SRMJEEE 2027 Sample Paper

SAMPLE PAPER

S A M P L E Q U E S T I O N P A P E R

SRMJEEE 2027
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME MARKING

105 105 150 Min +1 / 0

GENERAL INSTRUCTIONS

1. This paper contains 105 multiple-choice questions. All questions are compulsory.

2. Each question has four options — (A), (B), (C) and (D) — of which only one is correct.

3. Each correct answer carries 1 mark; there is no negative marking.

4. Total time allowed is 150 minutes. Manage your time across all sections.

5. Use of calculators, mobile phones or any electronic device is not permitted.

6. Attempt the paper first, then check your answers against the Answer Key at the end.

Candidate Name: Roll No.: Date:

SAMPLE PAPER

SRMJEEE 2027
SAMPLE QUESTION PAPER

Questions 105 Max Marks 105 Time 150 Min Marking +1 / 0

Attempt all questions. Choose the one correct option for each.

PHYSICS

1. The position of a particle is given by r = ( i + 2 j - k ) 2. A carrier is simultaneously modulated by two sine
and its linear momentum is given by p = ( 3 i + 4 j - 2 k ) . waves having modulation indices of 0.3 and 0.4. The total
Then its angular momentum, about the origin is modulation index will be:
perpendicular to
(A) 0.1
(A) yz-plane (B) 0.5
(B) z-axis (C) 0.7
(C) y-axis (D) 0.35
(D) x-axis

3. An AC generator of 220 V having internal resistance r = 4. Conductivity of semiconductors
10 Ω and external resistance R = 100Ω. What is the
(A) is maximum at 0 K
power developed in the external circuit?
(B) decreases with increase in temperature
(A) 484 W
(C) increases with increase in temperature
(B) 400 W
(D) is maximum at 300 K.
(C) 441 W

(D) 369 W

5. The ratio of minimum to maximum wavelength in 6. What is the shape of the graph between the speed and
Balmer series is kinetic energy of a body?

(A) 5:9 (A) Straight line

(B) 5:36 (B) Hyperbola

(C) 1:4 (C) Parabola

(D) 3:4 (D) Exponential

7. Sand drops vertically at the rate of 2 kg s⁻¹ on to a 8. What would be maximum wavelength for Brackett
conveyor belt moving horizontally with a velocity of 0.2 m series of hydrogen spectrum?
s⁻¹. Then the extra force required to keep the belt
(A) 74583 Å
moving is
(B) 22790 Å
(A) 0.4 N
(C) 40519 Å
(B) 0.08 N
(D) 18753 Å
(C) 0.04 N

(D) 0.2 N

9. The speed of a projectile at its maximum height is √3/ 10. If the force on a rocket, moving with a velocity of 300
2 times its initial speed. If the range of the projectile is P m s' is 210 N, then the rate of combustion of the fuel is
times the maximum height attained by it, then P is equal
(A) 0.07 kg s⁻¹
to
(B) 1.4 kg s⁻¹
(A) 4/3
(C) 0.7 kg s⁻¹
(B) 2
(D) 10.7 kg s⁻¹
(C) 4

(D) 3/4

11. The current through a coil of self inductance L = 2 mH 12. A current of (2/√3)A produces a deflection of 60° in a
is given by I = t²e⁻t at time t. How long it will take to tangent galvanometer. The reduction factor is
make the e.m.f. zero?
(A) (2/√3) A
(A) 1s (B) (2/3) A
(B) 2s (C) 2 A
(C) 3s (D) (3/2) A
(D) 4s

13. In a certain situation, Ē and S are not equal to zero 14. Sharp peak point A represents
but the work done is zero. From this, we conclude that

(A) F and S are in the same direction

(B) F and S are in opposite directions

(C) F and S are at right angles

(D) F >S

(A) characteristic X-ray

(B) continuous X-ray

(C) Bremsstrahlung

(D) discontinuous spectrum.

