PRADEEP AGARWAL ACADEMY 14.06.2020.
PRA D EEP AGA RW A L ACA D EM Y
I I T / M ED I C A L
Create an edge with the best IIT Faculty Combined JEE Advanced Test -1
TIME: 3 Hours Maximum Marks: 198 6. A block of mass m is placed on a wedge of mass 2m which rests
on a rough horizontal surface. There is no friction between the
PHYSICS block and the wedge. The minimum coefficient of friction
SECTION 1 (Maximum Marks: 30) between the wedge and the ground so
This section contains TEN questions. ONLY ONE of the that the wedge does not move is m
2m
four options is correct. (a) 0.167 (b) 0.20
4 50
+3 Marks will be awarded for correct option and –1 Marks (c) 0.23 (d) 0.33
for wrong option.
7. Two bodies of identical mass are tied by an ideal string
which passes over an ideal pulley. The co-efficient of
1. Three blocks A, B and C weighing 1 kg, 8 kg and 27 kg friction between the bodies and
respectively are connected as shown in the figure with an the plane is . The minimum
inextensible string and are moving on a smooth surface. value of for which the system
If T3 = 36 N, then T2 = starts moving is
2 1 2 1
T3
(a) cos 2 (b) cos
T1 T2 C
1 2
A B -1 -1
1
(a) 18 N (b) 9 N
(c) 3.375 N (d) 1.25 N 2 1 2
(c) cos -1 (d) cos–1
2
1 2 1
2. Block B moves to the right with a constant velocity v0. The
velocity of body A relative to B is 8. In the arrangement shown in the figure, there is friction
between the blocks of mass m and 2m. Block of mass 2m is
kept on a smooth horizontal plane. The mass of the
suspended block is m. If block
A is stationary with respect to
(a) v0 /2 towards left (b) v0 /2 towards right block B, the minimum value of
(c) 3v0 /2 towards left (d) 3v0 /2 towards right coefficient of friction between
m and 2m is m C
3. A block of mass M = 5 kg is resting on a rough horizontal
surface for which the coefficient of friction is 0.2. When a (a) 1 /2 (b) 1 / 2 A m
B 2m
force F = 40 N is applied, the acceleration of the block will (c) 1 / 4 (d) 1 /3
be (g = 10 m/s2)
(a) 5.73 m/sec2 9. Two masses A and B of 10 kg and 5 kg respectively are
(b) 8.0 m/sec2 connected with a string passing over a frictionless pulley
(c) 3.17 m/sec2 fixed at the corner of a table as
(d) 10.0 m/sec2 shown. The coefficient of static
friction of A with table is 0.2.
4. A block A of mass 100 kg is resting on another block B of The minimum mass of C that
mass 200 kg. As shown in figure, a horizontal rope tied to may be placed on A to prevent
a wall holds it. The coefficient of friction between A and it from moving is
B is 0.2 while coefficient of friction between B and the (a) 15 kg (b) 10 kg
ground is 0.3. The minimum force F required to start (c) 5 kg (d) 12 kg
moving B is
(a) 900 N 10. In the arrangement shown in figure,
(b) 100 N pulleys are massless and frictionless
(c) 1100 N and threads are inextensible. Block
(d) 1200 N of mass m1 will remain at rest if
5. For the arrangement shown in figure, the masses of the blocks 1 1 1
(a) m m m
are mA = 2 kg, mB = 1 kg, mC = 1 kg. The frictional force between 1 2 3
the blocks A and B and the tension in string connecting A and 4 1 1
B are respectively (coefficient (b)
m1 m2 m3
of friction between any two B
(c) m1 = m2 + m3
surfaces is 0.5) A
(a) 0, 5 N (b) 0, 0 1 2 3
(d) m m m
(c) 10 N, 5 N (d) 5 N, 0 C 1 2 3
PRADEEP AGARWAL ACADEMY 37, Housing Board Colony, Near Jyoti Hospital, Jharsa Road. 1
PRADEEP AGARWAL ACADEMY 14.06.2020.
