Test of Class 11th Advanced
Test of Class 11th Advanced
Paper-1
VP AIR TEST - 01
DURATION ::180
DURATION Minutes
90 Minutes DATE : 29/06/2025 M.MARKS : 180
Topics Covered
Physics: Mathematical Tools, Units and Measurements
Chemistry: Structure of Atom
Mathematics: Basic Maths, Sets
General Instructions:
[1]
SECTION-3 (Maximum marks: 12)
• This section contains FOUR (04) Matching List Sets.
• Each set has ONE Multiple Choice Question.
• Each set has TWO lists: List-I and List-II.
• List-I has Four entries (I), (II), (III) and (IV) and List-II has Five entries (P), (Q), (R), (S) and (T).
• FOUR options are given in each Multiple Choice Question based on List-I and List-II and ONLY ONE of these
four options satisfies the condition asked in the Multiple Choice Question.
• Answer to each question will be evaluated according to the following marking scheme:
Full Marks : +3 ONLY if the option corresponding to the correct combination 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.
OMR Instructions:
1. Use blue/black dark ballpoint pens.
2. Darken the bubbles completely. Don't put a tick mark or a cross mark where it is specified that you fill the bubbles
completely. Half-filled or over-filled bubbles will not be read by the software.
3. Never use pencils to mark your answers.
4. Never use whiteners to rectify filling errors as they may disrupt the scanning and evaluation process.
5. Writing on the OMR Sheet is permitted on the specified area only and even small marks other than the specified area may
create problems during the evaluation.
6. Multiple markings will be treated as invalid responses.
7. Do not fold or make any stray mark on the Answer Sheet (OMR).
[2]
IMPORTANT CONSTANTS
IMPORTANT VALUES
2 = 1.414 ln 10 = 2.303
3 = 1.732 log102 = 0.3010
5 = 2.236 log103= 0.4770
= 3.142 log107 = 0.845
e (Euler’s constant) = 2.718
[3]
PART-I (PHYSICS)
SECTION-1 7. If y = sin (8 sin–1 x) then (1 – x2)
Numerical Value Type Questions d2y dy
1. In a particular system of units, a physical quantity 2
− x = −ky , find the value of k
dx dx
can be expressed in terms of the electric charge e ,
d −1 1
electron mass me , Planck’s constant h, and use sin ( x ) =
dx 2
1 1 − x
coulombs constant k = , where 0 is the
40
permittivity of vacuum. In terms of these physical d2y
8. If 2sin(x) cos(y) = 1, then at , is
constants, the dimension of the magnetic field is dx 2
4 4
B = [e] me [h] [k ] –N. Find the value of N.
The value of + + + is
SECTION-2
[[B] = MT–2A–1] [ 0 ] = M–1L–3T4A2] One or More Than One Correct Type Questions
9. The intensity of polarised light through a polaroid
2. A vernier caliper (Non standard) is constructed is given by I = I0cos2 , where I 0 is intensity of
which has one main scale division of length 1mm
incident polarised light and is angle made by
and 20 vernier scale divisions measure 18mm. In
pass axis with line of incident polarised light. If
an experiment, zero of vernier scale lies between
I 0 and are measured as
0 cm and 0.1 cm on main scale and 2nd division
I0 = (10.0 0.1)W / m2 and = 45 1 . Then
of vernier scale coincides with a main scale
division (when jaws of vernier are in closed (A) Percentage error in measurement of I0 is 1%
position). When a cylinder whose diameter is to (B) Percentage error in measurement of is 4%
be measured is kept between the jaws of vernier (C) Percentage error in measurement of I is
caliper, the zero of vernier scale lies between 2.0 nearly 4.5%
(D) Percentage error in measurement of I is
cm and 2.1 cm on main scale and 12th division of nearly 6%
vernier scale coincide with a main scale division.
