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GOPREP TALENT SEARCH EXAM

QUESTION PAPER

INSTRUCTIONS:

The duration of the test will be 60 minutes. Use the time accordingly.

The test paper consists of 50 questions divided into four sections, Section A, Section B, Section C & Section D.

➢ Section A contains 15 questions of Physics. ➢ Section B contains 15 questions of Chemistry. ➢ Section C contains 15 questions of Biology. ➢ Section D contains 5 questions of Aptitude. ➢

Each question will have 4 choices, with the only single choice being correct. You will get 2 marks for every correct answer. There will be no negative marking for any wrong answer or unanswered question.

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SECTION |A|

PHYSICS

1. If in a p-n junction diode, a square input signal of 10V is applied as shown

Then the output signal across the load resistor RL will be

A. B. C. D.

2. A ring made of non-conducting material and of radius ‘R’ has a charge of ‘+Q’ uniformly

distributed on it. Which of the following statements is incorrect about the Electric Field

‘E’ and Electric Potential ‘V’ at any point on the ‘axis’ of the ring at a distance of ‘x’ from

it’s center.

A. The Maximum value of ‘V’ is at x = 0

B. The Electric Field ‘E’ is zero at x = 0

C. The Electric Field ‘E’ is maximum for

D. The Electric Field ‘E’ is maximum for

3. The activity of a radioactive sample falls from to in 20 minutes. What can

be the possible half-life of the radioactive sample? Assume

A. 19 min B. 15 min C. 10 min D. 8.2 min

4. Three capacitor are connected as shown in the figure. When key is closed then, find the

amount of charge flowing through the battery.

A. B. C. D.

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5. What is the ratio of the de-Broglie wavelengths of molecules of nitrogen and oxygen

which are at temperature and respectively?

A. B. C. D.

6. An iron-cored transformer assumed to be 100% efficient. The ratio of the secondary turns

to the primary turns is 1 : 30. Find the current in the primary coil.

A. 0.01 A B. 0.1 A C. 2 .1 A D. 10 A

7. Determine approximately how much power is dissipated through the 12Ω resistance.

Assume the internal resistance of the battery is 2.5Ω

A. 3 W B. 6 W C. 10 W D. 16 W

8. In Young's double slit experiment, the central maxima occur where path difference

between the interfering beams is zero. A glass plate of thickness 5 mm is inserted to cover

the upper slit completely. The slit separation is 10 mm and the diffraction patterns are

observed at the focal plane of the converging lens (focal length 35 mm). Which of the

following statement on the position of the central maximum is true? Assume the

refractive index of the glass is 2.5.

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A. Central maxima will shift up by 5 mm

B. The position of central maxima remains same.

C. Central maxima will shift down by 15 mm

D. None of these

9. When a ray of light is incident normally on one refracting surface of an equilateral prism

(Refractive index of the material of the prism = 1.5)

A. Emerging ray is deviated by

B. Emerging ray is deviated by

C. Emerging ray just grazes the second refracting surface

D. The rays undergoes total internal reflection at the second refracting surface

10. Following figure shows an adiabatic cylindrical container of volume divided by an

adiabatic smooth piston (area of cross-section = A) in two equal parts. An ideal

gas is at pressure P1 and temperature T1 in left part and gas at

pressure P2 and temperature T2 in right part. The piston is slowly displaced in right

direction and released at a position where it can stay in equilibrium. The final pressure of

the two parts will be (Suppose x = displacement of the piston)

A. B. C. D. Insufficient Data

11. The ratio of intensities between two coherent sound sources is 4:1. The difference of

loudness in dB between maximum and minimum intensities when they interfere in space

is

A. 10 log 2 B. 20 log 3 C. 10 log 3 D. 20 log 2

12. A pulse shown here is reflected from the rigid wall A and then from free end B. The shape

of the string after these 2 Reflection will be.

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A. B.

