JEE Main 2027 Sample Paper B.Tech

SAMPLE PAPER

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

JEE Main B.Tech 2027
Modelled on the actual exam pattern
.

QUESTIONS MAX MARKS TIME MARKING

75 300 180 Min +4 / −1

GENERAL INSTRUCTIONS

1. This paper contains 75 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 4 marks; 1 mark is deducted for each wrong answer.

4. Total time allowed is 180 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

JEE Main B.Tech 2027
SAMPLE QUESTION PAPER

Questions 75 Max Marks 300 Time 180 Min Marking +4 / −1

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

PHYSICS

1. L , C and R represents physical quantities inductance, 2. Light source having wavelength 331 nm is used to
capacitance and resistance respectively. The dimensional generate photo-electrons whose stopping potential is 0.2
formula M L2 T-4 A-2 corresponds to __________. V. The work function of the used metal in the experiment
is α × 10-19 J. The value of α is _____. ( h = 6.62 × 10-34 J
(A) R√(LC)
s, e = 1.6 × 10-19 C and c = 3 × 108 m/s)
(B) RLC
(A) 3.68
(C) C√(LR)
(B) 4.68
(D) 1R√LC
(C) 5.68

(D) 2.68

3. Two cars A and B are moving in the same direction 4. Two resistors of 200 Ω and 400 Ω are connected in
along a straight line with speeds 100 km/h and 80 km/h, series with a battery of 100 V. A bulb rated at 200 V, 100
respectively such that car A is moving ahead of car B . A W is connected across the 400 Ω resistance. The potential
person in car B throws a stone with a speed v so that it drop across the bulb is __________ V.
hits the car A with a speed of 5 m/s. The value of v is
(A) 25
_______ km/h.
(B) 50
(A) 18
(C) 66.6
(B) 28
(D) 100
(C) 38

(D) 48

5. When one moves from a point 16 km below the earth's 6. A 0.5 kg mass is in contact against the inner wall of a
surface to a point 16 km above the earth's surface. The cylindrical drum of radius 4 m rotating about its vertical
change in g is approximately α %. The value of α is ______. axis. The minimum rotational speed of the drum to
(Take radius of the earth = 6400 km.) enable the mass to remain stuck to the wall (without
falling) is 5 rad/s. The coefficient of friction between the
(A) 0.12
drum's inner wall surface and mass is __________. (Take g =
(B) 0.25
10 m/s2 )
(C) 0.50
(A) 0.1
(D) 0.75
(B) 0.5

(C) 0.7

(D) 0.3

7. One side of an equilateral prism is painted by a 8. The Young's modulus of steel wire of radius r and
transparent material of refractive index n . The length L is Y . If the radius r and length L of the wire are
2
refractive index of prism is 1.6 . The minimum value of n doubled then the value of Y
2
required for total internal reflection from painted face is
(A) increases by two times
__________.
(B) reduces by half

(C) remains unchanged

(D) becomes one fourth

(A) 3√(3)/1.6

(B) √(3)

(C) 3.2/√(3)

(D) 4√(3)/5

9. At t = 0 , a body of mass 100 g starts moving under the 10. Given below are two statements: one is labelled as
influence of a force (5i+10j) N. After 2 s its position is Assertion A and the other is labelled as Reason R
(2xi+5yj) m. The ratio x : y is _______. Assertion A: If the average kinetic energy of H and O
2 2
molecules, kept in two different sized containers are
(A) 1 : 2
same, then their temperatures will be same. Reason R:
(B) 2 : 5
The r.m.s. speed of H and O molecules are same at
2 2
(C) 5 : 2 same temperature. Choose the correct answer from the
(D) 5 : 4 options given below

