25-05-2025
9610WJA801491250007 JA
PHYSICS
SECTION-I (i)
1) A car travels 30 km at a uniform speed of 40km/h and the next 30 km at a uniform speed of 20
km/h. Find its average speed (in km/hr).
(A)
(B)
(C)
(D)
2)
A car moving with constant acceleration covers two successive kilometers in 30 sec and 20 sec
respectively. The acceleration of car is :-
(A) 5/3 m/s2
(B) 3/5 m/s2
(C) 2/3 m/s2
(D) 5/2 m/s2
3)
A body starts from rest and is uniformly accelerated for 15 s. The distance travelled in the first 5 s is
x1, next 5 s is x2 and the last 5 s is x3. Then x1 : x2 : x3 is the same as
(A) 1 : 2 : 4
(B) 1 : 2 : 5
(C) 1 : 3 : 5
(D) 1 : 3 : 9
4) Two objects A and B of masses 2 kg and 4kg are connected by a uniform rope of mass 4kg as
shown in the diagram. A force of magnitude 80N acts on A in vertically upward direction. Tension at
mid point of the rope is (g = 10 m/s2) :-
(A) 32 N
(B) 40 N
(C) 42 N
(D) 48 N
5) If system is in equilibrium, find value of m (all string are ideal) (shown angle are in degree) :-
(A) 3.46 kg
(B) 2.46 kg
(C) 1.67 kg
(D) 3.67 kg
6) A block of mass 5kg connected to ceiling of lift by an inextensible string. Three different observer
observes the block then select the correct statement.
(A) Obserever-1 observes block at rest. Therefore tension in the string is 50N.
Observer-2 observes block accelerates downwards with an acceleration of 5 m/s2. Therefore
(B)
tension in the string is 25 N.
Observer-3 observes block accelerate upwards with an acceleration of 5 m/s2. Therefore tension
(C)
in string is 75N.
(D) All the above.
SECTION-I (ii)
1)
Three blocks are connected by string and pulled by a force F = 60 N as shown in figure. If mA = 10
kg, mB = 5 kg & mC = 15 kg, then :
(A) Acceleration of the system is 2 m/s2
(B) T1 = 10 N
(C) T2 = 30 N
(D) Net force on block B will be 10 N
2) The system shown in the diagram is released from rest. Pulley and string are massless. Neglect
friction everywhere. (g = 10 ms–2)
(A) Tension in the string during motion is 20N
(B) Acceleration of blocks during motion is 5 ms–2
(C) Block B reaches ground in s
(D) All of the above statements are incorrect
3) The magnitude of the displacement is equal to the distance covered in a given interval of time if
the particle :
(A) moves with constant acceleration
(B) moves with constant speed
(C) moves with constant velocity
(D) Motion is in a straight line
4)
In the given figure, F = 17N and spring constant of all spring is 100 N/m then choose the correct
options. (Assume string and springs are ideal)
(A) Acceleration of 1 kg block connected at last is 2 m/s2
(B) Spring force between 1 kg and 2 kg blocks is 3 N
(C) Spring force between 2 kg and 3 kg block is 5 N
(D) Acceleration of 3kg block is 3 m/s2
5) Which of the following statements is/are correct regarding ideal pullies and strings?
If we pull the two ends of an ideal string with a force of 10N each, the tension in the string is
(A)
20N.
(B) The net force on an ideal pulley must be zero.
(C) The tension in an ideal string must be same at all points of the string.
(D) The acceleration of an ideal pulley must be zero.
6)
System is released from rest then :
Acceleration of 5 kg block is
(A)
Acceleration of 8 kg block is
(B)
(C)
Acceleration of 10 kg block is
(D) Acceleration of 5 kg block is zero.
SECTION-II
1) Position x of a particle moving along the x-axis is given by equation x = 2t3 – 21t2 + 36 t – 72,
where x is in meters and t is in seconds. Find time interval (in seconds) between the instants it
changes its direction of motion.
