JEE (MAIN+ADVANCED)

Academic Session: 2023-24

TARGET TEST PATTERN JEE (ADVANCED)

JEE (MAIN+ADVANCED)
EXAMINATION

TARGET YEAR 2024 TEST TYPE PRACTICE TEST

TEST CODE &

PAPER NO. ONE SEQUENCE
PRACICE TEST-1

PAPER CODE 1 MAX. MARKS 198 or 213

CLASS XII TEST DURATION 3 Hrs.

TEST DATE 20ST MARCH 2024

COURSE NAME VIJETA
TEST DAY WEDNESDAY
COURSE CODE JP
TOTAL NO. OF
PAGES IN PAPER 30
BATCH CODE(S) JAZP, IP BOOKLET

TEST PAPER DETAILS MARKING SCHEME

Partial Marks
Type No. Full
Subject If Three If Two If One If No (–)ve Total Subject
Qs. No. Section No. of of Marks
Sequence Options Options Option Option Marks Marks Total
Qs.* Qs. Per Qs.
Correct Correct Correct Chosen

01 to 04 1 MCQ 4 3 – – – 0 –1 12

05 to 10 2 MSQ 6 4 +3 +2 +1 0 –2 24
Physics ,
11 to 15 3 Chemistry , NVQ 5 3 – – – 0 0 15
66 or 71
Maths
16 to 19 4 CBQ 4 3 – – – 0 –1 12
MLQ
20 5 or 1 3 or 8 – – – 0 –1 3 or 8
CMQ
Total 20 MAXIMUM MARKS 198 or 213

* Please turn overleaf to understand the meaning of coding for types of Questions.
A. GENERAL INSTRUCTIONS B. DARKENING THE BUBBLES ON THE ORS :
1. Use a BLACK BALL POINT to darken the
1. Darken the appropriate bubbles on the original
bubbles in the upper sheet.
by applying sufficient pressure. 2. Darken the bubble COMPLETELY.
2. The original is machine-gradable and will be 3. Darken the bubble ONLY if you are sure of the
collected by the invigilator at the end of the answer.
examination. 4. The correct way of darkening a bubble is as
3. Do not tamper with or mutilate the ORS. shown here :
5. There is NO way to erase or "un-darkened
4. Write your name, roll number and the name of
bubble.
the examination centre and sign with pen in the 6. The marking scheme given at the beginning of
space provided for this purpose on the original. each section gives details of how darkened and
Do not write any of these details anywhere not darkened bubbles are evaluated.
else. Darken the appropriate bubble under each 7. Zero marks ‘0’ If none of the options is chosen
digit of your roll number. (i.e. the question is unanswered).

C. FOR INTEGER TYPE QUESTIONS OMR LOOKS D. FOR DECIMAL TYPE QUESTIONS OMR LOOKS
LIKE: LIKE:
1. For example, if answer ‘SINGLE DIGIT’ integer 1.
type below : COLUMN
0 1 2 3 4 5 6 7 8 9 1 2 . 3 4
2. For example, if answer ‘SINGLE DIGIT’ integer 0 0 0 0
with positive / negative type below : 1 1 1 1
0 2 2 2 2
– 1
3 3 3 3
2
4 4 4 4
3
5 5 5 5
4
6 6 6 6
5
7 7 7 7
6
8 8 8 8
7
8
9 9 9 9
9 2. If answer is 3.7, then fill 3 in either 1st or 2nd
3. For example, if answer ‘DOUBLEDIGIT’ integer column and 7 in 3rd or 4th column.
type below :
0 0 3. If answer is 3.07 then fill 3 in 1st or 2nd column ‘0’
1 1 in 3rd column and 7 in 4th column.
2 2 If answer is, 23 then fill 2 & 3 in 1st and 2nd
3 3 column respectively, while you can either leave
4 4 column 3 & 4 or fill ‘0’ in either of them.
5 5
6 6
7 7
8 8
9 9

TYPE WISE CODES FOR QUESTIONS

SR# QUESTION TYPE CODE
1 MULTIPLE CHOICE QUESTION (ONLY ONE CORRECT OPTION) MCQ
2 MULTIPLE SELECT (ONE OR MORE THAN ONE CORRECT OPTIONS QUESTION) MSQ
3 NUMERICAL VALUE QUESTION NVQ
4 COMPREHENSION / PARAGRAPH BASED QUESTION CBQ
5 MATCH THE LISTING QUESTION MLQ
6 COLUMN MATCH QUESTION CMQ
7 FILL IN THE BLANKS TYPE QUESTION FBQ
8 TRUE OR FALSE TYPE QUESTION TFQ
9 ASSERTION & REASON / STATEMENT TYPE QUESTION ARQ
10 SUBJECTIVE TYPE QUESTION STQ
 PHYSICS
PHYSICS

SECTION – 1 : (Maximum Marks : 12)

 This section contains FOUR (04) questions.
 Each question has FOUR options ONLY ONE of these four options is the correct answer.
 For each question, choose the correct option corresponding to the correct answer.
 Answer to each question will be evaluated according to the following marking scheme :
Full Marks : +3 If ONLY the correct option is chosen.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : –1 In all other cases.

