17-11-2024

4001CJA101021240080 JA

PART-1 : PHYSICS

SECTION-I (i)

1) When a metal surface is illuminated by light of wavelength 400 nm and 250 nm, the maximum
speed of photoelectrons are v and 2v respectively. The work function of metal is :

(A) 2hc × 106 J

(B) 2hc × 106 J
(C) hc × 106 J
(D) 0.5 hc × 106 J

2)

A flood light is covered with a filter that transmits red light. The electric field of the emerging beam
is represented by a sinusoidal plane wave
Ex = 36 sin (1.20 × 107 z – 3.6 × 1015 t) V/m. The average intensity of the beam will be :-

(A) 0.86 W/m2

(B) 1.72 W/m2
(C) 3.44 W/m2
(D) 6.88 W/m2

3) A cylindrical wire of mass has length and radius . The

maximum error in its density will be

(A) 1 %
(B) 3.5 %
(C) 4 %
(D) 5 %

4) A sinusoidal peak voltage of 15V connected between input terminals of circuit shown in figure.
Assume diodes are ideal. In the output wave form,
(A) Positive peaks of input clipped at +12V and negative peaks at –6V
(B) Positive peaks of input clipped at +6V and negative peaks at –12 V
(C) Positive peaks of input clipped at +12V and negative peaks at –12 V
(D) Positive peaks of input clipped at +6V and negative peaks at –6 V

SECTION-I (ii)

1) The figure shows the variation of photo current with anode potential for a photosensitive surface
for three different radiations. Let Ia, Ib and Ic be the intensities and fa, fb and fc be the frequencies for

the curves a, b and c respectively :

(A) fa = fb
(B) Ia < Ib
(C) fc < fb
(D) Ic > Ib

2) A student studied the photoelectric effect from two different metals by performing two separate
experiments. In the first experiment using a light source where frequency of the light can be varied,
the student obtained the following plot of stopping potential versus frequency. In the second
experiment using light source of frequency 1.2 f0, the student found the stopping potential for
photoelectrons released from sample A is 2.4 V larger than that for sample B. Given : f0 = 1 × 1015
Hz, Work function of metal of sample A is ϕA and that of sample B is ϕB.

(A) ϕA = 1.74 eV
(B) C = 0.42
(C) In second experiment VS for electrons from sample A is 3.23 volts.
(D) In second experiment VS for electrons from sample B is 0.83 volts.

3) Electric field component of an electromagnetic wave is expressed as

 in SI unit. Taking c = 3 × 108 m/s as speed of
electromagnetic wave in vacuum. Choose correct options.

(A)
(B) b = 2
–6
(C) Average energy density of wave is 6.5 × 10 ε0 in SI unit.
(D) Amplitude of magnetic field is 1.2 × 10–11 T.

4) Two resistance are R1 = 5.0 ± 0.2 Ω and R2 = 10.0 ± 0.1 Ω. Equivalent resistance with limit of
possible error is Rs and Rp when both resistances are connected in series and parallel respectively.

(A) Rs = 15.0 Ω ± 2%
(B) Rp = 3.3 Ω ± 3%
(C) Rs = 15.0 Ω ± 1%
(D) Rp = 3.3 Ω ± 2%

5) For the circuit shown in the figure:

(A) current through zener diode is 4 mA

(B) current through zener diode is 9 mA
(C) the output voltage is 50 V
(D) the output voltage is 40 V

6)

How much ice at –20° C can be mixed with 2.5 litre water at 20°C so that final temperature of the
mixture is 0°C ? ρW = 1002.5 kg/m3, Lice= 80 cal/gm, 2 × Sice = Sw = 1 Cal/gm –°C

(A) 500 gm
(B) 1 kg
(C) 5 kg
(D) 20 kg

7) A body of mass M is attached to the lower end of a metal wire, whose upper end is fixed. The
elongation of the wire is l.

(A) Loss in gravitational potential energy of M is Mgl

(B) The elastic potential energy stored in the wire is Mgl
(C) The elastic potential energy stored in the wire is 1/2 Mgl
(D) Heat produced is 1/2 Mgl
8) For the given logic circuit; pick the incorrect option

(A) For A = 1, B = 0, C = 0; Output = 1

(B) For A = 0, B = 1, C = 1; Out put = 1
(C) For A = 1, B = 1, C = 0; Output = 0
(D) For A = 0, B = 1, C = 1; Output = 0

SECTION-II

1) The first member of the Balmer series of hydrogen atom has a wavelength of 6561 Å. The
wavelength of the second member of the Balmer series (in nm) is :-

2) A He+ ion in ground state is fired towards a Hydrogen atom in ground state and at rest. What
should be the minimum kinetic energy (in eV) of He+ ion so that both single electron species may get
excited.

