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SECTION - I
Straight Objective Type
This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
Note: Questions with (*) mark are from syllabus of class XI.
1. Consider the two curves xy 
(A) C1 and C2 touch each other only at one point
(B) C1 and C2 touch each other exactly at two points
(C) C1 and C2 intersect (but do not touch) at exactly two points
(D) C1 and C2 neither intersect nor touch each other
Ans. 2
Sol.: Solving C1 and C2 simultaneously we get x2 - 2x + 1 = 0  (x- 1)2 = 0
At x = 1, y =  2.
Hence C1 and C2 touch each other exactly at two points (1, 2) and (1, -2).
2. If 0 < x < 1 , then 
(A) 
(B) x
(C) 
(D) 
Ans . 3
3. The edges of a parallelopiped are of unit length and are parallel to non-coplanar unit vectors  Then, the volume of the parallelopiped is
(A) 
(B) 
(C) 
(D) 
Ans .1
4. Let a and b be non-zero real numbers. Then the equation (ax2 + by2 + c)(x2 - 5xy + 6y2) represents
(A) four straight lines, when c = 0 and a, b are of the same sign
(B) two straight lines and a circle, when a = b, and c is of sign opposite to that of a
(C) two straight lines and a hyperbola, when a and b are of the same sign and c is of sign opposite to that of a
(D) a circle and an ellipse, when a and b are of the same sign and c is of sign opposite to that of a
Ans . 2
5. Let and n are integers, m  0 , n > 0 and let p be the left hand derivative of
(A) n = 1 , m = 1
(B) n = 1 , m = -1
(C) n = 2 , m = 2
(D) n > 2 , m = n
Ans. 3
6. The total number of local maxima and local minima of the function 
(A) 0
(B) 1
(C) 2
(D) 3
Ans . 3
Obliviously, x = -1 and x = 0 are point of local maxima and point of local minima respectively.
SECTION - II
Multiple Correct Answers Type
This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE is/ are correct.
7. A straight line through the vertex P of a triangle PQR intersects the side QR at the point S and the circumcircle of the triangle PQR at the point T. If S is not the centre of the circumcircle, then
(A) 
(B) 
(C) 
(D) 
Ans .2,4
Since PS= ST and QS = SR can't occur simultaneously, therefore equality in (iii) is not possible.
8. Let P(x1, y1) and Q(x2, y2) , y1< 0 , y2< 0 be the end points of the latus rectum of the ellipse x2 + 4y2 = 4 . The equations of parabolas with latus rectum PQ are
(A) 
(B) 
(C) 
(D) 
Ans .2,3
9. 
(A) 
(B) 
(C) 
(D) 
Ans. 1,4
10. Let f(x) be a non-constant twice differentiable function defined on  Then,
(A) f ''(x) vanishes at least twice on [0, 1]
(B) 
(C) 
(D) 
Ans .
SECTION - III
Reasoning Type
This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
11. Let f and g be real valued functions defined on interval (-1,1) such that g''(x) is continuous, g(0) 0 , g'(0) ,
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
(C) STATEMENT-1 is True, STATEMENT-2 is False.
(D) STATEMENT-1 is False, STATEMENT-2 is True.
Ans.1
12. Consider three planes  intersection of the planes P2 and P3 , P3and P1, and P1 and P2 , respectively.
STATEMENT-1: At least two of the lines L1 , L2 and L3 are non -parallel.
and
STATEMENT-2: The three planes do not have a common point.
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
(C) STATEMENT-1 is True, STATEMENT-2 is False.
(D) STATEMENT-1 is False, STATEMENT-2 is True.
Ans . 4
Line L3 is intersection of planes P1 and P2, then direction cosine of 
13. Consider the system of equations 
STATEMENT-1: The system of equations has no solution for k 3.
and
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
(C) STATEMENT-1 is True, STATEMENT-2 is False.
(D) STATEMENT-1 is False, STATEMENT-2 is True.
Ans. 1
Now the system of equations has infinite solutions or no solution depending on  x,y,z If at least one of the x,y,z is non-zero, then it has no solution otherwise infinite solutions.
Thus system of equations has no solution if k 3.
14.
and
STATEMENT-2: The probability that the system of equations has a solution is 1.
