2 , respectively. Find the ratio (I 1 /I 2 ) if r 1 > R and r 2 < R. 

Ans. 

(a) 

[c] 

2 

R 

r r 

1 2 

(b) 

R 

3 

2 

1r2 

r 

Q.8 A toy car of mass 2.0 kg is moving towards –ve Y-axis with a velocity of 0.5 m/s. It takes a turn towards 

X-axis with a velocity of 0.4 m/s. How much is the change in the linear momentum of the care due to the 

turn ? 

Ans. 

(a) ( 0.6î − 1.0ĵ) 

kg.m/s (b) ( 0.8î + 1.0ĵ) 

kg.m/s (c) ( 0.8î −1.0ĵ) 

kg.m/s (d) ( 0.8î + 0.6ĵ) 

kg.m/s 

[b] 

⎧E Q.9 The potential energy of particle of mass m varies as : U(x) = 0 for 0 ≤ x ≤ 1 

⎨ 

. The deBroglie wavelength 

⎩ 0 for x > 1 

of the particle in the range 0 ≤ x ≤ 1 is λ 1 and that in the range x > 1 is λ 2 . If the total energy of the particle is 

2E 0 , find λ 1 /λ 2 . 

Ans. 

(c) 

3 

2 

1 r2 

r 

R 

(d) 

4 

2 2 

1 r2 

(a) 2 (b) 3 (c) 1 / 2 

(d) 2 / 3 

[a] 

Q.10 A car moves around a curved road of radius R 1 at constant speed v without sliding. If we double the car's 

speed, what is the least radius that would now keep the car from sliding ? 

r 

R 

Ans. 

(a) 2R 1 (b) 4R 1 (c) 6R 1 (d) R 1 

[b] 



2 / 25



CAREER POINT 

Q.11 The figure shows the potential energy function U(x) for a system in which a particle is in one-dimensional 

motion. Arrange regions AB, BC, CD and DE according to the magnitude of the force on the particle in 

decreasing order. 

U(x) 

6 

5 

4 

3 

2 

1 

O A B C D E 

x 

Ans. 

(a) BC, DE, AB, CD (b) BC, AB, CD, DE (c) AB, CD, BC, DE (d) CD, AB, DE, BC 

[d] 

Q.12 The figure shows four arrangements of three particles of equal masses. Arrange them according to the 

magnitude of the net gravitational force on the particle labeled m, in decreasing order- 

Ans. 

D 

D 

m D 

D 

m 

d 

d 

d d 

m 

m 

(i) 

(ii) 

(iii) 

(iv) 

(a) (i), (iii) = (iv), (ii) (b) (i) = (iii), (ii), (iv) (c) (i), (ii), (iii), (iv) (d) (iv), (iii), (ii), (i) 

[a] 

Q.13 A point charge +q moves from point P to origin O along the path PQRO in a uniform electric field E r . Find 

the work done by the field- 

Y 

E r 

P(2a,b,O) 

O 

(4a,O,O) 

30º 

X 

45º 

Q 

(2a,–b,O) 

R 

Ans. 

(a) –2qEa (b) 2qEa (c) 8qEa (d) –4qEa 

[a] 

Q.14 In a new system of units called star units, 1 kg* = 10 kg, 1 m* = 1 km and IS* = 1 minute, what will be the 

value of IJ in the new system ? 

(a) 2.4 × 10 –5 J* (b) 3.6 × 10 –4 J* (c) 4.2 × 10 –3 J* (d) 4.2 × 10 –2 J* 

Ans. [b] 



3 / 25



CAREER POINT 

Q.15 A wooden box has a 4 m × 4 m × 10 cm metallic cover (K = 1.26 W/m-ºC). At some instant, the temperature 

outside is 40ºC and that inside is 26ºC. Neglecting convection, the amount of heat flowing per second into 

the box through the cover is- 

(a) 1832 W (b) 2212 W (c) 2822 W (d) 3122 W 

Ans. [c] 

Q.16 The following figure shows the Maxwell's speed distribution plots at four different temperatures T 1 , T 2 , T 3 

and T 4 . 

dN 

dν 

T 1 

T 2 

T 3 T4 

speed 

Which of the following gives the correct relation between temperatures ? 

Ans. 

(a) T 4 > T 3 > T 2 > T 1 (b) T 4 < T 3 < T 2 < T 1 (c) T 1 = T 2 = T 3 = T 4 (d) T 1 > T 2 , T 3 < T 4 

[a] 

Q.17 A thermodynamic state of a given sample of an ideal gas is completely described, if its- 

(a) pressure, volume and internal energy are known 

(b) pressure, volume, temperature and internal energy are known 

(c) pressure, volume and temperature are known 

(d) pressure and volume are known 

Ans. [d] 

Q.18 A cyclic process ABCA on the V-T diagram (shown below) is performed with a constant mass of an ideal 

gas. 

V C B 

A 

T 

Which of the following figures corresponds to the same process on a P-V diagram ? 

P 

P 

A B A B P 

P 

C B 

C 

C 

(i) 

V 

(ii) 

C 

V 

A 

(iii) 

V 

B 

(iv) 

A 

V 

(a) (i) (b) (ii) (c) (iii) (d) (iv) 

Ans. 

[b] 



4 / 25



CAREER POINT 

Q.19 The ratio of the radii of the nuclei 13 Al 27 and 52 Te 125 is- 

(a) 13 : 52 (b) 27 : 125 (c) 3 : 5 (d) 14 : 73 

Ans. [c] 

Q.20 How many NAND gates are needed to obtain OR gate ? 

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

Ans. [c] 

Q.21 A capacitor is discharged through a resistance in R-C circuit. The variation of log e i with time t is shown by a 

dotted line in the figure, where i is the discharging current. If the resistance in the circuit be doubled, the 

variation of log e i with time t would be best represented by the line - 

log e i 

S 

R 

Ans. 