1. The maximum angle to the horizontal at which a stone can be thrown so that it always moves away
from the stationery thrower will be :

 2 2 2  1   2
(A) sin–1 
 3 
(B) sin–1 
 3 
(D) sin–1 
 3 
(C) sin–1  
     3  

2. A particle of mass 'M' is moved under constant power P 0. At some instant after the start, its speed is v
and at a later instant, the speed is 2v. Neglecting friction, distance travelled by the particle as its speed
increases from v to 2v is :

12Mv 3 7Mv 3 9 Mv 3 Mv 3
(A) (B) (C) (D)
5P0 3P0 5 P0 3P0

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 PHYSICS
3. On a cart of mass 3 m, two blocks A and B, each of mass m are placed as shown. Upper surface of the cart

is smooth, but the vertical surface is rough having friction coefficient  = 0.5. The cart is pulled with a

constant force F. What should be the value of F so that neither static, nor kinetic friction acts on block A.

5
(A) 5 mg (B) mg (C) 7 mg (D) 10 mg
2

1
4. A worker wishes to pile a pyramid of sand with equilateral triangular base of side 3m. If   is the
3

co-efficient of static friction between each layer of sand along the slope of the sand, then maximum

height of the pyramid will be (neglect any complexities at the corners) :

1 1
(A) 3m (B) m (C) m (D) 2 3 m
2 3

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 PHYSICS
SECTION – 2 : (Maximum Marks : 24)
 This section contains SIX (06) questions.
 Each question has FOUR options ONE OR MORE THAN ONE of these four option(s) is(are) correct
answer(s).
 For each question, choose the option(s) corresponding to (all) the correct answer(s).
 Answer to each question will be evaluated according to the following marking scheme.
Full Marks : +4 If only (all) the correct option(s) is (are) chosen.
Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.
Partial Marks : +2 If three or more options are correct but ONLY two options are chosen and both of
which are correct.
Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct
option.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : –2 In all other cases.

5. Consider the condition shown in the figure. Pulley is massless and frictionless, springs are massless.
Both the blocks are released with the springs in their natural lengths. Choose the correct options.

4m1m2g
(A) Maximum elongation in the spring S1 is
K1(m1  m2 )
4m1m2g
(B) Maximum elongation in the spring S1 is
K 2 (m1  m2 )
(C) If m1 = m2 both the blocks will come to instantaneous rest simultaneously.
(D) If K1 = K2 both the blocks will come to instantaneous rest simultaneously.
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 PHYSICS
6. Consider three fixed surfaces shown in the figure. Three blocks each of mass m are released from rest
from top of the three surfaces. All blocks reach ground with same speed. Length of path travelled by the
blocks is same for second and third surface. If coefficient of friction of three surfaces are 1, 2 and 3
respectively then

(A) 1 = 2 (B) 1 > 2 (C) 2 = 3 (D) 2 < 3

7. In the arrangement shown, W 1 = 200 N, W 2 = 100 N and  = 0.25 for all surfaces in contact. The block
W 1 just slide under the block W 2

A
45
W2
P
W1

(A) a pull of 50 N is to be applied on W 1

(B) a pull of 90 N is to be applied on W 1.
(C) tension in the string AB is 10 2 N
(D) tension in the string AB is 20 2 N

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 PHYSICS
8. Two blocks A and B of equal mass m are connected through a massless string and arranged as shown

in figure. The wedge is fixed on horizontal surface. Friction is absent everywhere. When the system is

released from rest.

mg mg
(A) tension in string is (B) tension in string is
2 4

g 3
(C) acceleration of A is (D) acceleration of A is g
2 4

9. In given arrangement, 10 kg and 20 kg blocks are kept at rest on two fixed inclined planes. All strings

and pulleys are ideal. value(s) of m for which system remain in equilibrium are: (g = 10 m/s 2)

(A) m = 6 kg (B) m = 13 kg (C) m = 9 kg (D) m = 12 kg

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 PHYSICS
2
10. In the figure shown, there is no friction between B and ground and  = between A and B.
3

A M
B 2M F = Mg

(A) The net work done on block A with respect to B is zero

MgS
(B) The net work done on block A with respect to ground for a displacement ‘S’ is
3

2MgS
(C) The net work done on block B with respect to ground for a displacement ‘S’ is
3

(D) The work done by friction with respect to ground on A and B is equal and opposite in sign.