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
(C) STATEMENT-1 is True, STATEMENT-2 is False.
(D) STATEMENT-1 is False, STATEMENT-2 is True.
Ans . 2
SECTION - IV
Linked Comprehension Type
This section contains 3 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
Paragraph for Question Nos. 15 to 17
A circle C of radius 1 is inscribed in an equilateral triangle PQR. The points of contact of C with the sides PQ, QR, RP are D, E, F respectively. The line PQ is given by the equation  . Further, it is given that the origin and the centre of C are on the same side of the line PQ.
15. The equation of circle C is
(A) 
(B) 
(C) 
(D) 
Ans. 4
Equation of line CD in parametric form is
16. Points E and F are given by
(A) 
(B) 
(C) 
(D) 
Ans . 1
17. Equations of the sides QR, RP are
(A) 
(B) 
(C) 
(D) 
Ans . 4
Equation of line PR which is parallel to DE and passes through F is 
Similarly, equation of line QR which is parallel to DF and passes through the point E is 
Paragraph for Question Nos. 18 to 20
Consider the functions defined implicitly by the equation y3 - 3y + x = 0 on various intervals in the real line. If  the equation implicitly defines a unique real valued differentiable function  the equation implicitly defines a unique real valued differentiable function y = g(x) satisfying g(0) = 0
18 . If
(A) 
(B) 
(C) 
(D) 
Ans . 2
19. The area of the region bounded by the curve y = f(x) , the x-axis, and lines x = a and x = b , where 
(A) 
(B) 
(C) 
(D) 
Ans . 1
20. 
(A) 2g (-1)
(B) 0
(C) -2g (1)
(D) 2g (1)
Ans . 4
Paragraph for Question Nos. 21 to 23
Let A, B, C be three sets of complex numbers as defined below:
21. The number of elements in the set A BC is
(A) 0
(B) 1
(C) 2
(D) 
Ans . 2
Set A represents all the points in argand plane for which Im(z)  1.
Set B represents all the points on the circle and set C represents all the points on the straight line as shown in the figure.
Clearly, there is only one point 'z' which lies in ABC.
22. Let z be any point in 
(A) 25 and 29
(B) 30 and 34
(C) 35 and 39
(D) 40 and 44
Ans . 3
Since AB is the diameter of circle. Hence 
23. Let z be any point in ABC and let w be any point satisfying 
(A) -6 and 3
(B) -3 and 6
(C) -6 and 6
(D) -3 and 9
Ans . 2,3,4
PHYSICS
SECTION - I
Straight Objective Type
This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
24. Students I, II and III perform an experiment for measuring the acceleration due to gravity (g) using a simple pendulum. They use different lengths of the pendulum and / or record time for different number of oscillations. The observations are shown in the table.
Least count for length = 0.1 cm
Least count for time = 0.1 s
| Student |
Length of the pendulum (cm) |
Number of oscillations (n) |
Total time for (n) oscillations (s) |
Time period (s) |
| I |
64.0 |
8 |
128.0 |
16.0 |
| II |
64.0 |
4 |
64.0 |
16.0 |
| III |
20.0 |
4 |
36.0 |
9.0 |
If EI, EII and EIII are the percentage errors in g, i.e. 
for students I, II and III, respectively,
(A) EI = 0
(B) EI is minimum
(C) EI = EII
(D) EII is maximum
Ans2
25. Figure shows three resistor configurations R1, R2 and R3 connected to 3V battery. If the power dissipated by the configuration R1, R2 and R3 is P1, P2 and P3, respectively, then