15. A ray of light is incident on a 60° prism at the 16. The wireless communication frequency bands for
minimum deviation position. The angle of refraction at cellular mobile radio (mobile to base station) are in range
the first face (i.e., incident face) of the prism is of

(A) Zero (A) 76-88 MHz

(B) 30° (B) 900-1000 MHz

(C) 45° (C) 896-901 MHz

(D) 60° (D) 896-1000 MHz

17. An alternating current of rms value 10 A is passed 18. Which two of the following quantities are
through a 12Ω resistor. The maximum potential dimensionally equivalent? (i) Force (ii) Pressure (iii)
difference across the resistor is Young's Modulus (iv) Energy

(A) 20 V (A) (i) and (ii)

(B) 90 V (B) (i) and (iii)

(C) 169.68 V (C) (ii) and (iii)

(D) None of these (D) (ii) and (iv)

19. If the shift in a star light is towards red end, then 20. The temperature of the system decreases in the
process of
(A) the star is approaching the earth

(B) the star is receding from the earth (A) free expansion

(C) the apparent frequency is lesser than actual (B) adiabatic expansion

(D) both (b) and (c) (C) isothermal expansion

(D) isothermal compression

21. 1 mole of monatomic and 1 mole of diatomic gas are 22. The magnifying power of a compound microscope
mixed together. The value of Cν for the mixture is increases with

(A) 2R (A) the focal length of objective lens is increased and that of

(B) (3/2)R eye lens is decreased

(C) R (B) the focal length of eye lens is increased and that of
objective lens is decreased
(D) R/2
(C) focal lengths of both objects and eye-piece are increased

(D) focal lengths of both objects and eye-piece are
decreased.

23. Four identical plates each of area a are separated by 24. Red colour is used for danger signals because
a distance d. The connection is shown below. What is the
(A) it causes fear
capacitance between P and Q?
(B) it undergoes least scattering

(C) it undergoes maximum scattering

(D) it is in accordance with international convention.

(A) 2aεₒ/d

(B) aεₒ/(2d)

(C) aεₒ/d

(D) 4aεₒ/d

25. If the radius of a spherical liquid drop (of surface 26. The value of gravitational acceleration g at a height h
tension S) increases from r to r + Δr, the corresponding above the earth's surface is g/4 then (R = radius of earth)
increase in the surface energy is:
(A) h = R
(A) 8πrΔrS (B) h = R/2
(B) 4πrΔrS (C) h= R/3
(C) 16πrΔrS (D) h = R/4
(D) 2πrΔrS

27. In the meter bridge experiment shown in the figure, 28. A uniform rod of mass m, length L, area of cross-
the balance length AC corresponding to null deflection of section A and Young's modulus Y hangs from a rigid
the galvanometer is x. What would be the balance length support. Its elongation due to its own weight will be
if the radius of the wire AB is doubled?
(A) ( m g L )/( A Y )

(B) ( m g L )/( 2 A Y )

(C) ( 2 m g L )/( A Y )

(D) zero

(A) 4x

(B) 2x

(C) x

(D) x/2

29. The average kinetic energy of a gas molecule is 30. For sky wave propagation of 10 MHz signal, what
should be the minimum electron density in Inosphere?
(A) proportional to pressure of gas

(B) inversely proportional to volume of gas (A) ~ 1.2 x 10¹² m⁻³

(C) inversely proportional to absolute temperature of gas (B) ~10⁶ m⁻³

(D) proportional to absolute temperature of gas (C) ~ 2.3 x 10¹⁴ m⁻³

(D) ~10²² m⁻³

31. If units of force and length become 3 times then what 32. In a moving coil galvanometer, to make the field
will be the value of energy E=81 J, in new units? radial

(A) 81 J (A) coil is wound on wooden frame

(B) 9 J (B) magnetic poles are cylindrically cut

(C) 729 J (C) a horse shoe magnet is used

(D) 700 J (D) the number of windings in the coil is decreased

33. A diffraction pattern is obtained using a beam of red 34. An echo repeats four syllables. The distance of the
light. What happens if the red light is replaced by blue reflecting surface, if it takes one-fifth of a second to
light? pronounce or hear one syllable distinctly is (Velocity of
sound = 340 m s⁻¹)
(A) No change.

(B) Diffraction bands become narrower and crowded (A) 100 m

together. (B) 136 m

(C) Band become broader and farther apart. (C) 120 m

(D) Bands disappear altogether. (D) 50 m

35. A dynamometer D is attached to two blocks of masses
M = 6 kg and m = 4 kg. Forces F=20 N and f=10 N are
applied to the masses as shown. The dynamometer reads

(A) 10 N

(B) 20 N

(C) 6 N

(D) 14 N

CHEMISTRY

36. Which of the following reactions will not give a 37. Which of the following statements is incorrect?
primary amine?
(A) Relative lowering of vapour pressure is independent of
(A) the nature of the solute and the solvent.

