16-06-2024
9610WJA801259240002 JA
PART 1 : PHYSICS
SECTION-I (i)
1) = 5 units due to South-West
= 5 units due 53° North of East
= 10 units due 37° South of East
Then which of the following are correct ?
(A)
(B)
(C)
(D)
2) Choose the correct alternate(s) :-
(A) The dimensional formula for potential energy is ML2T–2.
(B) Dimensions of time in power is –3 in standard base unit system.
(C) The units of angular momentum (mvr) in CGS system are erg × s.
(D) Work, energy and torque have same dimensions.
3) Which of the following expressions have magnitude unity .
(A)
(B) when angle between and is 120°
(C)
(D) when angle between and is 60°
4) If this equation is dimensionally correct where all the letters represent
physical quantities then choose the correct statement(s) : (none is dimensionless)
(A)
Units of and are same.
(B)
Dimensional formulas of P and are same.
(C)
Dimensional formulas of P and are same.
(D)
Units of and X are same.
5) Two vectors and of magnitudes 2 units and 4 units respectively are shown in the figure.
Which of the following mathematical operations is/are CORRECT ?
(A)
(B)
(C)
(D)
6) A wave is propagating along x-axis in a medium, so that displacement y of particle at any position
x, at any time t is given by :
where a, b and c are constants. Choose the correct option (s).
(A) dimension of b is [T]
(B) dimension of a is [LT2]
(C) dimension of c is [L]
(D) is dimensionless
7) Which of following statement is/are correct ?
(A) x-component of is positive.
(B) y-component of is negative
(C) is positive
(D) Component of along is negative
8) Which of the following relation is/are correct
(A)
(B)
(C)
(D)
SECTION-I (ii)
1) Answer the following by appropriately matching the lists based on the information given
in the paragraph.
List–I List–II
(I) (P) 6
(II) (Q)
(III) (R)
(IV) (S) 0
(T) 12
(U)
(A) I → Q;II → P;III → T;IV → R
(B) I → S;II → R;III → P;IV → U
(C) I → Q;II → S;III → U;IV → P
(D) I → Q;II → P;III → U;IV → S
2) If a physical quantity x is given as , where F is force, A is area, x is distance and
P is power then match the following list.
List-I List-II
(P) Dimension of β is (1) M1/2L–1/2T–1/2
If y is velocity then 0 0
(Q) (2) M L1T
dimension of ω is
If y is velocity then
(R) (3) M–3/2L1/2T7/2
dimension of α is
If ω is dimensionless 0
(S) (4) M1L T–2
then dimension of y is
(5) M1L1T1
(6) M3/2L–1/2T5/2
(A) P → 2;Q → 1;R → 4;S → 3
(B) P → 2;Q → 1;R → 3;S → 4
(C) P → 1;Q → 3;R → 2;S → 4
(D) P → 4;Q → 2;R → 3;S → 1
3) List-I gives the direction of non-zero velocity vectors of the two particles A and B. List-II gives the
possible directions of vectors of relative velocity. (Relative velocity of A with respect to B is defined
as )
List-I List-II
(I) (P)
Velocity of B with respect to A
(II) (Q)
Velocity of A with respect to B
(III) (R)
Velocity of B with respect to A
(IV) (S)
Velocity of A with respect to B
(T)
(U)
(A) I → P,Q,R;II → S,T;III → P;IV → Q
(B) I → Q,R;II → P,Q;III → Q;IV → P
(C) I → P,R;II → R,T;III → R;IV → P
(D) I → R,S;II → Q,R;III → S;IV → R
4) In a new system of units, the fundamental physical quantities of mechanics-length, mass and time
are measured in “toof”, “dounf” and “shan” respectively. You know the following information.
1 toof = 10 m
1 dounf = 10 kg
1 shan = 0.1 s
Suggest suitable matches.
List-I List-II
(P) One unit of speed in the new system (1) 10–1 SI unit
(Q) One unit of force in the new system (2) 102 SI unit
(R) One unit of pressure in the new system (3) 103 SI unit
(S) One unit of energy in the new system (4) 104 SI unit
(5) 105 SI unit
(6) 10–2 SI unit
(A) P → 2;Q → 3;R → 1;S → 4
(B) P → 1;Q → 3;R → 4;S → 2
(C) P → 1;Q → 4;R → 2;S → 3
(D) P → 2;Q → 4;R → 2;S → 5
SECTION-II
1) The time period of oscillation of a body is given by
T=
K : Represents the kinetic energy, m mass, g acceleration due to gravity and A is unknown quantity.