PRA D EEP AGA RW A L ACA D EM Y
I I T / M ED I C A L
Create an edge with the best IIT Faculty Combined JEE Advanced Test -1
SECTION 2 (Maximum Marks: 36) 15. In the given figure, all surface are frictionless and strings
This section contains NINE questions. ONE OR MORE and pulleys are massless.Then,
THAN ONE of the four option(s) is(are) correct. A C
+4 Marks will be awarded for all correct options, Partial m m
Marks +1 for each correct option provided that NO incor-
m
rect option is marked and –2 Marks if even a single incor- m B
D
rect option is marked.
2m Wedge
11. Two blocks of equal masses (M) are connected by a string
and are kept on rough horizontal surface as shown in the (a) acceleration of block B is g/2.
figure. The coefficient of friction between the blocks and (b) acceleration of block B is zero.
the surface is . If 0 < F1 – F2 < 2Mg , then choose the (c) acceleration of wedge is zero.
correct statement B A (d) acceleration of wedge is g/2.
F2 F1
16. Figure shows a wedge of mass
(a) the direction of friction on block A is towards right. 2kg resting on a frictionless
(b) the direction of friction on block B is towards left. floor. A block of mass 1 kg is kept
(c) tension in the string must be zero. on the wedge and the wedge is
(d) friction force on block B must be zero. given an acceleration of 5 m/s2
towards right. Then
12. Two blocks of masses m and 2m are placed one over the (a) block will remain stationary w.r.t. wedge
other as shown in figure. The coefficient of friction between (b) block will have acceleration of 2 m/s2 w.r.t. wedge
m and 2m is and between 2m and ground is / 3 . If a (c) normal reaction on the block is 11 N
horizontal force F is applied on upper block and T is tension (d) net force acting on the wedge is 10 N
developed in string, then choose the correct alternatives
17. A trolley of mass 8 kg is standing on a frictionless surface
(a) If F mg / 3 , T = 0 m F inside which an object of mass 2 kg is suspended. A
(b) If F mg , T = 0 2m constant force F starts acting on the trolley as a result of
which the string gets inclined at an angle of 37 0 from the
(c) If F 2mg , T mg / 3 vertical. Then,
(d) If F 3mg , T = 0 (a) acceleration of the trolley
is (40/3) m/s2
13. Coefficient of friction between 2k g (b) force applied in 60 N
T1
the two blocks is 5/8 whereas (c) force applied is 75 N
3k g
the surface AB is smooth. T2 (d) tension in the string is 25 N
A B
(g =10 ms–2) 18. Two blocks A and B of equal mass m are connected through
(a) Acceleration of the system a massless string and arranged as shown in figure. Friction
of masses is 5 ms–2 10kg
is absent everywhere. When the system is released from rest.
(b) Tension T1 in the string is 22.5 N
(c) Tension T2 in the string is about 50 N
(d) Acceleration of 10 kg mass is 7.5 ms–2
14. A block P of mass 4 kg is placed on horizontal rough surface
A
with coefficient of friction = 0.6. Two blocks R and Q of Fixed
masses 2 kg and 4 kg are connected with the help of massless
30°
strings A and B respectively passing over frictionless pulleys B
as shown. Then (g = 10m/s2) (a) tension in string is mg/2
P
B A (b) tension in string is mg/4
4kg
(c) acceleration of A is g/2
= 0.6 (d) acceleration of A is 3g/4
19. A block is placed over a plank. The coefficient of friction
4kg 2kg between the block and the plank is µ = 0.2 . Initially both
Q R are at rest. Suddenly, the plank starts moving with accel-
(a) acceleration of block P is zero. eration a0 = 4 m/s2. The displacement of the block in 1s is
(b) tension in string A is 20 N. (g =10 m/s2)
(c) tension in string B is 40 N. (a) 1 m relative to ground (b) 1 m relative to plank
(d) contact force on block P is 20 5 N (c) zero relative to plank (d) 2 m relative to ground
PRADEEP AGARWAL ACADEMY 37, Housing Board Colony, Near Jyoti Hospital, Jharsa Road. 2
PRADEEP AGARWAL ACADEMY 14.06.2020.