(B) (B) Relative lowering in vapour pressure is a colligative

(C) property.

(D) (C) Vapour pressure of a solution is lower than the vapour
pressure of the solvent.

(D) Relative lowering of vapour pressure is directly
proportional to the original pressure.

38. The pH of 0.1 M solution of following increases in the 39. Which of the following compounds is not coloured?
order
(A) Na _ 2 [ CuCl _ 4 ]
(A) NaCl NH₄Cl NaCN HCl (B) Na _ 2 [ CdCl _ 4 ]
(B) HCl NH₄Cl NaCl NaCN (C) K _ 4 [ Fe ( N ) _ 6 ]
(C) NaCN NH₄Cl NaCl HCl (D) K _ 3 [ Fe ( CN ) _ 6 ]
(D) HCl NaCl NaCN NH₄Cl

40. In equimolar solutions of glucose, NaCl and BaCl _ 2 41. If m _ 1 gram of a metal A displaces m _ 2 gram of
the order of osmotic pressure is another metal B from its salt solution and if the
equivalent weights are E and E respectively then the
(A) Glucose > NaCl > BaCl _ 2 1 2
equivalent weight of A can be expressed by
(B) NaCl > BaCl _ 2 > Glucose
(A)
(C) BaCl _ 2 > NaCl > Glucose
(B)
(D) Glucose > BaCl _ 2 > NaCl
(C)

(D)

42. If x/m is the mass of adsorbate adsorbed per particle 43. The electron identified by quantum numbers n and l,
is 8 unit mass of adsorbent, p is the pressure of the (i) n =4,l = 1 (ii) n = 4, l = 0 (iii) n = 3, l = 2 (iv) n = 3, l =
adsorbate gas and a and b are constants which of the 1 can be placed in order of increasing energy from the
following represents “Langmuir adsorption isotherm"? lowest to highest as

(A) (A) (iv) く (ii) く(iii) く(i)

(B) (B) (ii) く (iv) く(i) く(iii)

(C) (C) (i) く (iii) く(ii) く(iv)

(D) (D) (iii) く (i) く(iv) く(ii)

44. Terywool shirts and trousers are made up of 45. The radioactive isotope _ 27 ^ 60 CO which is used in
the treatment of cancer can be made by (n, p) reaction.
(A) dacron + wool
For this reaction the target nucleus
(B) cotton + wool
(A) 28 29 Ni
(C) nylon + wool
(B) 27 59 CO
(D) rayon + wool
(C) 28 60 Ni

(D) 27 60 CO

46. In a reaction between A and B, the initial rate of 47. Which of the following is arranged in order of
reaction ro was measured for different initial increasing density?
concentrations of A and B as given below:
(A) Al Mg C (graphite) B

(B) B Al Mg C (graphite)

(C) C (graphite) Al B Mg
The
(D) Mg C (graphite) B Al

order of the reaction with respect to A is

(A) 1.5

(B) 0.5

(C) 1

(D) 2

48. In a set of reactions acetic acid yielded a product S. 49. pH of a 1.0 x 10 ^ - 8 M solution of HCl is
The structure of S would be
(A) 7.02

(B) 6.98

(C) 7.4

(A) (D) 6.8

(B)

(C)

(D)

50. According to Kohlrausch's law, the limiting value of 51. Which of the following molecule has the maximum
molar conductivity of an electrolyte,A2B is number of stereoisomers?

(A) (A)

(B) (B)

(C) (C)

(D) (D)

52. Emission of an alpha particle leads to a 53. The two monosaccharides of sucrose are held
together by a glycosidic linkage between
(A) decrease of 2 units in the charge of the atom

(B) increase of 2 units in the mass of the atom (A) C _ 2 of ��-glucose and C _ 1 of �� fructose

(C) decrease of 2 units in the mass of the atom (B) C _ 3 of ��-glucose and C _ 2 of �� fructose

(D) increase of 4 units in the mass of the atom (C) C _ 1 of ��-glucose and C _ 2 of �� fructose

(D) C _ 1 of ��-glucose and C _ 5 of �� fructose.

54. Which is correct about saccharin? 55. Which statement is incorrect for osmotic pressure
(π), volume (V) and temperature (T)?