Q 

P 

t 

(a) P (b) Q (c) R (d) S 

[b] 

Q.22 A container is filled with water (µ = 1.33) upto a height of 33.25 cm. A concave mirror is held 15 cm above 

the water level, and the image I of an object O placed at the bottom is formed 25 cm below the water level. 

The focal length of the mirror is roughly- 

15 cm 

33.25 cm IO 

25 cm 

Ans. 

O 

(a) 10 cm (b) 15 cm (c) 20 cm (d) 25 cm 

[c] 

Q.23 A current of 4.0 A is present in a wire of cross-sectional area 2.0 mm 2 . Find the number of free electrons in 

each cubic metre of the wire, if the drift velocity is 2.1 × 10 –4 m/s. 

(a) 6.0 × 10 28 m –3 (b) 3.6 × 10 29 m –3 (c) 7.0 × 10 30 m –3 (d) 8.2 × 10 32 m –3 

Ans. 

[a] 



5 / 25



CAREER POINT 

Q.24 Doubly charged Mg 24 ions are accelerated to kinetic energy 8 KeV and are projected perpendicularly into a 

magnetic field of magnitude 1.2 T. Find the radius of the circle formed by the ions- 

(a) 2.4 cm (b) 3.2 cm (c) 4.8 cm (d) 5.3 cm 

Ans. [d] 

Q.25 When two radiations of wavelengths λ 1 and λ 2 fall on a metallic surface, they produce photoelectrons with 

maximum energies k 1 and k 2 , respectively. Which of the following relations is used to estimate the Planck 

constant ? 

(a) h = 

k 

1 

− k 

c 

2 

λ1λ 

2 

λ − λ 

2 

1 

(b) h = 

k 

1 

+ k 

c 

2 

λ1λ 

2 

λ − λ 

2 

1 

Ans. 

(c) h = 

[a] 

k 

1 

− k 

c 

2 

λ1λ 

2 

λ + λ 

2 

1 

(d) h = 

k 

2 

1 − 

c 

k 

2 

2 

λ1λ 

2 

λ − λ 

2 

1 

Q.26 Which of the following phenomena establishes the wave nature of particles ? 

(a) Millikan oil drop experiment 

(b) Davisson-Germer experiment 

(c) Stern-Gerlach experiment 

(d) Franck-Hertz experiment 

Ans. [b] 

Q.27 Find the deBroglie wavelength for a 100 gm bullet moving at 900 m/s- 

(a) 3.7 × 10 –35 m (b) 7.4 × 10 –36 m (c) 7.8 × 10 –37 m (d) 8.2 × 10 –39 m 

Ans. [b] 

Q.28 The colours of the rings on a resistor are brown, yellow, green and gold as seen from the left to the right. 

The value of the resistance is- 

(a) (1.4 ± 0.07) MΩ (b) (2.4 ± 0.05) MΩ (c) (3.4 ± 0.05) MΩ (d) (1.4 ± 0.05) MΩ 

Ans. [a] 

Q.29 The ammeter, shown below, consists of a 360 Ω coil connected in parallel to a 40 Ω shunt. Find the reading 

of the ammeter. 

164Ω 

A 

+ – 

40 V 

Ans. 

(a) 0.35 A (b) 0.4 A (c) 0.25 A (d) 0.2 A 

[d] 



6 / 25



CAREER POINT 

Q.30 You are given four semiconductors P, Q, R and S with respective band gaps 4 eV, 3 eV, 2 eV and 1 eV for 

use in a photodetector to detect λ = 1400 nm. Select the suitable semiconductor- 

(a) P (b) Q (c) R (d) S 

Ans. [d] 

Q.31 When two waves of nearly equal frequencies ν 1 and ν 2 are produced simultaneously, the time interval 

between successive maxima is- 

(a) 

ν 

Ans. [a] 

1 

1 

− ν 

2 

(b) 

1 1 

− 

ν ν 

1 

2 

(c) 

1 1 

+ 

ν ν 

1 

2 

(d) 

1 

ν + ν 

1 

2 

Q.32 A particle emission line, detected in the light from a star, has a wavelength λ det = 1.1 λ, where λ is the proper 

wavelength of the line. What is the star's distance from us ? 

(a) 8.6 × 10 8 ly (b) 1.6 × 10 9 ly (c) 3.2 × 10 10 ly (d) 9.2 × 10 11 ly 

Ans. [b] 

Q.33 For sky wave propagation of 10 MHz signal, what should be the minimum electron density in ionosphere ? 

(a) ~1.2 × 10 12 m –3 (b) ~10 6 m –3 (c) ~2.3 × 10 14 m –3 (d) ~10 22 m –3 

Ans. [a] 

Q.34 Light from a source located in a medium (refractive index = µ 0 ) enters an optical fibre with core refractive 

index µ 1 and clad refractive index µ 2 , as shown in figure. The maximum value of incident angle θ which 

would undergo total internal reflection in the fibre is- 

θ 

µ 0 

µ 2 

µ 1 

Ans. 

⎛ 2 2 ⎞ 

−1⎜ 

µ 1 − µ 2 ⎟ 

−1 

⎡µ 

1 − µ 2 

⎤ 

(a) θ = cos ⎜ µ 

⎟ 

(b) θ = tan ⎢ ⎥ 

0 

⎝ ⎠ 

⎣ µ 0 ⎦ 

⎛ 2 2 ⎞ 

−1⎜ 

µ 1 − µ 2 ⎟ 

(c) θ = sin ⎜ µ 

⎟ 

(d) None of these 

0 

⎝ ⎠ 

[c] 

Q.35 A cyclotron is opened at an oscillator of 12 MHz and has a dee radius R = 50 cm. What is the magnitude of 

the magnetic field needed for a proton to be accelerated in the cyclotron ? 