2) A car is traveling at 20 m/s. The driver applies the brakes, and the car slows with 4.0 m/s2. The
stopping distance(in m) is x0. Then value of x0 is :-
3) Three monkeys are moving on vertical rope. Their acceleration are shown. For B velocity is
constant. Tension in the rope at rigid support is (g = 10 m/s2) in (N)
4) Diagram shows a block at rest in equilibrium on a fixed inclined plane. If for the given case F1 is
horizontal & F2 is along the incline, fill in OMR sheet.
5) A cube of side length 2m is shown in diagram. A particle moves from A to B. If displacement of the
particle is then a + b – c is :–
6) If the angle made by the vector with z-axis is radian. Then the value of x.
CHEMISTRY
SECTION-I (i)
1) Which of the following frequencies is required to eject a photo electron having work function of 6
eV having the kinetic energy of 3.4 eV
[h = 6.625 × 10–34 J Hz–1]
(A)
(B)
(C)
(D)
2) If λ0 is the threshold wavelength for photoelectric emission, λ wavelength of light falling on the
surface of metal, and m mass of electron, then de Broglie wave- length of emitted electron is
(A)
(B)
(C)
(D)
3) The potential energy curve for the H2 molecule as a function of inter nuclear distance is
(A)
(B)
(C)
(D)
4) The kinetic energy of an electron in the second Bohr orbit of a hydrogen atom is [a0 is Bohr
radius]
(A)
(B)
(C)
(D)
5) Which of the following relation is correct for Boron element.
Here P = Period number of Boron
N = Number of valence electrons in Boron
(A) (P + 1) > N
(B) (P + 1) < N
(C) (P + 1) = N
(D) P = N
6) The period number of K = x
Number of unpaired electron in Cr+ = y
The total number of s-subshell used in Ca = z
then find the value of (x + y + z)
(A) 10
(B) 11
(C) 12
(D) 13
SECTION-I (ii)
1) Considering the following ionisation steps :
A(g) → A+ (g) + e¯ ΔH = 100 eV
2+
A(g) → A (g) + 2e¯ ΔH = 250 eV
Select the correct statements :
(A) IE1 of A(g) is 100 eV
+
(B) IE1 of A (g) is 150 eV
(C) IE2 of A(g) is 150 eV
(D) IE2 of A(g) is 250 eV
2) ; This is the equation representing an orbital. Which of
the following is/are correct ?
(A) This equation is of 3s orbital
(B) Radial probability curve touches r-axis at three finite points
(C) Above equation can be used to deduce n & quantum numbers.
(D) Probability density curve shows two maximas
3) Select the correct graph for Bohr atom –
(A)
(B)
(C)
(D)
4) If 100 mL of 1 M H2SO4 solution is mixed with 100 mL of 9.8%(w/w) H2SO4 solution (d = 1 g/mL),
then the correct information(s) for the final solution is/are :
(Assume volume to be additive)
(A) Concentration of solution is 1M
(B) Volume of solution become 200 mL
(C) Mass of H2SO4 in the solution is 98 g
(D) Mass of H2SO4 in the solution is 19.6 g
5) The non-stoichiometric compound, titanium monoxide, has a continuous range of composition
from to Which of the following is/are the correct regarding the possible composition
of the compound ? [Ti = 48]
(A) The maximum percentage by mass of oxygen in the compound is 30.8.
(B) The minimum percentage by mass of titanium in the compound is 69.2.
(C) The minimum percentage by mass of oxygen in the compound is 18.7.
(D) The minimum percentage by mass of titanium in the compound is 81.3.
6) A quantity of 0.22 g of a gas occupies a volume of 112 ml at pressure of 1 atm and temperature of
273 K. The gas may be
(A) nitrogen dioxide (NO2)
(B) nitrous oxide (N2O)
(C) carbon dioxide (CO2)
(D) propane (C3H8)
SECTION-II
1) If in urea [CO(NH2)2] there are 20 g -atoms of nitrogen present then the mass of urea will be (in
gm).
2) Ratio of total energy of an e– in 1st orbit and potential energy of e– in 4th orbit of a H is (z = 1)
3) The time period of revolution of e– in the first excited state of He+ is X × 10–16 second, if time
period of revolution of Hydrogen electron in its ground state is 1.5 × 10–16 second. Then report the
value of "X".