(A) Both A and R are true and R is the correct explanation of
A

(B) Both A and R are true but R is NOT the correct
explanation of A

(C) A is true but R is false

(D) A is false but R is true

11. Given below are two statements: one is labelled as 12. A circular current loop of radius R is placed inside
Assertion A and the other is labelled as Reason R square loop of side length L (L R) such that they are co-
Assertion A: In electrostatics, a conductor does not store planar and their centers coincide. The permeability of
any net charge inside. Reason R: Inside the capacitor free space is μ . The mutual inductance between circular
0
(with no dielectric medium), the free charge carriers, if loop and square loop is __________.
placed between the plates of capacitor, experience force
(A) 2√(2) μ L2R
0
and drift. Choose the correct answer from the options
(B) √(2) μ L2R
given below 0
(C) √(2) μ R2L
(A) Both A and R are true and R is the correct explanation of 0
(D) 2√(2) μ R2L
A 0

(B) Both A and R are true but R is NOT the correct
explanation of A

(C) A is true but R is false

(D) A is false but R is true

13. Consider the following statements: A. Zeroth law of 14. The binding energy per nucleon of 209 Bi is __________
83
thermodynamics gives concept of temperature B. First MeV. [Take m(209 Bi) = 208.980388 u, m = 1.007825 u,
83 p
law of thermodynamics gives concept of internal energy m = 1.008665 u, 1 u = 931 MeV/c2]
n
C. In isothermal expansion of ideal gas, Δ Q ≠ Δ W D.
(A) 7.48
Product of intensive and extensive variables is extensive
(B) 7.84
E. The ratio of any extensive variable to mass will be an
extensive variable. Choose the correct combination of (C) 8.79

statements from the options given below: (D) 6.94

(A) C, D and E Only

(B) A, B and C Only

(C) A, B and D Only

(D) B, C and D Only

15. Consider a circuit consisting of a capacitor ( 20 μF ), 16. Refer to the figure given below, current between
resistor ( 100 Ω ) and two identical diodes as shown in terminals A and B is ________ A.
figure. The resistance of diode under forward biasing
condition is 10 Ω . The time constant of the circuit is α ×
10-3 s . The value of α is ________.

(A) 12.5

(B) 1.25

(C) 7.5
(A) 2.2
(D) 5
(B) 2.0

(C) 2.1

(D) 2.4

17. A rod of length 10 cm lies along the principle axis of a 18. An unpolarized light is incident on the plane interface
concave mirror of focal length 10 cm as shown in figure. of air-dielectric medium shown in figure. If the incident
The length of the image is ________ cm . angle is equal to Brewster angle, identify the expression
representing reflected wave.

(A) 2.5

(B) 5 (A) (E i + E j)(kx - kz - ω t)
x y

(C) 7.5 (B) (E i + E k)(kx + ky - ω t)
x z

(D) 7 (C) (E j + E k)(ky + kz - ω t)
x y
(D) (E i + E j + E k)(kx + ky - kz - ω t)
x y z

19. Refer to the figure given below. The values of I , I 20. Given below are two statements: one is labelled as
1 2
and I are ________. Assertion A and the other is labelled as Reason R
3
Assertion A: A diode under reverse-biased condition
provides very small current which is nearly independent
of voltage until a critical limit at which the current
increases drastically. Reason R: Below the critical voltage
limit, only majority charge carriers flow which increases
drastically above critical voltage. choose the correct
answer from the options given below

(A) Both A and R are true and R is the correct explanation of
(A) I = 2.5 A, I = 1.875 A, I = 1.875 A
1 2 3
A
(B) I = 1.875 A, I = 2.5 A, I = 1.875 A
1 2 3
(B) Both A and R are true but R is NOT the correct
(C) I = 1.875 A, I = 1.875 A, I = 2.5 A
1 2 3 explanation of A
(D) I = 2.5 A, I = 2.5 A, I = 1.875 A
1 2 3 (C) A is true but R is false

(D) A is false but R is true

21. A magnetic field vector in an electromagnetic wave is 22. A rigid dipole undergoes a simple harmonic motion
represented by B = B (2π vt - (2π x)/(λ))j . Its associated about its centre in the presence of an electric field E = E
0 1
electric field vector is _______. x . If another electric field E = 2E (y + z) is introduced
0 2 0
to the system, what will be the percentage change in the
(A) E = -vλ B (2π vt - (2π x)/(λ))k
0
frequency of the oscillation (approximate)?
(B) E = -vλ B (2π vt - (2π x)/(λ))i
0
(A) 73%
(C) E = vλ B (2π vt - (2π x)/(λ))k
0
(B) 63%
(D) E = vλ B (2π vt - (2π x)/(λ))i
0
(C) 83%