If [A] = Mx Ly Tz , then what is the value of x + y + z.
2) and value of is_______.
3)
The potential energy 'U' of a particle varies with distance 'x' from a fixed origin as .
where A and B are dimensional constants. Find the dimension of length in AB.
4) If and then component of along is -
5) When a sphere of radius 'r' is moving in a viscous medium with velocity 'v'. The viscous force on
the sphere is given by f = 6πηrv. If the dimension of [η] = [MaLbTc]. The value of |a + b + c| is
________.
6) A vector makes angles α, β, and γ with x-axis, y-axis and z-axis respectively. The value of (sin2 α +
sin2 β + sin2 γ) is _________.
PART 2 : CHEMISTRY
SECTION-I (i)
1) Select the correct order of radii :-
(A) Na+ > Al3+
(B) N3– > F–
(C) Li+ < Mg2+
(D) Cr > Mn
2) In which of the following set of atomic numbers, all elements are in the same group?
(A) 8, 16, 24
(B) 3, 11, 37
(C) 12, 38, 56
(D) 10, 18, 56
3) Hund’s rule is applicable for
(A) s-subshell
(B) p-subshell
(C) d-subshell
(D) f-subshell
4) Which is/are correct statements about 1.7 g of NH3 :
(A) It contain 0.3 mol H – atom
(B) it contain 2.408 × 1023 atoms
(C) Mass % of hydrogen is 17.65%
(D) It contains 0.3 mol N-atom
5) Which of the following have equal no. of atoms ?
(A) 12 g MgSO4
(B) 0.2 mole CO2
(C) 5.6 L SO2 at STP
(D) 24 g Ca
6) 1 kg mass is equivalent to ____________ amu. Choose the correct option :
(A) 6.023 × 1025
(B) 6.023 × 1026
(C) 6.023 × 1024
(D) 6.023 × 1023
7) Which of the following options is/are incorrect.
(A) 10 gm of Boron is having 5 mole of nucleons.
(B) One atom of an element weight 1.8 × 10–22 gm, then its atomic mass is 108.36
(C) 10 gm of CaCO3 contains 1 gm atom of C.
(D) Number of atoms in 2 moles of S8 is greater than 5.5 moles of SO2
8) If n + =5, then
(A) Number of possible orbitals are 4
Maximum number of electrons that can be filled with ms = +1/2 is 6 in an atom with above
(B)
condition
(C) for iron (Z = 26) atom, number of electron with above condition must be 1 only
(D) For Germanium (Z = 32), number of electron with above condition can be 5
SECTION-I (ii)
1)
List-I List-II
(P) Mass of one molecule of C12H22O11 (1) 12
(Q) Molar mass of C12H22O11 (2) 342 amu
(R) 1 amu (3) 342 gm
(S) Relative atomic mass of C12 (4) 1.66 × 10–27 Kg
(5) 12 gm
(6) 12 amu
The correct match is :
(A) P → 2;Q → 3;R → 4;S → 5
(B) P → 2;Q → 3;R → 4;S → 1
(C) P → 3;Q → 2;R → 4;S → 5
(D) P → 3;Q → 2;R → 3;S → 5
2) Match the quantities given in list-I with equivalent amount in list-II.
List-I List-II
(P) 0.4 mol CO2 (1) 45g
(Q) 2.5 mol H2O (2) 32g
23
(R) 3.01 × 10 molecules of SO2 (3) 6g
(S) 4.48L of C2H6(g) at 1 atm, 0°C (4) 17.6 g
(5) 45 amu
(6) 17.6 amu
(A) P → 1;Q → 2;R → 3;S → 4
(B) P → 4;Q → 1;R → 2;S → 3
(C) P → 4;Q → 1;R → 2;S → 6
(D) P → 6;Q → 5;R → 2;S → 3
3) If electrons are filled in the sub shells of an atom in the following order 1s, 2s, 2p, 3s, 3p, 3d, 4s,
4p, 4d, 4f......... then match the following element in List I with block in List II.
