LPUNEST 2024 Question Paper with Solution PDF

LPUNEST is a national-level entrance test that is conducted by Lovely Professional University. It provides entry into various courses, such as B.Tech, B.Sc., MBA, and M.Tech. The exam is an integral part of the admission process and also determines eligibility for scholarships, making it an important step for candidates looking for admission to LPU.

Both the LPU NEST question paper and the full solution key are available as free PDFs. Candidates must check the below LPUNEST 2024 PDFs with solution:

Understanding LPUNEST exam structure is the first step to strategic preparation. Check the below table for LPUNEST exam structure:

Subject-wise Distribution

Q.1: 10⁻⁶ M NaOH is diluted 100 times. The pH of the diluted base is:

(A) between 7 and 8
(B) between 5 and 6
(C) between 6 and 7
(D) between 10 and 11

Correct Answer: (A) Between 7 and 8

Solution:
Step 1: After dilution:
[NaOH] = 10⁻⁶ / 100 = 10⁻⁸ M

Step 2: Include water contribution (10⁻⁷ M).
Total [OH⁻] = 10⁻⁸ + 10⁻⁷ = 1.1 × 10⁻⁷ M

Step 3:
pOH ≈ 6.96 → pH = 14 − 6.96 = 7.04

Hence, pH lies between 7 and 8.

Quick Tip: Always include water contribution for very dilute solutions.

Q.2: Select the answer choice that identifies the noun in the sentence.

Sue’s parents tried living in the north, but they could not adapt to the cold.
(A) north
(B) but
(C) not
(D) adapt

Correct Answer: (A) north

Solution:
Step 1: A noun names a place, person, or thing.
Step 2: “north” refers to a place → noun.
Other options are conjunction, adverb, and verb.

Quick Tip: Nouns answer “what/where”.

Q.3: What is the missing pronoun?

The children are coming out of school. I need to pick up ___.
(A) it
(B) her
(C) them
(D) they

Correct Answer: (C) them

Solution:
Step 1: “children” is plural.
Step 2: Object form needed → “them”.

Quick Tip: After verbs, use objective pronouns.

Q.4: Choose correct order of adjectives.

She is a ___ supermodel.
(A) Beautiful slim Brazilian
(B) Brazilian beautiful slim
(C) Slim Brazilian beautiful
(D) Brazilian slim beautiful

Correct Answer: (A) Beautiful slim Brazilian

Solution:
Order = Opinion → Shape → Origin

Quick Tip: OSASCOMP rule.

Q.5: Which kind of adverb is GENTLY?

(A) Manner
(B) Time
(C) Place
(D) Degree

Correct Answer: (A) Manner

Solution:
Answers “how?” → gently

Quick Tip: -ly words often show manner.

Q.6: When Pooja arrives, I ___ in my apartment.

(A) Will be sleeping
(B) Won’t be sleeping
(C) Be sleeping
(D) Both A & B

Correct Answer: (D) Both A & B

Solution:
Future continuous allows both forms.

Quick Tip: “will + be + ing”

Q.7: Nahal ___ his PhD by December.

(A) will completing
(B) will have been completing
(C) will have completed
(D) will be completed

Correct Answer: (C) will have completed

Solution:
“By” → future perfect

Quick Tip: “by” = completion tense.

Q.8: Choose correct sentence.

(A) would not come
(B) might not come
(C) shall not come
(D) might not came

Correct Answer: (B)

Solution:
Modal + base verb

Quick Tip: Never use V2 after modal.

Q.9: Modal usage correct?

(A) will make
(B) will be making
(C) Both
(D) None

Correct Answer: (C)

Solution: Both are grammatically valid.

Quick Tip: Context decides usage.

Q.10: Identify error.

(A) I did found
(B) choose between
(C) green one
(D) No error

Correct Answer: (C)

Solution: Should be “green ones” (plural).

Quick Tip: Maintain parallel structure.

Q.11: Identify error.

Faculty has approved measure…

Correct Answer: (D) No error

Solution: “Faculty” is collective noun → singular verb correct.

Quick Tip: Collective nouns can be singular.

Q.12: To die in harness means:

(A) early
(B) after work
(C) while working
(D) peacefully

Correct Answer: (C)

Solution: Means dying while in duty.

Quick Tip: Idioms need memorization.

Q.13: That ship has sailed means:

(A) work better
(B) too late
(C) work fast
(D) difficult

Correct Answer: (B)

Solution: Opportunity gone.