(D) 53%

23. The increase in the pressure required to decrease the 24. In Young's double slit experiment, the fringe width of
volume (Δ V) of water is 6.3 × 107 N/m2 . The percentage the interference pattern produced on the screen is 2.4
decrease in the volume is ________. (Bulk modulus of water μm . If the experiment is carried out in another medium
= 2.1 × 109 N/m2 .) having refractive index 1.2, the fringe width will be _____
μm .
(A) 2 \%

(B) 3 \% (A) 1.2

(C) 6 \% (B) 2

(D) 4 \% (C) 2.4

(D) 2.88

25. A displacement current of 4.0 A can be set up in the
space between two parallel plates of 6 μF capacitor. The
rate of change of potential difference across the plates of
the capacitor is nearly α × 106 V/s. The value of α is
________.

(A) 0.58

(B) 0.67

(C) 0.82

(D) 0.75

CHEMISTRY

26. Among Fe2+ , Fe3+ , Cr2+ and Zn2+ , the ion that 27. Pairs of elements with the same number of electrons
shows positive borax bead test and with highest in their respective 4f orbital are [Atomic number: Eu-63,
ionisation enthalpy is : Gd-64, Dy-66, Ho-67, Tm-69, Yb-70, Lu-71, Hf-72] A. (Eu
and Gd) B. (Dy and Ho) C. (Yb and Hf) D. (Lu and Tm)
(A) Fe2+
Choose the correct answer from the options given below:
(B) Zn2+
(A) B and C Only
(C) Cr2+
(B) A and B Only
(D) Fe3+
(C) A and D Only

(D) A and C Only

28. The species having identical radii according to the 29. Given below are two statements : Statement I : In O
2
Bohr's theory are: A. H (first orbit) B. He^+ (first orbit) C. N-C H -⊕CH-C H -OCH , the carbocation is stabilised by
6 4 6 4 3
He^+ (Second orbit) D. Li2+ (first orbit) E. Be3+ (Second +R effect of -OCH group. Statement II : In O N-C H -CH-
3 2 6 4
orbit) Choose the correct answer from the options given C H -OCH , the carbanion is stabilised by -R effect of -
6 4 3
below: NO group. In the light of the above statements, choose
2
the correct answer from the options given below :
(A) A and C Only

(B) A and E Only (A) Both Statement I and Statement II are true

(C) B and E Only (B) Both Statement I and Statement II are false

(D) C and D Only (C) Statement I is true but Statement II is false

(D) Statement I is false but Statement II is true

30. Given below are two statements : Statement I : The 31. Consider the given graph showing variation of
second ionization enthalpy of B, Al and Ga is in the order reactant concentration with time. Three different
of B > Al > Ga. Statement II : The correct order in terms reactions were started with identical initial concentration
of first ionization enthalpy is Si < Ge < Pb < Sn. In the of reactants. Which of the following statement is correct?
light of the above statements, choose the correct answer / mol L-1 (y-axis) against t/s (x-axis), all three curves
from the options given below : starting from [R] and decreasing; curves labelled 1, 2
0
and 3 from top to bottom]
(A) Both Statement I and Statement II are true

(B) Both Statement I and Statement II are false

(C) Statement I is true but Statement II is false

(D) Statement I is false but Statement II is true

(A) The order of all the three reactions is same.

(B) The rate constant of reaction 3 is larger than the rate
constant of reaction 2 if the order of reaction is same for
both.

(C) The SI unit of rate constant of reaction 1 is s-1 .

(D) Thermal decomposition of HI on gold surface is an
example of reaction 2.

