18-05-2025

2001CJA101002250001 JA

PHYSICS

SECTION-I

1) Find a vector whose magnitude is 25 and which is parallel to vector

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

2) Which of the following pair of forces will never give a resultant force of 2 N ?

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

3) The resultant of makes an angle α with (a, b represent magnitudes of

respective vectors)

(A) α < β
(B) α < β if a < b
(C) α < β is a > b
(D) α < β if a = b

4) Let

(A) is always greater than

(B) it is possible to have

(C) is always equal to

(D) is never equal to

5) If then angle between is

(A)

(B) 0
(C) π
(D)

6) The (x, y, z) co-ordinates of two points A and B are given respectively as (0,3, –1) and (–2,6,4) The
displacement vector from A to B may be given by :

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

7) Given a function . What is rate of change in y with respect to x when x=0.25 ?

(A) Zero
(B) 0.5
(C) –0.5
(D) 1.5

8) Angle between two vectors and shown in diagram is

(A) 150º
(B) 30º
(C) 60º
(D) 90º

9) If , then find

(A)

(B)

(C)

(D)

10)

If is perpendicular to then value of α is

(A) 1
(B) –1
(C) 2
(D) –2

11) A vector having magnitude 10 units is shown in diagram. is unit vector along x axis and is

unit vector along y axis. In terms of and , can be written as .

(A)
(B)

(C)

(D)

12) (4x2 – 9x + ex) = ?

(A) ex – 1
(B) ex + 8
(C) 8x + ex – 9
(D) 0

13)

Find

(A) zero
(B)
(C)
(D)

14) Given ; then find the magnitude of component of vector along .

(A)

(B)

(C)
(D)

15) If y = x loge x then is

(A) loge x
(B) ex
(C) 1 + loge x
(D) x + loge x

16) Find the area of a parallelogram find by vectors , ?

(A) 2
(B)
(C) 10
(D) 6

17) If

the rate of change of y with respect to x at is

(A)
(B) 0
(C)

(D)

18) sin (120) × cos (150) is equal to

(A)

(B)

(C)

(D)

19) y = sin2(x) + sin(x2). Then is equal to

(A) 4 sin x cos x

(B) 4x ⋅ cos x2
(C) 2 sin x ⋅ cos x + 2x cos x2
(D) 2 sin (x) + cos (x)2
20) Find the slope of function at .

(A)
(B)

(C)

(D)

SECTION-II

1) Find maximum value of 5 + 3 sinθ is

2) The magnitude of sum of these 3 forces is equal to (in newton)

3) If the angle between the unit vectors is 60°, then is

4) If then value of at t = 2 is :

5) The resultant of two vectors both having equal magnitude units and inclind at an angle of 60°
with each other will be (in same unit)

CHEMISTRY

SECTION-I

1) Which of the following is NOT homogeneous mixture ?

(A) Pure air

(B) Alloy
(C) Sugar solution in water
(D) Sea water
2) 1.2 g of Mg (At mass 24) will produce MgO equal to -

(A) 0.05 mol

(B) 40 g
(C) 40 mg
(D) 4 g

3) Which one of the following contains maximum number of 'O'-atom

(A) 2g-molecule of dioxygen

(B) 3.011 × 1024 molecules of ozone
(C) 98g of H2SO4
(D) 44.8 L CO2 at (P = 1atm & T = 0°C)

4) What is the mass of oxygen atoms present in the 100g of CaCO3?

(A) 12 g
(B) 60 g
(C) 48 g
(D) 240 g

5) If water samples are taken from sea, rivers, clouds, lake or snow, they were found to contain H
and O in the approximate mass ratio of 1 : 8. This indicates the law of -

(A) Multiple proportion

(B) Definite proportion
(C) Reciprocal proportion
(D) None of these

6) A gas is found to have the formula (CO)x. It's vapour density is 70 the value of x must be:

(A) 3
(B) 4
(C) 5
(D) 7

7) One molecule of a compound contains 7 carbon atoms, 2 oxygen atoms and 6 amu of other
elements. The molecular mass of compound is (NA = 6 × 1023) :
[At.mass : C = 12, O = 16]

(A) 122
(B) 116
(C) 148
(D) 154

8) Which of the following contains maximum number of atoms in 100g sample -

(A) CO2
(B) N2O
(C) NO2
(D) H2O

9) At certain temperature two moles of A2 combines with five moles of B2 to produce two mole of C.
The formula of compound C is :-

(A) AB3
(B) A2B5
(C) AB5
(D) A5B2

10) What is the concentration of H+ in a solution that is prepared by mixing 50.0 mL of 0.50 M HCl
with 200.0 mL of 0.25 M HCl ?