(a) 0.72 T (b) 0.65 T (c) 0.39 T (d) 0.12 T 

Ans. [a] 



7 / 25



CAREER POINT 

Q.36 Which of the following expressions represents the relation between orbital magnetic moment and orbital 

angular momentum of an electron ? 

r 2m r 

e 

r r r e r r e r 

(a) µ orb = − Lorb 

(b) µ orb = −2meLorb 

(c) µ orb = − Lorb 

(d) µ orb = Lorb 

e 

2m 

2m 

Ans. [c] 

e 

e 

Q.37 In the following figure, the variation of electric field magnitude E versus time is shown for four uniform 

electric fields contained within identical circular regions. Arrange the fields according to the magnitudes of 

the magnetic fields they induce at the edge of the region, in decreasing order- 

E 

S 

P 

Ans. 

R 

Q 

t 

(a) P, R, Q, S (b) R, P, Q, S (c) Q, R, P, S (d) S, P, Q, R 

[a] 

Q.38 In a double slit experiment, the distance between slits is 5.0 mm and the slits are 1.0 m from the screen. Two 

interference patterns can be seen on the screen : one due to light of wavelength 480 nm and the other due to 

light of wavelength 600 nm. What is the separation on the screen between the third order bright fringes of 

the two interference patterns ? 

(a) 0.02 mm (b) 0.05 mm (c) 0.07 mm (d) 0.09 mm 

Ans. [c] 

Q.39 A LED is constructed from a p-n junction based on a certain Ga-As-P semiconducting material whose energy 

gap is 1.9 eV. Identify the colour of the emitted light- 

(a) blue (b) red (c) violet (d) green 

Ans. [b] 

Q.40 The binding energy per nucleon in a heavy nucleus is of the order of- 

(a) 8 MeV (b) 7 MeV (c) 5 MeV (d) 2 MeV 

Ans. [b] 

Q.41 In the following nuclear reaction, 235 U + n → X + Y + 2n, which of the following pairs cannot represent X 

and Y ? 

(i) 141 Xe and 93 Sr (ii) 139 Cs and 95 Rb (iii) 156 Nd and 79 Ge (iv) 141 Ba and 92 Kr 

(a) (iii) and (iv) (b) (i) and (ii) (c) (ii) and (iii) (d) (i) and (iv) 

Ans. [a] 



8 / 25



CAREER POINT 

Q.42 Which of the following fusion reactions will not result in the net release of energy ? 

(i) 6 Li + 6 Li 

(ii) 4 He + 4 He 

(iii) 12 C + 12 C 

(iv) 35 Cl + 35 Cl 

(a) (iv) (b) (iii) (c) (i) (d) (ii) 

Ans. [a] 

Q.43 For a damped harmonic oscillator of mass 250 gm, the values of spring constant (k) and damping constant 

(b) are 85 N/m and 70 gm/s, respectively. What is the period of motion ? 

(a) 2.5 s (b) 5.0 s (c) 6.25 s (d) 7.2 s 

Ans. [b] 

Q.44 

⎡πx 

⎤ 

A string oscillates according to the equation, y = (0.50 cm) sin ⎢ ⎥ cos [40πt]. Find the distance between 

⎣ 3 ⎦ 

nodes- 

(a) 1.5 cm (b) 2.5 cm (c) 3.0 cm (d) 3.5 cm 

Ans. [c] 

Q.45 Two point sources, which are in phase and separated by distance D = 1.5 λ, emit identical sound waves of 

Ans. 

wavelength λ. If a circle with a radius much greater than D, centered on the mid-point between the sources, 

what is the number of points around the circle at which the interference is fully constructive ? 

(a) 12 (b) 8 (c) 6 (d) 4 

[c] 

Q.46 The figure shows the temperature at four faces of a composite slab consisting of four materials S 1 , S 2 , S 3 and 

S 4 of identical thickness, through which the heat transfer is steady. Arrange the materials according to their 

thermal conductivities in decreasing order - 

25ºC 15ºC 10ºC –5ºC –10ºC 

S 1 S 2 S 3 S 4 

(a) S 2 , S 4 , S 1 , S 3 (b) S 2 = S 4 , S 1 , S 3 

Ans. 

(c) S 1 = S 2 , S 3 , S 4 (d) S 1 , S 2 , S 3 , S 4 

[b] 



9 / 25



CAREER POINT 

Q.47 The figure shows two identical copper blocks of mass 0.5 kg. When they were not in contact, block L was at 

temperature 60ºC and block R was at temperature 20ºC. But, when the blocks bring in contact, they come to 

the equilibrium temperature 40ºC. What is the net entropy change of the two block system during the 

irreversible process ? (Specific heat of copper = 386 J/kg.K) 

L 

R 

Ans. 

(a) 2.4 J/K (b) 3.6 J/K (c) 4.2 J/K (d) 5.2 J/K 

[a] 

Q.48 Two parallel large nonconducting sheets with identical (positive) uniform surface charge densities, and a 

sphere A with a uniform (positive) volume charge density are arranged as shown in figure. Rank the points 

1,2,3 and 4 according to the magnitudes of the net electric field in increasing order- 

+ 

+ 

+ 

+ 

+ 

+ 

1 

2 3 4 ⊕ 

+ 

+ 

+ 

+ 

+ 

Ans. 

d d d d 

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

[b] 

Q.49 Choose the electromagnetic radiation relevant to telecommunication- 

(a) ultraviolet (b) infrared (c) visible (d) microwave 

Ans. [d] 

Q.50 A microscope is focused at a point at the bottom of a beaker containing water. The microscope is then raised 

through 3 cm. To what height water must be added into the beaker to bring the point again in focus ? 

