Based on New Pattern
Time : 3 Hours
Syllabus : Physics : Calorimetry, K.T.G., Thermodynamics, Heat Transfer, Thermal expansion, Transverse wave, Sound wave, Doppler's effect, Atomic Structure, Radioactivity, X-ray, Nuclear Physics, Matter Waves, Photoelectric Effect, Practical Physics. Chemistry : Chemical Equilibrium, Acid Base, Ionic Equilibrium, Classification & Nomenclature, Isomerism , Hydrogen Family, Boron Family & Carbon Family, S-block elements, Nitrogen Family, Oxygen Family, Halogen Family & Noble Gas, Salt Analysis, Metallurgy, Co-ordination Compounds, Transitional Elements.
Mathematics: Point, Straight line, Circle, Parabola, Ellipse, Hyperbola, Vector, 3-D, Probability, Determinants, Matrices.
Instructions :
Section - I
• Question 1 to 9 are multiple choice questions with only one correct answer. +3 marks will be awarded for correct answer and -1 mark for wrong answer.
• Question 10 to 13 are Reason and Assertion type questions with only one correct answer in each. +3 marks will be awarded for correct answer and -1 mark for wrong answer.
• Question 14 to 19 are passage based single correct type questions. +4 marks will be awarded for correct answer and -1 mark for wrong answer.
Section - II
• Question 20 to 22 are Column Matching type questions. +6 marks will be awarded for the complete correctly matched answer and No Negative marks for wrong answer. However, 1 mark will be given for a correctly marked answer in any row.
6. The potential difference across the Coolidge tube is 20 kV and 10 mA current flows through the voltage supply. Only 0.5% of the energy carried by the electrons striking the target is converted into X-rays.
The power carried by X-ray beam is P.
(A) P = 0.1 W (B) P = 1 W (C) P = 2 W (D) P = 10 W
7. A radioactive sample consists of two distinct species is τ and that of the other is 5τ. The decay products in both cases are stable. A plot is made of the total number of radioactive nuclei as a function of time.
Which of the following figures best represents the form of this plot ?
(A) τ t N
(B) τ t N
(C) τ t N
(D) τ t N
8. A star initially has 1040 deutrons. It produces energy via the processes 1H2 + 1H2 → 1H3 + p and 1H2 + 1H3
→ 2He4 + n. If the average power radiated by the star is 1016 W, the deutron supply of the star is exhausted in a time of the order of
(The masses of nuclei are : m(H2) = 2.014 u, m(p) = 1.007 u, m(n) = 1.008 u, m(He4) = 4.001 u) (A) 106 s (B) 108 s (C) 1012 s (D) 1016 s 9. In an excited state of hydrogen like atom an electron
has total energy of – 3.4 eV. If the kinetic energy of the electron is E and its de Broglie wavelength is λ, then
(A) E = 6.8 eV, λ ~ 6.6 × 10–10 m (B) E = 3.4 eV, λ ~ 6.6 × 10–10 m (C) E = 3.4 eV, λ ~ 6.6 × 10–11 m (D) E = 6.8 eV, λ ~ 6.6 × 10–11 m
This section contains 4 questions numbered 10 to 13, (Assertion and Reason type question). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Use the following Key to choose the appropriate answer.
(A) If both (A) and (R) are true, and (R) is the correct explanation of (A).
(B) If both (A) and (R) are true but (R) is not the correct explanation of (A).
(C) If (A) is true, but (R) is false.
(D) If (A) is false, but (R) is true.
10. Assertion : In a standing wave formed in a stretched wire the energy of each element of wire remains constant.
Reason : The net energy transfer in a standing wave is zero.
11. Assertion : On a T-V graph (T on y-axis), the curve for adiabatic expansion would be a monotonically decreasing curve.
Reason : The slope of an adiabatic process represented on T-V graph is always + ve.