4)
Count the number of incorrect statement among the following :-
(A) The first ionisation potential of Al is less then the first ionisation potential of Mg
(B) Ionic radius of free H– is more than that of Br–
(C) The formation of S2– from sulphur atom is an endothermic process
(D) The first ionisation energies of carbon, silicon, germanium, tin, and lead change as C > Si > Ge
> Pb > Sn
5) When 800 mL of 0.5 M nitric acid is heated in a beaker, its volume is reduced to half and 11.5 g of
nitric acid is evaporated. The molarity of the remaining nitric acid solution is x × 10–2 M. (Nearest
Integer)
(Molar mass of nitric acid is 63 g mol–1)
6)
What volume (in ml) of 0.8 M - Ca(NO3)2 solution should be mixed with 40 ml of 0.6M - Al(NO3)3
solution to get a solution having NO3– ion concentration equal to 1.70 M ?
MATHEMATICS
SECTION-I (i)
1) If X = {x : 1 < x ≤ 9}
Y = {y : –2 < y < 5}
and Z = {z : –4 ≤ z ≤ 6} then (X ∪ Z) – Y is
(A) [–4, 9] – (–2, 5)
(B) [–4, 9] – [–2, 5]
(C) [–4, –2) ∪ (5, 9]
(D) [–4, –2) ∪ (5, 6]
2) Solve for x : + – 34 = 0
(A) x = 4 or x = –4
(B) x = 2 or x = –2
(C) x = 3 or x = –3
(D) x = 8 or x = –8
3) A = {x : x is a multiple of 3, x < 100, x ∈ N}
B = {x : x is a multiple of 5, x < 100, x ∈ N}
then value of n(A – B) is
(A) 27
(B) 6
(C) 13
(D) 19
4) If (x + 1)(x2 + 1)(x4 + 1)(x8 + 1) = , then value of x5 can be -
(A) 64
(B) 128
(C) 32
(D) 256
5) If the equation 4x2 – x + 1 = 0 and 3x2 + (λ + µ)x + λ – µ = 0 have a common root then the value
of λµ is (where λ, µ are rational)
(A) 0
(B)
(C)
(D)
6) If roots of the equation 2x3 – 4x2 + x + 2 = 0 are α, β and γ, then the value of
is :-
(A)
(B)
(C)
(D)
SECTION-I (ii)
1) If x2 – 3x + 2 is a factor of x4 – px2 + q, then-
(A) equation x4 – px2 + q = 0 has four distinct real roots
(B) equation x4 – px2 + q = 0 has two real and two imaginary roots
(C) p = – 5, q = – 4
(D) p = 5, q = 4
2) If p and q are roots of equation the ordered pair (p, q) is/are
(A) (0, 0)
(B) (1, 2)
(C) (1, –2)
(D) (2, 1)
3) consider the graph of y = ax2 + bx + c as shown in the figure below, then which of the following is
true:
(A) b > 0
(B) a – b + c < 0
(C) c < 0
(D) 4a + 2b + c = 0
4) If 8x3 + 27x2 – 9x – 50 is divided by (x + 2) then remainder is then
(A)
is equal to 4
(B)
If then (p + q) is divisible by 13 (where p & q are coprime)
(C) is a natural number
(D) ( – 2) is divisible by 3
5) If where x, y > 0
then which of the following is/are correct.
(A) x + y = 12
(B) x – y = 3
(C) x2 + y2 = 74
(D) x2 – y2 = 24
6) If A, B be any two sets, then (A ∪ B)' is equal to __________ (Here U is universal set).
(A) A' ∩ B'
(B) U – (A ∪ B)
(C) ((A – B) ∪ (B – A))'
(D) A' ∩ (U – B)
SECTION-II
1) Let Z be set of integers, If A = { x : x ∈ Z and } and B = { x : x ∈ Z and 1 < 2x + 1 < 4},
then the number of subsets of the set A × B is :
2) Suppose there are 100 people in a city C. Let X be the set of people who are engineers in the city
C, Y be the set of people whose age is above 40 years in the city C, Z be the set of people who has an
independent house in the city C. Now, study the following Venn diagram and answer the question
given below. Find the number of engineers who do not have an independent
house ?