PRA D EEP AGA RW A L ACA D EM Y
I I T / M ED I C A L
Create an edge with the best IIT Faculty Combined JEE Advanced Test -1
9. What would be the molality of 20% (mass/ mass) aqueous
CHEMISTRY solution of KI? (molar mass of KI = 166g mol–1)
SECTION 1 (Maximum Marks: 27) (a) 1.08 (b) 1.48
This section contains NINE questions. ONLY ONE of the (c) 1.51 (d) 1.35
four options is correct.
+3 Marks will be awarded for correct option and –1 Marks
for wrong option. SECTION 2 (Maximum Marks: 24)
This section contains SIX questions. ONE OR MORE THAN
1. 10 mL of gaseous hydrocarbon on combustion gives 40 ONE of the four option(s) is(are) correct.
mL of CO2 (g) and 50 mL of H2O (vapour). Using Gay +4 Marks will be awarded for all correct options, Partial
lussac’ law of gaseous volumes, The hydrocarbon is Marks +1 for each correct option provided that NO incor-
(a) C4 H5 (b) C8 H10 rect option is marked and –2 Marks if even a single incor-
(c) C4 H8 (d) C4 H10 rect option is marked.
2. Hydrochloric acid solutions A and B have concentrations
10. Which is Correct Match:
0.5 M and 0.1 M respectively. The volumes of solution A (a) 1 M glucose solution-- 1 mol solute per litre solution
and solution B required to make a 2-litre solution of 0.2 M (b) 3 M urea (NH2CONH2) solution - 180 g solute per litre
HCI are solution
(a) 0.5 L of A and 1.5 L of B (c) 3 M CH3COOH solution - % w/v = 18% (solution)
(b) 3.5 L of A and 0.5 L of B (d) 1 M H2SO4 solution- % w/v = 9.8% (solution)
(c) 1.0 L of A and 1.0 L of B
(d) 0.75 L of A and 1.25 L of B 11. In which of the following pairs do 1 g of each have an equal
number of molecules?
3. The percentage composition of carbon by mole in methane
(a) N2O and CO (b) N2 and C3O2
is:
(c) N2 and CO (d) N2O and CO2
(a) 80% (b) 25%
(c) 75% (d) 20% 12. Which is Correct Match:
4. 8 g of NaOH is dissolved in 18 g of H2O. Mole fraction of (a) 24 atoms of ‘O’ - 1.5 moles
NaOH in solution and molality (in mol kg–1) of the solutions (b) 2 mole of CaCO3 - 10 NA atoms
respectively are: (c) 5 moles of O2 - 200 g
(a) 0.167, 11.11 (b) 0.2, 22.20 (d) 24 g of ‘C’ atom - 2 atoms of C
(c) 0.2, 11.11 (d) 0.167, 22.20
13. Select the incorrect statement(s) :
5. In the reaction CrO5 + H2SO4 Cr 2(SO4)3 + H2O + O 2 [Take STP as 1 bar pressure & 273 K]
one mole of CrO5 will liberate how many moles of O2 (a) Mass of 6.022 × 1025 molecule of SO3 is 8 kg.
(a) 5/2 (a) 5/4 (b) Number of oxygen atoms in 4.8 g of O3 are 18.06 × 1023
(c) 9/2 (d) 7/4 (c) Mass of 22.7 ml of C2H6 at STP is 30 gm
(d) Volume of 51 mg of NH3 at STP is 68.1 l .