(a) 15 cm (b) 12 cm (c) 10 cm (d) 8 cm 

Ans. [b] 



10 / 25



Part B - CHEMISTRY 

CAREER POINT 

Q.51 One mole of compound, A, on heating with excess of conc. HI gave two moles of ethyl iodide. Compound, 

A, is - 

(a) ethoxy benzene 

(b) 1,2-dimethoxy ethane 

(c) methoxy ethane 

(4) ethoxy ethane 

Ans. [d] 

Q.52 The appropriate reagent(s) for the following transformation is (are) : 

O 

|| 

CH 3 (CH 2 ) 9 – C –OC 2 H 5 ⎯→ CH 3 (CH 2 ) 9 –CHO 

Ans. 

(a) SnCl 2 + HCl (b) DIBAL-H (c) CrO 2 Cl 2 (d) CO, HCl, anhyd. AlCl 3 

[b] 

Q.53 Which of the following reactions would provide the best synthesis of butan-2-ol ? 

O 

(a) MgBr + H ether H 3O + 

O 

(b) MgBr + H ether H 3O + 

Ans. 

(c) MgBr + 

[a] 

ether H 3 O + 

O (d) 

MgBr + 

CO 2 (s) H 3 O + 

Q.54 Pick out the electrophiles from following species 

BF 3 NH 3 Me 3 C⊕ HCl 

(a) BF 3 and NH 3 (b) Me 3 C⊕ and HCl (c) BF 3 and Me 3 C⊕ (d) NH 3 and HCl 

Ans. [c] 

Q.55 What reagent (s) is (are) needed to accomplish the following conversion ? 

εt R 

εt R 

? 

C=C 

O 

H H 

H H 

(a) (i) O 3 (ii) Zn/H + (b) KMnO 4 , O H 

(c) 

O 

CO 2 H 

(d) H 3 O + 

, cold 

Ans. 

Cl 

[c] 



11 / 25



CAREER POINT 

Q.56 Which of the following compounds is strongest acid ? 

Ans. 

H H 

H C=C H 

I 

H – C ≡ C– H 

II 

H 

H 

H C=C=C H 

III 

(a) I (b) II (c) III (d) IV 

[b] 

H 

H 

H 

H 

IV 

H 

H 

Q.57 Major products, A and B, of the following reactions are : 

O 

i) Cl 2 , NaOH, H 2 O 

ii) H 3 O + 

A + B 

(a) 

OH + CHCl3 

(b) 

CCl 3 

+ NaCl 

O 

O 

(c) 

O 

H 

+ 

O 

Cl 

(d) 

OH 

O 

+ NaCl 

Ans. 

[a] 

Q.58 The hydrolysis of which of the following takes the longest time ? 

(a) CH 3 COCl 

(b) (CH 3 CO) 2 O 

Ans. 

(c) CH 3 COOC 2 H 5 (d) CH 3 CONH 2 

[d] 

Q.59 In the given reaction, A, may be : 

H 2 O CH 3 

A 

H 2 SO 4 OH 

CH 3 

CH 3 

(c) (d) 

(a) 

(b) 

Ans. 

[c] 

Q.60 Wilinson's catalyst is used for - 

(a) epoxidation (b) hydrogenation (c) polymerization (d) substitution 

Ans. [b] 



12 / 25



CAREER POINT 

Q.61 For the following conversion, 

OH 

(A) 

OH 

Ans. 

reagent/reagents (A) is/are - 

(a) OsO 4 (b) O 3 

(c) I 2 and silver acetate under wet condition (d) peracid following by acid hydrolysis 

[d] 

Q.62 An ether solution of benzoic acid (A), aniline (B) and toluene (C) is extracted with aqueous NaOH. The ether 

layer will contain what compound (s) after the extraction ? 

(a) A (b) A + B (c) B + C (d) A + C 

Ans. [c] 

Q.63 Which of the free radical is most stable ? 

Ans. 

I II III IV 


[c] 

Q.64 The best reagent for converging 2-phenylpropanamide into 2-phyenylpropanamine is - 

(a) Br 2 in aqueous NaOH (b) excess of H 2 

(c) iodine in the presence of red phosphorus (d) LiaAlH 4 in ether 

Ans. [d] 

Cl 

Q.65 Which of the following compounds reacts faster with sodium methoxide (NaOCH 3 ) : 

Cl Cl Cl 

Cl OCH 3 

O 2 N 

NO 2 

I II III IV 


Ans. [a] 

Q.66 Which one of the following reaction is easily possible ? 

Cl 

OMe 

(a) 

Cl + MeO – Na + → Cl (b) + Cl + MeO– Na → +OMe 

(c) C 7 H 5 OH + HCl → C 6 H 5 Cl (d) C 6 H 5 MgCl + ether H 3 O + C 

O 

6 H 5 

OH 

Ans. [d] 



13 / 25



CAREER POINT 

Q.67 Which one of the following is hydride transfer reaction ? 

O 

O 

(a) 2C 6 H 5 

H 

Base C 6 H 5 OH + C 6 H 5 

O – 

∆ 

O i) Mg, Benzene 

(b) 2 ii) H 2 O 

OH OH 

OH 

O 

O 

base 

(c) 

Ans. 

(d) C 6 H 

[a] 

O 

H 

HCN, NaCN 

EtOH 

C 6 H 5 

OH 

H 

H 

Q.68 Which of the following has maximum number of lone pairs associated with Xe ? 

