**Physics**

**Section-A**

1. Zener breakdown occurs in a p-n junction having p and n both:

(a) lightly doped and have wide depletion layer.

(b) heavily doped and have narrow depletion layer.

(c) heavily doped and have wide depletion layer.

(d) lightly doped and have narrow depletion layer.

2. According to Bohr atom model, in which of the following transitions will the frequency be maximum?

(a) n = 2 to n = 1

(b) n = 4 to n = 3

(c) n = 5 to n = 4

(d) n = 3 to n = 2

3. An X-ray tube is operated at 1.24 million volt. The shortest wavelength of the produced photon will be:

(a) 10^{−}^{2} nm

(b) 10^{−}^{3} nm

(c) 10^{−}^{4} nm

(d) 10^{−}^{1} nm

4. On the basis of kinetic theory of gases, the gas exerts pressure because its molecules:

(a) suffer change in momentum when impinge on the walls of container.

(b) continuously stick to the walls of container.

(c) continuously lose their energy till it reaches wall.

(d) are attracted by the walls of container.

5. A circular hole of radius (a/2) is cut out of a circular disc of radius ‘a’ shown in figure. The centroid of the remaining circular portion with respect to point ‘O’ will be:

(a)

(b)

(c)

(d)

6. Given below are two statements:

Statement I: PN junction diodes can be used to function as transistor, simply by connecting two diodes, back to back, which acts as the base terminal.

Statement II: In the study of transistor, the amplification factor β indicates ratio of the collector current to the base current.

In the light of the above statements, choose the correct answer from the options given below.

(a) Statement I is false but Statement II is true.

(b) Both Statement I and Statement II are true.

(c) Statement I is true but Statement II is false.

(d) Both Statement I and Statement II are false.

7. When a particle executes SHM, the nature of graphical representation of velocity as a function of displacement is:

(a) elliptical

(b) parabolic

(c) straight line

(d) circular

8. Match List – I with List – II.

**List-I**

(a) Source of microwave frequency

(b) Source of infrared frequency

(c) Source of Gamma Rays

(d) Source of X-rays

**List-II**

(i) Radioactive decay of nucleus

(ii) Magnetron

(iii) Inner shell electrons

(iv) Vibration of atoms and molecules

(v) LASER

(vi) RC circuit

Choose the correct answer from the options given below:

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

(b) (a)-(vi),(b)-(iv),(c)-(i),(d)-(v)

(c) (a)-(ii),(b)-(iv),(c)-(vi),(d)-(iii)

(d) (a)-(vi),(b)-(v),(c)-(i),(d)-(iv)

9. The logic circuit shown below is equivalent to :

10. If the source of light used in a Young’s double slit experiment is changed from red to violet:

(a) the fringes will become brighter.

(b) consecutive fringe lines will come closer.

(c) the central bright fringe will become a dark fringe.

(d) the intensity of minima will increase.

11. A body weighs 49 N on a spring balance at the north pole. What will be its weight recorded on the same weighing machine, if it is shifted to the equator?

[Use and radius of earth, R = 6400 km.]

(a) 49 N

(b) 49.83 N

(c) 49.17 N

(d) 48.83 N

12. If one mole of an ideal gas at (P_{1}, V_{1}) is allowed to expand reversibly and isothermally (A to B) its pressure is reduced to one-half of the original pressure (see figure). This is followed by a constant volume cooling till its pressure is reduced to one-fourth of the initial value (B→C). Then it is restored to its initial state by a reversible adiabatic compression (C to A). The net work done by the gas is equal to:

(a) 0

(b)

(c)

(d) RTln2

13. The period of oscillation of a simple pendulum is Measured value of ‘L’ is 1.0 m from meter-scale having a minimum division of 1 mm and time of one complete oscillation is 1.95 s measured from stopwatch of 0.01 s resolution. The percentage error in the determination of ‘g’ will be:

(a) 1.33%

(b) 1.30%

(c) 1.13%

(d) 1.03%

14. In the given figure, a body of mass M is held between two massless springs, on a smooth inclined plane. The free ends of the springs are attached to firm supports. If each spring has spring constant k, the frequency of oscillation of given body is:

(a)

(b)

(c)

(d)

15. Figure shows a circuit that contains four identical resistors with resistance R = 2.0 Ω. Two identical inductors with inductance L = 2.0 mH and an ideal battery with emf E = 9.V. The current ‘i’ just after the switch ‘s’ is closed will be:

(a) 9 A

(b) 3.0 A

(c) 2.25 A

(d) 3.37 A

16. The de Broglie wavelength of a proton and α-particle are equal. The ratio of their velocities is:

(a) 4 : 2

(b) 4 : 1

(c) 1 : 4

(d) 4 : 3

17. Two electrons each are fixed at a distance ‘2d’. A third charge proton placed at the midpoint is displaced slightly by a distance x (x<<d) perpendicular to the line joining the two fixed charges. Proton will execute simple harmonic motion having angular frequency:

(m = mass o charged particle)

(a)

(b)

(c)

(d)

18. A soft ferromagnetic material is placed in an external magnetic field. The magnetic domains:

(a) decrease in size and changes orientation.