12. Assertion : Energy is released in nuclear fission.
Reason : Total binding energy of the fission fragments is larger than the total binding energy of the parents nucleus.
13. Assertion : If the accelerating potential in an X-ray tube in increased, the wavelength of the characteristic X-ray do not change.
Reason : When an electron beam strikes the target in an X-ray tube, part of kinetic energy is converted into X-ray energy.
This section contains 2 paragraphs; each has 3 multiple choice questions. (Question 14 to 19) Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Passage : I (No. 14 to 16)
In the following figure the spring is at its natural length. In both the chambers 'n' moles of monoatomic gas is filled at temperature T. Heat is supplied to the right chamber. Piston is non-conducting and vessel is non-conducting. Temperature of the left chamber does not change. Piston is displaced by L/4.
n, T K
n, T
14. Change in temperature of right chamber is – (A) 2T +
nR LK 16
5 2
(B) T/3 + nR 16
KL2
(C) 2T/3 + nR 16
KL 5 2
(D) 2T/3 + nR KL 5 2
15. Change in the internal energy of the right chamber is (A) nRT +
32
15KL2 (B) nRT + 32 KL2
(C) 2nRT + 15 KL2 (D) 3nRT + 32 15KL2
16. Heat transferred into the system is (A) 2nRT +
2 KL2
(B) nRT + 2 KL2
(C) 3nRT + 32 KL2
(D) nRT + 32 KL2
Passage : II (No. 17 to 19)
Two hydrogen like atoms A and B are of different masses and each atom contains equal number of protons and neutrons. The energy difference between the radiation corresponding to first Balmer lines emitted A and B is 5.667 eV when A & B moving with the same velocity, strikes a heavy target they rebound back with the same velocity. In this process the atom B imparts twice the momentum to the target the A imparts.
17. Ionization energy of Atom B is – (A) 27.2 eV (B) 13.6 eV (C) 10.2 eV (D) 54.4 eV 18. Atomic number of atom A is
(A) 1 (B) 2 (C) 3 (D) 4 19. Mass number of atom B & Atom A
(A) 2, 4 (B) 4, 2 (C) 2, 1 (D) 4, 1
The section contains 3 questions (Questions 20 to 22).
Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (P, Q, R, S) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example. If the correct matches are A-P, A-S, B-Q, B-R, C-P, C-Q and D-S, then the correctly 4 × 4 matrix should be as follows :
D C B A
P P P P
Q Q Q Q
R R R R
S S S S Q P R S
20. Consider a situation (i) that two sound waves, y1 = (0.2m) sin 504π (t – x/300) and y2 = (0.6 m) sin 490π (t – x/300) are superimposed. Consider another situation (ii) that two sound waves, y1 = (0.2m) sin 504π(t – x/300)
y2 = (0.4 m) sin 504π(t + x/300), are superimposed.
Match the Column-I with Column-II :
Column -I Column-II
(A) In situation (i) (P) Stationary waves are formed (B) In situation (ii) (Q) There will be the
phenomenon of 'Beats'
(C) When two waves of same frequency and amplitude and travelling in opposite directions
superimpose
(R) Amplitude of the resultant wave will vary periodically with position
(D) If the intensity of sound alternately increases and decreases periodically
as a result of superposition of waves of slightly different frequencies
(S) Amplitude of the resultant wave will vary periodically with time
21. The specific heat capacity of a material is given as C = AT, where A is a constant, T is temperature. The substance is heated from 27ºC to 127ºC. Unit of A is J/kg/K2. Then match quantities in column I to that in column II.