C. D.

13. Steel ruptures when a shear of 3.5 × 108 Nm‒2 is applied. The force needed to punch a 1

cm diameter hole in a steel sheet 0.3 cm thick is nearly:

A. 1.4 × 104 N B. 2.7 × 104 N C. 3.3 × 104 N D. 1.1 × 104 N

14. A stone dropped from a building of height h and it reaches after t seconds on earth. From

the same building if two stones are thrown (one upwards and other downwards) with the

same velocity u and they reach the earth surface after t1 and t2 seconds respectively, then

A. t = t1 – t2 B. C. D.

15. An aluminium container of mass 100 gm contains 200 gm of ice at -20°C . Heat is added

to the system at the rate of 100 cal/s. The temperature of the system after 4 minutes will

be (specific heat of ice = 0.5 and L = 80 cal/ gm, specific heat of Al = 0.2 cal/gm/°C)

A. 40.5°C B. 25.5°C C. 30.3°C D. 35.0°C

SECTION |B|

CHEMISTRY

Direction: The Ellingham diagram reveals the curves for MgO, ZnO and CO, Answer the

following questions on the basis of the given curves.

1. Carbon can reduce iron (II) oxide at

A. 500 K B. 1000 K

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C. Above 1000 K D. Above 500 K and below 1000 K

2. Calculate the accelerating potential must be imparted to a proton beam to give it an

effective wavelength of 0.005 nm.

A. 36.8 volts B. 32.8 volts C. 30.2 volts D. 39.8 volts

3. The precipitate of Ag2CrO4 (Ksp = 1.9 x 10-12) is obtained when equal volumes of the

following are mixed.

A. 10-4 M Ag+ + 10-4 M

B. 10-2 M Ag+ + 10-3 M

C. 10-5 M Ag+ + 10-3 M

D. 10-4 M Ag+ + 10-5 M

4.

A. 1-(S) , 2-(P,R), 3-(T), 4-(P,R,S,T)

B. 1-(P,R) , 2-(R), 3-(R,S), 4-(Q,S,T)

C. 1-(P,Q,R,T) , 2-(R), 3-(R,S), 4-(P,R,S,T)

D. 1-( P,R,S,T) , 2-(R,S), 3-(R,S), 4-(P,Q,R,T)

5. The reaction of K2Cr2O7 with acidified solution of H2O2 yields a blue color substance. The

change of oxidation state for Chromium observed in the above reaction is:

A. 0 B. 5 C. 6 D. 2

6. Consider the following ionisation reactions:

If monovalent positive ion of A, divalent positive ion of B and trivalent positive ion of C

have zero electron. Then incorrect order of corresponding I.E is :

A. C3 > B2 > A1 B. B1 > A1 > C1 C. C3 > C2 > B2 D. B2 > C3 > A1

7. One mole of nitrogen gas at 0.8 atm takes 38 second to diffuse through a pin hole

whereas one mole of an unknown compound of xenon with fluorine at 1.6 atm takes 57

second to diffuse through the same hole. The molecular formula of the compound is

A. B. C. D.

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8.

A. A – ii, B – v, C – vi, D – i, E – iii, F – iv

B. A –vi, B – iv, C – v, D – iii, E – ii, F – i

C. A – iii, B – iv, C – vi, D – ii, E – i, F – v

D. A – ii, B – vi, C – v, D – iii, E – i, F – iv

9. ;

Identify N and M

A. 6, 4 B. 6,6 C. 4, 4 D. 3,3

10. How many chiral centers are in the following compound?

A. 4 B. 5 C. 6 D. 7

11. Given:E0Fe

3+/Fe =–0.036V, E0

Fe2+

/Fe=–0.439V. The value of standard electrode potential for

the change, Fe3+ (aq) + e-→ Fe2+ (aq) will be:

A. -0.403 V B. 0.385 V C. 0.77V D. 0.403V

12. The distance between adjacent, oppositely charged ions in rubidium chloride is 3.285 Å,

in potassium chloride is 3.139Å, in sodium bromide is 2.981 Å and in potassium bromide

is 3.293 Å. The distance between adjacent oppositely charged ions in rubidium bromide

is

A. 3.147 Å B. 3.385 Å C. 3.393 Å D. 3.439 Å

13. What is formed when benzoyl chloride reacts with aniline in presence of sodium

hydroxide

A. Acetanilide B. Benzanilide C. Benzoic acid D. Azobenzene

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14. Consider the following sequence of reactions.

