)) CLASSROOM CONTACT PROGRAMME JEE(Main) UNIT TEST

)1001CJA136621002)(1001CJA136621002) Test Pattern

CLASSROOM CONTACT PROGRAMME(Academic Session : 2021 - 2022)

JEE(MAIN + ADVANCED) : NURTURE COURSE PHASE-III(A) & LIVE-II

Your Hard Work Leads to Strong Foundation

JEE(Main)UNIT TEST01-08-2021

Corporate Office : ALLEN CAREER INSTITUTE, “SANKALP”, CP-6, Indra Vihar, Kota (Rajasthan) INDIA-324005

+91-744-2757575 [email protected] www.allen.ac.in

En

glis

h

Name of the Candidate (in Capitals)

Form Number : in figures

: in words

Centre of Examination (in Capitals) :

Candidate’s Signature : Invigilator’s Signature :

Do not open this Test Booklet until you are askedto do so.Read carefully the Instructions on this Test Booklet.

Important Instructions :

1. Immediately fill in the form number on this page of the Test Booklet with Blue/Black Ball PointPen. Use of pencil is strictly prohibited.

2. The candidates should not write their Form Number anywhere else (except in the specified space)on the Test Booklet/Answer Sheet.

3. The test is of 3 hours duration.

4. The Test Booklet consists of 90 questions. The maximum marks are 300.

5. There are three parts in the question paper 1,2,3 consisting of Physics, Chemistry andMathematics having 30 questions in each subject and each subject having Two sections.

(i) Section-I contains 20 multiple choice questions with only one correct option.

Marking scheme : +4 for correct answer, 0 if not attempted and –1 in all other cases.

(ii) Section-II contains 10 Numerical Value Type questions. Attempt any 5 questions.First 5 attempted questions will be considered for marking.

Marking scheme : +4 for correct answer and 0 in all other cases.

6. Use Blue/Black Ball Point Pen only for writting particulars/marking responses on Side–1 and Side–2of the Answer Sheet. Use of pencil is strictly prohibited.

7. No candidate is allowed to carry any textual material, printed or written, bits of papers, mobilephone any electronic device etc, except the Identity Card inside the examination hall/room.

8. Rough work is to be done on the space provided for this purpose in the Test Booklet only.

9. On completion of the test, the candidate must hand over the Answer Sheet to the invigilator onduty in the Room/Hall. However, the candidate are allowed to take away this Test Bookletwith them.

10. Do not fold or make any stray marks on the Answer Sheet.

Paper : Physics, Chemistry &Mathematics

SECTION-I : (Maximum Marks: 80)This section contains 20 questions. Each questionhas 4 options for correct answer. Multiple-ChoiceQuestions (MCQs) Only one option is correct. Foreach question, marks will be awarded as follows: Full Marks : +4 If correct answer is selected. Zero Marks : 0 If none of the option isselected. Negative Marks : –1 If wrong option is selected.

1. Two vectors and are added, the magnitude

of resultant is 15 units. If is reversed and

added to resultant has a magnitude

units. The resultant of and a vector

perpendicular to and equal in magnitude to

has a magnitude

(A) 13 units

(B) 17 units

(C) 19 units

(D) 20 units

2. If instead of mass, length and time as

fundamental quantities, we choose velocity,

acceleration and force as fundamental

quantities and express their dimensions by V, A

and F respectively, then the dimensions of

pressure 'p' will be as expressed as :

(A) [FA V ] (B) [F V A]

(C) [FA V ] (D) [FAV ]

3. If A physical quantity x is given as x = ,

where F is force, A is area, x is distance and P is power

then match following list.