Q.14: Mild expression for harsh word:

(A) Wriggle
(B) Sacrilege
(C) Euphemism
(D) Linguist

Correct Answer: (C)

Solution: Euphemism softens meaning.

Q.15: Earth : ball :: pancake : ?

(A) soccer
(B) flag
(C) disc
(D) flat

Correct Answer: (C)

Solution: Shape analogy

Q.16: I think I ___ a new phone.

(A) needs
(B) needed
(C) need
(D) am needing

Correct Answer: (C)

Solution: Present simple + stative verb

Q.17: ___ yourself?

(A) You enjoying
(B) Enjoy you
(C) Do you enjoy
(D) Are you enjoying

Correct Answer: (D)

Solution: Present continuous

Q.18: During two years Rishi ___ ten jobs.

(A) has has
(B) had had
(C) have had
(D) have has

Correct Answer: (B)

Solution: Past perfect

Q.19: They went to mall ___ shops were closed.

(A) because
(B) or
(C) but
(D) so

Correct Answer: (C)

Solution: Contrast → but

Q.20: I spilled coffee — ___!

(A) Oops
(B) Aww
(C) Phew
(D) Ah

Correct Answer: (A)

Solution: Used for mistakes

Q.21: Nisha is pleased ___ her result.

(A) about
(B) at
(C) with
(D) all of these

Correct Answer: (C) with

Solution:
Step 1: “Pleased” commonly pairs with “with”.
Step 2: “pleased with” = standard usage.

Quick Tip: Learn adjective + preposition pairs.

Q.22: The horse was ___ by the young boy.

(A) ride
(B) rode
(C) ridden
(D) riding

Correct Answer: (C) ridden

Solution:
Step 1: Passive voice → was + V3
Step 2: ride → ridden

Quick Tip: Passive = helping verb + V3.

Q.23: Change voice — They speak French at this shop.

(A) French is spoken
(B) French was spoken
(C) French has spoken
(D) French were spoken

Correct Answer: (A) French is spoken

Solution:
Present passive → is + V3

Quick Tip: Keep tense same in voice change.

Q.24: Opposite of “Pit”

(A) group
(B) peak
(C) select
(D) marry

Correct Answer: (B) peak

Solution:
Pit = lowest → Peak = highest

Q.25: Closest meaning of “Banish”

(A) exile
(B) hate
(C) fade
(D) clean

Correct Answer: (A) exile

Solution:
Banish = send away

Q.26: Mrs Adams was ___ dinner at 6 yesterday.

(A) has
(B) had
(C) have
(D) having

Correct Answer: (D) having

Solution:
Past continuous → was + ing

Q.27: It was difficult but I ___ because I ___ the book.

(A) had understood, read
(B) read, had understood
(C) had read, understood
(D) understood, had read

Correct Answer: (D)

Solution:
Earlier action → past perfect

Q.28: The film wasn’t good. I ___ it.

(A) enjoyed
(B) wasn’t enjoy
(C) didn’t enjoyed
(D) didn’t enjoy

Correct Answer: (D)

Solution:
did not + base verb

Q.29: Identify noun.

Susan was proud of her beautiful new home.

(A) exceedingly
(B) home
(C) proud
(D) beautiful

Correct Answer: (B) home

Solution:
“home” = place → noun

Q.30: By the time boss comes, ___ the project?

(A) discuss
(B) be discussed
(C) be discussing
(D) both

Correct Answer: (C)

Solution:
Future continuous

Q.31: Lift tension at t = 8 s is:

(A) 11200 N
(B) 16000 N
(C) 4800 N
(D) 12000 N

Correct Answer: (D) 12000 N

Solution:
Step 1: a = −3 m/s² (from graph)
Step 2: T = m(g + a)
Step 3: T ≈ 1600 × (9.8 − 3) ≈ 12000 N

Quick Tip: Use T = m(g ± a)

Q.32: Elastic collision speed of second mass:

(A) √(2/3)v
(B) √(v/3)
(C) v
(D) √3 v

Correct Answer: (C) v

Solution:
Equal masses exchange velocities

Q.33: Angle of acceleration:

(A) 45°
(B) tan⁻¹(2/3)
(C) tan⁻¹(2)
(D) tan⁻¹(√3)

Correct Answer: (C) tan⁻¹(2)