The diameter of cylinder in cm is 10. The velocity, acceleration and force in two
systems of units are related as under:
3. Two complete turns of the circular scale of a
2
screw gauge covers a distance of 1mm on its main i. v' = v
scale. The number of divisions on the circular
scale is 50 . The screw gauge has a negative zero ii. a' = ( ) a
error of 0.03mm . If the main scale reading is 1
3mm and circular scale reading is 35 during the iii. F' = F
measurement of diameter of wire, then find the All the primed symbols belong to one system and
diameter of wire in mm . unprimed ones belong to the other system. and
are dimensionless constants. Which of the
4. The speed of light (c), gravitational constant (G) following is/are correct?
and plank's constant (h) are taken as fundamental (A) Length standards of the two systems are
unit in system. The dimension of time in this new
3
system is Ga hb Cc, then find the magnitude of related by: L' = 3 L.
value of a + b + c.
(B) Mass standards of the two systems are related
a3 a 1
5. If a1 a2 ,…..a10 are in G.P and = 4 then 9 = by: m' = 2 2 m.
a1 a5
(C) Time standards of the two systems are related
6. For very small angle , simplify the expression
sin
2 by: T' = 2 T .
1+
and find the value of E = to the
(D) Momentum standards of the two systems are
tan
+ cos 1
related by: P' = 3 P.
nearest integer.
[4]
11. Consider a Vernier Callipers in which each 1cm SECTION-3
on the main scale is divided into 8 equal divisions Matrix Match Type Questions
and a screw gauge with 100 division on its 15. A group of students were given a metal cylinder
Circular scale. In the Vernier Callipers, 5 and asked to measure the volume of metal in the
divisions of the Vernier scale coincides with 4 cylinder. The cylinder is open at both ends. The
divisions of main scale and in the screw gauge, students decided to measure the inner diameter d,
one complete rotation of the circular scale moves outer diameter D and the length L of the cylinder.
it by two divisions on the linear scale. For all the three measurements, they used a
(A) If the least count of screw gauge is 0.005mm, vernier callipers in which each main scale division
then the ratio of the pitch of screw gauge to is 1mm and 10 vernier scale divisions match with
least count of the vernier calipers is 2 9 main scale divisions. With the jaws closed, the
(B) If the least count of screw gauge is 0.01mm , zero of the vernier was found to be to the right of
then the ratio of pitch of the screw gauge and the zero of the main scale and the 4th vernier
least count of vernier calipers is 2 division coincided with a main scale mark.
(C) If the Least count of screw gauge is 0.01mm The cylinder was placed between the jaws to
then the ratio of least count of the linear scale measure its outer diameter. Three readings (at
of the screw gauge to least count of vernier different locations) were taken. The readings
scale is 2 recorded were
(D) If the least count of screw gauge is
0.005mm, then the ratio of the least count of
the linear scale of the screw gauge to least
count of the vernier scale is 2.
[5]
16. There are four Vernier scales, whose (A) I→S; II→Q; III→S; IV→T
specifications are given in List-I and the least (B) I→Q; II→S; III→R; IV→T
count is given in List-II. Match the List-I and List- (C) I→S; II→Q; III→T; IV→R
II with correct specification and corresponding (D) I→P; II→Q; III→R; IV→S
least count
(s = value of main scale division, n = number of 18. Match the following
marks on Vernier). Assume (n – 1) main scale List-I List-II
divisions are equal to n Vernier divisions. I If P –1
I
List-I
s = 1 mm, n = 10
List-II
P 0.05 mm
a =3 ( 8+2 7 − 8−2 7 , )
II. s = 0.5 mm, n = 10 Q 0.01 mm
b= ( 42)( 30) + 36 , then the
III. s = 0.5 mm, n = 20 R 0.1 mm
IV s = 1 mm, n = 100 S 0.025 mm value of log a b is equal to
PART-II (CHEMISTRY)
SECTION-1 then the number of α-particles deflected at 180°
Numerical Value Type Questions is_____.