List-I List-II

(P) Dimension of β is (1) M L T

(Q)If y is velocity then

dimension of ω is(2) M L T

(R) If y is velocity then

dimension of α is(3) M L T

(S) If ω is dimensionless

then dimension of y is(4) M L T

(A) P → 2; Q → 1; R → 4; S → 3

(B) P → 2; Q → 1; R → 3; S → 4

(C) P → 1; Q → 3; R → 2; S → 4

(D) P → 4; Q → 2; R → 3; S → 1

4. A stone is dropped from a building, 2sec later

another stone is dropped (both are dropped from

rest). How far apart are the two stones by the

time the first one has reached a speed of 30 m/s :-

(A) 80 m (B) 60 m

(C) 20 m (D) 40 m

ALLEN

PART-1 : PHYSICS

P Q

Q

P 113− −−√

P

P

Q

2 –4 2 –1

2 –1 –2

Page 1/12English / 01082021 Space for Rough Work

1/2 –1/2 –1/2

0 1 0

–3/2 1/2 7/2

1 0 –2

Nurture Course - III(A) & Live-II 1001CJA136621002

5. A groove is in the form of a broken line ABC

and the position vectors of these three points

are respectively, , ,

. A force of magnitude acts on

a particle of unit mass kept at a point A and

moves it along the groove to the point C. If the

line of action of the force is parallel to the

vector, find work done by the force

(all quantities are in SI units) :

(A)

(B)

(C)

(D)

6. Two vectors are arranged in such a

way that they form adjacent sides of a

parallelogram as shown in figure. Which of the

following options have incorrect relationship :-

(A)

(B)

(C)

(D)

7. If and

then find a vector whose magnitude is equal tocomponent of A along B and direction is alongA.

(A)

(B)

(C)

(D)

8. Three of your friends are pulling a objectplaced on ground with forces shown indiagram. When they are unable to push theobject, they call you for help. Instead of pullingthe object directly, you start calculating theminimum force required to move the object.(May be you are intelligent, may be you arelazy). You find that minimum force required inany direction should be 60 N. The minimumforce you should apply to move the object is.(Assume that your friends are still applyingforce in the earlier directions).

(A) 34 N (B) 20 N (C) 38 N (D) 60 N

ALLEN

2 − 3 + 2i j k 3 + 2 −i j k

+ +i j k 24 3–√

+ 2 +i j k

144 2–√

144 3–√

72 2–√

72 3–√

&P Q

= +Q P S

= +R P Q

= +R P S

= −S Q P

English / 01082021Page 2/12 Space for Rough Work

= + 2 + 3A i j k = 2 − + 2B i j k

2 (2 + 2 + 2 )i j k

14−−√

2 (2 + + 3 )i j k

14−−√

2 ( − 2 + 3 )i j k

14−−√

2 ( + 2 + 3 )i j k

14−−√


9. A diwali rocket moves vertically with constantacceleration of 5 ms . After some time itsfuel exhausted and then it falls freely. Ifmaximum height attained by the rocket is 60m.Then find its speeds when the fuel is justexhausted. (g = 10ms )

(A) 10 ms (B) 20 ms

(C) 30 ms (D) None of these

10. A ball is released from the top of a tower of heighth metre. It takes T second to reach the ground.

What is the position of the ball in second ?

(A) h/9m from the ground

(B) 7h/9m from the ground

(C) 8h/9 m from the ground

(D) 17h/18m from the ground

11. A particle is moving towards East with

velocity 10 ms and acceleration 5 ms

directed towards West. Find the distance

travelled in 8 seconds.

(A) 80 m (B) 70 m

(C) 100 m (D) 60 m

12. The position of a particle moving in a straight line

is described by the relation, x = 5 + 16 t – 4t .

Here x is in meters and t in minutes. The distance

covered by particle in first 5 minute is

(A) 52 m (B) 57 m

(C) 15 m (D) 21 m

13. A particle travels 10m in first 5 sec and 10m innext 3 sec. Assuming constant accelerationwhat is the distance travelled in next 2 sec ?

(A) 8.3 m (B) 9.3 m

(C) 10.3 m (D) None of above

14. A particle is projected vertically upwards froma point A on the ground. It takes t time toreach a point B but it still continues to moveup. If it takes further t time to reach the groundfrom point B then height of point B from theground is:

(A)

(B) gt t

(C)

(D)

15. A ball is thrown vertically upwards from the

ground. It crosses a point at the height of 25 m

twice at an interval of 4 secs. The ball was

thrown with the velocity of :

(A) 20m/sec. (B) 25 m/sec.

