29-06-2025

6021CJA300125PT05 JA

PHYSICS

SECTION A

1) The circuit shown above shows a steady state with S open. When S is closed :-

(A) No charge/current passes through S.

(B) A steady current of 30 A flows through S.
(C) 90µC of charge flows from B to A.
(D) 120 µC of charge flows from A to B.

2)

In the given circuit switch S is closed at t = 0. The current I in the figure at time t is :-

(A)

(B)

(C)

(D)

3) The circuit shown in the figure is in steady state for a long time. The connection to battery is
suddenly broken (switch S is opened up). What is the charge (in µC) on the capacitor after 0.001
sec?

(A) 100
(B) 100 e–2
(C) 100 e–4
(D) 0

4) In the RC circuit shown, switch is closed at t = 0. Graphs showing variation of potential (VR)
across resistor and potential (VC) across capacitor are given. Time constant of circuit is

approximately equal to :-

(A) 100 ms
(B) 145 ms
(C) 200 ms
(D) 300 ms

5) In the given circuit, find current through battery at t = 0. (Initially the capacitor is uncharged)

(A)

(B)

(C)

(D) 0

6) In the circuit shown, when the key k is pressed at time t = 0, which of the following statements
about current I in the resistor AB is true ? (Capacitor is uncharged at t = 0)
(A) I = 1 mA at all t.
(B) At t = 0, I = 0.5 mA and with time it goes to 1 mA.
(C) I = 0.5 mA at all t.
(D) At t = 0, I = 1 mA and with time it goes to 0.5 mA.

7) In the circuit shown in figure the capacitors are initially uncharged. The current through resistor

PQ just after closing the switch is

(A) 2 A from P to Q
(B) 2 A from Q to P
(C) 6 A from P to Q
(D) Zero

8) Consider a R–C circuit to be connected with closing the switch at t = 0. Initially the capacitor is

uncharged then,

List-I List-II

Rate of charging is
(P) (1) t = RC ln2
maximum

Rate of energy storage in

(Q) (2) t=0
capacitor is maximum

Capacitor is more than

(R) (3) t = RC
40% charged

Capacitor has more than

(S) (4)
50% energy
(A) P → 1 ; Q → 2 ; R → 3 ; S → 4
(B) P → 2 ; Q → 1 ; R → 1,3,4 ; S → 4
(C) P → 3 ; Q → 1,3 ; R → 2 ; S → 4
(D) P → 4 ; Q → 1 ; R → 2 ; S → 3

9) Let C be the capacitance of a capacitor discharging through a resistor R. Suppose t1 is the time
taken for the energy stored in the capacitor to reduce to half its initial value and t2 is the time taken
for the charge to reduce to one-fourth its initial value. Then the ratio t1/t2 will be :

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

10) Energy stored in capacitor at steady state is :-

(A) 0 µJ
(B) 8 µJ
(C) 16 µJ
(D) 32 µJ

11) In the circuit shown in figure, the capacitor is partially charged with a charge q0 = CV/2 and at t

= 0 switch is closed. Find the charge on capacitor as a function of time t.

(A)

(B)

(C)

(D)

12) In the figure, capacitor is completely charged and switch is closed at t = 0. The time after which
the current from the capacitor becomes 1/4th of its maximum value will be :-

(A) 2 RC ln2

(B)

(C) RC ln2

(D)

13) In figure R1 = 5.00 Ω, R2 = 10.0 Ω, R3 = 15.0 Ω, C1 = 5.00μF, C2 = 10.0 μF, and the ideal battery
has emf ∈ = 20.0 V. Assuming that the circuit is in the steady state, choose the correct option

(A)
Charge stored by C1 is μC

(B)
Charge stored by C2 is μC

(C)
Energy stored by C1 is

(D)
Energy stored by C2 is

14) For given circuit charge on capacitor C1 and C2 in steady state will be equal to:

