Date : 03.05.2023
Time : 3 Hrs
Single correct
MM 234
XII Adv. Paper-2
1.
The ordered pair (a, b) such that x 2  x  1 divides the polynomial ax 9  bx 8  1 is
(A) (–21, 34)
(B) (21, –34)
(C) (47, –58)
(D) (58, –47)
2.
The number of possible integral pairs (a, b) for which 2ab  5a  b
(A) 8
(B) 16
(C) 12
(D) 6
n
(1  2 k ) , then
k 0
k 
(A) f n  2  3 f n 1  2 f n
 55 is
n
3.
If f n 
(C)
4.

f n 2  5 f n 1  6 f n
f n2  3 f n  2 f n
(D) f n  2  6 f n 1  5 f n
(B)
A set contains 3n members. Let Pn be the probability that S is portioned into 3 disjoint subset
with n members in each subset such that the three largest numbers in S are in different subsets.
Then lim Pn is
n
2
(A)
7
1
(C)
9
1
7
2
(D)
9
(B)
5.
If a, b, c are in H.P. and p is the length of the perpendicular drawn from the origin to any member
of family of lines (a + c – 2ac) bx – 2acy + 7abc = 0 then p 
1
4
(A)  ,
9 

2
(C) (7, 9)
6.
7 

2
7
9 
,

2
2


(D) 

The sides of a triangle are the roots of the cubic equation x 3  13 x 2  54 x  72  0 then the
area of the triangle in square units is
1
455
2
1
(C)
394
2
(A)
7.

(B)  0,
1
455
4
1
(D)
394
4
(B)
f(x) is a polynomial function and (f( )2  (f ( ))2  0 then find lim
x 
f(x)  f (x) 

 where [.] denotes
f (x)  f(x) 
greatest integer function.
(A) 0
(C) –1
8.
(B) 1
(D) none of these
f(x) and g(x) are quadratic polynomials and f(x)  g(x) , x  R.
2
Also f(x)=0 have real roots.
Then number of distinct roots of equation h(x)h(x)  (h(x))  0 are (where h(x)=f(x)g(x)).
(A) 0
(B) 2
(C) 3
(D) 4
Multiple Correct Choice Type
This section contains 04 multiple choice questions. Each question has 4 choices (A), (B), (C) and (D)
for its answer, out of which only ONE OR MORE THAN ONE is/are correct
9.
If the equation
then p  q 
(A) 5
px 2  y 2  qz 2  2 yz  zx  3 xy  0 represents a pair of perpendicular planes,
(B) –5
5
(C)
2
10.
(D) 
dy
dx
y
 x and y (2)  1, then
dx
dy
(A) 2 x  y  3  0
If
(C) x  y  1  0
11.
5
2
If (1, 2, p ) , ( 2, 2 p , - 6) and
satisfies all the equations.
x3  8y  0
2
(D) x  4 y  0
(B)
( 2  2, 1, 1) are the ordered triplets of form (x, y, z) which
x y z
x y z
x y z
   1,    1 and    1 then  can be
a b c
b c a
c a b
(A) 2
(C) – 4
12.
(B) – 2
(D) 4
If f (x ) is a continuous and differentiable function such that
f (t k )  1 for k  1, 2, .....n, where
k
1
then
r 1 r ( r  1)(r  2)
1
(A) f    1
 4
1
(C) f    0
2
tk  
1
 1
2
1
(D) f    0
4
(B) f 
Comprehension Type
This section contains 3 groups of questions. Each group has 2 multiple choice question based on a
paragraph. Each question has 4 choices (A), (B), (C) and (D) for its answer, out of which only ONE is
correct
Paragraph for Questions 13 & 14
a
Consider the function h( n) 
 f ( x) g (nx) dx
o
13.
Let
f ( x)  2, g ( x )  | sin  x |, and n 
1
, where N is natural number. If h( n ) / a is
N
independent of n for N  1, 2, 3, 4 then minimum value of a is
(A) 2
(B) 3
(C) 4
(D) 12
14.
If
h(1)
is equal to
a a
1
(B)
3
1
(D)