32. The compound (X) on (i) on heating in the presence of 33. Arrange the following resultant mixtures in increasing
anhydrous AlCl and HCl gas gives 2,4-dimethyl pentane order of their pH values A. 10 mL 0.2 M Ca(OH) + 25 mL
3 2
(ii) aromatization gives toluene and (iii) cyclisation gives 0.1 M HCl B. 10 mL 0.01 M H SO + 10 mL 0.01 M Ca(OH)
2 4 2
methyl cyclohexane The correct name of compound (X) is C. 10 mL 0.1 M H SO + 10 mL 0.1 M KOH Choose the
2 4
: correct answer from the options given below:

(A) Hept-2-ene (A) B C A

(B) Hept-1,3,5-triene (B) C A B

(C) Heptane (C) C B A

(D) Hept-2,4,6-triene (D) A C B

34. Correct statements from the following are: A. 35. At 27 °C, 0.1 M, 1 L K [Fe(CN) ] aqueous solution and
4 6
Nitrogen in oxidation states from +1 to +4 0.1 M, 1 L FeCl aqueous solution are placed in a
3
disproportionates in acid medium. B. Nitrogen has the container separated by a semi permeable membrane AB.
ability to form dπ - pπ multiple bonds with itself and Assume complete dissociation of both the solutes. Which
other elements with small size and high of the following statement is correct ? and side 'y'
electronegativity. C. N-N single bond is stronger than P-P contains 0.1 M, 1 L FeCl ]
3
single bond. D. Nitrogen has highest density in its group
due to small size. E. The maximum covalency of nitrogen
is four since it has only four valence orbitals for bonding.
Choose the correct answer from the options given below:

(A) B, C and D Only

(B) C, D and E Only

(C) A, C and E Only

(D) A and E Only (A) Blue color is formed on both sides.

(B) Ionic solutes in aqueous solution can pass through semi-
permeable membrane.

(C) Solution on side 'y' is hypotonic.

(D) To cause the reverse flow of solvent during osmosis,
external pressure (any value) should be applied to side 'x'.

36. Consider the reaction aX arrow bY , for which the rate 37. For the following Friedel Craft's alkylation reaction,
constant at 30°C is 1 × 10-3 mol-1 L s-1 . Which of the which of the statements are correct? A. Major product is
following statements are true ? A. When concentration of n-propyl benzene. B. iso-propyl carbocation intermediate
'X' is increased to four times, the rate of reaction is also generated. C. Multiple substitution is inevitable.
becomes 16 times. B. The reaction is a second order D. Introducing electron-donating substituent on benzene
reaction. C. The half-life period is independent of the will not produce any alkyl benzene. Choose the correct
concentration of X. D. Decomposition of N O is an answer from the options given below:
2 5
example of the above reaction. E. ([R ])/([R]) (plotted
o
against time) is valid for the above reaction. Choose the
correct answer from the options given below :

(A) A and B Only

(B) A, B and C Only

(C) A, B, D and E Only

(D) C and D Only
(A) A and D only

(B) B and C only

(C) A and C only

(D) B and D only

38. Consider the first order reaction R arrow P . The 39. Consider the following molecules/species: (x) tropone
fraction of molecules decomposed in the given first order (cycloheptatrienone, a seven-membered ring with three
reaction can be expressed as C=C double bonds and one C=O ); (y) acetone, (CH ) C=O
3 2
; (z) acetate ion, CH -C(=O)-O(-) The correct order of
(A) 1 - ek t
1
3
carbon - oxygen double bond length is :
(B) 1 + ek t
1