(C) 30m/sec. (D) 35 m/sec.

16. If the displacement 's' travelled by a body intime 't' is given by

, then the acceleration equals

(A) (B)

(C) (D)

ALLEN

–2

–2

–1 –1

–1

T3

–1 –2

2


1

2

g( +12

t1 t2)2

1 2

g( +18

t1 t2)2

g12

t1 t2

s = + bat2

t2

+ 2b6at4

2st2

2b−2at3

st2


17. A car starts from rest travelling with constantacceleration. If distance covered by it in 10second of its journey is 19m, what will be theacceleration of car ?

(A) 4 m/s (B) 3 m/s

(C) 2 m/s (D) 1 m/s

18. A particle is moving Eastwards with a velocity

of 5 ms . In 10s, the velocity changes to 5 ms

Northwards. The average acceleration in this

time is

(A) ms towards North-East

(B) ms towards North

(C) zero

(D) ms towards North-West

19. A car moving with a speed of 50 kmh , can be

stopped by brakes after atleast 6 m. If the same

car is moving at a speed of 100 kmh , the

minimum stopping distance is

(A) 12 m (B) 18 m

(C) 24 m (D) 6 m

20. If s = 2t + 3t + 2t + 8 then the time at whichacceleration is zero, is :-

(A) t = (B) t = 2

(C) t = (D) Never

SECTION-II : (Maximum Marks: 40)This section contains 10 questions Candidates haveto attempt any 5 questions out of 10. If more than 5questions are attempted, then only first 5 attemptedquestions will be evaluated. The answer to each question is a Numerical ValueType questions. For each question, enter the correct numerical value(in decimal notation, truncated/rounded off to thesecond decimal place; e.g. 6.25, 7.00, –0.33, –.30,30.27, –127.30, if answer is 11.36777..... then both11.36 and 11.37 will be correct) Answer to each question will be evaluated accordingto the following marking scheme: Full Marks : +4 If ONLY the correct numericalvalue is entered as answer. Zero Marks : 0 In all other cases.

1. A rocket is projected vertically upward from

ground with resultant acceleration of 20 m/s in

upward direction. After 10 seconds, engine of

the rocket is swithced off and rocket falls under

gravity. After how much further time the

direction of the velocity changes. If your

answer is N, fill .

2. A car is moving with 54 km/h speed at t = 0. Its

break produces the retardation of 2.5 m/s . If he

applies break at t = 0 and produces constant

retardation till car stops then the displacement

(in m) travelled by car in 10 sec is X. Fill in

OMR sheet.

ALLEN

th

2 2

2 2

–1 –1

12–√

–2

12

–2

12–√

–2

–1

–1

3 2

121

2 2–√


2

N10

2

X5


3. A particle moves in a straight line, its position (in

m) as function of time is given by x = (at + b).

What is average velocity (in m/s) in time interval

t = 3 sec to t = 5 sec in m/s. (Where a and b are

constants and a = 1 m/s , b = 1 m.)

4. A ball is projected with velocity 40 m/s

vertically up. If the ball was found at of

maximum height at time t1 & t2 then find the

value of in seconds. (g = 10 m/s )

5. x-coordinate of a particle moving along x-axis

is x = . Here x is in metre and t in

second. The motion starts at t = 0. Find

acceleration of particle (in m/s ) when particle

comes to instantaneous rest.

6. A particle starting from rest have acceleration n

cm/s for nth second. If displacement travelled

by particle in 7s starting from t = 0 is X cm

then fill in OMR sheet.

7. Given that P = Q = R. If then the

angle between and is θ . If

then the angle between and

is θ then relation between θ & θ is given

by . Find the value of 3x.

8. A vector makes angle with +ve x-axis & +ve

y-axis respectively 45° & 60°, if the angle

made by the vector with +ve z-axis is 15n (in

degree). What is the value of n.