List-I List-II
(A) K (P) s-Block
(B) Fe (Q) p-Block
(C) Ga (R) d-Block
(D) Sn (S) f-Block
(V) not discovered
(W) not defined
(A) A → P;B → Q;C → R;D → S
(B) A → R;B → R;C → Q;D → S
(C) A → S;B → R;C → Q;D → P
(D) A → Q;B → R;C → R;D → S
4) Match the list:
List- I List- II
(species) (Properties)
(P) Be → Be– (1) Positive electron gain enthalpy
(Q) O– → O–2 (2) Negative electron gain enthalpy
(R) F → F– (3) Endothermic
(S) Cl → Cl– (4) Exothermic
(5) Highest electron gain enthalpy
(6) Exothemic and endothemic both
The correct option is
(A) P → 1,4;Q → 1,3;R → 2,4;S → 2,4
(B) P → 1,3;Q → 1,4;R → 2,4,5;S → 2,4
(C) P → 1,4;Q → 1,3;R → 2,4,5;S → 2,4,5
(D) P → 1,3;Q → 1,3;R → 2,4;S → 2,4,5
SECTION-II
1)
How many electrons in an atom with atomic number 105 can have (n + l) = 8?
2) Find the Zeff value of 4s electron in scandium.
3) Twenty molecules of SO3 will weigh as much as x molecules oxygen. 'x' is :
4) One molecule of a compound contains six carbon atoms, 2 × 10–23 g of hydrogen and 16 × 10–23 g
of other atoms. The gram-molecular mass of the compound is-
5) A sample of carbon dioxide contains 12C and 14C in 3 : 1 mole ratio and 16O and 18O in 4 : 1 mole
ratio. How many moles of neutrons are present in 45 gm sample? Write your answer to the nearest
integer.
6) A hypothetical element has an electron configuration where the highest energy electron occupies
a subshell with quantum number (n = 4, l = 1). If this electron transitions to a lower energy state
with (n = 3), How many of the values of quantum number is/are can be possible for given transition
?
(Values of quantum number = 0,1,2,3,4,5)
PART 3 : MATHEMATICS
SECTION-I (i)
1) Let A and B be two sets. Then
(A) A ∪ B ⊆ A ∩ B
(B) A ∩ B ⊆ A ∪ B
(C) A ∩ B = A ∪ B
(D) None of these
2) A and B are two sets such that n(A) = 3 and n(B) = 6, then
(A) minimum value of n(A ∪ B) = 6
(B) minimum value of n(A ∪ B) = 9
(C) maximum value of n(A ∪ B) = 6
(D) maximum value of n(A ∪ B) = 9
3) Three sets A, B, C are such that A = B∩C and B = C∩A, then Which of the following statements is
incorrect ?
(A) A ⊂ B
(B) B ⊂ A
(C) A = B
(D) A ⊂ B'
4) For two sets A and B if n(A) = 7, n(B) = 13 and n(A ∩ B) = 5, then the correct statement is
(A) n(A ∪ B) = 15
(B) n(A – B) = 6
(C) n(A × B) = 91
(D) n{(A ∪ B) × (A ∩ B)} = 75
5) Let A, B, C ⊆ X. Which of the following option(s) is/are true ?
(A) [A\(A ∩ B)] ∪ [B\(A ∩ B)] ∪ (A ∩ B) = A ∪ B
(B) [(A ∪ B)c ∪ B] ∩ [Bc ∪ (A ∪ B)] = (A\B)c
(C) [(A ∪ B) ∩ (A ∩ C)] ∩ Bc = (A\B)]\Cc
(D) [A ∩ (Bc ∩ Ac)c]c ∪ A = X
6) Let then
(A) t102 is not prime
(B) t951 is not prime
(C) t540 is not prime
(D) t91 is not prime
7) The value of :
(A) greater than 5
(B) less than 5
(C) greater than 4
(D) less than 4
8) Values of x satisfying the inequality |x – 1| + | x – 2| + |x – 3| > 6
(A)
(B)
(C)
(D)
SECTION-I (ii)
1)
If
List-I List-II
(P) Number of solution(s) (1) 1
(Q) Sum of all solution(s) (2) 2
(R) Product of all solution(s) (3) 4
(S) Absolute difference between any two solution(s) (4) 6
(5)
(6)
The correction options is
(A) P → 2;Q → 3;R → 5;S → 1
(B) P → 2;Q → 3;R → 6;S → 1
(C) P → 3;Q → 4;R → 6;S → 1
(D) P → 3;Q → 4;R → 1;S → 5
2) Answer the following by appropriately matching the lists based on the information given
in the paragraph.
'n' is the number of solution for ||x| + a | = 10, List-I contains the values of 'n'. List-II contains subset
of the set of all possible values of 'a' for corresponding value of 'n'.