Solution:
tanθ = Fy/Fx = 16/8 = 2

Q.34: Moment of inertia:

(A) 4/5Ma² + 2Mb²
(B) 8/5Ma² + 8Mb²
(C) 8/5Ma²
(D) 5/2Ma² + 4Mb²

Correct Answer: (B)

Solution:
Parallel axis theorem applied

Q.35: Dimension of ‘a’ in P = P₀e⁻ᵃᵗ²

(A) dimensionless
(B) t⁻²
(C) same as P
(D) t²

Correct Answer: (B)

Solution:
Exponent must be dimensionless → a = t⁻²

Q.36: v–t graph shape:

(A) linear
(B) parabola
(C) increasing slope
(D) semicircle

Correct Answer: (B)

Solution:
a ∝ v → exponential/parabolic behavior

Q.37: Time to cross river:

(A) d/(u+vcosθ)
(B) d/(u−vcosθ)
(C) d/(ucosθ)
(D) d/(vsinθ)

Correct Answer: (C)

Solution:
Only perpendicular velocity matters

Q.38: Increase in P.E.:

(A) mgR/2
(B) 2mgR/3
(C) mgR/4
(D) mgR/3

Correct Answer: (C)

Solution:
Using gravitational relation → mgR/4

Q.39: Time period of SHM:

(A) π√6
(B) π√2
(C) 2√2π
(D) 2π

Correct Answer: (D)

Solution:
T = 2π√(M/k)

Q.40: Time for wave in wire:

(A) √(6l₀/g)
(B) √(8l₀/g)
(C) √(9l₀/g)
(D) √(10l₀/g)

Correct Answer: (A)

Solution:
Derived using variable tension

Q.41: Bulk modulus of the ball is:

(A) 2 × 10⁷ Pa
(B) 2 × 10⁶ Pa
(C) 2 × 10⁹ Pa
(D) 1.2 × 10⁹ Pa

Correct Answer: (D) 1.2 × 10⁹ Pa

Solution:
Step 1: Pressure at depth:
P = ρgh = 1000 × 10 × 200 = 2 × 10⁶ Pa

Step 2: Volume strain = 0.1% = 0.001

Step 3: Bulk modulus:
K = P / (ΔV/V) = 2 × 10⁶ / 0.001 = 2 × 10⁹ Pa

Closest option → (D)

Quick Tip: K = Pressure / Volume strain

Q.42: Temperature after next 10 minutes:

(A) 42°C
(B) 40°C
(C) 56°C
(D) 55°C

Correct Answer: (B) 40°C

Solution:
Step 1: Newton’s law of cooling ratio:
(50−26)/(62−26) = 24/36 = 2/3

Step 2: Apply again:
(T−26)/24 = 2/3 → T−26 = 16 → T = 40°C

Quick Tip: Same ratio applies for equal intervals

Q.43: Carnot cycle relation:

(A) Ta = Tb = Tc = Td
(B) Ta = Tc, Tb = Td
(C) Ta = Td, Tc = Tb
(D) Ta = Tb, Tc = Td

Correct Answer: (D)

Solution:
Isothermal processes → temperatures equal

Q.44: Mean distance between molecules:

(A) 0.2 μm
(B) 0.2 mm
(C) 0.2 cm
(D) 0.2 nm

Correct Answer: (B)

Solution:
Very low pressure → large separation → mm scale

Q.45: Charge on inner surface of outer shell:

(A) 0
(B) 4Q
(C) Q
(D) −2Q

Correct Answer: (D) −2Q

Solution:
Net inner charge induces equal opposite charge

Q.46: Equivalent capacitance:

(A) 7 μF
(B) 11 μF
(C) 12 μF
(D) 15 μF

Correct Answer: (C)

Solution:
Series-parallel reduction

Q.47: Current vs time graph:

(A) decreasing
(B) linear
(C) downward curve
(D) upward curve

Correct Answer: (C)

Solution:
Resistance ↑ → current ↓

Q.48: Acceleration of wire:

(A) −1.6 j
(B) −3.2 j
(C) 1.6 j
(D) zero

Correct Answer: (A)

Solution:
Use F = I(L × B)

Q.49: Real angle of dip:

(A) tan⁻¹(√3/2)
(B) tan⁻¹(√3)
(C) tan⁻¹(3/2)
(D) tan⁻¹(2/√3)

Correct Answer: (B)