f ( x)  sin 2 x, g ( x) | cos x | then lim
2
3
1
(C)
2
(A)
Paragraph for Questions 15 & 16
In a ABC , AB  3, BC  4, CA  5. P is any point inside the ABC , such that
PAB  PBC  PCA  .
15.
cot  
1
(A
5
25
(C)
12
(B)
25
4
(D) 4
16.
Ratio of Areas of
(A)
PBC and PAB is
16
25
25
16
4
(D)
15
(B)
(C) 2
Paragraph for Questions 17 & 18
Using three basic colours (Red, Blue, Green) different colour are made by mixing these two or more
colours in equal proportion. The n vertical stripes are painted by all colours available, such that no two
consecutive stripes have same colour.
17.
The number of ways of painting n stripes such that only alternate stripes are painted by a basic
colour (n in odd) is
(A) 3
(C) 3
18.
n 1
2
.4
n 1
2
.4
n 1
2
(B) 7.12
n 1
2
(D) 7.12
n 1
2
n 1
2
If n stripes are painted such that no two consecutive stripes have any basic colour common, then
number ways of pointing n stripes is
1
 1 2
2
1
(C)  1  2
2
(A)



  1  2  
n 1
n

 1 2

n
n 1


1 
 1 2
2
3 
(D)
 1 2
2
(B)