Column -I Column-II
(A) Mean specific heat in the range 27ºC to 127ºC is
(P) 400 A (B) Actual specific heat at
127ºC is
(Q) 350 A (C) Graph of specific heat
versus temperature is
(R)
(D) Graph of amount of heat transferred versus temperature is
(S)
22. Match the Column-I with Column-II
Column -I Column-II
(A) An electron moves in an orbit in a Bohr atom
(P) Total Energy
= 2
Energy Potential (B) As a satellite moves
in a circular orbit around total earth
(Q) Kinetic Energy = Magnitude of Energy
(C) In Rutherford's α-scattering experiment, as an α-particle moves in the electric field of a nucleus
(R) Motion in under a central force
(D) As an object, release from some height above ground, falls towards earth, assuming negligible air resistance
(S) Mechanical energy is coserved
C HEMISTRY
Questions 1 to 9 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
1. For the reaction :
[Ag(CN)2]– Ag+ + 2CN–
The equilibrium constant at 25º C is 4 × 10–19. If a solution is 0.1 M in KCN and 0.03 M in AgNO3
originally, at equilibrium, the concentration of Ag+ is (A) 7.5 × 10–16 M (B) 7.5 × 10–18 M
(C) 1.25 × 10–19 M (D) 1.25 × 10–17
2. At 25º C, solubility product of Zn(OH)2 is 10–14. If NH4OH is 50% dissociated, then the concentration of Zn2+ in its 0.1 M solution is
(A) 2 × 10–12 (B) 1 × × 10–14 (C) 10–12 (D) 4 × 10–12
3. Which of the following pairs of compounds will have identical B.P ?
(A)
Me
Cl H
Et
&
Me
H Me
CH2Cl
(B)
CH3
Br H
CH3
OH H
&
OH
H H
CH3
CH3
Br
(C)
Me H
Me OH
H OH
H OH
&
Me H
Me OH
H OH
HO Me
(D) None of these
4. Which of the following statements are not correct ? (A) Me – CH = C = CH – Me is optically active (B)
Me
Me C
H
Me is optically inactive (C) All the compounds having chiral centre with L.P.
as one of the group, are non-resolvable.
(D) All geometrical isomers are diastereomers
5. Identify most acidic hydrogen in given compound.
OH
O – H S – H OH
O O
H d
b
c a
(A) a (B) b
(C) c (D) d
6. A yellow powder reacted with F2 to form a colourless gas X which is used as gaseous insulator in high power generators. It does not get hydrolysed. Another compound is obtained by reaction of sulphur dichloride with NaF. It can be easily hydrolysed and has see-saw shape. X and Y respectively are
(A) AgI, AgBr (B) SF6, SF4
(C) SF4, SF6 (D) SCl4,SCl6
7. Which of the following statement is true ? (A) Si–O bond is stronger than C–O bond
(B) Dimethyl ether acts as better lewis base but not disilyl ether
(C) (CH3)3SiO– is more stable than (CH3)3CO– (D) All of these
8. Here A, B, C and D are respectively (A) fused Na+ air 2CO3 (B) HEvaporation 2SO4 + H2O (C)
Yellow solution
Pb (CH3COO)2
Yellow ppt.
(D)
Orange Coloured Green
Solid
(A) FeSO4, FeCl3, Fe(OH)3, PbCl2
(B) FeCl2, FeSO4, Fe(OH)3, PbSO4
(C) Cr2O3, Na2CrO4, Na2Cr2O7, PbCrO4
(D) FeSO4, Fe2(CO3)2, Fe(OH)3, PbCO3
9. When sulphur is dissolved in oleum, a deep blue coloured solution containing polyatomic sulphur cation is obtained. The formula of cation present is (A) S 24+ (B) S 28+
(C)S 192+ (D) S 162+
This section contains 4 questions numbered 10 to 13, (Assertion and Reason type question). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Use the following Key to choose the appropriate answer.
(A) If both (A) and (R) are true, and (R) is the correct explanation of (A).
(B) If both (A) and (R) are true but (R) is not the correct explanation of (A).
(C) If (A) is true, but (R) is false.
(D) If (A) is false, but (R) is true.