(a) XeF 4 (b) XeF 6 (c) XeF 2 (d) XeO 3 

Ans. [c] 

Q.69 The number of types of bonds between two carbon atoms in calcium carbide is - 

(a) one sigma, one pi (b) two sigma, one pi (c) two sigma, two pi (d) one sigma, two pi 

Ans. [d] 

Q.70 The magnetic moment of transition metal ion is 15 B.M. The number of unpaired electrons present in it 

are - 

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

Ans. [d] 

Q.71 The structure of H 2 O 2 is - 

(a) planar (b) non planar (c) spherical (d) linear 

Ans. [b] 

Q.72 Which one of the following decides the shapes of orbitals in an energy shell - 

(a) Magnetic quantum number 

(b) Principal quantum number 

(c) Azimuthal quantum number 

(d) Spin quantum number 

Ans. [c] 

Q.73 The structure of paramagnetic nickel complex, [NiCl 4 ] 2– is - 

(a) tetrahedral 

(b) square planar 

(c) trigonal bipyramidal 

(d) distorted octahedral 

Ans. [a] 



14 / 25



CAREER POINT 

Q.74 The element Re, Os and Ir belong to - 

(a) First transition series 

(c) Third transition series 

Ans. [c] 

(b) Second transition series 

(d) Fourth transition sereies 

Q.75 Which of the following is not true ? 

(a) Halogens act as strong oxidizing agents 

(b) Fluorine oxidizes water to oxygen and ozone 

(c) Iodine has good solubility in water 

(d) Solubility of iodine in water much increases by adding KI due to formation of I – 3 ions 

Ans. [c] 

Q.76 Silica is attacked by - 

(a) Conc. HNO 3 (b) Conc. H 2 SO 4 (c) Aqua regia (d) Hydrofluoric acid 

Ans. [d] 

Q.77 [CO(NH 3 ) 3 Br] SO 4 and [CO(NH 3 ) 5 SO 4 ] Br are examples of which type of isomerism - 

(a) Linkage (b) Geometrical (c) Ionization (d) Optical 

Ans. [c] 

Q.78 Which of the following ions will exhibit colour in aqueous solution ? 

(a) Lu 3+ (Z = 71) (b) SC 3+ (Z = 21) (c) La 3+ (Z = 57) (d) Ti 3+ (Z = 22) 

Ans. [d] 

Q.79 The correct order of C–O bond length among CO, CO 2– 3 , CO 2 is - 

2– 

(a) CO < CO 2 < CO 3 (b) CO 2 < CO 2– 3 < CO 

(c) CO < CO 2– 3 < CO 2 

(d) CO 2– 3 < CO 2 < CO 

Ans. [a] 

Q.80 In Fe(CO) 5 , the Fe–C bond possesses - 

(a) Ionic character (b) σ character only (c) π character only (d) Both σ and π character 

Ans. [d] 

Q.81 The anion O – is isoelectronic with - 

(a) N 2– (b) F – (c) N 3– (d) Ne 

Ans. [a] 

Q.82 Which of the following oxides is most acidic ? 

(a) BeO (b) MgO (c) Al 2 O 3 (d) Cl 2 O 7 

Ans. [d] 



15 / 25



CAREER POINT 

Q.83 Analysis shows that a binary compound of X (atomic mass = 10) and Y (atomic mass = 20) contains 50 % X. 

The formula of the compound is - 

Ans. 

(a) XY (b) X 2 Y (c) XY 2 (d) X 2 Y 3 

[b] 

Q.84 The volume occupied by 16g of oxygen gas at S.T.P. is - 

(a) 22.4 L (b) 44.8 L (c) 11.2 L (d) 5.6 L 

Ans. [c] 

Q.85 If K sp of Ni(OH) 2 is 2.0 × 10 –15 M, the molar solubility of Ni(OH) 2 in 0.10 M NaOH is - 

(a) 2.0 × 10 –15 M 

(b) 2.0 × 10 –13 M 

(c) 2.0 × 10 –11 M 

(d) 2.0 × 10 –9 M 

Ans. [b] 

Q.86 Above the Boyle temperature, the compressibility factor of the real gases, Z, is - 

(a) 1 (b) < 1 (c) > 1 (d) ≤ 1 

Ans. [c] 

Q.87 The arsenic content of an agricultural insecticide was reported as 28 % AS 2 O 5 . What is the percentage of 

arsenic in this preparation ? 

(a) 16 % (b) 18 % (c) 15 % (d) 20 % 

Ans. [b] 

Q.88 Calculate the maximum work that can be obtained from the cell 

Zn | Zn 2+ (1 M) || Ag + (1 M) Ag 

where 

o 

E Zn = – 0.76 V and 

o 

E Ag = 0.8 V 

Ans. 

(a) 301.080 kJ (b) 201.830 kJ (c) 112.830 kJ (d) 212.630 kJ 

[a] 

Q.89 Which metal is protected from corrosion by a layer of its own oxide ? 

(a) Tl (b) Ag (c) Al (d) Au 

Ans. [c] 



16 / 25



CAREER POINT 

M 

Q.90 The ideal gas equation, PV = nRT, can be written in terms of density, ρ, as ρ/P = . The graph between 

RT 

ρ/P against P is given by : 

(a) ρ/P 

(b) ρ/P 

(c) ρ/P 

(d) ρ/P 

P 

P 

P 

P 

Ans. 

[b] 

Q.91 When a dilute solution of KNO 3 is mixed with a dilute solution of NaBr, the enthalpy change in expected to 

be - 

(a) Zero, O (b) > O (c) < O (d) All the above 

Ans. [a] 

Q.92 Which of the following represents the zero overlap : 

(a) – + + z 

(b) 

p x s 

(c) 

Ans. [d] 

+ – 

p x 

– + 

p x 

z 

+ + 

p x 

– – 

p x 

+ 

(d) + 

– s 

p x 

z 

p z 

Q.93 A compound alloy of copper and gold crystallises in a cubic lattice in which the copper atom occupy the 

centres of each of the cube faces and the gold atoms occupy the lattice point. The formula of compound is - 

Ans. 