The products A. and B. are, respectively,

A. B.

C. D.

15. At the point intersection of the two curves shown, the conc. Of B is given by ________

for, A → nB:

A. B. C. D. nA0

SECTION |C|

MATHEMATICS

1. If a polygon has 44 diagonals, then the number of its sides are

A. 7 B. 11 C. 8 D. 10

2. The coefficient of x5 in (1+2x+3x2+……….up to infinite term)-3/2 is

A. 21 B. 25 C. 26 D. 0

3. Solve :

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A. B.

C. D. None

4. The roots of (x – a) (x – b) = abx2

A. are always real

B. may be complex depending upon a & b

C. are real and equal if and only if a = b = 2

D. are real and distinct if and only if

5. If is defined by , where [x] denotes the greatest

integer function then is

A. Z, the set of all integers

B. N, the set of all natural numbers

C. , the empty set

D. R, the set of all real numbers

6. If , then is equal to

A. sin 1 B. 2 sin 1 C. D. 3 sin 1

7. If = 0 , then the value of is?

A. –abc B. abc C. 0 D. none of these

8. Divide 48 into 4 parts such that third term is A.M. of first 2 and fourth term is addition of

first 3. Find sum of first 2 parts.

A. 16 B. 24 C. 8 D. 28

9. For let and be three given

functions. If a function, J(x) satisfies (f2oJof1)(x) = f3(x) then J(x) is equal to :

A. f1(x) B. f2(x) C. D. f3(x)

10. Find the solution of the differential equation at y(1)=3

A. B. C. D.

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11.

A. B.

C. D.

12. The area enclosed by y = 3x - 5, y = 0, x = 3 and x = 5 is

A. 12 sq. units B. 13 sq. units C. sq. units D. 14 sq. units

13. Vector of length 3 unit which is perpendicular to and lies in the plane

of and

A. B.

C. D.

14. Find the length of the side of an equilateral triangle whose one of the side

is and its vertex is (1, 2)

A. B. C. D.

Direction: The question has FOUR options. ONLY ONE of these four options is the correct

answer.

15. If a is an integer lying in the closed interval [- 5 ,30], then the probability that the graph

of y=x2+2(a+4) x-5a+64 is strictly above the x-axis is

A. 2/9 B. 1/6 C. 1/2 D. 5/9

SECTION |D|

APTITUDE

1. The sum of the ages of Ram and his father at present is 7/6 of what it was 5 years ago.

Find the sum of their present ages.

A. 30 B. 35 C. 60 D. 70

2. An ant is moving around a few food pieces of different shape scattered on the floor. For

which food – piece would the ant have to take a longer round?

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A. Food piece (P) B. Food piece (Q)

C. Food piece (R) D. None of these

3. ....... is equal to:

A. B. C. D.

4. Arrange the following words according to English Dictionary.

1. Banal 2. Banana 3. Banish 4. Bandage

5. Bandit

A. 1, 3, 2, 4, 5 B. 1, 2, 4, 3, 5 C. 1, 2, 4, 5, 3 D. None of these

5. 1024, ______, 64, 16, 4

A. 254 B. 236 C. 256 D. 244

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HINT AND SOLUTIONS

SECTION |A|

PHYSICS

1. Ans. D.

The diode will only conduct for forward bias voltage.

2. Ans. D.

and , hence, V is max at x=0 and E has local

minima of E=0 at x=0 and whereas ‘E’ has it’s local maxima (and Global max)

at

3. Ans. A.

As we know activity

Half-life of sample is

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4. Ans. D.

The equivalent capacitance of the capacitor is

Initial charge on the capacitor is

After closing the switch, (Since left capacitors are short circuited)

Charge, ,

Amount of charge flow is,

5. Ans. B.

As we know de-Broglie wavelength is

RMS velocity of a gas particle is at given temperature T is

Therefore

6. Ans. A.

The equivalent primary load is

Current in the primary coil is

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7. Ans. B.