10. Assertion : KMnO4 is a coloured compound Reason : Colour of KMnO4 is due to charge transfer.
11. Assertion : [Co(NH3)5Cl]Cl2 reacts with excess of AgNO3 to form 2 moles of AgCl (white ppt)
Reason : [Co(NH3)6]Cl3 gives 2 moles of Cl– which react with AgNO3 to forms 2 moles of AgCl.
12. Assertion : AlF3 is almost insouble in anhydrous HF but dissolves in NaF.
Reason : NaF produces free F–
13. Assertion : Cu+ ion does not exist in solution.
Reason : Cu+ ion undergoes disproportionation in aqueous solution.
This section contains 2 paragraphs; each has 3 multiple choice questions. (Question 14 to 19) Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Passage : I (No. 14 to 16)
The stability of complexes depend upon stability constant. Higher the value of stability constant, more will be stability of complex. It can also be determined with the help of dissociation constant. Higher the value of dissociation constant, lesser will be stability.
Smaller cation, with higher charge can form more stable complex. Stronger the ligand, more stable will be complex. Polydentate ligands form more stable complex than unidentate ligand. If multidentate ligand is cyclic, it further increases the stability, it is called macrocyclic effect.
14. Formation of complex involves (A) exothermic, decrease in entropy (B) endothermic, decrease in entropy (C) exothermic, increase in entropy (D) endothermic, increase in entropy 15. Which of the following is most stable
(A) [Co(en)3]3+ (B) [Co(NH3)6]3+
(C) [Co(H2O)6]3+ (D) [CoF6]3–
16. Which of the following exist as dimer (A) Al(CH3)3 (B) CH3Li (C) Si(CH3)4 (D) Be(CH3)2
Passage : II (No. 17 to 19)
A black coloured compound (A) on reaction with dil H2SO4 form a gas 'B' and a solution of compound (C). When gas B is passed through solution of compound (C), a black coloured compound 'A' is obtained which is soluble in 50% HNO3 and forms blue coloured complex 'D' with excess of NH4OH and chocolate brown ppt. 'E' with K4[Fe(CN)6] 17. 'A' is
(A) CuS (B) FeS
(C) PbS (D) HgS
18. 'D' is
(A) Cu(OH)2 (B) [Cu(NH3)2]SO4
(C) [Cu(NH3)4](NO.3)2 (D) [Cu(NH3)6]SO4
19. 'E' is
(A) Cu2[Fe(CN)6] (B) [Cu4[Fe(CN)6] (C) Cu3[Fe(CN)6]2 (D) None of these The section contains 3 questions (Questions 20 to 22).
Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (P, Q, R, S) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example. If the correct matches are A-P, A-S, B-Q, B-R, C-P, C-Q and D-S, then the correctly 4 × 4 matrix should be as follows :
D C B A
P P P P
Q Q Q Q
R R R R
S S S S Q P R S
20. Match the following :
Column -I Column-II
(A) Compound show Geometrical isomerism
(P)
Me Me
(B) Compound is chiral (Q)
Me = C
H Me
H
(C) Compound having plane of symmetry
(R)
C = C
Me H
Me H
(D) Compound having centre of symmetry
(S) Me
H Me
H
21. Match the following :
Column -I Column-II
(A) Two electron three centre bond
(P) (BN)x
(B) Four electron three centre bond
(Q) B2H6
(C) sp3 hybrid orbitals (R) AlCl3
(D) Inorganic graphite (S) B4H10
22. Match the following :
Column -I Column-II
(A) KHCO3 (P) Exists in solid state (B) NaHCO3 (Q) Soluble in water (C) LiHCO3 (R) Hydrogen bonding (D) NH4HCO3 (S) Dimeric anion
MATHEMATICS
Questions 1 to 9 are multiple choice questions. Each question has four choices (A), (B), (C) and (D), out of which ONLY ONE is correct.