(a) Au 3 Cu (b) AuCu 3 (c) Au 2 Cu 3 (d) Au 1 Cu 2 

[b] 

Q.94 What volume of oxygen, at 18ºC and 75º torr, can be obtained from 110 gram of KClO 3 

(a) 32.6 L (b) 42.7 L (c) 3.26 L (d) 4.27 L 

Ans. [a] 

Q.95 CsBr crystallizes in a body centred cubic unit lattice with an edge length of 4.287 Å. How many molecules of 

CsBr will be present in the unit lattice ? 

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

Ans. [a] 



17 / 25



CAREER POINT 

Q.96 Arrange the following solutions in the increasing order of their osmotic pressure ? 

(i) 34.2 g/l sucrose (M = 342) (ii) 60 g/l urea (M = 60) 

(iii) 90 g/l glucose (M = 180) (iv) 58.5 g/l NaCl (M = 58.5) 

(a) Sucrose < Urea < Glucose < NaCl 

(b) Sucrose < Glucose < NaCl < Urea 

(c) Sucrose < Glucose < Urea < NaCl 

(d) NaCl < Urea < Glucose < Sucrose 

Ans. [c] 

Q.97 The magnitude of the charge on the electron is 4.8 × 10 –10 esu. What is the magnitude of the charge on the 

proton on the nucleus of helium atom ? 

(a) 4.8 × 10 –10 esu 

(b) 9.6 × 10 –10 esu 

(c) 6. 4 × 10 –10 esu 

(d) 14.4 × 10 –10 esu 

Ans. [b] 

Q.98 In free radical polymerization, the extent of conversion increasing with - 

(a) increase in temperature 

(b) increase in polymerization time 

(c) increase in monomer concentration (d) All the above 

Ans. [d] 

Q.99 100 ml of 0.1 M H 2 SO 4 is mixed with 100 ml of 0.1 NaOH. the normality of the solution obtained is - 

(a) 0.4 N (b) 0.05 N (c) 0.04 N (d) 0.2 N 

Ans. [b] 

Q.100 The thermodynamics equilibrium constant, K C , for the reaction : 

CuO(s) + H 2 (g) = Cu(s) + H 2 O(g) is given by - 

Ans. [d] 

[Cu][H2 O] 

(a) K C = 

(b) K C = 

[CuO][H ] 

2 

[H2 O] 

(c) K C = 

(d) K C = 

[CuO][H ] 

2 

[Cu][H2 

O] 

[H ] 

2 

[H2 

O] 

[H ] 

2 



18 / 25

SERIES-A (CODE-05) 


CAREER POINT 

Part C - MATHEMATICS 

Q.101 Let A ={(x, y) : y = e –x } and B = {(x, y) : y = – x}. Then - 

Ans. 

(a) A I B = ϕ 

(b) A ⊂ B 

(c) B ⊂ A (d) A I B = {(0, 1) , (0, 0)} 

[a] 

Q.102 The set of zeros of f(x) = 0 is a non-empty set, when f(x) = 

(a) e –x + x (b) |x| + (x – 2) 2 (c) x – log e x (d) x + e x 

Ans. [d] 

Q.103 Let f(x) = (x + 2) 2 – 2, x ≥ –2. Then f –1 (x) = 

Ans. 

(a) – 

[c] 

2 + x – 2 (b) 2 + x + 2 (c) 2 + x – 2 (d) – 2 + x + 2 

Q.104 Let z be the set of integers. Then the relation R = {(a, b) : 1 + ab > 0} on z is - 

(a) reflexive and transitive but not symmetric 

(b) symmetric and transitive but not reflexive 

(c) reflexive and symmetric but not transitive 

(d) an equivalence relation 

Ans. [c] 

Q.105 Let L denote the set of all straight lines in a plane. Let a relation R be defined by l 1 R l 2 if and only if the 

straight line l 1 is perpendicular to the straight line l 2 . Then R is - 

(a) symmetric (b) reflexive (c) transitive (d) none of these 

Ans. [a] 

Q.106 Which one of the following is not true ? 

(a) |sin x| ≤ 1 (b) – 1 ≤ cos x ≤ 1 

(c) |sec x| < 1 (d) cosec x ≥ 1 or cosec x ≤ – 1 

Ans. [c] 

Q.107 The general solution of sin 3x + sin x – 3 sin 2x = cos 3x + cos x – 3 cos 2x is - 

nπ π 

(a) + for n integer 

2 8 

nπ π (b) – for n integer 

2 8 

π 

(c) nπ + for n integer 

8 

π (d) nπ – for n integer 

8 

Ans. 

[a] 

⎡ –1 3 –1 2⎤ 

Q.108 The value of tan ⎢cos 

+ tan ⎥ is - 

⎣ 5 3 ⎦ 

(a) 18 (b) 2 (c) 9 (d) None of these 

Ans. [a] 



19 / 25



CAREER POINT 

6i – 3i 1 

Q.109 If 4 3i –1 = x + iy, then - 

20 3 i 

(a) x = 0, y = 1 (b) x = 1, y = 0 (c) x = 1, y = 1 (d) None of the above 

Ans. [d] 

⎛ 1+ 

i ⎞ 

Q.110 The smallest positive integer n for which ⎜ ⎟ 

⎝1 – i ⎠ 

n 

= 1, is - 

(a) 4 (b) 2 (c) 8 (d) 16 

Ans. [a] 

Q.111 If z 1 , z 2 and z 3 are complex numbers such that 

Ans. 