(b) may increase or decrease in size and change its orientation.

(c) increase in size but no change in orientation.

(d) have no relation with external magnetic field.

19. Which of the following equations represents a travelling wave?

(a)

(b) y = A sin(15x – 2t)

(c) y = Ae^{x} cos (ωt – θ)

(d) y = A sin x cos ωt

20. A particle is projected with velocity v0 along x-axis. A damping force is acting on the particle which is proportional to the square of the distance from the origin i.e. ma = −αx^{2}. The distance at which the particle stops:

(a)

(b)

(c)

(d)

**Section-B**

21. A uniform metallic wire is elongated by 0.04 m when subjected to a linear force F. The elongation, if its length and diameter is doubled and subjected to the same force will be ________ cm.

22. A cylindrical wire of radius 0.5 mm and conductivity 5 × 10^{7} S/m is subjected to an electric field of 10 mV/m. The expected value of current in the wire will be x^{3}π mA. The value of x is ____.

23. Two cars are approaching each other at an equal speed of 7.2 km/hr. When they see each other, both blow horns having frequency of 676 Hz. The beat frequency heard by each driver will be ________ Hz. [Velocity of sound in air is 340 m/s.]

24. A uniform thin bar of mass 6 kg and length 2.4 meter is bent to make an equilateral hexagon. The moment of inertia about an axis passing through the centre of mass and perpendicular to the plane of hexagon is ______×10^{−}^{1} kg m^{2}.

25. A point charge of +12 μC is at a distance 6 cm vertically above the centre of a square of side 12 cm as shown in figure. The magnitude of the electric flux through the square will be _____ ×10^{3} Nm^{2}/C.

26. Two solids A and B of mass 1 kg and 2 kg respectively are moving with equal linear momentum. The ratio of their kinetic energies (K.E.)_{A} : (K.E.)_{B} will be A/1. So the value of A will be ________.

27. The root mean square speed of molecules of a given mass of a gas at 270C and 1 atmosphere pressure is 200 ms^{−}^{1}. The root mean square speed of molecules of the gas at 127°C and 2 atmosphere pressure is The value of x will be __________.

28. A series LCR circuit is designed to resonate at an angular frequency ω_{0} = 10^{5}rad/s. The circuit draws 16W power from 120 V source at resonance. The value of resistance ‘R’ in the circuit is _______ Ω.

29. An electromagnetic wave of frequency 3 GHz enters a dielectric medium of relative electric permittivity 2.25 from vacuum. The wavelength of this wave in that medium will be _______ ×10^{−}^{2}

30. A signal of 0.1 kW is transmitted in a cable. The attenuation of cable is −5 dB per km and cable length is 20 km. The power received at receiver is 10^{−}^{x} The value of x is ______.

**Chemistry**

**Section-A**

1. The correct order of the following compounds showing increasing tendency towards nucleophilic substitution reaction is:

(a) (iv) < (i) < (iii) < (ii)

(b) (iv) < (i) < (ii) < (iii)

(c) (i) < (ii) < (iii) < (iv)

(d) (iv) < (iii) < (ii) < (i)

2. Match List-I with List-II

List-I List-II

(Metal) (Ores)

(a) Aluminium (i) Siderite

(b) Iron (ii) Calamine

(c) Copper (iii) Kaolinite

(d) Zinc (iv) Malachite

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

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

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

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

3. Match List-I with List-II

List-I List-II

(Salt) (Flame Colour wavelength)

(a) LiCl (i) 455.5 m

(b) NaCl (ii) 970.8 nm

(c) RbCl (iii) 780.0 nm

(d) CsCl (iv) 589.2 nm

Choose the correct Answer from the options given below:

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

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

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

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

4. Given below are two statements: one is labelled as Assertion A and the other is labelled as Reason R.

Assertion A: Hydrogen is the most abundant element in the Universe, but it is not the most abundant gas in the troposphere.

Reason R: Hydrogen is the lightest element.