6. SO2Cl2 reacts with water to give a mixture of H2SO4 and HCl.
How many moles of NaOH would be needed to neutralize the 14. The true statement out of the following is /are
solution formed by adding 1 mole of SO2Cl2 to excess water (a) Density of an ideal gas is proportional to (P/T)
(a) 1 (b) 3 (b) 1 g O, 1 g O2 and 1 g O3 has same number of atoms.
(c) 2 (d) 4 (c) Non- stoichiometric compounds do not obey law of
constant proportions.
7. An organic compound is estimated through Dumus method
(d) One g-atom of each element contains the same number
and when heated with dry CuO, was found to evolve 6
of atoms.
moles of CO2, 4 moles of H2O and 1 mole of nitrogen gas.
The formula of the compound is: 15. If 0.5 mol of BaCl2 is mixed with 0.20 mol of Na3PO4,
(a) C12 H8 N (b) C12H8N2 (a) The maximum amount of Ba3(PO4)2 that can be formed is
(c) C6H8N (d) C6H8N2 0.10 mol.
8. Total number of neutrons present in 4 g of heavy water (D2O) (b) The maximum amount of Ba3(PO4)2 that can be formed is
is : (Where NA represents Avogadro's number) (D represents 0.20 mol.
deuterium=1H2) (c) Na3PO4 is limiting reagent.
(a) 2.4 NA (b) 4NA (d) Na3PO4 is excess reagent.
(c) 1.2 NA (d) 2NA
PRADEEP AGARWAL ACADEMY 37, Housing Board Colony, Near Jyoti Hospital, Jharsa Road. 3
PRADEEP AGARWAL ACADEMY 14.06.2020.
PRA D EEP AGA RW A L ACA D EM Y
I I T / M ED I C A L
Create an edge with the best IIT Faculty Combined JEE Advanced Test -1
16. Which is Correct Match: 18. If Vapor Density of gaseous compound is 100. What is the
For 1 mole of reactant placed in open container in each reaction molecular formula of compound :
(a) C5H8O2 (b) C10H16O4
(a) PCl5 (g)
PCl3 (g) + Cl2(g) - 2N A product
(c) C15H2O8 (d) C4H8O2
molecules
19. Compute weight of carbon present in 2 mole of compound :
(b) CaCO3 (s)
CaO(s) + CO2 (g) - 67.2 litre gaseous (a) 240 g (b) 120 g
(c) 480 g (d) 60 g
product at STP
(c) 2HCl (g)
H2 (g) + Cl2 (g)- 22.4 litre gaseous PARAGRAPH 2
Questions No . 20 to 21 (2 questions) are based on the
product at STP
following comprehension.
(d) NH4COONH2 (s)
2NH3(g) + CO2(g) - 44.8 litre Limiting reagent is that reactant which (when completely
consumed) produces least amount of a particular product.
gaseous product at STP
20. 50 mL solution of BaCl2 (20.8% w/v) and 100 mL solution
of H2SO4 (9.8% w/v) are mixed
SECTION 3 (Maximum Marks: 15)
(Ba = 137, Cl = 35.5, S = 32)
This section contains TWO paragraphs. ONLY ONE of the
four options is correct. BaCl2 + H2SO4 BaSO4 + 2HCl
+3 Marks will be awarded for correct option and –1 Marks BaSO4 formed is :
for wrong option (a) 23.3 g (b) 46.6 g
(c) 29.8 g (d) 11.65 g
PARAGRAPH 1
21. Which is limiting reagent in the above case in question:
Questions No . 17 to 19 (3 questions) are based on the
(a) BaCl2 (b) H2SO4
following comprehension.
(c) both(a) and (b) (d) none of these
A compound CxHyOz was analysed on the mass basis and
pencentage of different element in compound was calcu-
lated as below : C = 60%, O = 32%, H = 8%
17. What is the empirical formula of compound.
(a) C5H8O2 (b) C10H16O4
(c) C15H2O8 (d) C4H8O2
PRADEEP AGARWAL ACADEMY 37, Housing Board Colony, Near Jyoti Hospital, Jharsa Road. 4
PRADEEP AGARWAL ACADEMY 14.06.2020.