19. If the value of shortest wavelength for balmer
a 21. If the distance (in m) travelled by an electron
series for hydrogen atom is where RH is
RH revolving in the second orbit of Be3+ ion in 100
rydberg constant then, find the value of a. revolutions is x × 10–8, the value of x is ___
(Radius of first bohr’s orbit is 0.529A°) [Round
20. In Rutherford’s α-particle scattering experiment, off upto two decimal places]
if the number of α -particles deflected at 60° is 16
[6]
E1, 2 30. For the configurations.
22. Calculate the value of A; A = where En,z :
2E 2,1
Energy of electron in nth orbit; Z = atomic
number of hydrogen like species.
Which of the following statement(s) is/are
23. The ratio of angular node of 3d orbital and correct?
angular nodes of 3p is x : 1 then what will be the (A) Q is a correct configuration according to
value of x?
Hund's rule.
(B) Order of multiplicity is S = Q < R < P
24. Find the sum of quantum numbers of excited
states of electrons in He+ ion, which on transition (C) Exchange energy is maximum for P
to ground state and first excited state emit two 5 5
(D) Total spin for P is either + or −
photons of wavelengths, 30.4 nm and 108.5 nm 2 2
respectively. (RH = 1.09 × 107 m–1)
[Round off to nearest integer]
31. If the Binding energy of 2nd excited state of
hypothetical H-like species is 12 eV, then:
25. The nuclei of helium and beryllium move with
same velocity. If the Simplest ratio of their de- (A) 1st excitation potential = 81 eV
Broglie wavelength 4+ : +2 is expressed as (B) II excitation energy = 96 eV
Be He
(C) Ionisation potential = 192 eV
x : y, what is the value of (y – x)?
(Atomic mass: He = 4; Be = 9) (D) Binding energy of 2nd energy state = 27 eV
26. The number of electrons for Zn2+ cation that 32. Choose the correct statement(s):
have the value of azimuthal quantum number (l) (A) For a particular orbital in hydrogen atom,
= 0 is___. the wave function may have negative value
SECTION-2
(B) Radial probability distribution function can
One or More Than One Correct Type Questions
never have negative value
27. As an electron jumps from the fourth orbit to the
second orbit in Be3+ ion, its (C) 3d 2 2 orbital has two angular nodes and
x –y
(A) kinetic energy increases. one radial node
(B) speed increases. (D) yz and xz planes are nodal planes for dxy
(C) frequency of revolution increases.
orbital.
(D) potential energy decreases.
SECTION-3
28. Which of the following is/are true statement(s)?
(A) Rest mass of an electron is 9.1×10–28 g Matrix Match Type Questions
(B) The order of energies of orbitals in H-like 33. Match the following:
species is 3s = 3p = 3d. List-I List-II
(C) Wavelength of an electron accelerated 54
I Isotopes P 26F , 26F56, 26F57, 26F58,
through a potential difference of 1 volt is
3 3
12.27 Å. II Isotones Q 1H , 2He
76
(D) e/m of an electron is 1.7 × 108 coulomb/g III Isodiaphers R 32Ge , 33As77
235 231
IV Isobars S 92U , 90Th
29. Which of the following statement(s) is / are 1 2 3
T 1H , 1D , 1T
correct?
(A) Spin multiplicity in Fe3+ is greater than Co3+ (A) I→T; II→P, Q; III→R; IV→S
(B) Ti3+, Cr+, Sc2+ are isoelectronic species. (B) I→P; II→S; III→Q; IV→T
(C) Value of (n+ l + m) for last electron in Na is 3. (C) I→P,T; II→R; III→S; IV→Q
(D) The number of radial nodes in 3p orbital is 1 (D) I→P; II→Q; III→S; IV→T, R
[7]
34. Neon gas is generally used on a sign board, it IV 3p S
emits radiations at 600 nm. Match the values
given in List II with the corresponding parameter
in List I and select the correct answer from the
codes given below:
List-I List-II
I Frequency of emission P 9×106 T
(in s–1)
II Distance travelled by it Q 3.31×10–22
(in km) in 30 s
III Energy of quantum (in R 5 × 1014
kJ) (A) I→P; II→S; III→Q; IV→R
IV Number of quanta S 6.04 × (B) I→S; II→Q; III→P; IV→T
present if it produces 1018 (C) I→T; II→R; III→S; IV→P
2J of energy (D) I→P; II→Q; III→R; IV→S
T 3.02×1018
(A) I→R; II→P; III→Q; IV→S 36. Match the atom/ions with the characteristics of
(B) I→P; II→R; III→S; IV→Q the electron they contain.