  1  2  
n 1
n

 1 2

n
n 1


SECTION – C
(One Integer Value Correct Type)
This section contains 5 questions. Each question, when worked out will result in one integer from 0 to 9
(both inclusive).
1.
Let L1 be the projection and L2 be the image of the z-axis in the plane 3 x  4 y  z  1  0. The
distance of the point (1, 2, 3) from the plane containing the lines L1 and L2 is ……
2.
x 2  y 2  6 x  24 y  72  0 and x 2  y 2  6 x  16 y  46  0 intersect at four
points. The sum of distances from these four points to the point  3, 2  is 10 k. Then value of k
The graphs of
is equal to
3.
Let A  [ a ij ] nn be a matrix such that
aij  i.2  j then find the value of limtrace A n  (where
1/ n
n 
n  N ).
4.
f ( x  1)  (1) x 1 x  2 f ( x ) for x  N and f (1)  f (1986).
Compute the sum of digit of number  f (1)  f ( 2)  ... f (1985) 
5.
Two rays begin at point A and form an angle of 43º with one another. Lines
l1 , l 2 , l 3 (no two
being parallel) each form an isosceles triangle with the original rays. If º is the largest angle of
triangle formed by l1 , l 2 and
l 3 then find value of 8 cos2 º 9º  .
PHYSICS
Single Option Correct Type Questions
Q.1
In the circuit shown, the galvanometer shows zero current. The value of resistance R is:
(A) 1
Q.2
(C) 4
(D) 9
Figure shows variation of potential V with distance y from origin along y-axis. What is electric field at
y = 2.5 m & y = 5.5 m.
(A)
Q.3
(B) 2
3ˆj , 5ˆj
(B) 2ˆj , – 5ˆj
(C) 3.5ˆj , 2.5ˆj
(D) 3.5ˆj , – 2.5ˆj
A uniform and constant magnetic field B is directed perpendicularly into the
plane of the page everywhere within a rectangular region as shown. A wire
circuit in the shape of a semicircle is uniformly rotated counterclockwise in the
plane of the page about an axis A. The axis A is perpendicular to the page at
the edge of the field and directed through the center of the straight-line portion
of the circuit. Which of the following graphs wedge approximates the magnetic
flux linked with the circuit as a function of time t?
(A)
(B)
(C)
(D)
Q.4
A sphere of radius 10 cm and density 500 kg/m3 is under water of density 1000 kg/m3. The acceleration of the sphere is 9.80 m/s2 upward. Viscosity of water is 1.0 centipoise. If g = 9.81 m/s 2, the
velocity of the sphere is :
(A) 9 m/s
(B) 10 m/s
(C) 11 m/s
(D) 12 m/s
Q.5
A uniform spherical planet (Radius R) has acceleration due to gravity at its surface g. Points P and Q
g
located inside and outside the planet have acceleration due to gravity . Maximum possible separation
4
between P and Q is
7R
3R
9R
(A)
(B)
(C)
(D) none
4
2
4
Q.6
An astraunaut in a strange planet observer that he can jump a maximum horizontal distance of 2m, if his
initial speed is 6 m/s. What is the acceleration due to gravity of the planet ?
(A) 3 m/s2
(B) 9 m/s2
(C) 18 m/s2
(D) 36 m/s2
Q.7
At night approximately 500 photons per second must enter an unaided human eye for an object to be
seen. A light bulb emits about 5.00 × 1018 photons per second uniformly in all directions. The radius of
the pupil of the eye is about 4 × 10–3 meters. What is the maximum distance from which the bulb could
be seen ?
(A) 2.0 × 104 m
(B) 2.0 × 105 m
(C) 20 m
(D) 5.0 × 103 m
Q.8
A ball is released from position A and travels 5m before striking the smooth
fixed inclined plane as shown. If the coefficient of restitution in the impact
is
1
, the time taken by the ball to strike the plane again is
2
(A) 1s
(B) 2 s
(C) 2.5 s
(D) 3 s
e=
Q.9
Two insects P and Q are firmly sitting at the ends of a massless semicircular wire of radius R and two
more insects A and B are firmly sitting at the bottom of the wire. The wire is given an angular velocity
0 about a vertical axis through its centre as shown in the figure. Mass of each insect is M. Now A and
B crawl to the opposite ends to meet P and Q. Final angular velocity attained by the rod is equal to
(A)
Q.10
0
4
(B)
0
2
(C)
0
Consider the TV diagram of a thermodynamic process. Using the
details shown in the figure, find out the molar heat capacity of the gas
at the point Q. Consider the gas to be ideal and monoatomic.
(A) 2.5R
(C) 4R
(B) 3R
(D) 5.2R
(D) 2
0
Multiple Option Correct Type Questions
Q.11 A capacitor of capacitance C is connected to two voltmeters A and B. A is an ideal voltmeter having
infinite resistance, while B has resistance R. The capacitor is uncharged and then the switch S is
closed at t = 0,
(A) Readings of B and A will be and zero at t = 0
(B) During time interval (0 t
) readings of B and A are changing
(C) Reading of A and B will be equal at t = RC ln 2
(D) None of these
Q.12
A thin lens of material of r.i. = 1.4 is formed with radii of curvatures of bounding surfaces 16cm and
24cm. Then:
(A) the focal length of the lens is 3m, if it is a bi-convex converging lens.
(B) the power of the lens is 5/6 D, if it is a concave-convex converging lens.
(C) the focal length of the lens is 24cm, if it is biconvex lens.
(D) the focal length of the lens is –76.8 cm, if it is biconvex lens and surrounded by a medium of
r.i. = 1.6.
Q.13
Two thermometers, one containing mercury and another spirit read same temperature. The mercury
thermometer has a lower emissivity than spirit thermometer. Both have the same area and heat capacity.
If both are brought in bright sun.
(A) The temperature rises at equal rate in both.
(B) The temperature rises at higher rate in spirit thermometer.
(C) Final steady state temperature will be the same in both.