3) In an electromagnetic wave, the amplitude of electric field is 10 V/m. The frequency of wave is 5
× 1014 Hz, the wave is propagating along z–axis, then total average energy density of E.M. wave is α
× 10–10 J/m3, find the value of α to the nearest integer.

4) Write the value of current i3 (in mA) in the circuit shown in the figure.

5) 10 gram ice at 0°C is mixed with 10 gram water at 100°C. What will be common temperature of
mixture in °C? (Lf = 80 cal/gram and Sw = 1 cal/gram/°C)

6) 100 g of ice at 0°C is mixed with 100 g of water at 100°C. The final temperature of the mixture is
5 × N °C. Determine the value of N.

PART-2 : CHEMISTRY

SECTION-I (i)

1) Which of the following is green ppt in aqueous solution ?

(A) Cu(CN)2
(B) Fe(OH)2
(C) Ag2S
(D) CuO

2) Which ion is not identified by precipitation reaction ?

(A) Pb+2
(B) Na+
(C) Hg2+
(D) All of these

3) The IUPAC name for the coordination compound Ba[BrF4]2 is

(A) Barium tetrafluorobromate (V)

(B) Barium tetrafluorobromine (III)
(C) Barium bis (tetrafluorobromate) (III)
(D) Barium tetrafluoridobromate (III)

4) Which of the following complex shows optical isomerism -

2–
(A) [Cd(CN)4]
(B) [Cr(H2O)3Cl3].3H2O
(C) [Zn(gly)2]°
(D) [Ni(dmg)2]°

SECTION-I (ii)

1) Consider the following reaction :

Among the following, the compound(s) whose osazone derivative(s) will have the same melting point
as that of X is/are

(A)
(B)

(C)

(D)

2) Which of the following statement is/are correct for given compounds -

(A) I & II compounds are epimers

(B) I & II compounds are related as diastereomers
(C) III & IV compounds are related as anomers
(D) III and IV compounds are related as diastereomers

3) Ethanoic acid P.
Product 'P' can not be

(A) Propanone
(B) 2-Pentanone
(C) Butanone
(D) 3-Pentanone

4) Which of the following compound will give positive Tollens test

(A) CH3CHO
(B)

(C)

(D)

5)

Consider the following reaction.

Which of the following statement is/are correct?

(A) Oxidation state of central atom in 'Y' is +3
(B) When 'Z' react with Pb(CH3COO)2 yellow ppt. is formed
(C) X = HgCl2, Y = CrO2Cl2
(D) Blue solution is unstable and it is stablised by the addition of amylalcohol

6) The correct statement(s) about Cr2+ and Mn3+ is(are)

[Atomic numbers of Cr = 24 and Mn = 25]

(A) Cr2+is a reducing agent

(B) Mn3+ has a tendency to be reduced to Mn2+
(C) Both Cr2+ and Mn3+ exhibit d4 electronic configuration
(D) When Cr2+ is used as a reducing agent, the chromium ion attains d5 electronic configuration

7) Identify the correct statement among the following.

(A) order of Atomic Radii Eu > Ce > Nd > Ho

(B) Sm3+ ion show colour
(C) Pm is radioactive lanthanide
(D) Cerium shows '+8' oxidation state.

8) Which of the following properties are similar between Lanthanides and Actinides ?
(A) Reducing properties
(B) Most of the cations are coloured
(C) Group number in periodic table
(D) Radio active properties

SECTION-II

1) Find the number of acidic radical(s) which can form colourless gas when treated with dilute H2SO4
?
, S2– , Cl– , , , ,

2) The total number of species which give black precipitate with H2S
Hg(NO3)2, CuSO4, AgNO3, Pb(NO3)2, Sn(NO3)2

3) If number of t2g and eg electrons are 3 and 2 respectively in hexa aqua complex of 3d series metal
ion M3+, find atomic number of metal M.

4) Number of 5 membered chelate ring in

[Co(edta)]–1 is x & [Ni(en)3]Cl2 is y
then (x + y)?

5) The number of chiral centers present in glucopyranose and fructofuranose are x and y
respectively, then find (x + y).

6) (a)

(b)
Sum of molecular mass of gas (A) + number of H-atoms in (B).