(A) π ∝ if T is constant.

(B) π ∝ V if T is constant.

(C) π ∝ T if V is constant.

(D) πV is constant if T is constant
(A)

(B) It is 550 times sweeter than sugar

(C) It is used as sweetening agent.

(D) All of the above.

56. In hexagonal close packing of spheres in three
dimensions

(A) In one unit cell there are 12 octahedral voids and all are 57.
completely inside the unit cell.
The chemical formulae of A, B and C are
(B) In one unit cell there are 6 octahedral voids and 12-
tetrahedral voids and all are completely inside the unit cell. (A) Ca(OH)₂ NaOH CaCO₃

(C) In one unit cell there are 6 octahedral void and of which (B) NaOH Ca(OH)₂ CaCO₃

there are completely inside the unit cell and other three are (C) NaOH CaO CaCO₃
partially inside the unit cell.
(D) CaO Ca(OH)₂ NaOH
(D) none of these.

58. Which of the following is correct for SF _ 4 ? 59. In the reaction,

(A) It has a see-saw shape.

(B) It has two lone pairs of electrons.

(C) It has a square planar geometry.
which of the following compound will be formed?
(D) It has 5 bonding pairs.

(A)

(B)

(C)

(D)

60. The alkane C₆H₁₀ producing OHC(CH₂)₄CHO on 61. Which of the following expressions between the van
ozonolysis is der Waals constant, 'b' and the radius y' of spherical
molecule is correct?
(A) 1-hexene

(B) 3-hexene (A)

(C) cyclohexene (B)

(D) 1-methylcyclohex-1-ene (C)

(D)

62. Mn²⁺ forms a complex with Br⁻ ion. The magnetic 63. Which one of the following statements is not true?
moment of the complex is 5.92 BM. The probable formula
(A) Buna-S is a copolymer of butadiene and styrene
and geometry of the complex, is
(B) Natural rubber is a polymer of isoprene
(A) [MnBr]²⁻; tetrahedral
(C) In vulcanization, the formation of sulphur bridges
(B) [MnBr₄]²⁻; square planar between different chains make rubber harder and stronger
(C) [MnBr₆]⁴⁻; octahedral (D) Natural rubber has the trans configuration at every
(D) [MnBr₅]³⁻; trigonal planar double bond.

64. Which of the following is not an antioxidant? 65. In Bragg's equation, n represents

(A) SO _ 2 (A) principal quantum number

(B) Butylated hydroxy toluene (B) number of atoms

(C) SO _ 3 ^ 2 - (C) number of electrons

(D) Alitame (D) order of diffraction (n = 1, 2....).

66. In the following sequence of reactions, the alkene 67. Aluminium oxide crystallises with aluminium ions in ⅔
affords the compound B. of the octahedral holes and ⅓ octahedral holes remaining
vacant in a closest packed array of oxide ions. The
The formula of aluminium oxide is

compound B is (A) Al₃O₂

(A) CH₃CHO (B) Al₂O₃

(B) CH₃CH₂CHO (C) AlO₂

(C) CH₃COCH₃ (D) Al₂O

(D) CH₃CH₂COCH₃

68. Nucleotides and nucleosides mainly differ from each 69. The formal charge on the central oxygen atom in O₃
other in molecule is

(A) presence of phosphate units (A) 0

(B) presence of base units (B) +1

(C) presence of nucleic acids (C) -1

(D) none of the above (D) -2

70. For a chemical reaction, ∆S =-0.035 kJ/K and ∆H = -20
kJ. At what temperature does the reaction turn non-
spontaneous?

(A) 5.14 K

(B) 571.4 K

(C) 57.14 K

(D) 5714.0 K

MATHEMATICS

71. Let t be a positive integer and Δ _ t = | array c c c 2 t - 72. The minimum value of x ^ 2 + x + 1 + sin x is given by
1&m^2-1&^2(m^2)\^mC_1&2^m&^2(m
(A) ¼
) \ 1 & m + 1 & ( m ^ 2 ) array | then the value of Σ _ t = 0
(B) ¾
^ m Δ _ t is equal to
(C) -¼
(A) 2 ^ m
(D) 7/4
(B) 0

(C) 2 ^ m ^ 2 ( 2 ^ m )