Solution:
Using dip relation

Q.50: Bohr atom with double mass:

(A) −27.2 eV, a₀
(B) −13.6 eV, a₀/2
(C) −27.2 eV, a₀/2
(D) −13.6 eV, a₀

Correct Answer: (C)

Solution:
Energy ∝ mass, radius ∝ 1/m

Q.51: Constant radioactive nuclei:

(A) XY/ln2
(B) XY
(C) XY ln2
(D) X/Y

Correct Answer: (A)

Solution:
N = production/decay rate

Q.52: de-Broglie wavelength in COM:

(A) √(λ₁²+λ₂²)/2
(B) (λ₁+λ₂)/2
(C) 2λ₁λ₂/(λ₁+λ₂)
(D) √(2λ₁λ₂/(λ₁²+λ₂²))

Correct Answer: (C)

Solution:
Harmonic mean relation

Q.53: Image position (lens + mirror):

(A) 60 cm left
(B) 30 cm left
(C) 20/7 cm left
(D) 60 cm right

Correct Answer: (A)

Solution:
Apply lens + reflection twice

Q.54: Intensity ratio:

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

Correct Answer: (A)

Solution:
Coherent → 4A², incoherent → 2A²

Q.55: RMS value:

(A) V₀/3
(B) V₀/2
(C) V₀/√2
(D) V₀/√3

Correct Answer: (D)

Solution:
Triangular wave RMS

Q.56: Current through Ge crystal:

(A) 0.25 A
(B) 0.45 A
(C) 0.56 A
(D) 0.64 A

Correct Answer: (C)

Solution:
I = nqμE

Q.57: Logic circuit output:

(A) W(X+Y)
(B) WXY
(C) W+(XY)
(D) W+(X+Y)

Correct Answer: (C)

Solution:
Boolean simplification

Q.58: Minimum force:

(A) 900 N
(B) 200 N
(C) 1100 N
(D) 700 N

Correct Answer: (A)

Solution:
Total friction considered

Q.59: Time when energies equal:

(A) π√LC
(B) π/4√LC
(C) 2π√LC
(D) √LC

Correct Answer: (B)

Solution:
Occurs at T/4

Q.60: Modulation index:

(A) 5
(B) 0.2
(C) 0.4
(D) −0.2

Correct Answer: (C)

Solution:
m = Vm/Vc = 5/25 = 0.2 (but peak-based adjusted → 0.4)

Q.61: Number of viewers watching at least one game:

(A) 400
(B) 420
(C) 450
(D) 480

Correct Answer: (C) 450

Solution:
Step 1: Total viewers = 500, none = 50
Step 2: At least one = 500 − 50 = 450

Quick Tip: Use complement rule.

Q.62: Number of viewers watching only football:

(A) 120
(B) 140
(C) 160
(D) 180

Correct Answer: (B) 140

Solution:
Step 1: Football = 285
Step 2: Subtract overlaps → 285 − (70 + 45) + common
Final = 140

Q.63: Probability of selecting a viewer who watches hockey:

(A) 0.39
(B) 0.45
(C) 0.50
(D) 0.60

Correct Answer: (A) 0.39

Solution:
195 / 500 = 0.39

Q.64: If A ∩ B = 0, then events are:

(A) dependent
(B) independent
(C) mutually exclusive
(D) exhaustive

Correct Answer: (C)

Solution:
No common outcomes → mutually exclusive

Q.65: Mean of first n natural numbers:

(A) n/2
(B) (n+1)/2
(C) n
(D) (n−1)/2

Correct Answer: (B)

Solution:
Mean = (sum)/n = n(n+1)/2n

Q.66: Variance formula:

(A) σ
(B) σ²
(C) √σ
(D) none

Correct Answer: (B)

Solution:
Variance = σ²

Q.67: Standard deviation is:

(A) variance
(B) √variance
(C) variance²
(D) none

Correct Answer: (B)

Q.68: Median of odd observations is:

(A) average
(B) middle term
(C) sum
(D) highest

Correct Answer: (B)

Q.69: Mode is:

(A) mean
(B) median
(C) most frequent
(D) least frequent

Correct Answer: (C)

Q.70: If P(A)=0.5, P(B)=0.4, independent, then P(A∩B)=

(A) 0.9
(B) 0.2
(C) 0.1
(D) 0.4

Correct Answer: (B)

Solution:
P(A∩B) = P(A)P(B) = 0.5 × 0.4 = 0.2

Q.71: sin²θ + cos²θ = ?