(A) P1 > P2 > P3
(B) P1 > P3 > P2
(C) P2 > P1 > P3
(D) P3 > P2 > P1
Ans . 3
26. Which one of the following statements is WRONG in the context of X-rays generated from a X-ray tube?
(A) Wavelength of characteristic X-rays decreases when the atomic number of the target increases
(B) Cut-off wavelength of the continuous X-rays depends on the atomic number of the target
(C) Intensity of the characteristic X-rays depends on the electric power given to the X-ray tube
(D) Cut-off wavelength of the continuous X-rays depends on the energy of the electrons in the X-ray tube
Ans . 2
27. Two beams of red and violet colours are made to pass separately through a prism (angle of the prism is 60o). In the position of minimum deviation, the angle of refraction will be
(A) 30o for both the colours
(B) greater for the violet colour
(C) greater for the red colour
(D) equal but not 30o for both the colours
Ans . 1
In case of minimum deviation, r = A /2 r = 30o
28. An ideal gas is expanding such that PT2 = constant. The coefficient of volume expansion of the gas is
(A) 
(B) 
(C) 
(D) 
Ans .3
29. A spherically symmetric gravitational system of particles has a mass density 
Where  0 is a constant. A test mass can undergo circular motion under the influence of the gravitational field of particles. Its speed V as a function of distance r(0 < r < ) from the centre of the system is represented by
(A) 
(B) 
(C) 
(D) 
Ans . 3
SECTION - II
Multiple Correct Answers Type
This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE is/ are correct.
30. Two balls, having linear momenta  , undergo a collision in free space. There is no external force acting on the balls. Let 
be their final momenta. The following option(s) is (are) NOT ALLOWED for any non-zero value of 
(A) 
(B) 
(C) 
(D) 
Ans . 1,4
Since initial linear momentum of two balls system is zero, therefore final linear momentum of the system must also be zero. Final linear momentum of the system can not be zero in case of options (A) and (D).
31. Assume that the nuclear binding energy per nucleon (B/A) versus mass number (A) is as shown in the figure. Use this plot to choose the correct choice(s) given below.
(A) Fusion of two nuclei with mass numbers lying in the range of 1 < A < 50 will release energy
(B) Fusion of two nuclei with mass numbers lying in the range of 51 < A < 100 will release energy
(C) Fission of a nucleus lying in the mass range of 100 < A < 200 will release energy when broken into equal fragments
(D) Fission of a nucleus lying in the mass range of 200 < A < 260 will release energy when broken into equal fragments
Ans . 2,4
When binding energy of product is greater than the binding energy of reactants, the energy will be released.
32. A particle of mass m and charge q, moving with velocity V enters Region II normal to the boundary as shown in the figure. Region II has a uniform magnetic field B perpendicular to the plane of the paper. The length of the Region II is  . Choose the correct choice(s).
(A) The particle enters Region III only if its velocity 
(B) The particle enters Region III only if its velocity 
(C) Path length of the particle in Region II is maximum when velocity 
(D) Time spent in Region II is same for any velocity V as long as the particle returns to Region I
Ans . 1,3,4
33. In a Young's double slit experiment, the separation between the two slits is d and the wavelength of the light is  . The intensity of light falling on slit 1 is four times the intensity of light falling on slit 2. Choose the correct choice(s).
(A) If d = , the screen will contain only one maximum
(B) If < d < 2, at least one more maximum (besides the central maximum) will be observed on the screen
(C) If the intensity of light falling on slit 1 is reduced so that it becomes equal to that of slit 2, the intensities of the observed dark and bright fringes will increase. (D) If the intensity of light falling on slit 2 is increased so that it becomes equal to that of slit 1, the intensities of the observed dark and bright fringes will increase
Ans . 1,2
SECTION - III
Reasoning Type
This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
34. STATEMENT-1 In a Meter Bridge experiment, null point for an unknown resistance is measured. Now, the unknown resistance is put inside an enclosure maintained at a higher temperature. The null point can be obtained at the same point as before by decreasing the value of the standard resistance.
and
STATEMENT-2 Resistance of a metal increases with increase in temperature.
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
(C) STATEMENT-1 is True, STATEMENT-2 is False.
(D) STATEMENT-1 is False, STATEMENT-2 is True.
Ans . 4
 
35. STATEMENT-1 An astronaut in an orbiting space station above the Earth experiences weightlessness.
and
STATEMENT-2 An object moving around the Earth under the influence of Earth's gravitational force is in a state of 'free-fall'
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
(C) STATEMENT-1 is True, STATEMENT-2 is False.
(D) STATEMENT-1 is False, STATEMENT-2 is True.
Ans . 1
36. STATEMENT-1 Two cylinders, one hollow (metal) and the other solid (wood) with the same mass and identical dimensions are simultaneously allowed to roll without slipping down an inclined plane from the same height. The hollow cylinder will reach the bottom of the inclined plane first.
and
STATEMENT-2 By the principle of conservation of energy, the total kinetic energies of both the cylinders are identical when they reach the bottom of the incline.