|z 1 | = |z 2 | = |z 3 | = 

1 

z 

1 1 

+ + = 1, then |z 1 + z 2 + z 3 | is - 

1 z2 

z3 

(a) 3 (b) 1 (c) greater than 3 (d) less than 1 

[b] 

Q.112 In a triangle the lengths of the largest and the smallest sides are 10 and 9 respectively. If the angles are in 

A.P., then the length of the third side is - 

(a) 91 (b) 8 (c) 3 3 (d) 5 

Ans. [a] 

Q.113 Consider an infinite geometric series with first term a and common ratio r. If its sum is 4 and the second term 

is 4 

3 , then - 

(a) a = 2, r = 2 

1 

(b) a = 2, r = 8 

3 

(c) a = 1, r = 4 

3 

(d) none of these 

Ans. [c] 

Q.114 If p, q are positive real numbers such that pq = 1, then the least value of (1 + p) (1 + q) is - 


Ans. [a] 

Q.115 If 49 n + 16n + p is divisible by 64 for all n ∈ N, then the least negative integral value of p is - 

(a) –2 (b) –3 (c) –4 (d) –1 

Ans. [d] 

n 

Q.116 If the 4 th ⎛ 1 ⎞ 5 

term in the expansion of ⎜ax + ⎟ is , for all x ∈ R, then the values of a and n are - 

⎝ x ⎠ 2 

1 1 

(a) ¸6 (b) 6, (c) 2, 6 


2 2 

Ans. 

[a] 



20 / 25



CAREER POINT 

Q.117 Let n be a positive integer. If the coefficients of second, third and fourth terms in the expansion of (1 + x) n 

are in A.P., then n = 


Ans. [c] 

Q.118 Total number of ways in which five '+' and three '–' signs can be arranged in a line such that no two '–' sign 

occur together is - 


Ans. [b] 

Q.119 A box contains 2 white balls, 3 black balls and 4 red balls. In how many ways can 3 balls be drawn from the 

box, if at least one black ball is to be included in the draw - 

(a) 64 (b) 24 (c) 3 (d) 12 

Ans. [a] 

Q.120 Let P = (–1, 0) \, O = (0, 0) and Q = (3, 3 3 ) be three points. Then, the equation of the bisector of the 

∠POQ is - 

(a) y = 3 x (b) 3 y = x (c) y = – 3 x (d) 3 y = – x 

Ans. [c] 

Q.121 The lines 2x – 3y = 5 and 3x – 4y = 7 are diameters of a circle of area 154 squares unit. Then the equation of 

the circle is - 

(a) x 2 + y 2 – 2x + 2y + 47 = 0 (b) x 2 + y 2 + 2x – 2y – 47 = 0 

(c) x 2 + y 2 – 2x + 2y – 47 = 0 (d) x 2 + y 2 – 2x – 2y – 47 = 0 

Ans. [c] 

Q.122 The line 2x + y + k = 0 is a normal to the parabola y 2 = – 8x, if k = 

(a) –24 (b) 12 (c) 24 (d) –12 

Ans. [c] 

Q.123 If t is a parameter, then x = a(sin t – cos t), y = b(sin t + cos t) represents - 

(a) circle (b) parabola (c) ellipse (d) hyperbola 

Ans. [c] 

Q.124 The eccentricity of the hyperbola 9x 2 – 16y 2 + 72x – 32y – 16 = 0, is - 

(a) 5/4 (b) 6/5 (c) 4/3 (d) 3/2 

Ans. [a] 

Q.125 The value of λ such that x – 4 = y – 2 = 2 

1 (z – λ) lies in the plane 2x – 4y + z = 7, is - 

Ans. 

(a) 7 (b) –7 (c) 4 (d) None of these 

[a] 



21 / 25



CAREER POINT 

log( 1+ 

ax) – log(1 – bx) 

Q.126 The f(x) = 

is not defined at x = 0. The value which should be assigned to f at x = 0, 

x 

so that it is continuous at x = 0 is - 

(a) a – b (b) a + b (c) b – a (d) none of these 

Ans. [b] 

Q.127 Let f : R → R be such that f(1) = 3, and f ' (1) = 6. Then 

x lim →0 

1 

x 

⎡ f (1 + x) ⎤ 

⎢ ⎥ 

⎣ f (1) ⎦ 

1 

(a) 1 (b) e 

2 

(c) e 2 (d) e 3 

Ans. [c] 

Q.128 If f(x) is differentiable and strictly increasing function, then the value of 

Ans. 

f (x ) – f (x) 

lim 

x→ 0 f (x) – f (0 ) 

2 

= 

(a) – 1 (b) 0 (c) 1 (d) 2 

[a] 

= 

Q.129 The angle between the tangents drawn from the point (1, 4) to the parabola y 2 = 4x is - 

(a) π/2 (b) π/6 (c) π/4 (d) π/3 

Ans. 

[d] 

Q.130 The difference between the greatest and the least values of the function 

⎡ ⎤ 

f(x) = sin 2x – x on ⎢ ⎥ 

⎣ 

– π π 

, 

2 2 

is - 

⎦ 

(a) π (b) 3 – π/3 (c) – 3 + π/3 (d) None of these 

Ans. [a] 

(x – 1) 

Q.131 

∫ 

dx = 

3 4 2 

x 2x – 2x +1 

(a) – 2 

1 

(c) 2 

1 

2 

2 1 

1 

2 – + + c (b) 

2 4 

log (2x 4 – 2x 2 + 1) + c 

x x 

2 

2 1 

2 – + + c (d) None of these 

2 4 

x x 

Ans. [c] 

π 

Q.132 

∫sin x[f (cos x)]dx = 

–π 

(a) 2f(π) (b) 2f(2) (c) 2f(1) (d) None of these 

Ans. 