(A) 0.30 M
(B) 0.35 M
(C) 0.40 M
(D) 0.45 M

11) Which one of the following modes of expressing concentration of solution is independent
of temperature -

(A) Molarity
(B) Molality
(C) % w/v
(D) Grams per litre

12) Equal weight of NaCl and KCl are dissolved separately in equal volumes of solutions. Molarity of
the solutions will be –

(A) Equal
(B) Greater for NaCl
(C) Greater for KCl
(D) Uncomparable.

13) Equal volumes of 10% (w/v) of HCl is mixed with 10% (w/v) NaOH solution. The resultant
solution be.

(A) basic
(B) neutral
(C) acidic
(D) can’t be predicted.

14) Molarity and Molality of a solute (M. wt = 50 ) in aqueous solution is 9 and 18 respectively. What
is the density of solution.

(A) 1 g/cc
(B) 0.95 g/cc
(C) 1.05 g/cc
(D) 2 g/cc

15) Statement-1 : The mass fraction of solute in a solution is always greater than its mole fraction.
Statement-2 : Mole fraction of solvent in an aqueous solution of ethanol must be greater than that
of solute.

(A) Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for
(B)
statement-1.
(C) Statement-1 is true, statement-2 is false.
(D) Statement-1 is false, statement-2 is true.

16) In the following reaction, 2A + B → C 8 mole of A and 5 moles of B will form

(A) 13 moles of C
(B) 4 moles of C
(C) 5 moles of C
(D) 8 moles of C

17) The density of gold is 19.7 g/cm3. The volume of 1 mole solid is : (Au = 197)

(A) 10 ml
(B) 1 ml
(C) 100 ml
(D) 1000 ml

18) For the following sequence of reaction

5A + 6B → 2C
3C + 4D →2E
5E + 6F → 2G
If, B, D and F are in excess . How many mole of A is required to produce 100 mole G. The % yield of
1st, 2nd and 3rd reaction are 50%, 50% and 50% respectively.

(A) 3450 mol

(B) 6350 mol
(C) 6250 mol
(D) 7500 mol

19) The mass of CaO that shall be obtained 20 kg of 90% pure lime-stone (CaCO3) is :

(A) 11.2 kg
(B) 8.4 kg
(C) 10.08 kg
(D) 16.8 kg

20) 28 gm of N2(g) reacts with 6 gm of H2(g) to produce 17 gm of NH3(g). Calculate % yield of the
reaction:

(A) 100%
(B) 75%
(C) 25%
(D) 50%

SECTION-II

1)

Find the total number of moles of N atom in mixture containing 46 g NO2, 63 g HNO3, 184 g N2O4.

2) The mole fraction of a solute in a solution is 0.1. At 298 K, molarity of this solution is the same as
its molality. Density of this solution at 298 K is 2.0 g cm–3. The ratio of the molecular weights of the

solute and solvent, , is

3) 4FeS2 + 11O2 → 2Fe2O3 + 8SO2

2SO2 + O2 → 2SO3 How many moles of SO3 are obtained if we start with 3 moles of FeS2?

4) A complex compound of iron has molar mass = 2800 and it contains 8% iron by weight. The
number of iron atoms in one formula unit of complex compound is: [Atomic weight of Fe = 56]

5)

How many gram ions of SO4–2 are present in 1.25 mole of K2SO4. Al2(SO4)3. 24H2O :

MATHEMATICS

SECTION-I

1) If 2576a 456b is divisible by 15, then possible value of 'a' can be

(A) 5
(B) 3
(C) 9
(D) None of these
2) The complete solution set of is

(A) x ∈ (–∞, ∞)
(B) x ∈ [1,2)
(C) x ∈ (1,2)
(D) x ∈ [1,2]

3) If A = {1, 2, 3, 4} then number of subsets of A is

(A) 4
(B) 16
(C) 216
(D) 8

4) If , then the value of is equal to

(A)

(B)

(C)

(D) None of these

5) Number of roots of equation

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

6) The complete solution set of inequality is

(A) [5, 8]
(B) (5, 8)
(C)
(D)

7) The value of is

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

8) The multiplication of a rational number ' x ' and an irrational number ' y ' is :

(A) always rational

(B) rational except when y = π
(C) always irrational
(D) irrational except when x = 0