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 PHYSICS
SECTION – 3 : (Maximum Marks : 15)
 This section contains FIVE (05) questions. The answer to each question is a NUMERICAL VALUE.
 For Online:
For each question, enter the correct numerical value of the answer using the mouse and the on-screen
virtual numeric keypad in the place designated to enter the answer. If the numerical value has more
than two decimal places, truncate/round-off the value to TWO decimal places.
 For Offline:
If the numerical value has more than two decimal places truncate/round-off the value to TWO decimal
placed.
 Answer to each question will be evaluated according to the following marking scheme :
Full Marks : +3 If ONLY the correct numerical value is entered.
Zero Marks : 0 In all other cases.

11. A particle of mass m = 1 kg is lying at rest on x-axis, experiences a net force given by law
F = x (3x – 2) Newton, where x is the x-coordinate of the particle in meters. The magnitude of minimum
velocity in negative x-direction to be imparted to the particle placed at x = 4 meters such that it reaches
P P
the origin is m/s. Find the value of .
27 1300

12. A 20kg block attached to a spring of spring constant 5 N/m is released from rest at A. The spring at this
instant is having an elongation of 1m. The block is allowed to move is smooth horizontal slot with the
help of a constant force 50N in the rope as shown. The velocity of the block (in m/s) as it reaches B is :
50N

3m

4m
A B

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 PHYSICS
13. A man in a boat wishes to cross a 400 m wide river flowing at the rate of 2 m/s. Speed of boat in still
water is 4 m/s. The person starts to row the boat perpendicular to the river flow from one bank of the
river. When he reaches the middle of the river, he starts to row the boat at an angle  with the direction
perpendicular to river flow so as to reach the point directly opposite to the starting point on the opposite
4
bank. The value of tan  is . Find value of n.
n

14. A wire is bent in a parabolic shape followed by equation x = 4y2. Consider origin as vertex of parabola.
A wire parallel to y axis moves with constant speed 4 m/s along x-axis in the plane of bent wire. Then
the acceleration of point of contact of straight wire and parabolic wire is  m/s2 (when straight wire has x
coordinate = 4 m). Find the value of 4.

15. A box of mass 20 kg is kept on a rough horizontal surface ( = 0.1). There is a spring mass system
having block of mass 20 kg and spring of spring constant 100 N/m in the box. There is no friction
between block and box and spring is initially relaxed. Now an external force of 120 N is applied on the
box, find acceleration of the box (in m/s2) just after applying the force.

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 PHYSICS
SECTION – 4 : (Maximum Marks : 12)
 This section contains TWO (02) paragraphs
 Based on each paragraph, there will be TWO questions.
 Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four option is correct 
 Marking scheme :
 Full Marks : +3 If ONLY the correct option is chosen.
 Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
 Negative Marks : –1 In all other cases
Paragraph for Question Nos. 16 to 17
A block B of mass M = 20 kg is placed on a horizontal surface and it is tied with an inextensible string to
a block A of mass m = 10 kg. Another block C of mass m 0 = 20 kg is placed on block B and the system
is released from rest as shown in figure. (string is ideal and all the contacts are smooth) (g = 10 m/s 2)
m0 C
M B

m A

16. Which of the following option is false ?

10
(A) The downward acceleration of the block A is m/sec2
3
(B) Initial acceleration of C is zero
200
(C) The tension in the string is N
3
10
(D) Initial acceleration of C is m/sec2
3

17. If a friction force exist between blockSpace

B andfor
theRough
horizontal
Worksurface with the coefficient of friction , and
minimum value of  for which the block A remains stationary is min
(A)min = 0.5
(B)min = 0.25
ém -  (m0 + M) ù
(C) If  < min, then the downward acceleration of A is ê úg
ê m+ m + M ú
ë 0 û
é m - M ù
(D) If  < min, then the downward acceleration of A is ê úg :
êm + m + M ú
ë 0 û

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 PHYSICS
Paragraph for Question Nos. 18 to 19
Figure shows top view of a horizontal surface. Two blocks each of mass m are placed on the surface

and connected with a string. The friction coefficient is  for each block. A horizontal force F is applied

on one of the block as shown in the figure. F is maximum so that there is no sliding at any contact.