List-I List-II
(I) n=0 (P) [–10,10]
(II) n=1 (Q) (10,∞)
(III) n ∈ {2,3} (R) [0,10]
(IV) n=4 (S) (–∞,–10]
(T) (–20,0]
(U) [–10, ∞)
Which of the following is the only INCORRECT combination ?
(A) I → U
(B) II → P,R
(C) III → U
(D) IV → P
3) Let
List-I List-II
(P) Equation has exactly 2 solution (1)
(Q) Equation has exactly 1 solution (2)
(R) Equation has more than 2 solution (3)
(S) Equation has no solution (4)
(A) P → 3;Q → 4;R → 2;S → 1
(B) P → 3;Q → 2;R → 1;S → 4
(C) P → 1;Q → 4;R → 3;S → 2
(D) P → 1;Q → 2;R → 4;S → 3
4) Match every entry of List-I with correct entries of List-II
LIST I LIST II
(P) (1)
The value of is
(Q) (2)
+ 64–1/2 – (32)4/5 is equal to
(R) (3)
Find the value of x when
(S) If 4x+2 = 30 + 4x, then x is equal to (4) 2
(A) P → 3;Q → 1;R → 2;S → 4
(B) P → 3;Q → 1;R → 4;S → 2
(C) P → 1;Q → 2;R → 3;S → 4
(D) P → 4;Q → 2;R → 3;S → 1
SECTION-II
1) If \(\sqrt {{x^2} - 6x + 9} + \sqrt {{e^y} - 1} + \sqrt {{{\tan }^2}\theta - 3} = 0\), then the
value of x + y + sec2θ is
2) Number of values of x satisfying is
3) If A = {(x, y)|xy = 8 and x, y ∈ I} then n(A) equal to
4) If n(P(B)) = 29 then n(B) = (where n(X) represent number of elements in set X and P(X) represents
power set of X)
5) Let U be set with number of elements in it is 2009 and A, B are subsets of U with n(A ∪ B) = 280.
If n(A′ ∩ B′) = + = + for some positive integers x1, x2 ,y1, y2then find the value of
(x1+x2+y1+y2).
6) Let U be set with number of elements in it is 2009. A is a subset of U with n(A) = 1681 and out of
these 1681 elements, exactly 1075 elements belong to a subset B of U. If n(A – B) = m2 + p1 p2 p3 for
some positive integer m and distinct primes p1, p2, p3 then for least m find (p1+p2+p3)
ANSWER KEYS
PART 1 : PHYSICS
SECTION-I (i)
Q. 1 2 3 4 5 6 7 8
A. B,C A,B,C,D A,B,C,D B,C,D A,B A,B,C,D A,B,C,D A,B,C
SECTION-I (ii)
Q. 9 10 11 12
A. D B A D
SECTION-II
Q. 13 14 15 16 17 18
A. 3.00 2.00 5.00 2.00 1.00 2.00
PART 2 : CHEMISTRY
SECTION-I (i)
Q. 19 20 21 22 23 24 25 26
A. A,B B,C B,C,D A,B,C A,B,D B A,C,D A,D
SECTION-I (ii)
Q. 27 28 29 30
A. B B B D
SECTION-II
Q. 31 32 33 34 35 36
A. 17.00 3.00 50.00 180.00 23.00 3.00
PART 3 : MATHEMATICS
SECTION-I (i)
Q. 37 38 39 40 41 42 43 44
A. B A,D A,B,D A,C,D A,B,C,D A,B,C,D B,C A,D
SECTION-I (ii)
Q. 45 46 47 48
A. B D A B
SECTION-II
Q. 49 50 51 52 53 54
A. 7.00 5.00 8.00 09.00 32.00 52.00
SOLUTIONS
PART 1 : PHYSICS
1)
2)
[PE] = [mgh] = MLT–2 × L
[mvr] = ⇒ units = erg × s
[Work] = [F × d] = ML2T–2
[Energy] =
[Torque] = = L × MLT–2
3)
Vector upon magnitude of vector is unit vector. Hence (A) & (C) is correct. If two vector each of
magnitude one at 120° then their resultant has magnitude one. Hence B & D is correct.