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
(C) STATEMENT-1 is True, STATEMENT-2 is False.
(D) STATEMENT-1 is False, STATEMENT-2 is True.
Ans . 4
37. STATEMENT-1 The stream of water flowing at high speed from a garden hose pipe tends to spread like a fountain when held vertically up, but tends to narrow down when held vertically down.
and
STATEMENT-2 In any steady flow of an incompressible fluid, the volume flow rate of the fluid remains constant.
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
(C) STATEMENT-1 is True, STATEMENT-2 is False.
(D) STATEMENT-1 is False, STATEMENT-2 is True.
Ans . 1
By equation of continuity, Av = constant
SECTION - IV
Linked Comprehension Type
This section contains 3 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
Paragraph for Question Nos. 38 to 40
A small spherical monoatomic ideal gas bubble
 
38. As the bubble moves upwards, besides the buoyancy force the following forces are acting on it
(A) Only the force of gravity
(B) The force due to gravity and the force due to the pressure of the liquid
(C) The force due to gravity, the force due to the pressure of the liquid and the force due to viscosity of the liquid
(D) The force due to gravity and the force due to viscosity of the liquid
Ans .4
39. When the gas bubble is at height y from the bottom, its temperature is
(A) 
(B) 
(C) 
(D) 
Ans . 2
40. The buoyancy force acting on the gas bubble is (Assume R is the universal gas constant)
(A) 
(B) 
(C) 
(D) 
Ans . 2
Paragraph for Question Nos. 41 to 43
In a mixture of H - He+ gas (He+ is singly ionized He atom), H atoms and He+ ions are excited to their respective first excited states. Subsequently, H atoms transfer their total excitation energy to He+ ions (by collisions). Assume that the Bohr model of atom is exactly valid.
41. The quantum number n of the state finally populated in He+ ions is
(A) 2
(B) 3
(C) 4
(D) 5
Ans . 3
Energy transfer by H atom to He+ is 10.2 eV. Subsequently He+ gets excited to n = 4.
42. The wavelength of light emitted in the visible region by He+ ions after collisions with H atoms is
(A) 6.5 × 10-7 m
(B) 5.6 × 10-7 m
(C) 4.8 × 10-7 m
(D) 4.0 × 10-7 m
Ans .3
Only the energy corresponding to transition for n = 4 to n = 3 falls in visible region.
43. The ratio of the kinetic energy of the n = 2 electron for the H atom to that of He+ ion is
(A) 
(B) 
(C) 1
(D) 2
Ans . 1
Paragraph for Question Nos. 44 to 46
A small block of mass M moves on a frictionless surface of an inclined plane, as shown in figure. The angle of the incline suddenly changes from 60o to 30o at point B. The block is initially at rest at A. Assume that collisions between the block and the incline are totally inelastic (g = 10 m/s2)
44. The speed of the block at point B immediately after it strikes the second incline is
(A) 
(B) 
(C) 
(D) 
Ans .2
Let speed of block just before it strikes the second inclined plane be v then,
Speed of block immediately after it strikes the second incline is  (because in perfectly inelastic collision the component of velocity along line of impact becomes zero.)
45. The speed of the block at point C, immediately before it leaves the second incline is
(A) 
(B) 
(C) 
(D) 
Ans .2
46. If collision between the block and the incline is completely elastic, then the vertical (upward) component of the velocity of the block at point B, immediately after it strikes the second incline is
(A) 
(B) 
(C) 0
(D) -
Ans. 3
CHEMISTRY: Paper-I (Code: 0)
SECTION - I
Straight Objective Type
This section contains 6 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
47. Hyperconjugation involves overlap of the following orbitals
(A)  -
(B) - p
(C) p - p
(D)  -
Ans . 2
Hyperconjugation involves overlapping of C-H bonding electrons with p-orbital of unsaturated system, carbocation or carbon free radical.
Correct choice: (B)
48. The major product of the following reaction is
(A) 
(B) 
(C)
(D) 
Ans . 1
The given compound is an alkyl as well as an aryl halide. PhS- being a weak base cannot cause nucleophilic substitution by benzyne mechanism. SNAr mechanism is also ruled out because NO2 group is present at the meta position with respect to fluorine atom. So, the compound will react by SN2 mechanism.