Rearranging the circuit,

Resistance of Arm QT is

The effective resistance of the circuit is

Therefore, current passing through the circuit is

Potential difference across Q and T is

Therefore, power dissipated as heat due to resistance 12Ω

is

8. Ans. D.

Additional optical path introduced in beam which is coming from the upper slit.

Let central maxima is formed at point P. The path difference will be

For central maxima,

So,

Central maxima will shift by distance

9. Ans. D.

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10. Ans. C.

As finally the piston is in equilibrium, both the gases must be at same pressure Pf . It is

given that displacement of piston in final state is x and if A is the area of cross-section of

the piston, the final volumes of the left and right part finally can be given by figure as

and

As it is given that the container walls and the piston are adiabatic, so in left side the gas

undergoes adiabatic expansion and on the right side the gas undergoes adiabatic

compression. Thus we have for initial and final state of gas on left side

.....(i)

Similarly for gas in right side, we have

.....(ii)

From eq. (i) and (ii)

⇒

Now from equation (i)

11. Ans. B.

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Given that the ratio of intensities two coherent source is,

Loudness,

20 log 3

12. Ans. A.

After reflection from fixed end, a phase change of π occurs, and the pulse will be inverted

as it travels in the opposite direction. After refection from free end, no phase change

occurs and it just travels in the reverse direction.

Incident pulse

After one reflection

After another reflection.

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13. Ans. C.

The shear is experienced along the surface area of the punch. The surface of the punch

is cylindrical with the diameter of 1 cm and a height of 0.3 cm which is the thickness of

the sheet.

Therefore force needed to oppose the shear force is = force needed to punch the hole in

the steel sheet

14. Ans. C.

If a stone is dropped from height h

then …(i)

If a stone is thrown upward with velocity u then

…(ii)

If a stone is thrown downward with velocity u then

…(iii)

From (i), (ii) and (iii) we get

…(iv)

…(v)

Dividing (iv) and (v) we get

or

By solving, we get

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15. Ans. B.

Let the final temperature is T

Heat added = heat added to Aluminium + heat added to water.

Power × time = mAl SAl ΔT +mw Sw ΔT

100 × 60 × 4 = 100 × 0.2 × (T + 20 ) + 200 × 20 × 0.50 + 200 × 80 + 200 x 0.5 x T

Solving for T

T = 25.5°C

SECTION |B|

CHEMISTRY

1. Ans. C.

The carbon can reduce the metal at the temperature above which the lines cross.

2. Ans. B.

Atomic weight of hydrogen is 1.008 amu.

weight of 1 mole of proton = 1.008 g.

weight of 1 proton =

= 0.167 × 10–26 kg.

We have,

Kinetic energy =

= 5.26 × 10–18 J

=

= 32.8 eV.

As the magnitude of charge of a proton is the same as that an electron, the potential

required is equal in magnitude to the number of eV, i.e., 32.8 volts.

3. Ans. B.

Precipitation occurs when the ionic product exceeds Ksp value. When equal volumes of

two solutions are mixed, the concentration of each is reduced to half because total

volume becomes 2V. Also,

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Concentration= moles/2V

Therefore,

In first case,

Ionic product, I.P. =

As, I.P. < Ksp

No precipitation occurs.

In second case,

I.P. =

As, I.P. > Ksp

Precipitation occurs.

In third case,

I.P. =

As, I.P. < Ksp

No precipitation occurs.

In fourth case,

I.P. =

As, I.P. < Ksp

No precipitation occurs.

4. Ans. C.

A.

B.

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C.

D. MgO ⇒ Ionic; SO2 : covalent

Hybridization of S : sp2,

Planar

pp-dp bonds = 1

5. Ans. A.

The oxidation number of Cr does not change in the reaction. In K2Cr2O7, the central metal

Cr is in +6 oxidation state. The reaction is given below:

K2Cr2O7 + H2O2 + H2SO4 CrO5 + K2SO4 + H2O

The product CrO5 is :

From the figure we can see that there are two peroxy linkages and one double bonded

oxygen. Hence the total oxidation number will be: 1+1+1+1+2=6 (Here 1 is for each

oxygen of the peroxy linkage and 2 is for the double bonded oxygen).