(C) 1 + e-k1 t

(D) 1 - e-k1 t

(A) x > y > z

(B) y > z > x

(C) z > x > y

(D) x > z > y

40. Benzyl isocyanide can be obtained from A. B. [Figure: 41. Correct statements regarding alkyl halides (R - X)
benzylamine ( C H CH NH ) with CHCl / Aq NaOH arrow among the following are : A. Alcohol being less polar
6 5 2 2 3
] C. [Figure: bromobenzene ( C H Br ) + AgCN arrow ] D. solvent as compared to water, alcoholic KOH favours
6 5
[Figure: aniline ( C H NH ) with CHCl / Aq NaOH arrow ] elimination reaction with R - X. B. Order of reactivity
6 5 2 3
E. [Figure: (2-phenylethyl) bromide ( C H CH CH Br ) + towards S 1 mechanism is C H -CH -Cl > C H -CHCl-C H
6 5 2 2 N 6 5 2 6 5 6
KCN arrow ] Choose the correct answer from the options . C. Non substituted aryl halides exhibit properties
5
given below: similar to alkyl halides. D. Vinyl chloride is an example of
haloalkene and allyl chloride is an example of haloalkyne.
E. R - Cl can be prepared by reacting R - OH with SOCl
2
but Ar - Cl cannot be prepared by reacting Ar - OH with
SOCl . Choose the correct answer from the options given
2
below :

(A) A, B and C Only

(B) B and D Only

(A) A and B Only (C) A and E Only

(B) A and C Only (D) D and E Only

(C) B and D Only

(D) D and E Only

42. Given below are two statements : Statement I : 43. Identify the correct statements. A. Glucose exists in
Among Zn, Mn, Sc and Cu, the energy required to remove two anomeric forms. B. Anomers of glucose differ in
the third valence electron is highest for Zn and lowest for configuration at C-1 in cyclic hemiacetal structure. C.
Sc. Statement II : The correct order of the following Melting point of α - anomer of glucose is greater than β -
complexes in terms of CFSE is [Co(H O) ]2+ [Co(H O) ]3+ anomer. D. Specific rotation of α - anomer is +19° while
2 6 2 6
[Co(en) ]3+ . In the light of the above statements, choose for β - anomer is +112° E. α and β - anomers of glucose
3
the correct answer from the options given below : are prepared by crystallization of saturated glucose
solution at 303 K and 371 K respectively. Choose the
(A) Both Statement I and Statement II are true
correct answer from the options given below:
(B) Both Statement I and Statement II are false
(A) A and B Only
(C) Statement I is true but Statement II is false
(B) B and C Only
(D) Statement I is false but Statement II is true
(C) A, B and D Only

(D) A, B and E Only

44. First order gas phase reaction A arrow B + C p = 45. Which of the following is correct set of 4 quantum
i
initial pressure of gas A, p = total pressure of the numbers of 19th electron in Chromium (Atomic number =
t
reaction mixture at time t Expression of rate constant (k) 24) in accordance with Aufbau principle?
is
(A) n = 3, l = 2, m = +2, s = +(1)/(2)
(A) (1)/(t) (p )/(2p - p ) (B) n = 3, l = 2, m = -2, s = +(1)/(2)
i i t
(B) (1)/(t) (2p )/(p - p ) (C) n = 4, l = 1, m = 0, s = +(1)/(2)
i i t
(C) (1)/(t) (p )/(3p - 2p ) (D) n = 4, l = 0, m = 0, s = +(1)/(2)
i i t
(D) (1)/(t) (3p )/(4p - p )
i i t

46. What is the ratio of wave number of first line (lowest 47. Match the LIST-I with LIST-II List-I (Compound): A. B.
energy line) of Balmer series of H atomic spectrum to [Figure: ring with NH group (an amine)] C. [Figure: ring
2
first line of its Brackett series? with CHO group (an aldehyde)] D. [Figure: aromatic
benzene ring with OH group (phenol)] List-II (Test): I.
(A) 5:1
Hinsberg's reagent test II. Phthalein dye test III. Lucas
(B) 5:0.81
test IV. Tollen's test Choose the correct answer from the
(C) 5:1.75 options given below:
(D) 5:27