3) If α, β are roots of the equation x2 – 6x + 4 = 0, then value of is
4) α, β are the roots of the equation . If K1 & K2 are the two values of K for which
the roots α, β are connected by the relation . Find the value of .
5) Suppose p, q, r and s ∈ N satisfying the relation , then find the value of (pq + rs).
6) If , then find the value of the expression .
ANSWER KEYS
PHYSICS
SECTION-I (i)
Q. 1 2 3 4 5 6
A. B C C D A C
SECTION-I (ii)
Q. 7 8 9 10 11 12
A. A,C,D A,B,C C,D A,D B D
SECTION-II
Q. 13 14 15 16 17 18
A. 5.00 50.00 1580.00 8.00 4.00 4.00
CHEMISTRY
SECTION-I (i)
Q. 19 20 21 22 23 24
A. B A C C C D
SECTION-I (ii)
Q. 25 26 27 28 29 30
A. A,B,C A,B,C A,B,C A,B,D A,B,C B,C,D
SECTION-II
Q. 31 32 33 34 35 36
A. 600.00 8.00 3.00 0.00 54.00 40.00
MATHEMATICS
SECTION-I (i)
Q. 37 38 39 40 41 42
A. A A A C A B
SECTION-I (ii)
Q. 43 44 45 46 47 48
A. A,D A,C A,B,C A,B,C A,C,D A,B,D
SECTION-II
Q. 49 50 51 52 53 54
A. 8.00 18.00 257.00 254.00 23.00 17.00
SOLUTIONS
PHYSICS
1)
We known that,
So, let the time taken to cover first 30 km is t1
hours = hours
and let the time taken to cover next 30 km is t2
hours = hours
So, the total time = hours
Average speed = =
Average speed = km/hr.
2)
⇒ 6u + 90 a = 200 ....(i)
⇒ u + 40a = 50 ....(ii)
Solving (i) & (ii) we get a = 2/3 m/s2
3)
If body starts from rest and have uniform acceleration is will cover distance in the ratio 1 : 3 :
5 : 7 in equal interval of time.
4)
a = 2m/s2( )
60 – T = 12
T = 48 N
5) ... (i)
Also T = mg ... (ii)
from (i) & (ii)
6)
Force is frame independent.
Frame-1 and frame-2 are non-inertial frame.
7)
a=
T1 = 10 × 2 = 20N
T2 = 15 × 2
T2 = 30 N
Net force on B = 5 × 2 = 10N
8) Acceleration of system = = = 5 ms–2
For block A, T – 10 = 2 × 5 ⇒ T = 20 N
Time taken by block B to reach ground
2= (5)t2 ⇒ t = s
9) If paricle moves in a single direction.
10)
11)
Theoretical
12) 8 kg block will not leave contact and also acceleration of other two blocks is also zero.
13) v = 6t2 – 42 t + 36
v = 0 ⇒ t2 – 7t + 6 = 0
t = 6 and t = 1
14) v2 = u2 – 2as
0 = (20)2 – 2 × 4 × x0
0
x = = 50
15)
T – (60 + 50 + 40) g =
T – (1500) = 60 × 2 – 40 × 1
T = 1580 N
16)
28 + F1 cos θ = mg sin θ
17) ,
Displacement, =
a = 0, b = 2, c = –2, a + b – c = 4
18) cos θ =
cos θ =
cosθ =
θ= =
x=4
CHEMISTRY
19)
20)
21)
Theory based
22) According to Bohr’s model
For H – atom, r = n2a0
For n = 2 (second orbit)
23)
24) x = 4
y=5
z=4
25)
26) According to equation, l = 0, it has 2 roots, so this equation is for 3s orbital. radial part of
equation gives n and quantum numbers.
27)
(A) mvr = n
(B) r = 0.529
(C)
(D)
28)
(A) Molarity of second solution is = 1 M
Molarity of final solution =
(B) Volume = 100 + 100 = 200 mL
(D) Mass of H2SO4 = × 98 = 19.6 g.
29) For Ti0.75O = 0.75 × 48 + 16 = 52
Percentage of Ti
and percentage of O = 30.8%
For TiO0.69 = 48 + 16 × 0.69 = 59.04
Percentage of Ti
and percentage of O = 18.7%
30) Molar mass of gas .