 Top view

18. If  < 45° then the maximum magnitude of F

(A) mg sec  (B) mg (C) mg cosec  (D) mg tan 

19. If  > 45° then the maximum magnitude of F

(A) 2mg sec  (B) mg sin  (C) 2mg sin  (D) 2mg tan 

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 PHYSICS
SECTION – 5 : (Maximum Marks : 03)
 This section contains ONE (01) questions.
 Each question has TWO matching lists: LIST-I and LIST-II.
 FOUR options are given representing matching of elements from LIST-I and LIST-II. ONLY ONE of these
four options corresponds to a correct matching.
 For each question, choose the option corresponding to the correct matching.
 For each question, marks will be awarded according to the following marking scheme:
 Full Marks : +3 If ONLY the correct option is chosen.
 Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
 Negative Marks : –1 In all other cases.

20. Initially both blocks are at rest on a horizontal surface and string is just tight. At t = 0, two constant
horizontal forces F1 and F2 start acting on blocks as shown. f1 and f2 are friction forces acting on 10 kg
and 20 kg block (co–efficient of friction between blocks and ground are 0.5). Values of F 1 and F2 are
given in list–I. Then match magnitudes of f1, f2 and direction of f1 with corresponding values of F1 and
F2 given in list–I. [g = 10 m/s2].

List–I List–II
(P) F2 = 120 N, F1 = 40 N (1) f2 = 100 N , f1 = 20 N
(Q) F2 = 160 N, F1 = 40 N (2) f2 = 20 N , f1 = 50 N
(R) F2 = 60 N, F1 = 90 N (3) f2 = 70 N , f1 = 50 N
(S) F2 = 20 N, F1 = 90 N (4) f2 = 80 N , f1 = 50 N
Codes :
P Q R S
(A) 1 1 2 2
(B) 1 1 3 4
(C) 2 3 4 1
(D) 2 1 4 3
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 CHEMISTRY
CHEMISTRY
Atomic masses : [H = 1, D = 2, Li = 7, C = 12, N = 14, O = 16, F = 19, Na = 23, Mg = 24, Al = 27, Si = 28,
P = 31, S = 32, Cl = 35.5, K = 39, Ca = 40, Cr = 52, Mn = 55, Fe = 56, Cu = 63.5, Zn = 65, As = 75,
Br = 80, Ag = 108, I = 127, Ba = 137, Hg = 200, Pb = 207]
SECTION – 1 : (Maximum Marks : 12)
 This section contains FOUR (04) questions.
 Each question has FOUR options ONLY ONE of these four options is the correct answer.
 For each question, choose the correct option corresponding to the correct answer.
 Answer to each question will be evaluated according to the following marking scheme :
Full Marks : +3 If ONLY the correct option is chosen.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : –1 In all other cases.

21. In a hypothetical compound Cax(CO3)y (OH)z, ratio of hydrogen to oxygen atoms is 1 : 4. Variation of its
mass with moles is given as

Which of the following is incorrect?

(A) ratio of no. of atoms of Ca to C is 2 : 3
(B) ratio of no. of atoms of Ca to O is 3 : 8
(C) ratio of no. of atoms of C to H is 1 : 1
(D) value of x + y + z = 7.

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 CHEMISTRY
22. When Rydberg's equation is written in terms of frequency of photon produced for electronic transition
from n2 to n1 , then how is this frequency related to the debroglie wavelength 2 and 1 in respective
orbits ?
c c c c
(A)  =  (B)  = 
 2 1 1  2

h  1 1  h  1 1 
(C)  =  2  2  (D)  =  2  2 
2m  1  2  2m   2 1 

23. Match this graph with appropriate x & y axes?

x
x y
(A) r 200 (r)
(B) r Radial probability density of 1s
(C) r Radial probability of 311
(D) r Radial wave function of n = 2,  = 1, m = 0

24. An ammonia-ammonium chloride buffer has pH value of 9 when [NH 3] = 0.25 M. What will be new pH, if
500 ml of 0.1 M KOH solution is added to 200 ml of the buffer solution. Kb of NH3 = 2×10–5.
(A) 8.4 (B) 9.6 (C) 5.4 (D) 6.6

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 CHEMISTRY
SECTION – 2 : (Maximum Marks : 24)
 This section contains SIX (06) questions.
 Each question has FOUR options ONE OR MORE THAN ONE of these four option(s) is(are) correct
answer(s).
 For each question, choose the option(s) corresponding to (all) the correct answer(s).
 Answer to each question will be evaluated according to the following marking scheme.
Full Marks : +4 If only (all) the correct option(s) is (are) chosen.
Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.
Partial Marks : +2 If three or more options are correct but ONLY two options are chosen and both of
which are correct.
Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct
option.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : –2 In all other cases.