4)
5)
(A)
(B)
(C)
(D)
6) y =
⇒ [b] = T & [C] = [L] &
& is dimensionless
7)
8)
...(i)
...(ii)
From (i) & (ii)
9)
(I)
(II) Angle between and is 120°
So
(III) Angle between and is 60°
(IV)
10)
(Q)
ω = M1/2L–1/2T–1/2
(R)
11)
(I)
(II)
(III)
(IV)
12)
[speed] =
(A)
(B)
(C) [pressure] = ML–1T–2 =
(D) [Energy] = ML2T–2 =
13) [T] = = =
0
⇒ [A] = M L T2
x = 0, y = 1, Z = 2
x+y+z=3
14)
15)
∴ [B] = L2
ML2T–2 =
∴ A = ML3T–2
AB = ML5T–2
16)
Component of along = A cos θ =
17)
|a + b + c| = |1 - 1 - 1| = 1
18)
cos2 α + cos2 β + cos2 γ = 1
(1 – sin2 α) + (1 – sin2 β) + (1 – sin2 γ) = 1
PART 2 : CHEMISTRY
19)
(A) Na⨁ > Al+3
in isoelectronic species, higher number of proton increases (Zeff)
⇒size decreases
(B) N3– > F⊝
in isoelectronic species, higher number of proton increases (Zeff)⇒ size decreases
(C) Li+ > Mg2+
(D) Sc > Ti > V > Cr < Mn > Fe > Co Ni < Cu < Zn (order of radius)
20)
3, 11, 37 – all belong to group-1 (alkali metals)
12, 38, 56 – all belong to group-2 (alkaline earth metal)
21)
22)
Mole of NH3 = = 0.1 mole
Mole H atom = 0.3
Total atoms = 0.4 × 6.02 × 1023 = 2.408 × 1023
%H= × 100 = 17.65 %
23)
A → 12 g MgSO4 =
B → 0.2 × NA × 3 = 0.6 NA
C→
D→
24)
1 amu = g= kg
23 3
1 kg = 6.023 × 10 × 10 amu
1 kg = 6.023 × 1026 amu
25)
(A) 10 gm of Boron is having 10 mole of nucleons.
(B) Atomic mass = 1.8 × 10–22 × 6.023 × 1023 = 108.36 gm
(C) gm atom of C =
(D) Number of atom in S8 = 2 × 8 = 16
Number of atom in SO2 = 5.5 × 3 = 16.5
26)
If n + =5,
m = +1 or -1
n=4 l=1 4p
n = 3 l = 2 3d
no. of posible orbitals = 4
27)
(P) Mass of one molecule of C12H22O11 = 12 × 12 + 22 × 1 + 11 × 16 = 342 amu
(Q) Molar mass of C12H22O11 = 342 gm
(R) 1 amu = gm = 1.66 × 10–27 kg
(S) Relative atomic mass of C12 = 12 (unitless).
28)
(P) 0.4 mole CO2
W = 0.4 × 44 = 17.6 = n × MW
(Q) = 2.5 × 18 = 45.0 gram (n × MW)
(R) = 0.5 mole SO2
= 0.5 × 64 = 32.0 g
(S) W=6g
29)
(A)R ; (B)R ; (C)Q ; (D)S
(a) K(19) → 1s2,2s2,2p6,3s2,3p6,3d1 last electron in d–subshell ⇒ d–block element
(b) Fe(26) → 1s2,2s2,2p6,3s2,3p6,3d8 last electron in d–subshell ⇒ d–block element
(c) Ga(31) → 1s2,2s2,2p6,3s2,3p6,3d10,4s2,4p1 last electron in p–subshell ⇒ p–block element
(d) Sn(50) → 1s2,2s2,2p6,3s2,3p6,3d10,4s2,4p6,4d10, 4f4 last electron in f–subshell ⇒ f–block element
30)
(P) Be → Be–
EC = ns2 (fully filled)
ΔH = +ve (Endothermic)
(P) → 1, 3
(Q) O– → O–2
Here, second Electron gain enthalpy is always positive or endothermic.
(Q) → 1, 3
(R) F → F–
Electron gain enthalpy = –ve (exothermic)
R → 2, 4
(S) Cl → Cl–
Electron gain enthalpy = –ve (Exothermic)
It has the highest electron gain enthalpy in periodic table.
S → 2, 4, 5
14
31) 5f , 6d3
5f14 = (n + l) = 5 + 3 = 8
6d3 = (n + l) = 6 + 2 = 8
32)
=3
33)
20 × 80 = x × 32
34)
Weight of a molecule
= 30 × 10–23 g
Gram molecular mass = 30 × 10–23 × 6 × 1023 = 180 g
35)
Avg. molar mass of CO2
no. of moles of CO2 in sample =
Avg. number of neutrons per molecule
=
no. of moles of neutrons = 0.993 × 23.3 = 23.13
36)
for n =3
Possible value of l = 0, 1, 2
but = 3, 4 and 5 are not possible because 3f, 3g and 3h Subshells do not exist.