(D) m ^ 2

73. If the curve y=f(x) passing through the point (1, 2) 74. The function f ( x ) = ( x )/( 1 + | x | ) x R then which of
and satisfies the differential equation x d y + ( y + x ^ 3 the following is true ?
y ^ 2 ) d x = 0 then
(A) f(x) is differentiable everywhere and 01
(A) xy = 1/2 (B) At x = 0, '(x) is minimum
(B) x ^ 3 y = 2 (C) x = 0, gives points of inflexion so f(x) is twice
(C) ( 1 )/( x y ) = 2 differentiable at x=0

(D) None of these (D) f(x) is not differentiable at x = ± 1

75. array l ∫ √ x + √ x ^ 2 + 2 d x \ = k ( x + √ x ^ 2 + 2 ) 76. The two consecutive terms in the expansion of ( 3 + 2
^ p / 2 - 2 ( x + √ x ^ 2 + 2 ) ^ ( q )/( 2 ) + C array then x ) ^ 74 , whose coefficients are equal, is/are
k,p,q are respectively
(A) 30th and 31st terms
(A) 4/3 , 3/2 ,1 (B) 29th and 30th terms
(B) ⅓ , 3 , 1 (C) 31st and 32nd terms
(C) -2 , ⅓ ,1 (D) 28th and 29th terms
(D) None of these

77. In any triangle ABC, ( ( A )/( 2 ) + ( B )/( 2 ) + ( C )/( 2 ) 78. Σ _ r = 0 ^ n - 1 ^ n C _ r ^ π C _ r + ^ n C _ r + 1 is
)/( A + B + C ) = equal to

(A) a + b + c a ^ 2 + b ^ 2 + c ^ 2 (A) ( n ( n + 1 ) )/( 2 )

(B) ( a + b + c ) ^ 2 a ^ 2 + b ^ 2 + c ^ 2 (B) ( n + 1 )/( n - 1 )

(C) a ^ 2 + b ^ 2 + c ^ 2 ( a + b + c ) ^ 2 (C) ( n + 1 )/( 2 )

(D) none of these (D) n/2

79. If x, y, z are in A.P., then the value of determinant | 80. Length of intercept made by the circle x ^ 2 + y ^ 2 -
array c c c p + 2 & p + 3 & p + 4 \ p + 3 & p + 4 & p + 5 \ 16 x + 4 y - 36 = 0 on x - axis is
p + 2 x & p + 2 y & p + 2 z array | equals
(A) 20
(A) 42 (B) 10
(B) 0 (C) 5
(C) - 4a (D) None of these
(D) 1

81. Let a, b, c ∈ R+ (i.e. a, b, c are positive real numbers) 82. The length of perpendicular from O (0,0,0) to the
then the following system of equations in x, y, z array l x plane passing through three non collinear points a , b , c
^2a^2+y^2b^2-z^2c^2-1,x^2a^2-y^ is
2 b ^ 2 + z ^ 2 c ^ 2 = 1 and \ - x ^ 2 a ^ 2 + y ^ 2 b ^ 2
(A) 2 [ a b c ] a × b + b × c + c × a
+ z ^ 2 c ^ 2 - 1 has array
(B) [ a b c ]
(A) No solution
(C) [ a b c ] | a × b - b × c - c × a |
(B) Unique solution
(D) none of these
(C) Infinitely many solution

(D) Finitely many solution

83. The mid point of the chord 16x + 9y = 25 to the 84. The inverse of the function f ( x ) = _ 2 ( x + √ x ^ 2 +
ellipse x ^ 2 9 + y ^ 2 16 = 1 is 1 ) is

(A) (1, -1) (A) 2 ^ x + 2 ^ - x

(B) (-1,-1) (B) 2 ^ x + 2 ^ - x 2

(C) (-1, 1) (C) 2 ^ - x - 2 ^ x 2

(D) (1,1) (D) 2 ^ x - 2 ^ - x 2

85. The value of the expression is ^ 23 C _ 6 + Σ _ j = 1 ^ 86. If x ^ m occurs in the expansion of ( x + 1 x ^ 2 ) ^ 4
5 28 - i C _ 5 + Σ _ k = 1 ^ 5 33 - k C _ 28 - k is n then the coefficient of x ^ m is

(A) 33 C _ 6 (A) ( ( 4 n ) ! )/( ( ( 4 n - m )/( 3 ) ) ! · ( ( 8 n + m )/( 3 ) ) ! )