Hence, the correct option is A.

6. Ans. D.

7. Ans. A.

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=252

n = 6

Molecular formula = XeF6

8. Ans. C.

9. Ans. A.

So, the value of N will be 2 + 1 + 2 + 1 = 6.

Since enantiomers have nearly same physical properties, II and III as well as IV an V can’t

be separated, hence the number of isomers (M) will be

1 + 1 + 1 + 1 = 4.

10. Ans. C.

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11. Ans. C.

Fe2+ + 2e → Fe, E ° = –0.439V

To Find,

Fe3+ + e → Fe2+

Fe3+ +3e → Fe, Eo = -0.036V ......eq 1

Fe → Fe2+ + 2e, Eo = 0.439V ..... eq 2

Adding eq 1 and 2

Fe3+ + e → Fe2+ Eo = ?

ΔG = ΔG1 + ΔG2

-nFEo = -nFE1 -nFE2

-1×E = -3×-0.036 - 2×0.439

-E = -0.77V

E= 0.77V

Hence, option C is correct.

12. Ans. D.

= 3.285 Å

= 3.139 Å …..(2)

= 2.981

= 3.293 Å …..(4)

(2) – (4)

= – 0.154 Å

– 0.154 = 3.285

= 3.439 Å

13. Ans. B.

It is known as Schotten Baumann reaction.

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14. Ans. C.

15. Ans. C.

From the fig. [A]left = [B]formed = n × [A]decayed

Option(C) is correct answer

SECTION |C|

MATHEMATICS

1. Ans. B.

Let n be the number of sides.

∴nC2 – n = 44

n2 – 3n – 88 = 0

n = 11

2. Ans. D.

(1+2x+3x2+………)–3/2

=((1–x)–2)–3/2

= (1 − x)3 = 1 − 3x + 3x2 − x3

∴coefficient of x5 = 0.

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3. Ans. A.

put

4. Ans. A.

⇒

D = (a + b)2 + 4ab (ab – 1)

for all a, b.

Hence the roots are always real.

Also for the roots to be real and equal D = 0.

∴ ⇒

⇒

⇒ a = b = 0

5. Ans. C.

The set contains no elements, since gives

which is not true since , i.e, the given set is the empty set.

6. Ans. C.

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∴

7. Ans. B.

The given determinant is:

[Taking a, b, c from R1, R2 and R3 respectively]

= (abc)

[Performing R1 → R1 + R2 + R3 and taking (1/a+1/b+1/c+1) common]

= (abc)( )

[C1 → (C1 − C3) and C2 → (C2 − C3)]

= (abc)( )

[Expanding by 1st row]

= (abc)(

= (abc) (0 + 1)

= abc

8. Ans. A.

Take the parts as a,b,c,d respectively

According to the question,

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Also,

Also,

Find the value of c as:

Therefore,

9. Ans. D.

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10. Ans. D.

Let

Integrating both sides we get

Putting value of u we get

Given y(1)=3

Thus y=3 at x=1

Putting value of x and y

11. Ans. A.

.

Put then

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.

12. Ans. D.

y = 3x – 5

∴

∴ Required area ABCD

13. Ans. D.

Let

Required vector perpendicular to and perpendicular to the plane

of and

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= -7i+8j-k

Required vector

Hence, option (D) is correct.

14. Ans. C.

Distance from the point to the line meets mid-point of the other side of triangle.

In a triangle the angle is 6 0ۣ°

15. Ans. A.

D < 0

(a+4)2+5a-64<0

⇒ -16<a<3

But a ∈ [- 5 ,30]∴ a contains 8 values

∴ Probability = 8/36 =2/9

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SECTION |D|

APTITUDE

1. Ans. D.

Let Ram’s and his father’s present ages be x and y.

Then, according to the given statement

x + y = 7/6 (x – 5 + y – 5);

x + y = 70

2. Ans. B.

3. Ans. D.

4. Ans. C.

5. Ans. C.

The series goes like: , , ,

= 1024

=16 = 256

=8 = 64

=4 = 16

= 2 = 4

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