(A) C1(VA – VC), C2(VC – VB) respectively

(B) C1(VA – VB), C2(VA – VB) respectively
(C) (C1 + C2) (VA – VB) on each capacitor
(D)
(VA – VB) on each capacitor

15) In the shown circuit, all three capacitor are identical and have capacitance C μF each. Each
resistor has resistance of RΩ. An ideal cell of emf V volts is connected as shown. Then the magnitude

of potential difference across capacitor C3 in steady state is :

(A)

(B)

(C)

(D)

16) Calculate the amount of charge on capacitor of 4 µF. The internal resistance of battery is 1Ω :

(A) 8 µC
(B) zero
(C) 16 µC
(D) 4 µC

17) The time constant of the circuit shown is :

(A)

(B)

(C)
(D)

18) In the circuit shown, the charge on the 3μF capacitor at steady state will be

(A) 6 μC
(B) 4 μC

(C)
μC
(D) 3 μC

19) In steady state, the charge (in micro Coulomb) stored in the capacitor C = 2µF in the circuit

below is

(A) 6
(B) 12
(C) 18
(D) 24

20) In the circuit shown below, the switch is initially open and the capacitors are uncharged. The
ratio of current through 2Ω resistor, just after the switch is closed and a long time after the switch is

closed:

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

SECTION B

1) In the given figure magnetic field at the center of ring (O) is T. Now it is turned through an
angle of 90° about xx' axis, so that two semicircular parts are mutually perpendicular. Find the value
of magnetic field (in Tesla) at centre.

2) A circular loop of radius r carries a current i. A long, straight wire carrying a current 4i should be
placed in the plane of the circle so that the magnetic field at the centre becomes zero. If the distance

of wire from centre of circle is , then value of x is.

3) A long straight wire of radius a carries a steady current i. The current is uniformly distributed

across its cross-section. The ratio of the magnetic field at and 2a from axis is:

4) Two long parallel wires P and Q are held perpendicular to the plane of the paper with a distance
of 5m between them. If P and Q carry current of 2.5 amp and 5 amp respectively in the same
direction, then the magnetic field at a point half-away between the wires is Then N will

be

5) A current of 25 A flows through an overhead power cable from the North to South direction. The
magnitude of magnetic field at a point 5 m below the cable is where n is

CHEMISTRY

SECTION A

1) Among the given reactions, which is the best example of SN2 reaction ?

(A)

(B)

(C)
(D)

2) Which of the following compound does not give rearranged product in SN1 reaction ?

(A) (CH3)3CCH2Cl
(B) PhCH2CH2Cl
(C) CH2 = CH – CH2 –CH2Cl

(D)

3) Which of the following on heating with aqueous KOH, produces acetaldehyde?

(A) CH2ClCH2Cl
(B) CH3CHCl2
(C) CH3COCl
(D) CH3CH2Cl

4) The correct order of rate of SN1 is:

(A)

(B)

(C)

(D)

5) The mechanism of SN1 reaction is given as:

A student writes general characteristics based on the given mechanism as:
(a) The reaction is favoured by weak nucleophiles
(b) would be easily formed if the substituents are bulky
(c) The reaction is accompained by recemization
(d) The reaction is favoured by non-polar solvent.
Which observation are correct

(A) b and d
(B) a and c
(C) a, b and c
(D) a and b

6) Which compound undergoes hydrolysis by the SN1 mechanism at the fastest rate?

(A)

(B)

(C)

(D)

7) Consider the following bromides :-

The correct order of SN1 reactivity is :

(A) A > B > C

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

8) In SN2 reactions, the correct order of reactivity for the following compounds :
CH3Cl, CH3CH2Cl, (CH3)2CHCl and (CH3)3CCl is :

(A) CH3CH2Cl > CH3Cl > (CH3)2CHCl > (CH3)3CCl

(B) (CH3)2CHCl > CH3CH2Cl > CH3Cl > (CH3)3CCl
(C) CH3Cl > (CH3)2CHCl > CH3CH2Cl > (CH3)3CCl
(D) CH3Cl > CH3CH2Cl > (CH3)2CHCl > (CH3)3CCl

9) The reaction of SOCl2 on alkanols to form alkyl chlorides gives good yields because

(A) Alkyl chlorides are immiscible with SOCl2

(B) The other products of the reaction are gaseous and escape out
(C) Alcohol and SOCl2 are soluble in water
(D) The reaction does not occurs via intermediate formation of an alkyl chloro sulphite.