PART-3 : MATHEMATICS

SECTION-I (i)

1) equals

(A)
(B)

(C)

(D)

2) The value of is, where

(A) π/2
(B) 1
(C) π/4
(D) None of these

3) Let y = y (x) be the solution of the differential equations If

y(1) = 2, then y(2) is equal to

(A)

(B)

(C)

(D)

4) There are 10 engineering colleges and five students A, B, C, D, E. Each of these students got offer
from all of these 10 engineering colleges. They randomly choose college independently of each

other. The probability that all get admission in different colleges can be expressed as where a & b
are co-prime numbers then the value of a + b is

(A) 814
(B) 731
(C) 1013
(D) 502

SECTION-I (ii)

1) If , then
(A) I is an irrational number
(B)
(C) I = 3.72
(D) I is a rational number

2) Solution of differential equation , is (where 'c' is integration

constant)

(A) xy = sinx + c cosx

(B) xy secx = tanx + c
(C) xy + sinx + c cosx = 0
(D) xy – sinx + c cosx = 0

3)

The differential equation is

(A) linear differential equation

(B) order 1
(C) degree 2
(D) order 2

4) If ,
And h(x) = min{ƒ(x), g(x)} then which of the following is/are true ?

(A) The number of non-differentiable points of h(x) in (–1, 1) is one

(B)
Local maximum value of h(x) is

(C)
The area bounded by y = h(x) & x-axis is sq. units

(D)
h(x) is concave up in

5) Three different numbers are chosen at random without replacement from {1, 2, 3, ..., 15}, Let E1
be the event that minimum of the chosen numbers is 5 and E2 be the event that their maximum is 10,
then

(A)

(B)
(C)

(D)

6) If A and B are two events such that denotes the event complementary to B, then

(A)

(B)

(C)
accordingly as

(D)

7)

(A) V1 = 72
(B) V2 = 288
(C) V1 + V2 = 288

(D)

8) Let E denote the parabola y2 = 8x. Let P(–2, 4) and let Q and Q' be two distinct points on E such
that the lines PQ and PQ' are tangents to E. Let F be the focus E. Then which of the following
statements is (are) TRUE?

(A) The triangle PFQ is a right-angled triangle.

(B) The triangle QPQ′ is a right-angle triangle.
(C) The distance between P and F is
(D) F lies on the line joining Q and Q′.

SECTION-II

1) is equal to :

then value of k is-

2) Let , then is :
[where [x] is greatest integer less than or equal to x]

3) The value of 'c' for which the area of the figure bounded by the curves and y = c
is are c1 and c2 then [ c1 + c2] is, where [.] is greatest integer function.

4) Four fair dice are thrown simultaneously. If the probability that the highest number obtained is 4

is then 'a' is equal to

5) A tangent to the ellipse meets the ellipse at P and Q. Let angle between

tangents at P and Q of the ellipse is then k =

6) If the shortest distance between the line

and is , then the integral value of a is

equal to
 ANSWER KEYS

PART-1 : PHYSICS

SECTION-I (i)

Q. 1 2 3 4
A. B B C A

SECTION-I (ii)

Q. 5 6 7 8 9 10 11 12
A. A,B,D A,B,C,D A,C,D A,B B,C B,C,D A,C,D A,C,D

SECTION-II

Q. 13 14 15 16 17 18
A. 486 255 4 18 10 2

PART-2 : CHEMISTRY

SECTION-I (i)

Q. 19 20 21 22
A. B B D C

SECTION-I (ii)

Q. 23 24 25 26 27 28 29 30
A. B,C A,B,C,D B,C,D A,B,C B,D A,B,C A,B,C A,B,C

SECTION-II

Q. 31 32 33 34 35 36
A. 4 4 026 8 9 54

PART-3 : MATHEMATICS

SECTION-I (i)

Q. 37 38 39 40
A. B C C A

SECTION-I (ii)

Q. 41 42 43 44 45 46 47 48
A. A,B A,B,D B,C A,B,C,D A,B,C,D A,B,C,D A,C A,B,D
 SECTION-II

Q. 49 50 51 52 53 54
A. 40 7 12 7 2 2
 SOLUTIONS

PART-1 : PHYSICS

1) ... (i) ... (ii)

4 × (i) – (ii)

ϕ = 2 × 106 hc J

2)

= 1.72 W/m2

3)

⇒ % error in density

4) Positive cycle : D1 - forward, D2 - reverse

Negative cycle D1 - reverse, D2 - forward

6)

Also hf0 (1 – c) = 2.4 eV

So C = 0.42 and ϕA = Chf0 = 1.74 eV
In second experiment 1.2 hf0 – ϕ = eVs

For sample A →

For sample B →

7)

So, is direction of propagation of wave.

 dir. of propagation

6 + 3b = 0
b = –2

Avg. energy density =

= 6.5 × 10-6 ε0 SI unit

8) R1 = 5.0 ± 0.2Ω ; R2 = 10.0 ± 0.1Ω

Equivalent resistance Rs : when R1 and R2 is connected in series
Rs = R1 + R2
ΔRs = ΔR1 + ΔR2 = 0.3 Ω

% error =
⇒ RP = 15.0Ω ± 2%
Equivalent resistance RP : when R1 and R2 is connected in parallel.