[d] 



22 / 25



CAREER POINT 

Q.133 The area bounded by the curves y = x and y = x 3 is equal to - 

1 

1 

(a) 0 (b) (c) 4 2 

(d) 1 

Ans. 

[c] 

Q.134 The area bounded by the curves y = e x , y = e –x , the ordinates x = 0 and x = 1 is given by - 

(a) e + e –1 – 2 (b) e – e –1 (c) e + e –1 (d) e + e –1 + 2 

Ans. [a] 

Q.135 The differential equation of all non-vertical lines in a plane is - 

Ans. 

(a) 

[a] 

d 

2 

dx 

y 

2 

dy 

= 0 (b) = 0 dx 

dx (c) = 0 dy 


2 

⎛ dy ⎞ dy 

Q.136 A solution of the differential equation ⎜ ⎟⎠ – x + y = 0 is - 

⎝ dx dx 

(a) y = 2x (b) y = – 2x (c) y = 2x – 4 (d) y = 2x + 4 

Ans. [c] 

Q.137 If â and bˆ are unit vectors such that â + 3 bˆ is perpendicular to 7 â – 5 bˆ , then the angle between â and bˆ 

is - 

π 

(a) (b) π/6 (c) 2π/3 (d) None of these 

3 

Ans. 

[a] 

Q.138 The unit vector perpendicular to vectors î + ĵ and î – ĵ forming a right handed system is - 

(a) kˆ 

(b) 2 kˆ 

(c) – kˆ (d) None of these 

Ans. [c] 

Q.139 Let → a = î + ĵ + kˆ , → b = î – ĵ + kˆ and → c = î – ĵ – kˆ be three vectors. A vector → v in the plane of → a 

Ans. 

and → b , whose projection on → c is 

1 , is given by - 

3 

(a) 3 î + ĵ – 3 kˆ 

(b) 3 î – ĵ+ 3 kˆ (c) 3 î + ĵ + 3 kˆ (d) – 3 î + ĵ + 3 kˆ 

[b] 

Q.140 Max z = x + y 

Subject to y ≤ |x| – 1 

y ≤ 1 – |x| 

x, y ≥ 0 

The Max z = 

(a) 0 (b) 1 (c) 2 (d) –1 

Ans. [b] 



23 / 25



CAREER POINT 

Q.141 Max z = 2x + 3y 

Subject to y ≤ x – 1 

y ≥ x + 1 

x, y ≥ 0 

The max z 

(a) is 2 (b) is 3 (c) does not exist (d) is 10 

Ans. [c] 

Q.142 For any two events A and B, which of the following result does not hold true in general - 

(a) P (A ∪ B) = P(A) + P(B) – P(A ∩ B) (b) P(A) = P(A ∩B) + P (A ∩ B ) 

(c) P(B) = P(A ∩ B) + P( A ∩ B) 

(d) P(A ∪ B) = P(A) + P(B) 

Ans. [d] 

Q.143 A fair die is rolled. The probability that the first time 1 occurs at the odd throw is - 

5 

6 

1 

(a) (b) (c) 11 11 6 

31 

(d) 36 

Ans. 

[b] 

⎡α 0⎤ 

⎡1 

0⎤ 

Q.144 If A = ⎢ ⎥ and B = 

⎣1 

1 

⎢ ⎥ , then value of α for which A 2 = B is 

⎦ ⎣5 

1 ⎦ 

(a) α = 1 (b) α = – 1 (c) α = 4 (d) No real value of α 

Ans. [d] 

x 3 7 

Q.145 The number of positive roots of the equation 2 x 2 = 0 is - 

7 6 x 

(a) 1 (b) 2 (c) 3 (d) 0 

Ans. [b] 

⎡cosθ 

– sin θ⎤ 

Q.146 If A = ⎢ 

⎥ , then A 3 = 

⎣sin 

θ cosθ 

⎦ 

⎡– cos3θ 

– sin 3θ⎤ 

⎡ cos3θ 


(a) ⎢ 

⎥ (b) 

⎣ sin 3θ 

cos3θ 

⎢ 

⎥ ⎦ ⎣– sin 3θ 

cos3θ 

⎦ 

⎡cos3θ 


⎡– cos3θ 

sin 3θ 

⎤ 

(c) ⎢ 

⎥ (d) 

⎣sin 3θ 

cos3θ 

⎢ 

⎥ ⎦ ⎣– sin 3θ 

– cos3θ 

⎦ 

Ans. [c] 

⎡sin 

θ 

Q.147 The value of 

⎢ 

⎢ 

sinβ 

⎢⎣ 

sin δ 

cosα 

cosβ 

cosδ 

sin( α + γ) 

⎤ 

sin( β + γ) 

⎥ 

⎥ 

is - 

sin( γ + δ) 

⎥⎦ 

(a) sin α sin β sin δ (b) cos α cos β cos δ (c) 1 (d) 0 

Ans. [d] 



24 / 25



CAREER POINT 

Q.148 The numbers of real tangents that can drawn from (1, 1) to the circle x 2 + y 2 – 6x – 4y + 4 = 0, is - 

(a) 1 (b) 2 (c) 0 (d) 3 

Ans. [c] 

Q.149 The line x = my + C is normal to x 2 = – 4ay if C = 

(a) – 2 am – m 3 a (b) 2am + am 3 (c) – 2am – am 3 (d) 2 am + am 3 

Ans. [d] 

Q.150 If P is a point (x, y) and P 1 = (3, 0), P 2 = (–3, 0) and 16x 2 + 25y 2 = 400, then PP 1 + PP 2 = 

(a) 8 (b) 10 (c) 5 (d) 4 

Ans. [b] 



25 / 25

AMU-2013 - Career Point

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?