9. A force = (5î + 2ĵ + ) N displaces a body

from a point of coordinate (1, 1, 1) m to

another point of coordinates (2, 0, 3) m.

Calculate the work done (in J) by the force.

10. The angle of banking θ for a cyclist taking a curve

is given by , where v is velocity of

cyclist, r is radius of curve and g is acceleration

due to gravity. Then fill the value of n.

ALLEN

2

2

34

| − |t2 t1 2

+ − 3tt3

3t2

2

2

X10


+ =P Q R

P R 1

+ + =P Q R 0 P

R 2 1 2

=θ1θ2x

tan(θ) =vn

rg



1. What will be the CORRECT representation ofperiodic table (initial three periods) whenpossible value of ℓ = 0 to (n+1). All other rulesare same as present system –

(A)

(B)

(C)

(D)

2. All the lobes of which of the following orbitalis present in the nodal plane of p orbital.

(A) (B) d

(C) d (D)

3. Ratio of number of fully occupied tounoccupied orbitals present upto outermostshell of Cr atom is.

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

4. Within each pair of elements of Sc & Zn, La & Luand Al & Ga, respectively, the larger elements are -

(A) Sc, La and Al (B) Zn, La and Ga

(C) Sc, Lu and Ga (D) Zn, La and Al

5. If bond length of A = 2.4Å and bond length ofB = 6Å then bond length of A-B will be :- (E.N. of A = 1, E.N. of B = 3)

(A) 4.2 (B) 4.1 (C) 4.02 (D) 4.00

6. Select the correct graph between I.E. v/s Z for13 group elements

(A) (B)

(C) (D)

7. Element A has successive ionization energies

8.2, 16.4, 102.5, 122.4 (in eV/atom). Element B

has corresponding values 10.4, 19.2, 35.6, 49.2,

166.5, 208.7 (eV/atom)

What would be the likely formula for a

compound that may be formed from A and B

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

8. Electron affinities of O, F, S and Cl are in theorder of :-(A) F > Cl > S > O (B) O < S < F < Cl

(C) F > Cl > O > S (D) S < O < F < Cl

ALLEN

PART-2 : CHEMISTRY

z

d −x2 y2 zx

yz dz 2

158

35

32

37


2

2

th

4 3 2 2 2 3


9. If the compound A–O–H to be more acidic thanB–O–H then, (A & B are elements of periodictable) :-(A) Electronegativity of A must be more than B

(B) Electronegativity of B must be more than A

(C) Electronegativity of A = Electronegativity of B

(D) Acidic nature does not depend onelectronegativity of either A or B

10. It is CORRECT for periodic property "x".

(A) Atomic radius (B) First ionisation energy

(C) Electron affinity (D) Electronegativity

11. Which of the following compound showsamphoteric behaviour ?

(A) Ca(OH) (B) Mg(OH)

(C) CO (D) Pb(OH)

12. In given cycle,

Calculate H.E. of B (g), if HE[A (g)] = –50J/mole,

Lattice energy A B (s) = 90 J/mole, ΔH

[A B (s)] = –100 J/mole

(A) +30 J/mole (B) –30 J/mole

(C) –140 J/mole (D) +140 J/mole

13. Order of hydration energy is :-

(A) Na = Mg = Al (B) Na > Mg > Al

(C) Al > Mg > Na (D) Al > Mg < Na

14. Which one of the following has the greatestLattice energy.(A) MgO (B) NaCl (C) LiCl (D) MgCl

15. Which of the following statement is INCORRECT?(A) "F" is more Electro-negative than "Cl"-atom

(B) "Na" is more reducing nature than "Li" in water

(C) F has strongest oxidising nature amongthe halogen in water

(D) P has more electron affinity than N

16. X, Y and Z are consecutive elements in aperiod & order of their size is X < Y < Z. Whatwill be the order of ionic mobility of respectiveions i.e. Z , Y and X is