In the light of the above statements, choose the correct Answer from the given below

(1) A is false but R is true

(2) Both A and R are true and R is the correct explanation of A

(3) A is true but R is false

(4) Both A and R are true but R is NOT the correct explanation of A

(a) A is false but R is true

(b) Both A and R are true and R is the correct explanation of A

(c) A is true but R is false

(d) Both A and R are true but R is NOT the correct explanation of A

5.** Statement-I:** The parameter “Biochemical oxygen demand” as an important criteria for survival of aquatic life.

**Statement-II : **The optimum “Biochemical oxygen demand” is 6.5.

(a) Both Statement I and Statement II are false

(b) Statement I is false but Statement II is true

(c) Statement I is true but Statement II is false

(d) Both Statement I and Statement II are true

6. Which one of the following carbonyl compounds cannot be prepared by addition of water on an alkyne in the presence of HgSO_{4} and H_{2}SO_{4}?

7. Which one of the following compounds is non-aromatic?

8. The incorrect statement among the following is:

(a) VOSO_{4} is a reducing agent

(b) Red color of ruby is due to the presence of CO^{3+}

(c) Cr_{2}O_{3} is an amphoteric oxide

(d) RuO_{4} is an oxidizing agent

9. According to Bohr’s atomic theory:

(A) Kinetic energy of electron is ∝ Z^{2}/n^{2}

(B) The product of velocity (v) of electron and principal quantum number (n). ‘v_{n}’ ∝ z^{2}

(C) Frequency of revolution of electron in an orbit is ∝ Z^{3}/ n^{3}

(D) Coulombic force of attraction on the electron is ∝ Z^{3}/n^{4}

Choose the most appropriate Answer from the options given below

(a) (C) Only

(b) (A) and (D) only

(c) (A) only

(d) (A), (C) and (D) only

10. Match List-I with List-I

**List-I List-II**

(a) Valium (iv) Tranquilizer

(b) Morphine (iii) Analgesic

(c) Norethindrone (i) Antifertility drug

(d) Vitamin B12 (ii) Pernicious anemia

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

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

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

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

11. The Correct set from the following in which both pairs are in correct order of melting point is

(a) LiF > LiCl ; NaCl > MgO

(b) LiF > LiCl ; MgO > NaCl

(c) LiCl > LiF ; NaCl > MgO

(d) LiCl > LiF ; MgO > NaCl

12. The calculated magnetic moments (spin only value) for species [FeCl_{4}]^{2}^{−}, [Co(C_{2}O_{4})_{3}]^{3}^{−} and MnO_{4}^{2}^{−} respectively are:

(a) 5.92, 4.90 and 0 BM

(b) 5.82, 0 and 0 BM

(c) 4.90, 0 and 1.73 BM

(d) 4.90, 0 and 2.83 BM

13. Which of the following reagent is suitable for the preparation of the product in the following reaction?

(a) Red P + Cl_{2}

(b) NH^{2}^{−}NH_{2}/ C_{2}H_{5}O^{−}Na^{+}

(c) Ni/H_{2}

(d) NaBH_{4}

14. The diazonium salt of which of the following compounds will form a coloured dye on reaction with β-Naphthol in NaOH?

15. What is the correct sequence of reagents used for converting nitrobenzene into m- dibromobenzene?

16. The correct shape and I-I-I bond angles respectively in I_{3}^{−} ion are:

(a) Trigonal planar; 120º

(b) Distorted trigonal planar; 135º and 90º

(c) Linear; 180º

(d) T-shaped; 180º and 90º

17. What is the correct order of the following elements with respect to their density?

(a) Cr < Fe < Co < Cu < Zn

(b) Cr < Zn < Co < Cu < Fe

(c) Zn < Cu < Co < Fe < Cr

(d) Zn < Cr < Fe < Co < Cu

18. Match List-I and List-II.

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

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

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

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

19. In polymer Buna-S: ‘S’ stands for

(a) Styrene

(b) Sulphur

(c) Strength

(d) Sulphonation

20. Most suitable salt which can be used for efficient clotting of blood will be:

(a) Mg(HCO_{3})_{2}

(b) FeSO_{4}

(c) NaHCO_{3}

(d) FeCl_{3}

**Section-B**

21. The magnitude of the change in oxidising power of the MnO^{4}^{−}/Mn^{2+} couple is x × 10^{–4} V, if the H+ concentration is decreased from 1M to 10^{–4} M at 25°C. (Assume concentration of MnO^{4–} and Mn^{2+} to be same on change in H^{+} concentration). The value of x is _____. (Rounded off to the nearest integer).

[Given: 230RT/F = 0.059]

22. Among the following allotropic forms of sulphur, the number of allotropic forms, which will show paramagnetism is ______.