31) Moles of N-atom = 20 moles
Moles of urea = 10 moles
Mass of urea = = 600 gm
32) Total energy of 1st orbit = P.E. (4th orbit) = 2. (T.E.)
=2
=8
33)
= = 3 × 10–16 s = X × 10–16 s
X=3
34)
(a) Mg = 1s2 2s2 2p6 3s2 ; Al = 1s2 2s2 2p6 3s2 3p1 As electron is to be removed from stable
completely filled s-orbital of Mg as compared to partially filled p-orbital of Al.
(b) Ionic radius of free H– is more than that of Br–
(c) S → S–2 (endothermic process)
35)
= 0.4 mole
= 0.4 – 0.1825
= 0.2175
Molarity =
=
= 0.5437 mole/lit.
mole/lit.
= 54 × 10–2 mol/lit.
36)
Let the volume of 0.8 M Ca (NO3)2
be V ml
then moles of Ca (NO3)2
then moles of =
⇒ moles of 40 ml
0.6 M Al(NO3)3 is
then moles of
total moles of
then molarity of
then
1.6V + 72 = 1.7V + 1.7 × 40
72 – 68 = 1.7 V – 1.6V
4 = 0.1V
MATHEMATICS
37)
(X ∪ Z) ∈ [–4, 9]
(X ∪ Z) – Y = (X ∪ Z) – (X ∪ Z) ∩ Y
∈ [–4, 9] – (–2, 5)
38) Observe, = (3)2 – =1
=1
Let
– 34t + 1 = 0
⇒ t = 17 ± 12 =
Observe,
⇒ x = 4 or x = –4
39) A = {3,6,9,.....99}
B = {5,10,15,....95}
A ∩ B = {15,30,45,60,75,90}
n(A) = 33, n(A ∩ B) = 6
n(A – B) = 27
40) x16 – 1 = 65535
x16 = 65536
x16 = (±2)16
x = ±2
41)
∴ and
42) 2x3 – 4x2 + x + 2 = 2(x – α)(x – β)(x – γ)
put x = –1
= (α + 1)(β + 1)(γ + 1)
put x = 2
(2 – α)(2 – β)(2 – γ) = 2 = (α + β)(β + γ)(γ + α)
43) (x – 1) (x – 2) is a factor of x4 – px2 + q
⇒ x = 1, 2 are roots
⇒ 1 – p + q = 0 and 16 – 4p + q = 0
on solving, p = 5, q = 4
∴ equation : x4 – 5x2 + 4 = 0
⇒ (x2 – 4) (x2 –1) = 0
4 real and distinct roots.
44)
from given quadratic equation x2 + px + q = 0 roots are p, q so
p+q=-p pq = q
pq - q = 0
Now at p = 1 at q = 0
q = -2 p=0
so ordered pair (p, q) will be (0, 0) and (1, -2)
45)
lie in IIIrd quadrant
f(–1) < 0 ⇒ a – b + c < 0
46)
Put x = -2
remainder = 8x(-8) + 27 × 4 - 9(-2) - 50
= -64+108+18-50
= 12
47)
x=
x2 - 7x = 0 x=7
y=
y2 - y - 20 = 0
(y -5) (y +4) = 0
y = 5, -4
x = 7, y =5
48)
(A ∪ B)' = (1)
(A) A' = (1), (4)
B' = (1), (2)
(B) U – (A ∪ B) = (1)
(C) A – B = (2), B – A = (4)
((A – B) ∪ (B – A))' = (1), (3)
(D) A' = (1), (4)
A ∪ (U – B) = (1)
49) A = {0, 1, – 1} B = {1}
n(A × B) = 3
Total number of subset = 23 = 8
50)
Engineers who do not have independent House = X – Z = 11 + 7 = 18
51) α2 – 6α + 4 = 0 ⇒ (α – 2)2 = 2α
& β2 – 6β + 4 = 0 ⇒ (β – 6) =
Now
52)
Given,
⇒
⇒
⇒
Two roots of it are
53)
∴p=1 ∴
q=3 ∴
r = 4 and s = 5
Hence pq + rs = (3) + (20) = 23
54)
Substituting in the given expression
We get