(A) Z > Y > X (B) Z < Y < X

(C) Z = Y = X (D) X > Z >Y

17. The maximum covalency is equal to :-

(A) Number of unpaired p-electrons

(B) Number of paired d-electrons

(C) Number of unpaired s and p-electrons

(D) Total number of unpaired electron inground/excited state

18. Formal charge on I, II and III nitrogen atomrespectively in

is :

(A) –2, +1, 0 (B) 0, +1, –2

(C) +1, 0, –2 (D) 0, –2, +1

ALLEN

2 2

2 2

–2 +3

2 3 solution

2 3


+ +2 +3 + +2 +3

+3 2+ + +3 +2 +

2

2

+(aq)

+2(aq)

+3(aq)

+(aq)

+2(aq)

+3(aq)

+(aq)

+2(aq)

+3(aq)

+(aq)

+2(aq)

+3(aq)

+3(aq)

+(aq)

+2(aq)

≡NI

NII

→ NIII

−


19. Which of the following properties areINCORRECTLY matched?

(A) Atomic radius : Y < La

(B) IE : O < N

(C) EA : N > P

(D) Electronegativity : Be > Ba

20. Condition suitable for high solubility of ionic

compound in solvent should be :

(A) High lattice energy and low hydrationenergy

(B) Low lattice energy and high hydrationenergy

(C) Lattice energy must be equal to hydrationenergy

(D) Solubility is independent of lattice orhydration energy


1. Maximum number of electrons having samevalue of σ in Cu.

2. The atomic number of element “Unnilquadium”

is X. Calculate the value of .

3. Number of species having 10 exchanges intheir d-subshell. Cr , Mn , Cr, Fe , Co , Mn

4. If an element ‘X’ belongs to 4th period and 7thgroup in long form of periodic table then findthe magnetic moment (spin only) in Bohrmagneton(B.M.) of X

5. Given : M(s) → M (aq.) ΔH =

and ΔH (M(s)) = 80.5 KJ/mole ΔH (M (g)) = –591 KJ/mole –ΔH (M ) in KJ/mole?

6. From atomic number 3 to 17, how manyelement(s) is/are having higher ionisationenergy than fluorine?

7. If Z (as per Slater's rule) of 3s electron in Fe

is 'x' then find out the value of .

8. (C, O), (N, P), (S, Se), (Ne, F), (H, He)

Number of pairs where first element have

higher EA than second are :-

9. Find the number of elements, whose E.N. onpauling scale is greater than 'B' S, N, Cl, F, C, Al, Mg

10. In the electronic configuration of Zn (Z = 30)

find the total number of occupied orbitals

which do not possess any nodal plane :-

ALLEN

1

1


29

( )X− 425

+ +2 +3 +2

3+

+ −400.5 KJmole

sub

Hyd +

eg+

eff x10



1. If roots of the equation px + qx + r = 0 are in

ratio 4 : 3, then is equal to

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

2. Sum of maximum and minimum values of

y = is –

(A) 9 (B) 1

(C) –1 (D) Not defined

3. Number of real roots of (5 – x) + (3 – x) = 16 is

(A) 0 (B) 1

(C) 2 (D) 4

4. If α, β, γ are the roots of the equation x – 5x + 3 = 0,

then the value of (α – 2) (β – 2) (γ – 2) is

(A) 629 (B) 729

(C) 829 (D) 0

5. If α and β (α, β ≠ 0) are roots of quadratic

equation x – 5αx – 7β = 0, then β is –

(A) –28 (B) –25

(C) 5 (D) 32

6. If α, β are roots of 9x – 11x + 1 = 0 then value

of is-

(A) (B)

(C) (D)

7. If α & β are the roots of the quadratic equationx – (k – 2)x – k + 1 = 0, then minimum valueof α + β is -

(A) 1 (B) 2 (C) 5/4 (D) 3/4

8. Graph of y = ax + bx + c is given in theadjacent figure, then which of the following iscorrect -

(where α, β are the zeros of ax + bx + c)