(B) 23 C _ 16 (B) ( ( 4 n ) ! )/( n ! ( 4 n - m ) ! )

(C) 33 C _ 7 (C) ( ( 4 n ) ! 3 ! 3 ! )/( ( 4 n - 3 ) ! )

(D) None of these (D) none of these

87. The position vector of the foci of an ellipse are b and - 88. The point of contact of the circles x ^ 2 + y ^ 2 - 4 x+
b and the length of major axis is 2a. The equation of 6 v - 3 = 0 and x ^ 2 + y ^ 2 + 16 x + 6 y + 37 = 0 is
ellipse is
(A) (-8, -3)
(A) a ^ 4 - a ^ 2 ( r ^ 2 + b ^ 2 ) + ( b × r ) ^ 2 = 0 (B) (2, -3)
(B) a ^ 4 - a ^ 2 ( r ^ 2 + b ^ 2 ) + ( b · r ) ^ 2 = 0 (C) (-2,-3)
(C) a ^ 4 + a ^ 2 ( r ^ 2 + b ^ 2 ) + ( b · r ) ^ 2 = 0 (D) None of these
(D) a ^ 4 - a ^ 2 ( r ^ 2 - b ^ 2 ) + ( b · r ) ^ 2 = 0

89. Let f : R - \ n \ arrow R be a function defined by f ( x ) 90.  If Σ _ i = 1 ^ 25 a _ i = 625 such that a _ 1 , a _ 2 , a _
= ( x - m )/( x - n ) such that m ≠ n then 3 … A . P then Σ _ i = 1 ^ 13 a _ 2 j - 1

(A) f is one-one into function (A) 25

(B) f is one-one onto function (B) 15625

(C) f is many one into function (C) 325

(D) f is many one onto function (D) 125

91. If ASC is a focal chord of the parabola y ^ 2 = 4 a x 92. The value of λ , if the equation 2 x ^ 2 + 2 λ x y + 3 y
and AS=5, SC = 9 then length of latus rectum of the ^ 2 + 4 x + 2 y + 2 = 0 represent a pair of straight lines,
parabola equals is

(A) 90/7 (A) -1

(B) 7/90 (B) 2

(C) 45/14 (C) -2

(D) None of these. (D) 1

93. The ratio of the areas of a triangle formed with 94. The value of �� for which the lines ( x - 1 )/( 2 ) = ( 2 y -
vertices A ( a t _ 1 ^ 2 , 2 a t _ 1 ) , B ( a t _ 2 ^ 2 , 2 a t _ 2 1 )/( 3 ) = ( 1 - 3 z )/( α ) and ( x + 1 )/( 2 ) = ( 3 y - 5 )/( 2 )
) and C ( a t _ 3 ^ 2 , 2 a t _ 3 ) lies on the parabola y ^ 2 = ( z - 4 )/( 3 ) are perpendicular to each other is
= 4 a x and triangle formed by the tangents at A, B, C is
(A) 3
(A) 1:2 (B) 2
(B) 2:1 (C) -3
(C) 2:3 (D) 5
(D) 3:2

95. Let f ( x , y ) : y ^ 2 = 4 [ √( y ) ] x and g ( x , y ) : 4 [ 96. If ^ - 1 x + ^ - 1 ( 1 - x ) = ^ - 1 ( - x ) then x satisfies
√( x ) ] y = x ^ 2 where [.] denote greatest integer the equation
function, then the area enclosed by f(x, y) and g(x, y)
(A) 2 x ^ 2 - x + 2 = 0
within the square formed by the lines x = 1 = y & x=4 = y
(B) 2 x ^ 2 - x = 0
equals
(C) 2 x ^ 2 + x - 1 = 0
(A) 121/3
(D) 2 x ^ 2 - 2 x = 3
(B) 11/3

(C) 3/11

(D) None of these

97. The mean deviation of items x,x+y,x+2y,...,x+2ny 98. If √ b ^ 2 + c ^ 2 , √ c ^ 2 + a ^ 2 , √ a ^ 2 + b ^ 2 are
from mean is the three sides of a triangle, then the area of the triangle
is
(A) ( n ( n + 1 ) y )/( 2 n + 1 )