Correct choice: (A)
49. Aqueous solution of Na2S2O3 on reaction with Cl2 gives
(A) Na2S4O6
(B) NaHSO4
(C) NaCl
(D) NaOH
Ans . 2
Cl2 is a stronger oxidising agent than I2. So Na2S2O3 on oxidation gives NaHSO4 rather than sodium tetrathionate.
Correct choice: (B)
50. Native silver metal forms a water soluble complex with a dilute aqueous solution of NaCN in the presence of
(A) nitrogen
(B) oxygen
(C) carbon dioxide
(D) argon
Ans . 2
Sol.: Silver metal is oxidized by oxygen in presence of cyanide ion to Ag+, which then forms a complex with CN -, i.e.[Ag(CN)2] - .
51. Under the same reaction conditions, initial concentration of 1.386 mol dm-3 of a substance becomes half in 40 seconds and 20 seconds through first order and zero order kinetics, respectively. Ratio  of the rate constants for first order (k1) and zero order (k0) of the reactions is
(A) 0.5 mol-1 dm3
(B) 1.0 mol dm-3
(C) 1.5 mol dm-3
(D) 2.0 mol-1 dm3
Ans. 1
Sol.: For Ist order reaction, 
For zero order reaction,
Correct choice: (A)
52. 2.5 mL of  weak monoacidic base (Kb = 1 × 10-12 at 25°C) is titrated with  M HCl in water at 25°C. The concentration of H+ at equivalence point is (Kw = 1 × 10-14 at 25°C)
(A) 3.7 × 10-13 M
(B) 3.2 × 10-7 M
(C) 3.2 × 10-2 M
(D) 2.7 × 10-2 M
Ans .4
BOH + HCl  BCl + H2O
h = 0.27 (We cannot ignore the value of h w.r.t. 1 because it is more than 0.1)
 [H+] = 0.1 × 0.27 = 2.7 × 10-2 M.
Correct choice: (D)
SECTION - II
Multiple Correct Answers Type
This section contains 4 multiple correct answer(s) type questions. Each question has 4 choices (A), (B), (C) and (D), out of which ONE OR MORE is/are correct.
53. The correct statement(s) about the compound given below is(are)
(A) The compound is optically active.
(B) The compound possesses centre of symmetry.
(C) The compound possesses plane of symmetry.
(D) The compound possesses axis of symmetry.
Ans . 1,4
The given compound can be represented in saw-horse projection as
This does not have a plane or a centre of symmetry. So it is optically active. The compound on rotation about C1-C2, keeping C2 fixed and C1 rotated by 180° gives the structure.
The compound possesses 180° axis of symmetry (two fold axis of symmetry) passing through point z perpendicular to the plane of paper.
Correct choice: (A) & (D)
54. The correct statement(s) concerning the structures E, F and G is (are)
(A) E, F and G are resonance structures.
(B) E, F and E, G are tautomers.
(C) F and G are geometrical isomers.
(D) F and G are diastereomers.
Ans . 2,3,4
Sol.: (E) is a keto form and (F) & (G) are its enol forms. (F) and (G) are also geometrical isomers, which also come under the category of diastereomers. Correct choice: (B), (C) & (D)
55. A solution of colourless salt H on boiling with excess NaOH produces a non-flammable gas. The gas evolution ceases after sometime. Upon addition of Zn dust to the same solution, the gas evolution restarts. The colourless salt(s) H is (are)
(A) NH4NO3
(B) NH4NO2
(C) NH4Cl
(D) (NH4)2SO4
Ans . 1,2
Sol.: The colourless salt (H) must be an ammonium salt because on boiling with excess of NaOH it produces NH3 (non-flammable) gas. To this solution, when Zn dust is added, only nitrates and nitrites will liberate NH3 again (Zn acts as a reducing agent).
Correct choice: (A) & (B)
56. A gas described by van der Waals equation
(A) behaves similar to an ideal gas in the limit of large molar volumes.
(B) behaves similar to an ideal gas in the limit of large pressures.