(A) α + β > 0, αβ < 0 (B) b < 0, D < 0

(C) b > 0, D > 0 (D) α + β < 0, αβ < 0

9. If larger root of (2015x) – (2014)(2016)x – 1 = 0is α and smaller root of x + 2014x – 2015 = 0 is β,

then value of is :-

(A) 1 (B) 2

(C) 3 (D) 4

ALLEN

PART-3 : MATHEMATICS

2

4 4

3 2

3 3 3

2


2

2

2 2

2

2

2

2


10. If equations ax + bx + a = 0, a, b N andx + 2x – 2x – 1 = 0 have two rootscommon, then minimum value of (2a + 3b)is :-

(A) 5 (B) 11 (C) 13 (D) 17

11. If p > q > 0 are two real numbers, then thevalue of

is -

(A) independent of q

(B) independent of p

(C) independent of both p and q

(D) dependent on both p and q.

12. The number of positive integral solutionsof x – y = 1572 is -

(A) 0 (B) 1

(C) 2 (D) 4

13. The number of solutions of the equation||x – 2| – 5| = 5, is -

(A) 0 (B) 1

(C) 2 (D) 3

14. Let , then the value of

is -

(A)

(B)

(C)

(D)

15. Consider equation |x – 2| + 2|x – 5| = 7 thenwhich of the following statement is/are true

(A) Number of solutions of the given equationis 3

(B) Sum of all solutions of the given equationis 8

(C) Sum of all solutions of the given equation

is

(D) Number of solution of the given equationis 1

16. If x – y = a and x + y = b, then the value ofx – y is

(A) (B)

(C) (D) a + b

17. Ten times the number is

(A)

(B)

(C)

(D)

18. The value of is

(A) a integer

(B) an irrational number

(C) a rational number which is not integer

(D) none of these

ALLEN2

3 2

pq+ (p− q) pq+ (p− q) pq+ (p− q) pq+. . . . . . .− −−−−−−−−√− −−−−−−−−−−−−−−−−−−−

√− −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

√− −−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−−

√

4 4

x = 5+ 2 ( )6–√

+x−−√1x−−√

13−−√

8–√

12−−√

6–√


143

2 2

3 3

− 3aba3

23ab− a3

2

3ab− 5a3

22

10101034

10101035

10( +1)101034

10101134

10111034

( )2–√2√ 8√


19. If positive integer x satisfies the equation , then value of x is

(A) 105 (B) 125

(C) 225 (D) 243

20. If then is :–

(A) (B)

(C) (D)


1. The least prime integral value of '2a' such that

the roots α, β of the equation 2x + 6x + a= 0

satisfy the inequality is

2. Suppose α, β are roots of x – 7x + 8 = 0, with

α > β, then evaluate

3. Number of integral values which satisfies the

inequality , is

4. Consider f(x) =

(where a, b, c are distinct real number). If 'p'

denotes the number of natural numbers in the

range of f(x), then unit digit of (p + 8) is

5. If the equations x + 3x + 4 = 0 and 2ax + 3bx + 4c = 0,

a, b, c N have a common root, then minimum value

of (a + b + c) is

6. If x + y = 8 and x + y = 10, then value of

is

7. Number of natural number 'n' for which

is a natural number, is

8. If 2x – 3x + 4x – 3x + 9 is divided by (x – 1)

then the remainder is

9. If x + y + 12xy = 64 where x ≠ y then value

of is equal to

10. If then value of is

ALLEN

+ + =3–√ 27−−√ 75−−

√ x−−√

x = 5− 2 6–√ ( − )x−−√1x−−√

2 2–√ −2 2–√

2 3–√ −2 3–√

2

+ < 2αβ

βα

2

+ + α+ β16α

16β


2015

2 2

2 2

+∣∣x3 y3 ∣∣10

+ n+ 12n2

n

5 4 2

3 3

x+ y16

=2x

1+ 2x14

7 ( )8x

1+ 8x


Space for Rough Work


English / 01082021Page 12/12

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)) CLASSROOM CONTACT PROGRAMME JEE(Main) UNIT TEST