10) The synthesis of alkyl fluoride is best accomplished by :

(A) Finkelstein reaction

(B) Swarts reaction
(C) Free radical fluorination
(D) Sandmeyer's reaction

11) . The product A will be :

(A)

(B)

(C) H2C = CH2

(D)

12) The ascending order of relative rate of solvolysis of following compounds is

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

13) . Here y is

(A) Ethylmethyl amine

(B) n – propylamine
(C) Isopropylamine
(D) Ethyl amine

14) Among the given reactions, which is the best example of SN2 reaction?

(A)

(B)

(C)

(D)

15) The order of reactivity of following alcohols with halogen acids is

(I)

(II)
(III)

(A) (I) > (II) > (III)

(B) (III) > (II) > (I)
(C) (II) > (I) > (III)
(D) (I) > (III) > (II)

16) Rate of nucleophilic substitution is maximum in :

CH3 – CH2 – Br
(A)

(B)

(C)
CH2 = CH – Br
CH3 – CH2 –
(D)

17) In SN2 reactions, the correct order of reactivity for the following compounds:
CH3Cl, CH3CH2Cl, (CH3)2CHCl and (CH3)3CCl is :

(A) CH3CH2Cl > CH3Cl > (CH3)2CHCl > (CH3)3CCl

(B) (CH3)2CHCl > CH3CH2Cl > CH3Cl > (CH3)3CCl
(C) CH3Cl > (CH3)2CHCl > CH3CH2Cl > (CH3)3CCl
(D) CH3Cl > CH3CH2Cl > (CH3)2CHCl > (CH3)3CCl

18) The increasing order of the reactivity of the following halides for the SN1 reaction is

(A) (III) < (II) < (I)

(B) (II) < (I) < (III)
(C) (I) < (III) < (II)
(D) (II) < (III) < (I)

19) Which of the following compound do not undergo substituion by SN1 as well as SN2 mechanism
(A)

(B)

(C) CH3–O–CH2–Cl

(D)

20)

Which one of the following compounds will give (d) and form in reaction (as major product)

(A)

(B)

(C)

(D)

SECTION B

1) How many of the following undergo solvolysis by 50% aqueous ethanol, faster than
on mild heating.
2)

Number of the following reaction, in which the stereochemistry of the product has been correctly
shown

(A)

(B)

(C)

(D)

3) In how many of the following compounds SN2 reaction takes place at appreciable rate ?
(i) CH3Cl (ii) CH3CH2Cl (iii) CH2=CH–Cl
(iv) CH2=CH–CH2Cl, (v) Ph–CH2Cl

(vi) (vii)

(viii)

4)

How many of the following alcohols undergo dehydration with change in the skeletal framework?
5) Total number of polar aprotic solvents among the following :
(i) acetone (ii) DMF
(iii) NH3 (iv) Diethyl ether
(v) MeCN (vi) DMSO
(vii) H2O (viii) Alcohol
(ix) acetic acid

MATHS

SECTION A

1) Consider the function

, then

(A)

(B)
(C) g(x) is continuous for all x except at x = 0
(D) g(x) is differentiable for all x except at x = 0

2) The value of k, if

is both continuous & differentiable is -

(A) 0

(B)

(C)

(D) does not exist

3) If ƒ(x) = (x2 – 9)|x3 – 6x2 + 11x – 6| + , then the number of points where ƒ(x) is non-
differentiable
(A) 1
(B) 2
(C) 3
(D) 4

4)