PRA D EEP AGA RW A L ACA D EM Y
I I T / M ED I C A L
Create an edge with the best IIT Faculty Combined JEE Advanced Test -1
SECTION 2 (Maximum Marks: 28)
MATHEMATICS This section contains SEVEN questions. ONE OR MORE
SECTION 1 (Maximum Marks: 21) THAN ONE of the four option(s) is(are) correct.
+4 Marks will be awarded for all correct options, Partial
This section contains SEVEN questions. ONLY ONE of the Marks +1 for each correct option provided that NO incor-
four options is correct. rect option is marked and –2 Marks if even a single incor-
+3 Marks will be awarded for correct option and –1 Marks rect option is marked.
for wrong option
8. The correct statement is / are
1. The equation whose roots are sec2 and cosec2 can be (a) If x1 and x2 are roots of the equation 2x2 – 6x – b = 0
(Given that sin 2 2sin cos ) x x
(b > 0), then 1 2 2
(a) 2x2 – x – 1 = 0 (b) x2 – 3x + 3 = 0 x2 x1
(c) x – 9x + 9 = 0
2
(d) x2 + 3x + 3 = 0 (b) Equation ax2 + bx + c = 0 has real roots if a < 0, c > 0 and
b R
2. If a, b, c are real distinct numbers satisfying the condition (c) If P(x) = ax2 + bx + c and Q(x) = –ax2 + bx + c, where
a + b + c = 0 then the roots of the quadratic equation 3ax2 ac 0 and a, b, c R, then P(x).Q(x) has at least
+ 5bx + 7c = 0 are two real roots.
(a) always equal (d) If both the roots of the equation (3a + 1)x2 – (2a +3b)x +
(b) always imaginary 3 = 0 are infinite then a = 0 and b R
(c) always real and distinct
(d) can be real as well imaginary 9. If 1 2 3 4 5 6 , then the equation
( x 1 )( x 3 )( x 5 ) 3( x 2 )( x 4 )( x 6 ) 0 has
3. The set of values of ‘a’ for which the inequality (x – 3a) (x – a
(a) three real roots (b) no real root in (, 1 )
– 3) < 0 is satisfied for all x in the interval 1 x 3
(a) (1/3, 3) (b) (0, 1/3) (c) one real root in (1 , 2 ) (d) no real root in ( 5 , 6 )
(c) (–2, 0) (d) (–2, 3) 10. Equation 2x2 – 2(2a + 1)x + a(a + 1) = 0 has one root less than
4. If p and q are distinct reals, then 2 {(x – p) (x – q) + (p – x) (p 'a' and other root greater than 'a', then
– q) + (q – x) (q – p)} = (p – q)2 + (x – p)2 + (x – q)2 is satisfied (a) 0 < a < 1 (b) –1 < a < 0
by (c) a > 0 (d) a < –1
(a) no value of x (b) exactly one value of x 11. Graph of y = ax2 + bx + c = 0 is given adjacently. What
(c) exactly two values of x (d) infinite values of x conclusions can be drawn y
5. The value of 'a' for which the expression from this graph -
(a) a > 0
y x 2a a 3 x 4 is perfect square, is -
2 2
(b) b < 0 O x
(a) 4 (b) 3 (c) c < 0
(d) b2 – 4ac > 0 Vertex
(c) 2 (d) a (, 3] [ 3, )