⇒ = 0.03

% error ⇒
RP = 3.3Ω ± 3%

9) Potential difference across zener diode = 120 – 70 = 50 V

Zener current = 14 – 5 = 9 mA

10) Minimum mass of ice required

m1 × (0 – (– 20)) + m1 × 80
= 2.5 × 1.0025 × (20 – 0)
m1 0.557 kg
Maximum mass

m2 × (0–(–20)
= 2.5 × 1.0025 × [(20 – 0) + 80]
m2 25 kg
0.557 kg < mass of ice required < 25 kg

12)

13)

For Balmer series,

λ2 =
λ2 = 4860 Å = 486 nm

14)

Let mass of hydrogen atom be m and initial velocity of helium be u.

Therefore from momentum conservation (for maximum loss of energy)

4mu = 4mv1 + mv1 ⇒ v1 =

Loss in kinetic energy = =

Loss in K.E. must be equal to the sum of excitation energy for helium and hydrogen atom

∴ 10.2 eV + 40.8 eV = KEi ⇒ KEi = (51) × 5 eV = 255 eV

15) New Ans. 2 by Vivek Chauhan Sir

16) 5 × 103 I1 = 60

Potential difference across

10 kΩ = 240 – 60 = 180 V
So, I3 × 10 × 103 = 180
⇒ I3 = 18 mA
I2 = I3 – I1 = 6 mA

18) Let the final temperature of mixture be θ.

 Then miceLf + mices (θ – 0) = mws (100 – θ)
100 × 80 + 100(θ – 0) = 100 × 1 × (100 – θ)
Solving, we get θ = 10°C
∴N=2

PART-2 : CHEMISTRY

21) (A) Wrong name

(B) Barium tetra fluorobromate (III)
(C) wrong name

22) (A) [Ma4] tpye tertrahedral complex.

(B) [Ma3b3] type octahedral complex
(C) [Zn(gly)2] is [M(AB)2] type tetrahedral complex, so it shows optical activity.

23)
⇒ (A) → L–glucose
(B) → D- fructose
(C) → D- Mannose
They also give similar osazone having melting point as x.

26) Tollens test given By

– A;dehyde
– Hemiacitol
– α-Hydroxy Ketone
– Formic Acid

27) X = NaCl, Y = CrO2Cl2, Z = Na2CrO4, Blue solution ⇒ CrO5

 29) (A) Atomic radii ∝ no of shell ∝
(B) Sm3⊕ ⇒ [Xe] 4f5 (unpaired e⊝ present)
(C) Among all lanthanides Pm is the only radioactive substance
(D) Most common oxidation states shown by cerium are +3, +4.

32) Ag2S, HgS, CuS, PbS, black precipitate.

33)

electronic configuration of M3+ is [Ar] d5 i.e. M will have e– configuration [Ar] d6s2 so metal is
Fe.

34) x = 5
y=3

PART-3 : MATHEMATICS

37)

Let
÷ by x4 in numerator & denominator

⇒ {Put }

38)

ƒ'(x) = 0 ⇒ ƒ(x) = c
39)
Put,

Given that : x = 1

Now put, x = 2

40) Total no. of cases = 105

All students want different colleges so no. of cases =

Probability = =
a + b = 189 + 625 = 814

41)
apply king & add

esecx = t

42)
 xcosx + y(xsinx + cosx) = 1

= eℓnsecx+ℓnx
= xsecx

∴ y.xsecx =
xysecx = tanx + C

xy = sinx + cosx

43)

So, order = 1, degree = 2.

44)

45)

46) (A)

(B)
(C) If

(D)

48)

50)

51)
52) 4 must be obtained on atleast one dice
x = number of dice on which 4 is obtained
required probability
= P(x = 1) + P(x = 2) + P(x = 3) + P(x = 4)

53) Equation of tangent to

point

Equation of chord of contact of R (h, k)

are identical

(h, k) lies on director circle of ellipse

54) a1 = (–1,0,3)
a2 = (0,–1,2)
b1 = (1,–a,0) dr’s of line (1)
b2 = (1,–1,1) dr’s of line (2)
Squaring an both the side

After solving a = 2,