If ; x ≠ 0 and ƒ(x) is continuous at x = 0 then ƒ(0) is

(A) 0
(B) 1
(C) e
(D) e–1/2

5) Number of points where ƒ(x) = (x – 1)|x2 – 3x + 2| + cos|x| + sin|x| is non differentiable is -

(A) 0
(B) 1
(C) 2
(D) 3

6) If is continuous for x ∈ [–2, 10], then value of (α + β) is -

(A) 2
(B) 5
(C) 3
(D) 6

7) Let, be given by where denotes the greatest integer

less than or equal to t. The number of points, where f is not continuous, is:

(A) 5
(B) 6
(C) 4
(D) 3

8) Which of the following functions is differentiable at x = 0 ?

(A) cos(|x|) + |x|

(B) cos(|x|) – |x|
(C) sin(|x|) + |x|
(D) sin(|x|) – |x|

9) is
continuous at x = π, then

(A) ƒ(π) = 1

(B)

(C)

(D)

10) If ƒ(x) is continuous function (where n being odd integer),

then

(A) bn – an = 1
(B) b2n+1 – a2n+1 = 2
(C) bn – an = –1
(D) bn – an = 0

11)

The point of discontinuity of function is :

(A)

(B) x = 0

(C)

(D) Continuous every where

12)

If f(x) = min {1, x2, x3}, then :

(A) f(x) is continuous, ∀ x ∈ R

(B) f(x) is differentiable ∀ x ∈ R
(C) f(x) is not differentiable but continuous, ∀ x ∈ R
(D) f(x) is not differentable for two values of x
13) If f(x) = is continous at x = 0 ({} denotes fractional part function), then

(A) It is differnentiable at x = 0
(B) k = 1
(C) Continous but not differentiable at x = 0
(D) Continous every where in its domain

14) Let ƒ(x) = be

differentiable ∀ x ∈ , then is

(A) 0.6
(B) 2.7
(C) 1.80
(D) 0.75

15) Number of points of non-differentiability of the function

ƒ(x) = |x – 1| + |x – 2| + |x – 3| is

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

16) If , then number of points, where ƒ(x) is discontinuous is ([.] is

greatest integer function)

(A) 0
(B) 1
(C) 2
(D) Infinite

17) Let [t] denote the greatest integer less than or equal to t. Let f(x) = x – [x], g(x) = 1 – x + [x], and
h(x) = min{f(x), g(x)}, x ∈ [–2, 2]. Then h is :

(A) Continuous in [–2, 2] but not differentiable at more than four points in (–2, 2)
(B) Not continuous at exactly three points in [–2, 2]
(C) Continuous in [–2, 2] but not differentiable at exactly three points in (–2, 2)
(D) Not continuous at exactly four points in [–2, 2]

18) Let and then

(A) Both f(x) and g(x) are non differentiable at 5 points
(B) f(x) is not differentiable at 5 points and g(x) is non differentiable at 7 points
(C) Number of points of non differentiability for f(x) and g(x) are 7 and 5 respectively
(D) Both f(x) and g(x) are non differentiable at 3 and 5 points respectively

19) Let ƒ(x) = sin(4π [x]) (where [x] is the greatest integer less than or equal to x)

(A) ƒ'(x) does not exist

(B) ƒ'(x) exists but is non-zero
(C) ƒ'(x) = 0 for all x
(D) ƒ'(x) = 0 but 'ƒ' is not a constant function.