(a) α-sulphur (b) β-sulphur (c) S_{2}^{−} form

23. C_{6}H_{6} freezes at 5.5ºC. The temperature at which a solution of 10 g of C_{4}H_{10} in 200 g of C_{6}H_{6} freeze is ________ C. (The molal freezing point depression constant of C_{6}H_{6} is 5.12C/m).

24. The volume occupied by 4.75 g of acetylene gas at 50°C and 740 mmHg pressure is _______L. (Rounded off to the nearest integer)

(Given R = 0.0826 L atm K^{–1} mol^{–1})

25. The solubility product of PbI_{2} is 8.0 × 10^{–9}. The solubility of lead iodide in 0.1 molar solution of lead nitrate is x × 10^{–6} mol/L. The value of x is ________ (Rounded off to the nearest integer)

Given √2 = 1.41

26. The total number of amines among the following which can be synthesized by Gabriel synthesis is _______

27. 1.86 g of aniline completely reacts to form acetanilide. 10% of the product is lost during purification. Amount of acetanilide obtained after purification (in g) is ____× 10^{–2}.

28. The formula of a gaseous hydrocarbon which requires 6 times of its own volume of O_{2} for complete oxidation and produces 4 times its own volume of CO_{2} is C_{x}H_{y}. The value of y is

29. Sucrose hydrolysis in acid solution into glucose and fructose following first order rate law with a half-life of 3.33 h at 25ºC. After 9h, the fraction of sucrose remaining is f. The value of is _________× 10^{–2} (Rounded off to the nearest integer)

[Assume: ln10 = 2.303, ln2 = 0.693]

30. Assuming ideal behavior, the magnitude of log K for the following reaction at 25ºC is x × 10^{–1}. The value of x is __________. (Integer Answer)

3HC ≡ CH(g) ⇌ C_{6}H_{6} (l)

[Given: Δ_{f}G° (HC = CH) = –2.04 × 10^{5}] mol^{–1}; Δ_{f}G°(C_{6}H_{6}) = – 1.24 × 10^{5} J mol^{–1};

R = 8.314 J K^{–1} mol^{–1}]

**Mathematics**

**Section-A**

1. Let a, b ∈ If the mirror image of the point P(a, 6, 9) with respect to the line is (20, b, −a, −9), then |a + b| is equal to:

(a) 86

(b) 88

(c) 84

(d) 90

2. Let f be a twice differentiable function defined on R such that f(0) = 1, f'(0) = 2 and f'(x) ≠ 0 for all x ∈ If for all x ∈ R, then the value of f(1) lies in the interval:

(a) (9, 12)

(b) (6, 9)

(c) (3, 6)

(d) (0, 3)

3. A possible value of is :

(a) 1/2√2

(b) 1/√7

(c) √7 – 1

(d) 2√2 – 1

4. The probability that two randomly selected subsets of the set {1, 2, 3, 4, 5} have exactly two elements in their intersection, is:

(a) 65/2^{7}

(b) 135/2^{9}

(c) 65/2^{8}

(d) 35/2^{7}

5. The vector equation of the plane passing through the intersection of the planes and the point (1, 0, 2) is:

(a)

(b)

(c)

(d)

6. If P is a point on the parabola y = x^{2} + 4 which is closest to the straight line y = 4x − 1, then the co-ordinates of P are :

(a) (–2, 8)

(b) (1, 5)

(c) (3, 13)

(d) (2, 8)

7. Let a, b, c be in arithmetic progression. Let the centroid of the triangle with vertices (a, c), (2, b) and (a, b) be (10/3, 7/3). If α, β are the roots of the equation ax^{2} + bx + 1 = 0, then the value of α^{2} + β^{2} − αβ is:

(a) 71/256

(b) −69/256

(c) 6/9/256

(d) −71/256

8. The value of the integral, where [x] denotes the greatest integer less than or equal to x, is:

(a) −4

(b) −5

(c) −√2 – √3 − 1

(d) −√2 – √3 + 1

9. Let f : R → R be defined as

Let A = {x ∈ R : f is increasing}. Then A is equal to :

(a) (−5, −4) ∪ (4,∞)

(b) (−5, ∞)

(c) (−∞,−5) ∪ (4, ∞)

(d) (−∞,−5) ∪ (−4, ∞)

10. If the curve y = ax^{2} + bx + c,x ∈ R passes through the point (1, 2) and the tangent line to this curve at origin is y = x, then the possible values of a, b, c are:

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

(b) a = −1, b = 1, c = 1

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

(d) a = 1/2, b = 1/2 ,c = 1

11. The negation of the statement ~p ∧ (p ∨ q) is∶

(a) ~ p ∧ q

(b) p ∧ ~ q

(c) ~ p ∨ q

(d) p ∨ ∼ q

12. For the system of linear equations: x − 2y = 1, x − y + kz = −2, ky + 4z = 6,k ∈ R

Consider the following statements:

(A) The system has unique solution if k ≠ 2,k ≠ −2.