PART 3 : MATHEMATICS
37)
(A) A ∪ B ⊆ A ∩ B False
(B) A ∩ B ⊆ A ∪ B True
(C) A ∩ B = A ∪ B False
38)
n(A ∪ B) is minimum when n(A ∩ B) is maximum i.e. 3.
∴ minimum n(A ∪ B) = 6
n(A ∪ B) is maximum when n(A ∩ B) is minimum i.e. 0
∴ maximum n(A ∪ B) = 9
39)
From venn Diagram , A ∩ C = A
Hence, A, B are equal sets (A and B are inter changeable) in both equation
40)
n(A) = 7 ; n(B) = 13
n(A – B) = n(A) – n(A ∩ B) = 7 – 5 = 2
n(A ∪ B) = n(A) + n(B) – n(A ∩ B)
= 7 + 13 – 5 = 15
n(A × B) = n(A) × n(B) = 7 × 13 = 91
n{(A ∪ B) × (A ∩ B)} = 15 × 5 = 75
41)
(A) Correct
(B) Correct
(C) Correct
(D) Correct
42)
Sum of digits of t102 = 102 which is divisible by 3 Hence not prime.
Sum of t951 digits = 951 = 9+5+1 = 15 which is divisible by 3 so not prime.
Sum of digits of t540 = 540 which is divisible by 3 so not prime.
so not prime.
A, B, C, D all are correct.
43)
⇒
⇒
⇒
⇒
⇒ (∵ x > 0)
44)
|x – 1| + |x – 2| + |x – 3| ≥ 6
Let f(x) = |x – 1| + |x – 2| + |x – 3|
for f(x) ≥ 6
⇒ x ∈ (–∞, 0] ∪ [4, ∞)
∴ Option D is correct answer.
45)
|x – 1| + |x – 3| = 4|x – 2|
(P) x ≥ 3 then, x – 1 + x – 3 = 4 (x – 2)
⇒ x = 2 (reject)
(Q) 2 < x < 3 then, x – 1 + 3 – x = 4(x – 2)
⇒x=
(R) 1 < x ≤ 2 then, x – 1 + 3 – x = 4(2 – x)
⇒x=
(S) x ≤ 1 then, 1 – x + 3 – x = 4(2 – x)
⇒ x = 2 (reject)
* Number of solution = 2
* Sum of solution = 4
* Product of Solution =
* Absolute difference between any two sol. = 1
46) ||x| + a| = 10
for n = 0
a ∈ (10,∞)
for n = 1, a ∈ {10}
for n = 2, a ∈ (–10,10)
for n = 3, a ∈ {–10}
for n = 4, a ∈ (–∞,–10)
47)
49)
\(\sqrt {{{(x - 3)}^2}} + \sqrt {{e^y} - 1} + \sqrt {{{\tan }^2} - 3} = 0\)
⇒ x = 3, y = 0, tan2θ = 3
50)
case-1
x2 + 5x + 5 = 1
x2 + 5x + 4 = 0
(x + 4) (x + 1) = 0
case-2
x2 – 10x + 21 = 0
(x–7) (x–3) = 0
case-3
If x2 + 5x + 5 = –1
x2 + 5x + 6 = 0
(x + 3) (x + 2) = 0
x = –3, –2
at x = –3 at x = –2
2
x –10x + 21 x2 – 10 x + 21
=(–32) – 10 (–3) + 21 = (–2)2 – 10 (–2) +21
=60 (even) = 45 (odd)
Hence x = –4, –1, 3, 7, –3
No. of values of x = 5
51)
xy = 8
A = {(1, 8), (2, 4), (4, 2), (8, 1), (–1, –8),
(–2, –4), (–4, –2), (–8, –1)}
52)
Given n(P(B)) = 29
⇒ B has 9 elements
i.e. n(B) = 25
53)
n(A ∪ B) = 280
Now n(A' ∩ B') = n(A ∪ B)' = 2009 – n(A ∪ B) = 2009 – 280 = 1729 = 123 + 13 = 103 + 93
54)
n(A – B) = 1681 – 1075 = 606 = 4 + 2 × 301 = 4 + 2 × 7 × 43 = (2) 2 + 2 × 7 × 43
