SJS MEGA TRIALS, 2025

CONTEST 1

ROUND ONE
FUNDAMENTALS

PREAMBLE: Consider the Gibbs free energy equation ΔG = ΔH − TΔS, where ΔG is the
change in Gibbs free energy, ΔH= change in enthalpy, T= absolute temperature in Kelvin, ΔS
= change in entropy. Using the equation, explain why;

1. An endothermic reaction (ΔH > 0) can be spontaneous at high temperatures. Explain

how this happens.
Ans: When ΔH is positive, a large positive ΔS and high temperature T make the
TΔS term large enough to outweigh ΔH, causing ΔG to become negative and the
reaction to be spontaneous.

2. A reaction with negative ΔH and negative ΔS might be spontaneous at low

temperatures but not at high temperatures. Explain.
Ans: At low temperatures, the −TΔS term is small, so the negative ΔH dominates,
making ΔG negative (spontaneous). At high temperatures, the positive TΔS term
can outweigh ΔH, making ΔG positive and the reaction nonspontaneous.

3. A reaction with negative ΔH and positive ΔS is always spontaneous. Explain.

Ans: Since ΔH is negative (exothermic) and ΔS is positive (entropy increases),
both terms make ΔG=ΔH−TΔS negative at all temperatures, so the reaction is
always spontaneous.

4. Why can a reaction with positive ΔH and negative ΔS never be spontaneous at any
temperature?
Ans: Both ΔH and −TΔS are positive terms, so ΔG is always positive, meaning
the reaction cannot be spontaneous at any temperature.

PREAMBLE: Give the main product(s) that will be formed from the each of the following
reactions of 2-butene with the given reagent and condition(s)

1. concentrated aqueous acidified KMnO4 accompanied by heat Ans: Ethanoic acid

2. Dilute aqueous K2Cr2O7 in the cold Ans: No products formed
3. warm aqueous concentrated H2SO4 Ans: 2-Ethanol
4. Bromine water Ans: 3-Bromo butan-2-ol or 3-bromo-2-butanol

1
 1. What is the language origin of the word ‘enzyme’? Ans: Greek
2. What is the Greek word origin of the word ‘enzyme’? Ans: enzymos
3. What is the meaning of enzyme? Ans: “in yeast” or “leavened”
4. What triggers the dispatch of enzymes in animals?
Ans: Hormonal triggers/neural signals /presence of substrate

PREAMBLE: Name the phyla that comprises organisms with the following distinct features;

1. Soft, unsegmented body often protected by a shell Ans: Mollusca

2. Jointed appendages and exoskeleton Ans: Arthropoda
3. Radially symmetrical and spiny skin Ans: Echinodermata
4. Presence of stinging cells (collar cells) Ans: Porifera

PREAMBLE: A mass spectrometer has five main components. The vapourization chamber,
ionization chamber, the electric field, the magnetic field and the detector. To calculate the
abundance and number of species in a sample, the species carrying a velocity of V were
passed through a magnetic field of flux density B and are deflected in a circular path based on
their mass-to-charge ratio q/m. Find the degree of deflection r, and the angular velocity of a
species with the given values of B, V, and q/m.