1. The line joining A(b cos α, b sin α) and B (a cos β, is circumscribed about the triangle OAB. If m and n are the distances of the tangent to the circle at the origin from the points A and B respectively, the diameter of the circle is
(A) m(m + n) (B) m + n
4. The coordinates of the end point of the latus rectum of the parabola (y – 1)2 = 2(x + 2), which does not lie then a nonzero vector r satisfying r.a = α, for some scalar α, a × r = b is
9. If the probability of choosing an integer k out of 2m integers 1, 2, 3, ...., 2m is inversely proportional to k4(1 ≤ k ≤ 2m), then the probability that chosen number is odd, is
(A) equal to 1/2 (B) less than ½ (C) greater than 1/2 (D) less than 1/3
This section contains 4 questions numbered 10 to 13, (Assertion and Reason type question). Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Use the following Key to choose the appropriate answer.
(A) If both (A) and (R) are true, and (R) is the correct explanation of (A).
(B) If both (A) and (R) are true but (R) is not the correct explanation of (A).
(C) If (A) is true, but (R) is false.
(D) If (A) is false, but (R) is true.
10. Assertion : If A and B are two 3 × 3 matrices such then determinant equals zero.
12. Assertion : If A and B are two events such that concurrent lines is zero.
This section contains 2 paragraphs; each has 3 multiple choice questions. (Question 14 to 19) Each question has 4 choices (A), (B), (C) and (D) out of which ONLY ONE is correct.
Passage : I (No. 14 to 16)
Let k be the length of any edge of a regular tetrahedron. (A tetrahedron whose edges are all equal in length is called a regular tetrahedron.) The angle between a line and a plane is equal to the complement of the angle between the line and the normal to the plane whereas the angle between two planes is equal to the angle between the normals. Let O be the origin of reference and A, B and C vertices with position vectors a, b and c respectively of the regular tetrahedron.
14. The angle between any edge and a face not containing the edge is
(A) cos–1(1/2) (B) cos–1 (1/4)
Area of triangle with vertices A, B and C is given by 2
(C) altitude through vertex A
(D) perpendicular bisector of the side BC
The section contains 3 questions (Questions 20 to 22).
Each question contains statements given in two columns which have to be matched. Statements (A, B, C, D) in Column I have to be matched with statements (P, Q, R, S) in Column II. The answers to these questions have to be appropriately bubbled as illustrated in the following example. If the correct matches are A-P, A-S, B-Q, B-R, C-P, C-Q and D-S, then the correctly 4 × 4 matrix should be as follows :
D
20. Column –I Column-II (A) Centroid of the triangle with
vertices A(2, 3, 7), B(6, 7, 5), C(1, 2, 3)
(P) (1, 6, 5)
(B) Mid-point of the line joining the points A(7, 9, 11) and B(–5, 3, –1)
(Q) (3, 4, 5)
(C) A point on the line 2
x= 3 y=
5
z , at a distance 2 from the origin.
(R) (3, 3, 2)
(D) Coordinates of the point dividing the join of (5, 5, 0) and (0, 0, 5) in the ratio 2:3.
(S) (4/ 38 , 6/ 38 , 10/ 38 )
21. Let ak = nCk for 0 ≤ k ≤ n and Ak =
−
k 1 k
a 0
0
a and
B =
∑
−=
+ 1 n
1 k
1 k k.A
A =
b 0
0 a ,
Column -I Column-II
(A) a (P)
1 n
n 2
+ (2nCn) (B) a – b (Q) 0
(C) a + b (R) 2nCn+1
(D) a/b (S) 1
22. Cards are dealt one by one from wellshuffled pack of 52 playing cards until r (1 ≤ r ≤ 4) aces are obtained.
If pr denotes the probability of drawing r aces for the first time at the nth draw (with n ≥ 4), and Pr = (52Cn)Pr, then
Column -I Column-II
(A) P1 (P) 52 – nC3
(B) P2 (Q) (n – 1) (52 – nC2) (C) P3 (R) (n – 1C2) (52 – nC1)
(D) P4 (S) n –1C3