20) Which of the following function is discontinuous at x = 0, if ƒ(0) = 1

(A)
; (x ≠ 0)
(B) ƒ(x) = (1 + x)(sgn(x)) + x2 ; (x ≠ 0) (where sgn(x) is signum function)
(C) ƒ(x) = (ln(1 + tan2x))(cosec((ex – 1)2)); (x ≠ 0)
(D) ƒ(x) = (1 + sin2x)cosec x; (x ≠ 0)

SECTION B

1) Number of points where ƒ(x) = |(2x – 1).(3x – 3)x.(x – 1).(x – 2)| is not differentiable

2) The number of functions out of the following

(i) ƒ(x) = |x3| (ii) ƒ(x) = x3|x| (iii) |x| sin3x (iv) ƒ(x) = x|tan3x| which is/are differentiable at x = 0, is

3) The number of points where the function is not differentiable are

4) If ƒ(x) = {x} + {2x} + {3x} is not differentiable at 7 points in [0, n), (where, n ∈ N and {.} is
fractional part function) then n is equal to :-

5) Let f(x) = maximum {4, 1+x2, x2 – 1}, ∀ x ∈ R. Then, the total number of points, where f(x) is not
differentiable, .....
 ANSWER KEYS

PHYSICS

SECTION A

Q. 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20
A. C D C B A D D B D C C D C A C A A B B C

SECTION B

Q. 21 22 23 24 25
A. 8 4 1 2 1

CHEMISTRY

SECTION A

Q. 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45
A. C D B B B B B D B B A A A C B B D B D B

SECTION B

Q. 46 47 48 49 50
A. 4 1 5 3 5

MATHS

SECTION A

Q. 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70
A. C D B B C C C D C B C A A D C A A B C B

SECTION B

Q. 71 72 73 74 75
A. 1 4 2 2 2
 SOLUTIONS

PHYSICS

1)

Charge initially

Charge finally

for this charge arrangement to happen, 90μC charge has to flow upwards.

2)

Ceq. =
T = Red Ced = RC

3)

p.d across capacitor = 20 v

Q = CV = 5 × 20 = 100 µC
After S is open
4) VR = ε.e–t/RC
VC = ε[1 – e–t/RC]
At t = 100 ms
VR = VC
⇒ e–t/RC = 1/2

5)

At t = 0 capaciter behaves as open circuit.

6) (i) At t = 0, capacitor is uncharged, so it behaves as zero resistance

i= = 1mA
(ii) Now at t = ∞ ie. steady state, there is no current in capacitor branch

so i =

7) Conceptual

8) P → 2 ; Q → 1 ; R → 1,3,4 ; S → 4

9)

⇒ t1 =
10)
Potential difference across capacitor is 12 volt.

11) Loop equilibrium for this loop at time t

12) Here Req = R' =

Now,

or

13)

Concept:- In steady state the capacitor gets fully charged and no current flows across it.
Step by step solution:-

Step 1:- Try to find out a closed loop with no capacitor.

Step 2:- Look A BCDEFA with no capacitor. Current flows continuously in this look after steady
state is reached.

Step 3:- Using Kirchhoff’s Loop rule –

Step 4:- Now C1 is in parallel with R1 hence using Kirchhoff’s Loop rule charge stored by C1

Step 5:- Charge stored by C2

Energy
Hence option (C) is correct.

14) No current will flow through the resistance at steady state.

15)
No current passes through capacitors in steady state. Assume potential at point 'g' to be zero.

Then points '1' and '2' are at same potential .

Hence C1 and C2 can be taken in parallel.

The potential at point 3 is .

∴ Equivalent circuit of all three capacitors is shown
Hence potential difference across capacitor C3 is
16) On simplifying circuit we get

No current in upper wire.

∴ VAB = × 4 = 4 v.
∴ θ = (Ceq)v
⇒ 2 × 4 = 8 µC

17)

Equivalent battery

For Qmax

Potential on C = Potential on 2R resistance

Charge on capacitor ,
18) In steady state , no current flows through the capacitors From
KVL = 2V – i R – 1 – 2Ri = 0

i=
Now Form A to B

VA – 2i + 2 = VB = VB – VA = 2– 2i =

ΔV3μF = VB – VA = V
Q = CV

Q = (3μF)

19)
Q = 6 × 2 = 12

20) Just after

I1 = 6/2 = 3A
After long time

I2 = 6/6 = 1A

21) Given
∴ In 2nd case,
 22)

from centre of ring

23)

24)

25) Magnitude of the magnetic field is given by

CHEMISTRY

26) In case of (C) option, CH3O– is a strong nucleophile in DMSO and confirms SN2.