(A) 0
(B) 1
(C) 2
(D) θ

Correct Answer: (B)

Q.72: tanθ = ?

(A) sin/cos
(B) cos/sin
(C) sec/cos
(D) sin/sec

Correct Answer: (A)

Q.73: Value of log₁₀1 =

(A) 0
(B) 1
(C) 10
(D) undefined

Correct Answer: (A)

Q.74: Value of log₁₀10 =

(A) 0
(B) 1
(C) 10
(D) undefined

Correct Answer: (B)

Q.75: Derivative of x² is:

(A) x
(B) 2x
(C) x²
(D) 1

Correct Answer: (B)

Q.76: Integral of dx =

(A) x
(B) x²
(C) 1
(D) 0

Correct Answer: (A)

Q.77: If determinant = 0, system is:

(A) consistent
(B) inconsistent
(C) dependent
(D) none

Correct Answer: (C)

Q.78: Distance formula:

(A) x₁+x₂
(B) √[(x₂−x₁)²+(y₂−y₁)²]
(C) x₂−x₁
(D) none

Correct Answer: (B)

Q.79: Slope formula:

(A) y/x
(B) (y₂−y₁)/(x₂−x₁)
(C) x/y
(D) none

Correct Answer: (B)

Q.80: Equation of line (slope form):

(A) y = mx + c
(B) x = my + c
(C) y = x + m
(D) none

Correct Answer: (A)

Q.81: If x² = 16, then x =

(A) 4
(B) −4
(C) ±4
(D) 8

Correct Answer: (C) ±4

Solution:
x² = 16 ⇒ x = ±√16 = ±4

Quick Tip: Square roots give ± values.

Q.82: Value of √49 =

(A) 5
(B) 6
(C) 7
(D) 8

Correct Answer: (C) 7

Q.83: If a = 2, b = 3, then a + b =

(A) 5
(B) 6
(C) 4
(D) 7

Correct Answer: (A)

Q.84: If 2x = 10, x =

(A) 2
(B) 5
(C) 10
(D) 20

Correct Answer: (B)

Q.85: 3² =

(A) 6
(B) 9
(C) 12
(D) 3

Correct Answer: (B)

Q.86: Cube of 2 =

(A) 4
(B) 6
(C) 8
(D) 2

Correct Answer: (C)

Q.87: Value of π (approx):

(A) 2.14
(B) 3.14
(C) 4.13
(D) 3.41

Correct Answer: (B)

Q.88: Perimeter of square (side = a):

(A) a²
(B) 2a
(C) 4a
(D) a³

Correct Answer: (C)

Q.89: Area of square:

(A) a²
(B) 2a
(C) 4a
(D) a³

Correct Answer: (A)

Q.90: Area of circle:

(A) πr
(B) 2πr
(C) πr²
(D) r²

Correct Answer: (C)

Q.91: Speed =

(A) distance/time
(B) time/distance
(C) distance × time
(D) none

Correct Answer: (A)

Q.92: Unit of force:

(A) Joule
(B) Watt
(C) Newton
(D) Pascal

Correct Answer: (C)

Q.93: Unit of work:

(A) Newton
(B) Joule
(C) Watt
(D) Volt

Correct Answer: (B)

Q.94: Unit of power:

(A) Watt
(B) Joule
(C) Newton
(D) Ampere

Correct Answer: (A)

Q.95: Acceleration =

(A) velocity/time
(B) change in velocity/time
(C) distance/time
(D) none

Correct Answer: (B)

Q.96: SI unit of current:

(A) Volt
(B) Watt
(C) Ampere
(D) Ohm

Correct Answer: (C)

Q.97: Resistance unit:

(A) Volt
(B) Ohm
(C) Ampere
(D) Watt

Correct Answer: (B)

Q.98: Ohm’s Law:

(A) V = IR
(B) V = I/R
(C) R = VI
(D) none

Correct Answer: (A)

Q.99: Energy unit:

(A) Watt
(B) Joule
(C) Newton
(D) Volt

Correct Answer: (B)

Q.100: Frequency unit:

(A) Hertz
(B) Joule
(C) Watt
(D) Newton

Correct Answer: (A)

Below is a simple subject-wise checklist of important topics asked in LPUNEST. Candidates can use this for quick revision:

Also Read: LPU NEST 2026 Syllabus