(A) A-III, B-I, C-IV, D-II

(B) A-III, B-IV, C-I, D-II

(C) A-I, B-III, C-II, D-IV

(D) A-I, B-II, C-III, D-IV

48. The 1st ionization enthalpy for Mg is +737 kJ/mol. The 49. Given below are two statements: Statement I: The
most probable estimated value of the 2nd ionization covalency of oxygen is generally two but it can exceed
enthalpy of Mg is __________. upto four. The oxidation state of oxygen in SO is -2 and
2
in OF it is +2 . Statement II: The anomalous behaviour of
(A) -906 kJ/mol 2
oxygen when compared to the other elements of group
(B) -856 kJ/mol
16 is due to its small size and high electronegativity. In
(C) +1450 kJ/mol the light of the above statements, choose the correct
(D) +590 kJ/mol answer from the options given below

(A) Both Statement I and Statement II are true

(B) Both Statement I and Statement II are false

(C) Statement I is true but Statement II is false

(D) Statement I is false but Statement II is true

50. Given below are two statements: Statement I: Sodium
dichromate and potassium dichromate are classified as
primary standards in titrimetric analysis. Statement II:
Phenolphthalein is a weak base, therefore it dissociates
in acidic medium. In the light of the above statements,
choose the correct answer from the options given below

(A) Both Statement I and Statement II are ture

(B) Both Statement I and Statement II are false

(C) Statement I is true but Statement II is false

(D) Statement I is false but Statement II is true

MATHEMATICS

51. Consider the system of linear equations in x, y, z : x + 52. In an equilateral triangle PQR, let the vertex P be at
2y + tz = 0 , 6x + y + 5tz = 0 , 3x + t2y + f(t)z = 0 , where (3, 5) and the side QR be along the line x + y = 4 . If the
f : R → R is a differentiable function. If this system has orthocentre of the triangle PQR is (α, β) , then 9(α + β) is
infinitely many solutions for all t R , then f equal to:

(A) is a constant function (A) 16

(B) is strictly increasing on R (B) 27

(C) is strictly decreasing on R (C) 36

(D) has two critical points (D) 48

53. A letter is known to have arrived by post either from 54. If the quadratic equation (λ + 2)x2 - 3λ x + 4λ = 0 , λ
KANPUR or from ANANTPUR. On the envelope just two ≠ -2 , has two positive roots, then the number of possible
consecutive letters AN are visible. The probability, that integral values of λ is:
the letter came from ANANTPUR, is:
(A) 1
(A) (7)/(10) (B) 2
(B) (10)/(17) (C) 3
(C) (12)/(19) (D) 4
(D) (7)/(19)

55. Let the vertex A of a triangle ABC be (1, 2) , and the 56. The area of the region bounded by the curves x + 3y2
mid-point of the side AB be (5, -1) . If the centroid of this = 0 and x + 4y2 = 1 is equal to:
triangle is (3, 4) and its circumcenter is (α, β) , then 21(α
(A) (1)/(3)
+ β) is equal to:
(B) (2)/(3)
(A) 309
(C) (4)/(3)
(B) 403
(D) (5)/(3)
(C) 497

(D) 524

57. Σ 10((528)/(n(n+1)(n+2))) is equal to: 58. The square of the distance of the point of intersection
n=1
of the lines r = (i + j - k) + λ(ai - j) , a ≠ 0 and r = (4i - k)
(A) 65
+ μ(2i + ak) from the origin is:
(B) 130
(A) 5
(C) 220
(B) 10
(D) 440
(C) 17

(D) 26

59. Let P (3α, 2α) , α ≠ 0 , be a point on the ellipse (x2 60. Let the circles C : |z| = r and C : |z - 3 - 4i| = 5 , z C ,
1 2
)/(9) + (y2)/(4) = 1 , Q be a point on the circle x2 + y2 - be such that C lies within C . If z moves on C , z
2 1 1 1 2
14x - 14y + 82 = 0 and R be a point on the line x + y = 5 moves on C and |z - z | = 2 , then |z - z | is equal to :
2 1 2 1 2
such that the centroid of the triangle PQR is (2 + α, 3 +
(A) 12
(2)/(3)α) . Then the sum of the ordinates of all possible
(B) 17
points R is:
(C) 22
(A) 6
(D) 24
(B) 2