(D) Final steady state temperature will be higher in spirit thermometer.
Q.14
Charge is sprayed onto a large non conducting belt above the left hand roller.
The belt carries charge with a uniform surface charge density , as it moves
with a speed v between the rollers as shown. The charge is removed by a
wiper at right hand roller. For a point just above the sheet mark the
correct option.
(A) magnetic field is
0
v
, out of the plane of the page, parallel to axis of roller..
2
(B) magnetic field is 0 , out of the plane of the page, perpendicular to axis
(C) electic field is
0
perpendicular to the plane of sheet
2
(D) If an electron moves parallel to V just above the sheet it will experience an upward magnetic
force.
Q.15
Consider a tuning fork oscillating in air. Assume the wavefronts to be similar to that in a plane wave.
Mark the correct statements about that plane sound wave.
(A) Compression pulse is formed at equilibrium position of prong's simple harmonic oscillation with
prong moving in the direction of wave propagation.
(B) Rarefaction pulse is formed at extreme position of prong's simple harmonic oscillation.
(C) The maximum density occurs at the centre of compression.
(D) When the prongs are at extreme position of their simple harmonic oscillation, pressure has no
variation.
Q.16
A box is accelerating with acceleration = 20 m/s 2. A block of mass 10 kg
placed inside the box and is in contact with the vertical wall as shown. The
friction coefficient between the block and the wall is = 0.6 and take g =
10 m/s2
(A) The acceleration of the block will be 20 m/s2
(B) The friction force acting on the block will be 100 N
(C) The contact force between the vertical wall and the block will be 100 5 N
(D) The contact force between the vertical wall and the block is only electromagnetic in nature
Q.17
Q.18
The potential energy of a particle of mass 0.1 kg, moving along the x-axis, is given by U = 5x (x – 4)J,
where x is in metres. It can be concluded that :
(A) the particle is acted upon by a constant force.
(B) the speed of the particle is maximum at x = 2 m.
(C) the particle executes simple harmonic motion
(D) the period of oscillation of the particle is /5 s.
a
( V b) = nRT where P is the
V2
pressure, V is the volume, T is the absolute temperature, R is the molar gas constant and a, b are van
der Waals' constants. Which of the following have the same dimensions as those of PV?
(A) nRT
(B) a/V
(C) Pb
(D) ab/V2
The van der Waals' equation for n moles of a real gas is: P
Integer Type Questions
Q.19
In a Young’s double slit experiment, 60 fringes were seen in the field view for light of wavelength
7200Å. The number of fringes observed when light of wavelength 5400 Å is used, are:-
Q.20
A stone of mass 1 kg tied to a light inextensible string of length L = 10/3 m is whirling in a circular path
of radius L in a vertical plane . If the ratio of the maximum tension in the string to the minimum tension
in the string is 4 and if g is taken to be 10 m/sec2, the speed of the stone (in m/s ) at the highest point
of the circle is:-
Q.21
A block of mass 2kg hits a spring while moving with a velocity of 1m/s along the spring length as
shown. The maximum compression of the spring ( in cm ) is : (Assume friction is absent)
Q.22
When a gas A is introduced into an evacuated flask kept at 25°C, the pressure is found to be one
atmosphere. If an equal mass of another gas B is then added to the same flask, the total pressure
becomes 3 atm. Assuming ideal gas behaviour, calculate the value the ratio of the molecular weights
(MA / MB):-
CHEMISTRY
Only one option
Q1
(a.) 80%
(b.) 40%
(c.)
60%
(d.) 20%
(a.)
(b.)
(a.)
(b.)
(c.)
(d.)
(a.)
(b.)
(c.)
(d.)
(a.)
(b.)
(c.)
(d.)
Q2
(c.)
(d.)
Q3
Q4
Q5
Q6
(a.)
(b.)
(c.)
(d.)
Q7
(a.)
Q8
Q9.
2
2
(b.) eg t 2 g
4
0
(d.) eg t 2g
(c.)
What is the hybridization of Xe in cationic part of solid XeF6 at low temperatures?
3 3
3 2
3
(b.) sp d
(c.) sp d
(a.) sp d
(d.) sp
3
The following electrochemical cell is taken.
Cu | Cu2+(aq) || Ag+ (aq) | Ag, and has emf E1> 0. By which of the following actions, E1 increases?
(a.) Adding NH3 to the cathodic chamber.
(b.) Adding HCl to the cathodic chamber.
(c.) Adding AgNO3 to the anodic chamber.
(d.) Adding NH3 to the anodic chamber.
Q10
(a.) 8.5
(b.) 6.8
(c.)
13.6
(d.) 15.2
More than one
Q11
?
(a.)
(b.)
(c.)
(d.)
Q12 Which of the following are aromatic?
(a.)
Q13
(b.)
(c.)
(d.)
Periodic acid is generally used for the oxidation of vicinal diols or α-hydroxycarboxyl compounds. Which of the
following statements are correct for this reaction?
(a.) oxidative cleavage takes place in the above reactions
(b.) final products are generally carbonyl compounds or carboxylic acids
(c.) HΙO4 reduced into HIO3
(d.) Intermediate of this reaction for a vicinal diol is
Q14
(a.)
(b.)
(c.)
(d.)
Q15
Which of the following statements is/are correct?
(a.)
(b.)
(c.)
(d.)
Q16
Which of the following are more basic than HN(SiH3)2?
(a.) NH3
(b.) H2N(SiH3)
(c.)
HN(CH3)2
(d.)
Q17
Which of the following transition in H-atom would result in emission of radiations of same frequency?
(a.) 4 s → 3s
(b.) 4 d → 3 p
(c.) 4 p → 3 p
(d.) 3s → 2 p
Q18
Which of the following statements is/are correct about Henry’s constant KH?
(a.) KH is characteristic constant for a given gas-solvent system
(b.) It is temperature dependent
(c.) Higher the value of KH, lower is solubility of gas for a given partial pressure of the gas.
(d.) KH increases with temperature.
Integer
19.
19.
20.
21.