25. A gaseous substance AB2(g) converts to AB(g) in presence of solid A(s) as

AB2(g) + A(s) 2 AB(g)
The initial pressure and equilibrium pressure are 0.7 bar and 0.95 bar. Now the equilibrium mixutre is
expanded reversibly and isothermally till the total gas pressure falls to 0.4 bar. Then select correct
option(s) ?
(A) Mole percent of AB(g) at final equilibrium is nearly 27%
(B) Mole percent of AB2(g) at final equilibrium is nearly 32.5%
5
(C) Kp for the equilibrium is
9
(D) Ratio of equilibrium pressure of AB2(g) at initial and final equilibrium is more than 2 but less than 3

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 CHEMISTRY
26. (I) For the reaction X(g) Y(g) + 2C(g). Initially only X(g) was taken.

A
B

Effect 1 Effect 2 t
Vapour density and  are plotted w.r.t. time, then choose the correct options, if effect 2 is addition of
inert gas at constant pressure.
(A) Graph ‘A’ is vapour density and Graph ‘B’ is ‘’
(B) Graph ‘A’ is  and graph ‘B’ is vapour density
MX
(C) The vapour density of the mixture would be given by
2(1  2)
(D) All of these

27. The following graphs represent the behavior of BaCO 3 under different circumstances. In each case the
vertical axis indicates the solubility of the BaCO 3 and the horizontal axis represents the concentration of
some other reagent.

Which of the following is correct?

(A) Curve (i) represents addition of Na2CO3 to a solution containing BaCO3.
(B) Curve (ii) represents addition of NaNO3 to a solution containing BaCO3.
(C) Curve (iii) represents addition of HNO3 to a solution containing BaCO3.
(D) None of the above statements are correct.

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 CHEMISTRY
28. Photocurrent (i) versus anode potential (V) is plotted for two experiments of photoelectric effect done on
the same metal. Which of the following statement is/are true?

(A) Intensity of incident light is same in both experiments.

(B) Frequency of incident light is same in both experiments.
(C) Stopping potential is same in both experiments.
(D) KE of fastest photoelectron is same in both experiments.

29. The ratio of slopes of Kmax vs  and V0 vs  curves in the photoelectric effect does not give
(= frequency, Kmax = maximum KE, V0 = stopping potential )
(A) Charge of electron (B) Planck's constant
(C) De Broglie wavelength () (D) Work function (w)

30. A 150 ml of solution of I2 is divided into two unequal parts.  part reacts with hypo solution in acidic
medium. 15mL of 0.4 M hypo was consumed.  part was added to 100 ml of 0.3M NaOH solution
Residual base required 10 ml of 0.3 M H2SO4 solution for complete neutralization. The initial
concentration of I2 and total millimoles of I2 consumed are –
  – + S 4O 6
2– 2–
Reactions are I 2 + S2O3 
–
I2 + OH–  – + O3
(A) 15 m mole (B) 0.1 M (C) 20 m mole (D) 0.2 M

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 CHEMISTRY
SECTION – 3 : (Maximum Marks : 15)
 This section contains FIVE (05) questions. The answer to each question is a NUMERICAL VALUE.
 For Online:
For each question, enter the correct numerical value of the answer using the mouse and the on-screen
virtual numeric keypad in the place designated to enter the answer. If the numerical value has more
than two decimal places, truncate/round-off the value to TWO decimal places.
 For Offline:
If the numerical value has more than two decimal places truncate/round-off the value to TWO decimal
placed.
 Answer to each question will be evaluated according to the following marking scheme :
Full Marks : +3 If ONLY the correct numerical value is entered.
Zero Marks : 0 In all other cases.

31. A natural gas sample contains 84% (by mole) of CH4, 10% of C2H6, 3% of C3H8 and 3% of N2. If a
series of catalytic reactions could be used for converting all the carbon atoms of the gas into butadiene,
C4H6, with 100% efficiency, how much butadiene (in kg) could be prepared from 6 kg of the natural
gas? (Give answer by rounding off to nearest integer).

32. A certain transition in H sample from an excited state to the ground state in one or more steps gives
rise to total 28 lines. How many of these belong to the UV spectrum?

33. When the Bayer process is used for recovering aluminium from siliceous ores, some aluminium is
always lost because of the formation of an unworkable 'mud' having the following average formula :
3Na2O.3Al2O3.5SiO2.5H2O. Since Al3+ & Na+ are always in excess in the solution from which this
precipitate is formed, the precipitation of the silicon in the 'mud' is complete. A certain ore contained
15% (by mole) kaolin (Al2O3.2SiO2.2H2O) and 85% gibbsite (Al2O3.3H2O) what percent of the total
aluminium in the ore is recoverable in the Bayer's process?