(C) I→Q; II→R; III→P; IV→T List-I List-II
(D) I→R; II→Q; III→P; IV→T I H P Radius of 4th orbit
= 0.53 × 4 Å
35. Match the list-I with list-II II He + Q Energy of 2nd orbit
List-I List-II = –13.6 eV
(Orbital) (R vs, r Graph) III Be 3+ R Radius of 2nd orbit
I 3s P = 0.53 × 4 Å
IV Li 2+ S Velocity of electron in
the 3rd orbit = 2.18×106
m/sec
T Energy of 4th orbit
II 4s Q = –13.6 eV
(A) I→P; II→Q; III→R, S; IV→T
(B) I→S; II→P; III→P, T; IV→S
(C) I→R; II→Q; III→P, T; IV→S
III 2p R (D) I→P; II→Q; III→S, T; IV→R
PART-III (MATHEMATICS)
SECTION-1 39. A school offers 3 different languages – Hindi,
Numerical Value Type Questions English and French. There are 50 students of
37. Simplify: which each is enrolled in at least one of the three
1 3 classes. If 18 students study both Hindi and
log5 9 log 6 3 2 English. 15 study both Hindi and French, 13
81 +3
409
( )
7 log25 7 − (125)
log25 6
=?
study both English and French, and 7 study all
three languages, then number of students
studying at least two languages is equal to
38. Find number of solutions of the following
equation
x −1 + x − 2 + x − 3 = 9
[8]
40. If n 0 and exactly 15 integers satisfy ( x − 8)( 2 − x )
( x + 6)( x − 4)( x − 5)( 2x − n ) 0 , then sum of 0 and 2x−3 − 31 0
10
digits of the least possible value of n is log0.3 ( log2 5 − 1)
7
41. Let a, b, c be three distinct positive real number is A then which of the following is(are) true?
(A) A is a singleton set
such that ( a ) = ( bc )
lna lnb
and blnb = alnc . Then (B) Set A has two elements
(C) sum of value(s) of x in A is 10
1 lna lna
3
the value of − is (D) sum of value(s) of x in A is 8
2 lnb lnb
49. If a and b are the solutions of equation :
42. If x2 − 5 x − 14 0, then sum of all its integral 1
log5 log64 x − + 25x = 2 x , then
solutions is 2
(A) a + b = 0 (B) a2 + b2 = 128
43. If A and B are two sets such that n(A) = 7, n(B)=
(C) ab = 64 (D) a −b =8
6 and ( A B ) . Then the greatest possible
value of n ( A Δ B ) , is 50. The solution set of
x −1 2 ( ) x −1 2 ( ) is (0, a) (a, d)
log 4− x log 1+ x
−x
( x − 3) x ( x − 4)2 (17 − x ) (b, c) then which of the following is (are) true?