1. 𝑞𝑞/𝑚𝑚 = 2.5 × 108 𝐶𝐶/𝑘𝑘𝑘𝑘, 𝑣𝑣 = 2.0 × 106 𝑚𝑚 𝑠𝑠 −1 , 𝐵𝐵 = 5.0 𝑚𝑚𝑚𝑚

Ans: 𝑟𝑟 = 1.6𝑚𝑚 , 𝑤𝑤 = 1.3 × 106 𝑟𝑟𝑟𝑟𝑟𝑟/𝑠𝑠

2. 𝑞𝑞/𝑚𝑚 = 4.5 × 108 𝐶𝐶/𝑘𝑘𝑘𝑘, 𝑣𝑣 = 3.0 × 106 𝑚𝑚 𝑠𝑠 −1 , 𝐵𝐵 = 1.5 𝑚𝑚𝑚𝑚

Ans: 𝑟𝑟 = 4.4𝑚𝑚 , 𝑤𝑤 = 6.8 × 105 𝑟𝑟𝑟𝑟𝑟𝑟/𝑠𝑠

3. 𝑞𝑞/𝑚𝑚 = 2.7 × 108 𝐶𝐶/𝑘𝑘𝑘𝑘, 𝑣𝑣 = 1.8 × 106 𝑚𝑚 𝑠𝑠 −1 , 𝐵𝐵 = 5.0 𝑚𝑚𝑚𝑚

Ans: 𝑟𝑟 = 1.3𝑚𝑚 , 𝑤𝑤 = 1.4 × 106 𝑟𝑟𝑟𝑟𝑟𝑟/𝑠𝑠

4. 𝑞𝑞/𝑚𝑚 = 3.6 × 108 𝐶𝐶/𝑘𝑘𝑘𝑘, 𝑣𝑣 = 2.4 × 106 𝑚𝑚 𝑠𝑠 −1 , 𝐵𝐵 = 6.0 𝑚𝑚𝑚𝑚

Ans: 𝑟𝑟 = 1.1𝑚𝑚 , 𝑤𝑤 = 2.2 × 106 𝑟𝑟𝑟𝑟𝑟𝑟/𝑠𝑠

PREAMBLE: Find the work done when the point of application of the constant force 𝐹𝐹
undergoes the displacement d.

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 1. 𝐹𝐹 = (7.0𝚤𝚤̂ + 2.0𝚥𝚥̂) 𝑁𝑁 and 𝑑𝑑 = (2.0𝚤𝚤̂ − 1.5𝚥𝚥̂) 𝑚𝑚. Ans: 11 𝐽𝐽

2. 𝐹𝐹 = (−9.0𝚤𝚤̂ + 4.5𝚥𝚥̂) 𝑁𝑁 and 𝑑𝑑 = (2.0𝚤𝚤̂ + 6.0𝚥𝚥̂) 𝑚𝑚. Ans: 9.0 𝐽𝐽

3. 𝐹𝐹 = (5.0𝚤𝚤̂ − 9.0𝚥𝚥̂) 𝑁𝑁 and 𝑑𝑑 = (6.0𝚤𝚤̂ − 4.0𝚥𝚥̂) 𝑚𝑚. Ans: 66 𝐽𝐽

4. 𝐹𝐹 = (7.0𝚤𝚤̂ − 21𝚥𝚥̂) 𝑁𝑁 and 𝑑𝑑 = (6.0𝚤𝚤̂ + 2.0𝚥𝚥̂) 𝑚𝑚. Ans: 0

PREAMBLE: Determine the range of values of x for which the expansion is valid
1 1 1
1. (1 – 3x)1/3 Ans: �𝑥𝑥 ∶ − 3 < 𝑥𝑥 < 3� or �𝑥𝑥 ∶ |𝑥𝑥| < 3
�
1 1 1
2. (1+ 2x)-1/4 Ans: �𝑥𝑥 ∶ − 2 < 𝑥𝑥 < 2� or �𝑥𝑥 ∶ |𝑥𝑥| < 2
�
1 1 1
3. (4x - 1)1/2 Ans: �𝑥𝑥 ∶ − 4 < 𝑥𝑥 < 4� or �𝑥𝑥 ∶ |𝑥𝑥| < 4
�
1 1 1
4. (1+5x)-1/6 Ans: �𝑥𝑥 ∶ − 5 < 𝑥𝑥 < 5� or �𝑥𝑥 ∶ |𝑥𝑥| < 5
�

PREAMBLE: Find the nth term, Un and identify the given series completely if the sum of
the first n terms is Sn

1. Sn = 7n – 1
Ans: Un = 6 (7n – 1). It is an exponential or geometric series with first term 6 and
common ratio 7

2. Sn = 4n +1
Ans: 3 (4n-1). It is an exponential or geometric series with first term, 3 and common
ratio 4

3. Sn = 4n2 -7n + 3
Ans: Un = 8n – 11. It is an arithmetic or a linear series with first term, -3 and common
difference 8

4. Sn = 9n – 1
Ans: Un = 8 (9n-1). It is an exponential or geometric series with first term, 8 and
common ratio 9

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 ROUND TWO

SPEEDRACE

1. Before the electrolysis of Aluminium Oxide to extract Aluminium, what substance is

used to decrease the melting point of Aluminium oxide Ans: Cryolite
2. How many atoms are in 3 formula units of Octan-3-ol Ans: 81 atoms
3. To 3 s.f.,what percentage of Iron, Fe, is in Iron Sulphide FeS (Take Fe= 56.0, S=
32.0)
Ans: 63.6%

4. Which class does garden snail belong? Ans: Class Gastropoda

5. Who is widely regarded as the father of modern microbiology? Ans: Louis Pasteur
6. What is the mode of reproduction of Euglena? Ans: longitudinal binary fission

7. What is the resonance frequency of a tuned RLC circuit, If the inductor were tuned to
2.0 × 10−8 𝐻𝐻 and the capacitor to 72 𝑝𝑝𝑝𝑝? Ans: 130 𝑀𝑀𝑀𝑀𝑀𝑀
8. What is the moment of inertia of a hollow sphere of radius 5.0 𝑐𝑐𝑐𝑐 and mass 90.0 𝑔𝑔
about an axis passing through its center? Ans: 1.5 × 10−4 𝑘𝑘𝑘𝑘 𝑚𝑚2
9. What is the magnitude of the impulse of a 14 𝑁𝑁 force that acts for 15 𝑚𝑚𝑚𝑚?
Ans: 0.21 𝑁𝑁 𝑠𝑠