(B) ( ( n + 1 ) y )/( 2 n + 1 ) (A) √ a ^ 2 + b ^ 2 + c ^ 2

(C) ( n y )/( 2 n + 1 ) (B) √ b ^ 2 c ^ 2 + c ^ 2 a ^ 2 + a ^ 2 b ^ 2

(D) ( ( 2 n + 1 ) y )/( n ( n + 1 ) ) (C) √( a + b + c )

(D) none of these

99. Let P ( n ) : 2 ^ n > n n N and 2 ^ k > k , n = k then 100. _ 2 x + 3 ( 6 x ^ 2 + 23 x + 21 ) = 4 - _ 3 x + 7 ( 4 x ^
which of the following is true k ≥ 2 ? 2 + 12 x + 9 ) then x equals

(A) 2 ^ k > 5 k > 1 (A) -4

(B) 2 ^ k + 1 > 2 k > k + 1 (B) – 2

(C) 2 ^ k > 2 ( k + 1 ) > k (C) -1/4

(D) None of these (D) None of these

101. If �� and �� are roots of the equation x ^ 2 - 15 x + 1 = 0 102. The common roots of the equations x ^ 3 + 2 x ^ 2 +
, then the value of ( ( 1 )/( α ) - 15 ) ^ - 2 + ( ( 1 )/( β ) - 15 2 x + 1 = 0 and 1 + x ^ 200 + x ^ 2023 are (ω , is non real
) ^ - 2 is cube root of unity)

(A) 225 (A) - ω , 1

(B) 900 (B) ω ^ 2 , ω

(C) 223 (C) ω - ω ^ 2 , 1

(D) None of these (D) - ω ^ 2 , 1

103. The system AX=B of (n-1) equations in (n-1) 104. The solution of the differential equation ( x + y ( d y
unknowns has infinetely many solutions if )/( d x ) )/( y - x ( d y )/( d x ) ) = x ^ 2 + 2 y ^ 2 + y ^ 4 x
^2
(A) det A = 0 , ( adj A ) ( B ) = 0

(B) | A | ≠ 0 , ( adj A ) ( B ) = 0 (A) ( y )/( 4 ) + 1 x ^ 2 + y ^ 2 = c

(C) | A | = 0 , ( adi A ) ( B ) ≠ 0 (B) ( 2 y )/( x ) - 1 x ^ 2 + y ^ 2 = c

(D) None of these (C) ( x )/( y ) - 1 x ^ 2 + y ^ 2 = c

(D) None of these

105. If the value of Δ = | array c c c a ^ n & a ^ n + 2 & a
^2n\1&a^p&p\a^n+5&a^p+6&a^2n+5
array | = 0 then p equals to

(A) a ^ n

(B) n+1

(C) either (a) or (b)

(D) both (a) or (b)

ANSWER KEY

1. (D) 2. (B) 3. (B) 4. (C) 5. (A) 6. (C) 7. (A)

8. (C) 9. (C) 10. (C) 11. (B) 12. (B) 13. (C) 14. (A)

15. (B) 16. (C) 17. (C) 18. (C) 19. (D) 20. (B) 21. (A)

22. (D) 23. (A) 24. (B) 25. (A) 26. (A) 27. (C) 28. (B)

29. (D) 30. (A) 31. (B) 32. (B) 33. (B) 34. (B) 35. (D)

36. (C) 37. (D) 38. (B) 39. (B) 40. (C) 41. (B) 42. (D)

43. (A) 44. (A) 45. (C) 46. (A) 47. (D) 48. (A) 49. (B)

50. (D) 51. (D) 52. (A) 53. (C) 54. (D) 55. (B) 56. (B)

57. (A) 58. (A) 59. (C) 60. (C) 61. (D) 62. (A) 63. (D)

64. (D) 65. (D) 66. (A) 67. (B) 68. (A) 69. (B) 70. (D)

71. (B) 72. (C) 73. (B) 74. (A) 75. (B) 76. (A) 77. (B)

78. (D) 79. (B) 80. (A) 81. (B) 82. (D) 83. (D) 84. (D)

85. (A) 86. (A) 87. (B) 88. (C) 89. (A) 90. (C) 91. (A)

92. (A) 93. (B) 94. (D) 95. (B) 96. (B) 97. (A) 98. (D)

99. (B) Get Free Sample101.
100. (C) Papers,
(C)Question Papers,
102.Mock
(B)Tests & Study Material
103. (A) at
104. (B) 105. (D)