44. If 0 , then number (A) dbc = 12
− x ( − x2 + x − 1) (|x| − 32 ) (B) 2d + b + c = 9
of integral values of x satisfying the inequality is 1
(C) a + b − c + d =
2
SECTION-2 9
(D) d − b − c = −
One or More Than One Correct Type Questions 2
45. The equation log x+1 ( x − 0.5) = log x−0.5 ( x + 1)
has SECTION-3
(A) two real solutions Matrix Match Type Questions
(B) no prime solution 51. Match the set in List I with its superset in List II
(C) one integral solution List-I List-II
(D) no irrational solution I {32n – 8n – 1 : n N} P {49(n – 1) : n N}
II {23n –1 : n N} Q {64(n – 1) : n N}
III {32n –1 : n N} R {7n : n N}
46. Let f ( x ) = x2 − 4x + 3 −2 . Which of the IV {23n – 7n – 1 : n N} S {8n : n N}
following is/are correct? T {3n : n W}
(A) f ( x ) = m has exactly two real solutions of (A) I→Q, II →P, III→S, IV→T
different signm 2 (B) I→Q, II→R, III→S, IV→P
(C) I→S, II→P, III→Q, IV→R
(B) f ( x ) = m has exactly two real solutions (D) I→R, II→S, III→T, IV→Q
m ( 2, ) 0
(C) f ( x ) = m has no solutions m 0 x2 − 6 x + 5
52. Let f ( x ) =
(D) f ( x ) = m has four distinct real solution x2 − 5x + 6
List-I List-II
m ( 0,1) I If – 1 < x < 1 then f(x) P 0 < f(x) < 1
satisfies
47. Let A = n N : n is a 3-digit number} II If 1< x < 2, then f(x) Q f(x) < 0
satisfies
B = 9k + 2 : k N III If 3 < x < 5, then f(x) R f(x) > 0
and C = {9k + l : k∈N} for some l ( 0 l 9 ) . If satisfies
IV If x > 5, then f(x) S f(x) < 1
the sum of all the elements of the set A(B C) satisfies
is 274 × 400, then l can be equal to _____. T f(x) = 0
(A) 7 (B) 5 (A) I→P,R,S II →Q,S III→Q,S IV→P,R,S
(C) 8 (D) 3 (B) I→P,R,T II→P,Q,S III→Q,S,T IV→S,Q
(C) I→Q,S II→P,R,S III→P,R,S IV→S,T
48. If the solution set of values of x satisfying (D) I→R,T II→P,R,S III→T,S IV→R
simultaneously the inequalities
[9]
53. Match the following 54. List-I contains some modulus
List-I List-II equations/inequations. List -II contains number
I If x1 and x2 satisfy the equation P 9 of non-negative integral value of x.
xlog10x = 100x then value of x1 List-I List-II
x2 equals I |x2–2x|+|x–4|=|x2–3x+4|is P 2
II Sum of squares of roots of Q 17 II |x–1|<2is Q 4
( ) = 3 − x is
x III x − 2 x − 15
2 R 1
log2 9 − 2 0
x| + 3
III The least positive integer x, R 10 is
2x − 1 IV |x2–x|<|x–2|is S 3
for which is T 5
3
2x + 3x2 + x (A) I→S, II →T, III→Q, IV→U
positive, is equal to (B) I→R, II→P, III→S, IV→Q
IV logba = 3,logbc = −4 and if S 1 (C) I→Q, II→S, III→T, IV→P
value of x satisfying the (D) I→T, II→S, III→R, IV→Q
equation a3x = c x−1 is
expressed in form of p/q
where p & q are coprime then
p + q is
T 2
(A) I→R, II →P, III→S, IV→Q
(B) I→Q, II→R, III→P, IV→S
(C) I→S, II→Q, III→R, IV→P
(D) I→R, II→S, III→P, IV→Q
PW Web/App - https://smart.link/7wwosivoicgd4
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[10]
Test Analysis Sheet
● Student Name : Max. Marks:
● PW Registration No.: Marks Obtained:
● Batch Code: Percentage:
● Test Name/Type: Date of Exam :
1. Subject-wise Performance
Physics
Chemistry
Mathematics
Calculation
mistake
Silly mistake
Marked incorrect
option, however
solved correctly
Conceptual Error
Others
[11]
3. Unattempted Questions Analysis
Reason Physics Chemistry Maths Remark
Forgot the concept / Formula
Solved correctly but didn't
have confidence to mark it on
OMR
Missed the class /Didn’t
revise
Got confused with the
concept
Others
4. Weaknesses Identified
(List topics/chapters where you lost marks)
Physics :
Chemistry :
Mathematics :
4. What would you like to improve emotionally/mentally for the next test? :
[12]