12. The adjoining figure shows the graph of y = ax2 + bx + c.
6. Set of values of 'K' for which roots of the quadratic Then y
x2 – (2K – 1)x + K(K – 1) = 0 are - (a) a > 0 Vertex
(a) both less than 2 is K (1, ) (b) b > 0
(b) of opposite sign is K (,0) (1, ) (c) c > 0
(d) b2 < 4ac x1 x2 x
(c) of same sign is K (,0) (1, )
(d) both greater than 2 is K (2, ) 13. Which of the following is correct for the quadratic equation
x2 + 2 (a – 1) x + a + 5 = 0
1 1 (a) the equation have positive roots, if a (5, 1)
3
7. The number of real roots of x x 0 is
x x (b) the equation have roots of opposite sign, if a (, 5)
(a) 0 (b) 2
(c) the equation have negative roots, if a [4, )
(c) 4 (d) 6
(d) none of these
PRADEEP AGARWAL ACADEMY 37, Housing Board Colony, Near Jyoti Hospital, Jharsa Road. 5
PRADEEP AGARWAL ACADEMY 14.06.2020.
PRA D EEP AGA RW A L ACA D EM Y
I I T / M ED I C A L
Create an edge with the best IIT Faculty Combined JEE Advanced Test -1
14. Which of the following is true for all real solutions
( x, y ) of the equations x2 + y2 – 8x – 8y = 20 and xy + 4x SECTION 4 (Maximum Marks: 8)
+ 4y = 40 Following question contains statements given in two
(a) There are four distinct pair of solutions columns, which have to be matched. The statements in
(b) All real solutions lie on a straight line Column-I are labelled as A, B, C and D while the statements in
(c) | x – y | = 10 for all solutions Column-II are labelled as p, q, r and s. Any given statement in
(d) All real solutions are integral Column-I can have correct matching with ONE OR MORE
statement(s) in Column-II.
SECTION 3 (Maximum Marks: 9) +2 Marks will be awarded if all the correct options are marked
This section contains TWO paragraphs. ONLY ONE of the corresponding to the condition given in Column-I and
four options is correct. 0 Marks will be awarded in all other cases
+3 Marks will be awarded for correct option and –1 Marks
for wrong option 18. Consider the equation x2 + 2(a – 1)x + a + 5 = 0, where
‘a’ is a parameter. Match of the real values of ‘a’ so that
PARAGRAPH 1 the given equation has
Each question has a conditional statement followed by a Column-I Column-II
result statements.
If condition result, then condition is sufficient and 8
(A) imaginary roots (p) ,
7
If result condition, then condition is necessary
(B) one root smaller than 3 and other root greater than 3
If condition is necessary as well as sufficient for the result, (q) (–1, 4)
mark (A) (C) exactly one root in the interval (1, 3) and 1 and 3 are
If condition is necessary but not sufficient for the result, not the root of the equation
mark (B)
If condition is sufficient but not necessary for the result, 4 8
(r) ,
mark (C) 3 7
If neither necessary nor sufficient for the result, (D) one root smaller than 1 and other root greater than 3
mark (D) 4
Consider the following example : (s) ,
3
Condition : a > 0, b > 0
Result : a+b>0
Here, if a > 0 and b > 0, then it always implies that a + b is
positive but if a + b is positive, then a and b both need
not to be positive. So condition result but result does
not always implies condition hence condition is sufficient
but not necessary for the result to be hold. So answer is
‘C’.
15. Condition : Let f(x) = x2 + bx + c, f(2) > 0 and b2 – 4c > 0
Result : Both roots of the quadratic equation x2 + bx + c =
0 are distinct and more than 2
16. Condition : x2 + bx + c = 0 has integral roots
Result : The quadratic equation x2 + bx + c = 0 have b 2 –
4c as a perfect square of an integer and b, c Integer
17. Condition : One of the root of the quadratic equation ax2
+ bx + c = 0, (a, b, c R) is 2 3
Result : Other root of the quadratic equation ax2 + bx + c
= 0, (a, b, c R) is 2 3
PRADEEP AGARWAL ACADEMY 37, Housing Board Colony, Near Jyoti Hospital, Jharsa Road. 6