9) Solution set of is given by

(A) (–∞, 4)
(B) (–∞, –5]
(C) (–4, –3) ∪ (–3, –2] ∪ [–1, ∞]
(D) (–5, –3) ∪ (–3, –2) ∪ (–1, ∞)

10) The least integral value of x satisfying is

(A) 2
(B) 3
(C) 4
(D) 5

11) If then the complete solution set of x is

(A) (–∞,1]
(B) (–∞,2]
(C)
(D) ϕ

12) If (a + b) : (a – b) = 15 : 1, then the value of is

(A)

(B)

(C) 15
(D) None of these

13) If then

(A) {5}
(B) 5
(C) ϕ
(D)

14) In a class of 60 students, 25 students play cricket and 20 students play tennis, and 10 students
play both the games. Then, the number of students who play neither is

(A) 0
(B) 25
(C) 35
(D) 45

15) If (x - 1) (x - 2)2 (x - 5) > 0, then

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

16) If , then

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

17) If x and y are positive real numbers such that x3 + 8y3 + 24xy = 64, then the value of (x + 2y) is

(A) 8
(B) 4
(C) 2
(D) 1

18) Let and . Then,

(A) (4, 5]
(B) (4, 5)
(C) [4,5)
(D) [4, 5]

19) If , then

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

20) If , then

(A)
(B)
(C)
(D) None of these

SECTION-II

1) If a + b + c = 5 and ab + bc + ca = 10 then value of a2 + b2 + c2 is

2) If then the value of (31/4 –1)x is

3) LCM of is . Find a + b (where a and are co-prime)

4) If a, b, c are real and distinct numbers, then the value of is :

5) If a, b, c ∈R and then value of (a + b + c)2

 ANSWER KEYS

PHYSICS

SECTION-I

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

SECTION-II

Q. 21 22 23 24 25
A. 8.00 10.00 1.00 1.25 3.00

CHEMISTRY

SECTION-I

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

SECTION-II

Q. 46 47 48 49 50
A. 6.00 9.00 6.00 4.00 5.00

MATHEMATICS

SECTION-I

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

SECTION-II

Q. 71 72 73 74 75
A. 5.00 8.00 23 3.00 36.00
 SOLUTIONS

PHYSICS

8)

9)

10)

11)

13)

15) y = x log x

= 1 + loge x

17) y = sinx + cosx

20)

at

CHEMISTRY

28)
Class notes

29) Level : Easy

Concept : POAC can be used to deremine moles as mass of a compound from a sample.
Solution (C) :

no. of moles of CaCo3 = =1

no. of moles of oxygen in 1 mole CaCo3 = 1 3 = 03
mass of 3 mole oxygen atom = 3 16 = 48g

33)

(A) CO2 = moles =

(B) N2O = moles =

(C) NO2 = moles =

(D) H2O = moles =

H2O contains maximum number of moles.

34) Ratio of volumes = A : B : C = 2 : 5 : 2

Ratio of no. of molecules in A, B and C = 2 : 5 : 2 or 1 : 5/2 : 1
1 molecule C contains 1 molecule (i.e. 2 atom) of A and 5/2 molecules (i.e. 5/2 × 2 atoms) of B
Hence the formula of C is A2B5

35) M1V1 + M2V2 = M(V1 + V2)

50× 0.5 200× 0.25 M(50+200)
25 + 50 = M(250)
75 = M(250)

M= = 3 × 10–1
+
⇒ [H ] = 0.3 M

36)

Molality is temperature independent.

37)

NaCl KCl
let weight = Wgm Wgm

molarity =
38)

Since, equal volumes are mixed, let us assume 100 ml of each.

+
100 ml will 100 ml will
contain 10 gm HCl contain 10 gm NaOH

nNaOH =
HCl + NaOH → NaCl + H2O

(excess) L.R.
Final solution will be acidic.

39)

d = 0.95 gm/ml = 0.95 gm/cm3

40)

Statement:2 aq. solution of ethanol

i.e. ethanol + H2O
solute solvent
Here mole-fraction of H2O is greater than C2H5OH

46)

Mole =

47) (Mw)Solvent × 1.8 = (Mw)Solvent × 0.9 + (Mw)Solvent × 0.1

⇒
mole of solute = 0.1
mole of solvent = 0.9

Molarity = Molality =
Wsolvent = Vsolution

(Mw)solvent × 0.9 =

49) Percentage mass of an Fe

 8= ⇒x=4

MATHEMATICS