27)

28)

CH3CHCl2
29)

30) Conceptual
Unit-8, Page no. 175. Q - 35

31) Rate of SN1 ∝ stability of formed carbocation

most stable carbocation

32)
for SN1 compare stability of carbocation

B > C > A stability of carbocation

33) Crowding decreases reactivity of SN2 reaction

CH3 — Cl > 1° > 2° >>>> 3°

34) R – OH + SOCl2 → R – Cl + HCl ↑ + SO2 ↑

Gas Gas

35) Swarts reaction

36)

37)

Solvolysis or SN1 ∝ stability of carboccation

Stability order
38)

39)

40)

(III) > (II) > (I)

41)

42)

CH3Cl > CH3CH2Cl > (CH3)2CHCl > (CH3)3CCl

43)

(II) < (I) < (III)

44)

45)

46) b,c,d,f

47)
 Reaction of alcohol with SOCl2 / Pyridine involues attack of Nucleophile from back side.
So D is correct.

48)

49)

Theory based

50)

Conceptual

MATHS

51)
and

52) 3 – 2k – 2 = 0

for continuity for differentibility

ƒ'(1–) = ƒ'(1+)
1 = –2k
 ∴ No value of k.

53) ƒ(x) = (x2 – 9)|x3 – 6

54)

55) It is non differentiable at x = 2,0

56)
α=2

eβ – 1 = α – 1
β=1

57)

58)

59)

and ƒ(π) = –1
60) at x = 2n, n is odd

an + 1 = bn – 1
bn – an = 2

61) dis at 4x = ±x =

62)
f(x) is continuous x ∈ R

63) f(x) = 0 { x2 = 0 and {e1/x} is a bounded function} k=0

= x{e1/x} = 0
f'(0) = 0
not continuous at x = log2e, log3e, ..... etc.

64) For continuity

4a + 2b + 2 = 8a + 8b
4a + 6b = 2 ⇒ 2a + 3b = 1

ƒ'(x) =
R.H.S. = 4a + b ; LHD = 8a + 12b
8a + 12b = 4a + b
4a + 11b = 0

65) If we draw the graph of y = ƒ(x) then its is clearly seen that
sharp corners appear at x = 1,2,3 so non differentiable at 3 points.

66) is always an integer

⇒ ƒ(x) = tannπ = 0, always continous.

67) min{x – [x], 1 – x + [x]}

h(x) = min{x – [x], 1 – [x – [x])}

⇒ always continuous in [–2, 2]

but non differentiable at 7 Points

68) f (x) is non– differentiable at x = α,β,0,γ,δ and g(x) is non – differentiable at x = α, β, γ,

δ, 0, –2, 2 ⇒ (B)

69) ƒ(x) = sin(4π[x])

Since sinnπ = 0, where 'n' is any integer
∴ ƒ(x) = 0 ∀ x ∈ R

70) (a)

(b)
LHL = –1

(c) RHL = LHL

(d)

71) ƒ(x) = |(2x – 1).(3x – 3)x.(x – 1).(x – 2)|

ƒ(x) is not differentiable at x = 2

72)

All function are differentiable

73)

so at 2 points x = α, y curve has sharp corners.

74) ƒ(x) = {x} + {2x} + {3x}

{x} is not differentiable at x ∈ N
⇒ x = {1, 2, 3, ...}
{2x} is not differentiable at 2x ∈ N

{3x} is not differentiable at 3x ∈ N

∴ ƒ(x) is N.D. at

∴ ƒ(x) is N.D. at 7 points in [0, 2)

∴ n = 2 Ans.

75) Sketching maximum {4, 1 + x2, x2 – 1} as

OR
Thus, from above graph, we can simply say f(x) is not differentiable at ;
∴ Not differentiable at 2 points.