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 CHEMISTRY
34. The isothermal variation of pressure (in atm) with respect to time for each gas is shown in the following
curve for the homogenous equilibrium reaction

A(g) + nB(g) 
 mC(g)
The reaction is being conducted in a rigid container. What is the value of (m + n)?

35. One of the healing & air purifying effects of yajan(Hawan) performed by putting ghee in Agni is to
produce heat, CO2 and H2O which in turn can react together in inverted pyramid shaped to form
formaldehyde (with antibacterial and antiseptic properties) as
CO2(g) + H2O(g) + 112000 cal HCHO + (g) O2(g) ; Kp.
If the temperature is increased from 800 K to 823 K, how many times Kp will be increased? Assume H
to be constant in the given temperature range.
[Take R = 2 cal K–1 mol–1, ln 10 = 2.3, log 2 = 0.3, log 3 = 0.48, log 7 = 0.85].

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 CHEMISTRY
SECTION – 4 : (Maximum Marks : 12)
 This section contains TWO (02) paragraphs
 Based on each paragraph, there will be TWO questions.
 Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four option is correct 
 Marking scheme :
 Full Marks : +3 If ONLY the correct option is chosen.
 Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
 Negative Marks : –1 In all other cases

Paragraph for Question Nos. 36 to 37

A weak base BOH is titrated with a strong acid HA. When 10 ml of HA is added, the p H is 10.3 and
when 25 ml of HA is added the pH is 9.3.
In another experiment 40g of the salt BA is dissolved in water to make 1L aq. solution. The pH of
solution is found to be 5.15. If salt BA forms NaCl type crystal having rB  = 8Å and rA – = 1.2Å

(log 2 = 0.3, NA = 6 × 1023).

36. Find pKb of BOH:

(A) 4 (B) 5 (C) 5.3 (D) 3.7

37. Find density of BA crystal in g/ml.

(A) 6.66 (B) 8.33 (C) 12.33 (D) 9.66

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 CHEMISTRY
Paragraph for Question Nos. 38 to 39

Characteristics of equilibrium constant & factors affecting it :



  Equilibrium constant does not depend upon concentration of various reactants, presence of
catalyst, direction from which equilibrium is reached
 The equilibrium constant does not give any idea about time taken to attain equilibrium.
  K depends on the stoichiometry of the reaction.

38. When 10 gram-molecules of iodine (vapour) are allowed to react with 10 gram-molecules of hydrogen
at 945ºC an equilibrium H2(g) + 2(g) 2H(g) is set up. Select incorrect option :
Given : KC = 49 at 945ºC.
(A) Kp = Kc
(B) Kp = 49
(C) Moles of H2 present at equilibrium is 2.3 mol.
(D) Moles of HI formed at equilibrium is 7.7 mol.

39. An arbitrary compound P2Q decomposes according to reaction :

2P2Q (g) 2P2 (g) + Q2 (g)
If one starts the decomposition reaction with 4 moles of P2Q and value of equilibrium constant Kp is
numerically equal to total pressure at equilibrium. Then which option is incorrect at equilibrium ?
(A) Moles of P2Q nP Q  = Moles of Q nQ2 
2
2

(B) Moles of P2 nP2  = (8/3)

(C) Total number of moles at equilibrium is 12.
(D) Total number of moles of products (P2 & Q2) at equilibrium is 4

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 CHEMISTRY
SECTION – 5 : (Maximum Marks : 8)

 This section contains ONE questions

 Each question contains two columns, Column I and Column II
 Column I has four entries (A),(B), (C) and (D)
 Column II has five entries (P),(Q), (R), (S) and (T)
 Match the entries in Column I with the entries in Column II
 One or more entries in Column I may match with one or more entries in Column II
 The ORS contains a 4 × 5 matrix whose layout will be similar to the one shown below :

(A)
(B)
(C)
(D)

 For each entry in Column I, darken the bubbles of all the matching entries. For example, if entry (A) in
Column Imatches with entries (P), (Q), and (R), then darken these three bubbles in the ORS.
Similarly, for entries (B), (C) and (D).