(C) is characterized by van der Waals coefficients that are dependent on the identity of the gas but are independent of the temperature.
(D) has the pressure that is lower than the pressure exerted by the same gas behaving ideally.
Ans . 1,2,3
Sol.: A real gas following van der Waals equation behaves like an ideal gas at low pressures (or large molar volumes). Van der Waals coefficients ('a' and 'b') are characteristic of a gas and are independent of the temperature. The pressure exerted by the real gas is smaller than the pressure exerted by the gas under ideal conditions as some pressure is lost by the real gas due to inter molecular attractions.
Correct choice: (A), (C) & (D).
SECTION - III
Reasoning Type
This section contains 4 reasoning type questions. Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
57. STATEMENT-1: Bromobenzene upon reaction with Br2/Fe gives 1,4-dibromobenzene as the major product.
and
STATEMENT-2: In Bromobenzene, the inductive effect of the bromo group is more dominant than the mesomeric effect in directing the incoming electrophile. (A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
(C) STATEMENT-1 is True, STATEMENT-2 is False.
(D) STATEMENT-1 is False, STATEMENT-2 is True.
Ans . 2
STATEMENT-2 is true because inductive effect is permanent effect and inductive effect of halogen always dominates its mesomeric effect. But this statement is unable to explain the formation of 1,4-dibromobenzene as the major product. The correct reason for the formation of given product is that Br is ortho/para directing due to resonance stabilization of arenium ion. The prominent attack of Br+ takes place at para position due to steric effect.
Correct choice: (B)
58. STATEMENT-1: Pb4+ compounds are stronger oxidizing agents than Sn4+ compounds.
and STATEMENT-2:
The higher oxidation states for the group 14 elements are more stable for the heavier members of the group due to 'inert pair effect'.
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
(C) STATEMENT-1 is True, STATEMENT-2 is False.
(D) STATEMENT-1 is False, STATEMENT-2 is True.
Ans . 3
Pb4+ is less stable than Sn4+, therefore Pb4+ is a stronger oxidizing agent than Sn4+. Due to inert pair effect, stability of higher oxidation state of group 14 elements decreases down the group. Thus, STATEMENT-1 is true and STATEMENT-2 is false.
Correct choice: (C)
59. STATEMENT-1: The plot of atomic number (y-axis) versus number of neutrons (x-axis) for stable nuclei shows a curvature towards x-axis from the line of 45° slope as the atomic number is increased.
and
STATEMENT-2: Proton-proton electrostatic repulsions begin to overcome attractive forces involving protons and neutrons in heavier nuclides.
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
(C) STATEMENT-1 is True, STATEMENT-2 is False.
(D) STATEMENT-1 is False, STATEMENT-2 is True.
Ans .1
Proton-proton repulsions begin to dominate over attractions between protons and neutrons as the value of Z increases. Therefore, STATEMENT-2 is true. In order to stabilize the heavier nuclides, more number of neutrons are to be added so that the attractive forces between protons and neutrons overcome the repulsive forces among protons. Therefore, STATEMENT-2 is the correct explanation of STATEMENT-1.
Correct choice: (A)
60. STATEMENT-1: For every chemical reaction at equilibrium, standard Gibbs energy of reaction is zero.
and
STATEMENT-2: At constant temperature and pressure, chemical reactions are spontaneous in the direction of decreasing Gibbs energy.
(A) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is a correct explanation for STATEMENT-1.
(B) STATEMENT-1 is True, STATEMENT-2 is True; STATEMENT-2 is NOT a correct explanation for STATEMENT-1.
(C) STATEMENT-1 is True, STATEMENT-2 is False.
(D) STATEMENT-1 is False, STATEMENT-2 is True.
Ans . 4
For every chemical reaction at equilibrium, Gibbs free energy change (G) of reaction is zero but standard Gibbs free energy change (G°) may not be zero. Thus STATEMENT-1 is false but STATEMENT-2 is true.
Correct choice: (D)
SECTION - IV
Linked Comprehension Type
This section contains 3 paragraphs. Based upon each paragraph, 3 multiple choice questions have to be answered. Each question has 4 choices (A), (B), (C) and (D), out of which ONLY ONE is correct
Paragraph for Question Nos. 61 to 63
In the following reaction sequence, products I, J and L are formed. K represents a reagent.