(B) The system has unique solution if k = −2.

(C) The system has unique solution if k = 2.

(D) The system has no-solution if k = 2.

(E) The system has infinite number of solutions if k ≠ −2.

Which of the following statements are correct?

(a) (B) and (E) only

(b) (C) and (D) only

(c) (A) and (D) only

(d) (A) and (E) only

13. For which of the following curves, the line x + √3y = 2√3 is the tangent at the point (3√3/2, 1/2)?

(a) x^{2} + 9y^{2} = 9

(b) 2x^{2} − 18y^{2} = 9

(c)

(d) x^{2} + y^{2} = 7

14. The angle of elevation of a jet plane from a point A on the ground is 600. After a flight of 20 seconds at the speed of 432 km/hour, the angle of elevation changes to 300. If the jet plane is flying at a constant height, then its height is:

(a) 1200√3 m

(b) 1800√3 m

(c) 3600√3 m

(d) 2400√3 m

15. For the statements p and q, consider the following compound statements:

(a) (~ q ∧ (p → q)) → ~p

(b) ((p ∨ q)) ∧ ~ p) → q

Then which of the following statements is correct?

(a) (a) is a tautology but not (b)

(b) (a) and (b) both are not tautologies

(c) (a) and (b) both are tautologies

(d) (b) is a tautology but not (a)

16. Let A and B be 3 × 3 real matrices such that A is symmetric matrix and B is skew-symmetric matrix. Then the system of linear equations (A^{2}B^{2} − B^{2}A^{2})X = O, where X is a 3 × 1 column matrix of unknown variables and O is a 3 × 1 null matrix, has:

(a) a unique solution

(b) exactly two solutions

(c) infinitely many solutions

(d) no solution

17. If n ≥ 2 is a positive integer, then the sum of the series ^{n+1}C_{2} + 2(^{2}C_{2} + ^{3}C_{2} + ^{4}C_{2} + …. + ^{n}C_{2}) is

(a)

(b)

(c)

(d)

18. If a curve y = f(x) passes through the point (1, 2) and satisfies then for what value of b,

(a) 5

(b) 62/5

(c) 31/5

(d) 10

19. The area of the region: R{(x, y): 5x^{2} ≤ y ≤ 2x^{2} + 9} is:

(a) 9√3 square units

(b) 12√3 square units

(c) 11√3 square units

(d) 6√3 square units

20. Let f(x) be a differentiable function defined on [0, 2] such that f’(x) =f'(2 − x) for all x ∈ (0, 2), f(0) = 1 and f(2) = e^{2}. Then the value of is:

(a) 1 + e^{2}

(b) 1 – e^{2}

(c) 2(1 – e^{2})

(d) 2(1 + e^{2})

**Section-B**

21. The number of the real roots of the equation (x + 1)^{2} + |x – 5| = 27/4 is _______.

22. The students S_{1}, S_{2}, … S_{10} are to be divided into 3 groups A, B, and C such that each group has at least one student and the group C has at most 3 students. Then the total number of possibilities of forming such groups is _____.

23. If a + α = 1, b + β = 2 and then the value of the expression is________.

24. If the variance of 10 natural numbers 1, 1, 1, …,1, k is less than 10, then the maximum possible value of k is ___________.

25. Let λ be an integer. If the shortest distance between the lines x − λ = 2y − 1 = −2z and x = y + 2λ = z − λ is √7/2√2, then the value of |λ| is _________.

26. Let and n = [|k|] be the greatest integral part of |k|. Then is equal to ________.

27. Let a point P be such that its distance from the point (5, 0) is thrice the distance of P from the point (−5, 0). If the locus of the point P is a circle of radius r, then 4r^{2} is equal to _________.

28. For integers n and r, let

The maximum value of k for which the sum

exists, is equal to_________.

29. The sum of first four terms of a geometric progression (G.P.) is 65/12 and the sum of their respective reciprocals is 65/18. If the product of first three terms of the G.P. is 1, and the third term is α then 2α is________

30. If the area of the triangle formed by the positive x-axis, the normal and the tangent to the circle (x − 2)^{2} + (y − 3)^{2} = 25 at the point (5, 7) is A, then 24A is equal to ________.

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