10. Find the number of sides of a polygon if in its regular form, an interior angle is 13
times its exterior angle. Ans: 28 sides
11. Find the number of digits if 1113 is expressed as a number in base 4.
Ans: 6 digits
12. Factorize x4 – 21x2 + 80 Ans: (𝒙𝒙 − 𝟒𝟒)(𝒙𝒙 + 𝟒𝟒) (x2 -5)

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 ROUND THREE

TRUE OR FALSE

1. The electronic configuration of Neon is 1s2 2s2 2p6 3s2 3p6 False

2. The electronic configuration of Chloride ion is 1s2 2s2 2p6 3s2 3p6 True

3. The electronic configuration of Argon is 1s2 2s2 2p6 3s2 3p6 True

4. The electronic configuration of Ca2+ is 1s2 2s2 2p6 3s2 3p6 True

1. NaCl and HCl constitute a buffer system. False

2. NaOH and HBr constitutes a buffer system False

3. Na 2CO3 and CO2 constitutes a buffer system. False

4. NaF and HF constitutes a buffer system True

1. Myrmecology is scientific study of spiders False (ants)

2. Palaeontology is the study of fossils which are preserved remains or the traces
of organisms that lived in the past, and are now extinct. True
3. Sericulture is related to the rearing of different strains of silkworms for the
production, transportation and marketing of silk at commercial level. True
4. Apiculture is rearing and maintenance of bees for the production and
marketing of honey and wax at the commercial level. True

1. The water potential of a turgid plant cell is higher than that of a flaccid cell.
True
2. Water potential is a scalar quantity, meaning it has both magnitude and
direction. False
3. In a hypotonic solution, water potential is higher outside the cell than inside.
True
4. In a closed system, the pressure potential is always zero. False

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1. Neglecting air resistance, the kinetic energy of an object thrown vertically upward
increases as the object rises. False

2. Because energy is conserved, the kinetic energy of an object thrown vertically upward
remains the same as the object rises. False

3. Air resistance causes the kinetic energy of an object thrown vertically upward to
decrease as the object rises. False

4. The KE of an object thrown vertically upwards increases as the object returns to the
thrower because air resistance is less coming down than going up. False

1. The acceleration of an object oscillating vertically at the end of a vertical

spring attains it maximum magnitude at the equilibrium position.
False

2. The acceleration of an object oscillating vertically at the end of a vertical

spring attains it maximum magnitude at its extreme positions.
True

3. The speed of an object oscillating vertically at the end of a vertical spring

attains it maximum magnitude at its extreme position. False

4. The total energy of a system made up of an object oscillating vertically at the

end of a vertical spring attains it maximum value at the equilibrium position
and its minimum value at the extreme positions. False

1. sin-1 0 = π False
2. cos-1 (0) = π/2 True
3. cos-1(-1/2) = -π/3 False
4. tan-1 (-1) = 3π/4 False

The pair of lines with equations

1. x + 2y = -5 and 2x + y = 5, are perpendicular False
2. 3x + 5y = -10, 5x – 3y = 10 are perpendicular True
3. y = 4x + 5 and x = 5 – 4y are perpendicular True
4. 2x + y = 10 and y = 2x + 10 are parallel False

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 ROUND FOUR

RIDDLES

1. I am a four digits odd number

2. I am a palindromic number
3. My digits are simply binomial coefficients
4. My first and last digits are identical and an identity
5. I sit in pascals triangle rule with pride
6. The sum of my digits is 8
Who am I? 1331

1. I am a mechanical property of an object

2. I act along the path you trace, speeding you up in a circular race
3. My name hints at a break from the original direction
4. Changes in speed is where I shine
5. Combine me with centripetal, and see the outcome
6. I help describe full circular velocity
Who am I? TANGENTIAL ACCELERATION

1. I was an English chemist who lived between the years of 1837-1898

2. I contributed significantly to the periodic law.
3. In 1864 I published the concept of the periodicity of the chemical elements
4. I arranged elements in order of atomic weight.
5. I grouped elements in octaves.
Who am I? JOHN NEWLAND

1. I am a small, primitive wingless insect

2. I’m an ancient creature, older than dinosaurs might
3. I love the dark and damp
4. I’m not a swimmer though my name might make you think
5. My name is a giveaway, I’m silver and I’m a fish in looks
Who am I? SILVER FISH