61. The structure of the product I is
(A) 
(B) 
(C) 
(D) 
Ans. 4
62. The structures of compounds J and K, respectively, are
(A) 
(B) 
(C) 
(D) 
Ans . 1
Correct choice: (A)
63. The structure of product L is
(A) 
(B) 
(C) 
(D)
Ans .3
Correct choice: (C)
Paragraph for Question Nos. 64 to 66
There are some deposits of nitrates and phosphates in earth's crust. Nitrates are more soluble in water. Nitrates are difficult to reduce under the laboratory conditions but microbes do it easily. Ammonia forms large number of complexes with transition metal ions. Hybridization easily explains the ease of sigma donation capability of NH3 and PH3. Phosphine is a flammable gas and is prepared from white phosphorus.
64. Among the following, the correct statement is
(A) Phosphates have no biological significance in humans.
(B) Between nitrates and phosphates, phosphates are less abundant in earth's crust.
(C) Between nitrates and phosphates, nitrates are less abundant in earth's crust.
(D) Oxidation of nitrates in possible in soil.
Ans . 3
Nitrates are less abundant than phosphates in earth's crust as they are soluble in water. Moreover, they can also be reduced by numerous microbes present in the earth's crust.
Correct choice: (C)
65. Among the following, the correct statement is
(A) Between NH3 and PH3, NH3 is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional.
(B) Between NH3 and PH3, PH3 is a better electron donor because the lone pair of electrons occupies sp3 orbital and is more directional.
(C) Between NH3 and PH3, NH3 is a better electron donor because the lone pair of electrons occupies sp3 orbital and is more directional.
(D) Between NH3 and PH3, PH3 is a better electron donor because the lone pair of electrons occupies spherical 's' orbital and is less directional.
Ans .3
NH3 is a better electron donor than PH3 because the lone pair of electrons on N-atom occupies sp3 orbital and is more directional due to smaller size of N-atom.
66. White phosphorus on reaction with NaOH gives PH3 as one of the products. This is a
(A) dimerization reaction.
(B) disproportionation reaction.
(C) condensation reaction.
(D) precipitation reaction.
Ans . 2
This is an example of disproportionation reaction.
Paragraph for Question Nos. 67 to 69
Properties such as boiling point, freezing point and vapour pressure of a pure solvent change when solute molecules are added to get homogeneous solution. These are called colligative properties. Applications of colligative properties are very useful in day-to-day life. One of its examples is the use of ethylene glycol and water mixture as anti-freezing liquid in the radiator of automobiles.
A solution M is prepared by mixing ethanol and water. The mole fraction of ethanol in the mixture is 0.9.
Given:
In answering the following questions, consider the solutions to be ideal dilute solutions and solutes to be non-volatile and non-dissociative.
67. The freezing point of the solution M is
(A) 268.7 K
(B) 268.5 K
(C) 234.2 K
(D) 150.9 K
Ans .4
As the mole fraction of ethanol in the mixture is 0.9. So ethanol is the solvent and water is solute. The freezing point of the solution assuming water to be the non-volatile solute should be less than the freezing point of the pure solvent (ethanol). Hence, freezing point of solution should be less than 155.7 K. (D) is the obvious choice.
Correct choice: (D)
68. The vapour pressure of the solution M is
(A) 39.3 mm Hg
(B) 36.0 mm Hg
(C) 29.5 mm Hg
(D) 28.8 mm Hg
Ans .2
Vapour pressure of solution  (It is given that solute is to be treated as non-volatile and non-dissociative)
= 40 × 0.9
= 36.0 mm Hg.
Correct choice: (B)
69. Water is added to the solution M such that the mole fraction of water in the solution becomes 0.9. The boiling point of this solution is
(A) 380.4 K
(B) 376.2 K
(C) 375.5 K
(D) 354.7 K
Ans .2
Mole fraction of water in solution = 0.9.
Water becomes the solvent and ethanol is solute and has to be considered has non-volatile and non-dissociative.
Mole fraction of ethanol in solution = 0.1
Molality of ethanol in solution =
Boiling point of the solution = 373 + 3.2 = 376.2 K.
Correct choice: (B)
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