 Marking scheme :
For each entry in Column I
+2 If only the bubble(s) corresponding to all the correct match(es) is (are) darkened
0 If none of the bubbles is darkened
–1 In all other cases

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 CHEMISTRY
40. For an experiment of photoelectric effect: (h is Planck's constant, e is electronic charge, c is speed of
light, º is threshold frequency, º is threshold wavelength)

Column-I Column -II

(A) Graph between maximum kinetic energy (P) Linear with negative intercept
v/s frequency of incident radiation function of metal

(B) Graph between maximum kinetic energy (Q) Linear and negative intercept equal to hº
1
v/s where  is wavelength of

incident radiation

h º
(C) Graph between stopping potential (R) Linear and negative intercept equal to
e
v/s frequency of incident radiation

(D) Graph between stopping potential (S) Linear and negative intercept equal to
1 hc
v/s where  is wavelength of
 ºe
incident radiation

(T) Using slope of linear graph and/or some

other constants (c and e) value of Planck's
constant can be determined.

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 MATHEMATICS
MATHEMATICS
SECTION – 1 : (Maximum Marks : 12)
 This section contains FOUR (04) questions.
 Each question has FOUR options ONLY ONE of these four options is the correct answer.
 For each question, choose the correct option corresponding to the correct answer.
 Answer to each question will be evaluated according to the following marking scheme :
Full Marks : +3 If ONLY the correct option is chosen.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : –1 In all other cases.

41. If x5 + x2 + 1 = 0 have roots x1,x2, x3, x4, x5 and g(x) = x2 + 4 then the value of g(x1). g(x2). g(x3). g(x4).
g(x5) is
(A) 1033 (B) 1096 (C) 998 (D) 994

r 3  (r 2  1)2
42.  (r
r 1
4
 r 2  1)(r 2  r)
=

3
(A) (B) 1 (C) 2 (D) infinite
2

1 1
43. If and are the roots of the equation, ax2 + bx + 1 = 0 (a  0, b  R), then the equation,
 
x(x + b3) + (a3 – 3abx) = 0 has roots
(A) 3/2 and 3/2 (B) 1/2 and 1/2  (C)  and  (D) –3/2 and –3/2

44. The number of x  [0, 2] for which 2 sin4 x  18 cos2 x  2 cos4 x  18 sin2 x = 1 is

(A) 6 (B) 4 (C) 8 (D) 2

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 MATHEMATICS
SECTION – 2 : (Maximum Marks : 24)
 This section contains SIX (06) questions.
 Each question has FOUR options ONE OR MORE THAN ONE of these four option(s) is(are) correct
answer(s).
 For each question, choose the option(s) corresponding to (all) the correct answer(s).
 Answer to each question will be evaluated according to the following marking scheme.
Full Marks : +4 If only (all) the correct option(s) is (are) chosen.
Partial Marks : +3 If all the four options are correct but ONLY three options are chosen.
Partial Marks : +2 If three or more options are correct but ONLY two options are chosen and both of
which are correct.
Partial Marks : +1 If two or more options are correct but ONLY one option is chosen and it is a correct
option.
Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
Negative Marks : –2 In all other cases.

45. If a,b,c, are in A.P with non – zero common difference and x, y, z are in G.P. , then the point’s (a,x) ,
(b,y) and (c,z) are collinear, if
(A) y2 = z (B) x = z2 (C) x2 = y (D) x = y = z

(a  x)(b  x)
46. If y = where a, b > c and x > – c, then which of the following is/are true ?
(c  x)

(A) minimum value of y is ( a – c + b – c )2

(B) minimum value of y occurs at x = (a – c)(b – c) – c

(C) minimum value of y is ( a – c – b – c )2

(D) None of these

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 MATHEMATICS
47. Consider the equation x4 + 2ax3 + x2 + 2ax + 1 = 0, where aR. Then which of the following is/are true.
 –3 
(A) If equation has atleast two distinct positive real roots, then a   – ,
 4 

3 
(B) If equation has atleast two distinct negative real roots, then a   ,  
4 
(C) If exactly two roots are positive and two roots are negative, then number of integral values of 'a' is 0
(D) If exactly two roots are positive and two roots are negative, then number of integral values of 'a' is 1

48. Three numbers in AP are removed from first 'n' consecutive natural numbers and average of remaining
43
numbers is found to be . Then which of the following is/are true
4
(A) Number of prime numbers less than 'n' is 7
(B) Number of prime numbers less than 'n' is 11
(C) Number of sets of three removed numbers is 5
(D) Number of sets of three removed numbers is 6

49. If cot = (a3 + a2 + a)1/2, cot = (a + a–1 + 1)1/2, cot = (a–3 + a–2 + a–1)–1/2, where a > 0 then which of the
following may be true.
(A)  +  –  = 0 (B)  +  +  = 0 (C)  +  –  =  (D)  +  +  = 

50. Which of the following is/are true
(A) sec40° + sec80° + sec160° = 6 (B) tan2 40° + tan2 80° + tan2 160° = 33
1 1
(C) cos40° cos80° cos160° = (D) cos40° cos80° cos160° = –
8 8