(C) 4

(D) 8

61. Let f be a real polynomial of degree n such that f(x) = 62. The mean and variance of n observations are 8 and
f'(x)f''(x) , for all x R . If f(0) = 0 , then 36(f'(2) + f''(2) + ∫ 16, respectively. If the sum of the first (n - 1)
2 f(x)dx) is equal to: observations is 48 and the sum of squares of the first (n -
0
1) observations is 496, then the value of n is :
(A) 42

(B) 46 (A) 21

(C) 56 (B) 16

(D) 66 (C) 13

(D) 7

63. The value of the integral ∫ (π)/(3)((4 - cosec2 x)/( 64. For 10 observations x , x , ..., x , if Σ 10 (x + 2)2
(π)/(6) 1 2 10 i=1 i
4 x))dx is: = 180 and Σ 10 2
(x - 1) = 90 , then their standard
i=1 i
deviation is:
(A) 11√(3)

(B) 16√(3) (A) 2

(C) 323√(3) (B) √(3)

(D) 643√(3) (C) 2√(2)

(D) 3

65. Let the vectors a = -i + j + 3k and b = i + 3j + k . For 66. Let the smallest value of k N , for which the
some λ, μ R , let c = λa + μb . If c · (3i - 6j + 2k) = 10 and coefficient of x3 in (1 + x)3 + (1 + x)4 + (1 + x)5 + ... + (1
c · (i + j + k) = -2 , then |c|2 is equal to : + x)99 + (1 + kx)100 , x ≠ 0 , is (43n + (101)/(4))(100C )
3
for some n N , be p . Then the value of p + n is:
(A) 8

(B) 12 (A) 10

(C) 14 (B) 11

(D) 15 (C) 12

(D) 13

67. The square of the distance of the point (-2, -8, 6) from 68. Let the sum of the first n terms of an A.P. be 3n2 + 5n
the line (x - 1)/(1) = (y - 1)/(2) = (z)/(-1) along the line (x . Then the sum of squares of the first 10 terms of the A.P.
+ 5)/(1) = (y + 5)/(-1) = (z)/(2) is equal to: is:

(A) 3 (A) 10220

(B) 6 (B) 12860

(C) 8 (C) 15220

(D) 12 (D) 19780

69. The number of functions f : \1, 2, 3, 4\ → \a, b, c\ , 70. Suppose that the mean and median of the non-
which are not onto, is: negative numbers 21, 8, 17, a, 51, 103, b, 13, 67, (a > b) ,
are 40 and 21, respectively. If the mean deviation about
(A) 48
the median is 26, then 2a is equal to:
(B) 45
(A) 109
(C) 51
(B) 117
(D) 35
(C) 161

(D) 131

71. Let A, B , where A, B (-(π)/(2), (π)/(2)) , be the roots of 72. Let a, b C . Let α, β be the roots of the equation x2 +
the quadratic equation x2 - 2x - 5 = 0 . Then 202 ax + b = 0 . If β - α = √(11) and β2 - α2 = 3i√(11) , then (β
((A+B)/(2)) is equal to: 3 - α3)2 is equal to:

(A) 10 + √(10) (A) 160

(B) 10 - 2√(10) (B) 176

(C) 10 - 3√(10) (C) 194

(D) 10 - √(10) (D) 187

73. The number of ways, of forming a queue of 4 boys 74. Let f(x) be a polynomial of degree 5, and have
and 3 girls such that all the girls are not together, is: extrema at x = 1 and x = -1 . If ((f(x))/(x3)) = -5 ,
x→0
then f(2) - f(-2) is equal to :
(A) 5040

(B) 3050 (A) 0

(C) 3410 (B) 50

(D) 4320 (C) 92

(D) 112

75. The sum of all the integral values of p such that the
equation 32 x + 12 x - 3 = p , x R , has at least one
solution, is:

(A) -54

(B) -60

(C) -75

(D) -84

ANSWER KEY

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

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

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

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

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

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

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

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

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

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

71. (C) 72. (B) 73. (D) 74. (D) 75. (C)