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 MATHEMATICS
SECTION – 3 : (Maximum Marks : 15)
 This section contains FIVE (05) questions. The answer to each question is a NUMERICAL VALUE.
 For Online:
For each question, enter the correct numerical value of the answer using the mouse and the on-screen
virtual numeric keypad in the place designated to enter the answer. If the numerical value has more
than two decimal places, truncate/round-off the value to TWO decimal places.
 For Offline:
If the numerical value has more than two decimal places truncate/round-off the value to TWO decimal
placed.
 Answer to each question will be evaluated according to the following marking scheme :
Full Marks : +3 If ONLY the correct numerical value is entered.
Zero Marks : 0 In all other cases.

51. If 4a2x4 + 8x3 + 33x2 + 4ax + 16 is a perfect square then find

2  a 
5

7
52. Find maximum value of 'a' if the inequality 1 + log 2(2x2 + 2x + )  log2 (ax2 + a) posseses at least one
2
solution

 
1 a a  b
53. If the value of 
i0 j0 5i5 j
is
b
(where a & b are co-prime natural numbers) then find value of
2
(i  j)

1
54. If cos4 sec2, , sin4cosec2  are in AP then find the value of (cos8 sec6+ sin8 cosec6)
2

55. If ax2 + bx – 6 = 0 does not have distinct real roots then find maximum value of
3a  b .
3

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 MATHEMATICS
SECTION – 4 : (Maximum Marks : 12)
 This section contains TWO (02) paragraphs
 Based on each paragraph, there will be TWO questions.
 Each question has FOUR options (A), (B), (C) and (D). ONLY ONE of these four option is correct 
 Marking scheme :
 Full Marks : +3 If ONLY the correct option is chosen.
 Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
 Negative Marks : –1 In all other cases

Paragraph for Question Nos. 56 to 57

We know that arithmetic mean of the positive numbers lie between them. Let S1 > S2 > 0 and
1
Sn+1 = (Sn + Sn–1), n  2, n  N. Then answer the following questions.
2
56. Which of following is/are true
(A)The sequence {S2n}, n  N is increasing and the sequence {S2n+1}, n  N is decreasing
(B) The sequence {S2n}, n  N is decreasing and the sequence {S2n+1}, n  N is increasing
(C) The sequence {S2n}, n  N is decreasing and the sequence {S2n+1}, n  N is decreasing
(D) can't say anything

57. (S2n+1 – S2) must be equal to

( S1 – S 2 )  1  ( S1 – S 2 )  1 
(A)  1  2n – 1  (B) 1  2n 
3  2  3  2 

(S1 – S 2 )  1  ( S1 – S 2 )  1 
(C) 1 – 2n –1  (D) 1 – 2n 
3  2  3  2 

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 MATHEMATICS
Paragraph for Question Nos. 58 to 59

If roots of f(x) = x2 + ax + b = 0 are ,  and g(x) = x2 + px + q = 0 are + h, + h. If least value of f(x)
1 7
is and least value of g(x) occurs at x = then
4 2

58. The least value of g(x) is

1 1 5
(A) 1 (B) (C) (D)
4 2 2

59. Value of q is
3
(A) 12 (B) – 15 (C) (D) 7
2

SECTION – 5 : (Maximum Marks : 12)

 This section contains ONE (01) questions.
 Each question has TWO matching lists: LIST-I and LIST-II.
 FOUR options are given representing matching of elements from LIST-I and LIST-II. ONLY ONE of these
four options corresponds to a correct matching.
 For each question, choose the option corresponding to the correct matching.
 For each question, marks will be awarded according to the following marking scheme:
 Full Marks : +4 If ONLY the correct option is chosen.
 Zero Marks : 0 If none of the options is chosen (i.e. the question is unanswered).
 Negative Marks : –1 In all other cases.

60. Match List I with List II : –

List - I List - II
(A) Equation x2 + a | x| + 1 = 0 has two real roots then a  (P) –1

(B) If x R then minimum value of x6 – 8x4 +19x2 – 12x +11 is (Q) –2

(C) If x2 – (a – 3) x + 2 < 0  x  (– 2, – 1), then a can be (R) 1

(D) Roots of equation x2 – bx + cSpace for

= 0 are Rough
two Work
consecutive (S) 
integer then b – 4c =
2

(T) –3

(A) (A)  Q ; (B)  S ; (C)  R ; (D)  R

(B) (A)  P ; (B)  R ; (C)  T ; (D)  S
(C) (A)  Q ; (B)  P ; (C)  S ; (D)  T
(D) (A)  Q ; (B)  P ; (C)  S ; (D)  S

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