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Sections: PhysicsChemistryMathematics
Q1. Chemistry
Which of these is a noble gas?
A. Clâ‚‚
B. Nâ‚‚
C. Xenon
D. Oâ‚‚
Correct Answer: C
Xenon (Xe) is a noble gas. Clâ‚‚, Nâ‚‚, Oâ‚‚ are diatomic gases.
Q2. Physics
A ball dropped from height h hits the ground with speed v. The value of v is proportional to:
Correct Answer: B
v = √(2gh) → v ∠√h.
Q3. Chemistry
The coordination number in NaCl crystal structure is:
Correct Answer: B
NaCl has face-centered cubic (FCC) structure with each Na⺠surrounded by 6 Cl⻠and vice versa.
Q4. Chemistry
The color of phenolphthalein in basic medium is:
A. Colorless
B. Pink
C. Blue
D. Yellow
Correct Answer: B
Phenolphthalein is colorless in acid and pink in base (pH > 8.3).
Q5. Physics
A wire of resistance R is stretched to double its length. New resistance will be:
Correct Answer: C
When length is doubled (L' = 2L), cross-sectional area halves (A' = A/2). R' = ÏL'/A' = Ï(2L)/(A/2) = 4ÏL/A = 4R.
Q6. Chemistry
Which gas is known as "Laughing Gas"?
A. NOâ‚‚
B. Nâ‚‚O
C. CO
D. COâ‚‚
Correct Answer: B
Nitrous oxide (Nâ‚‚O) is called laughing gas due to its euphoric effects when inhaled.
Q7. Mathematics
The value of ∫₀¹ x² dx is:
Correct Answer: C
∫₀¹ x² dx = [x³/3]₀¹ = 1/3 - 0 = 1/3.
Q8. Mathematics
The sum of angles in a triangle is:
A. 90°
B. 180°
C. 180°
D. 360°
Correct Answer: C
Sum of interior angles of a triangle = 180°.
Q9. Physics
In SHM, the acceleration is maximum at:
A. Mean position
B. Equilibrium position
C. Extreme position
D. Same everywhere
Correct Answer: C
a = -ω²x. Acceleration is maximum at extreme positions (x = ±A) and zero at mean position.
Q10. Physics
A car accelerates uniformly from rest to 20 m/s in 10 s. The acceleration is:
A. 1 m/s²
B. 2 m/s²
C. 0.5 m/s²
D. 4 m/s²
Correct Answer: B
a = (v-u)/t = (20-0)/10 = 2 m/s².
Q11. Chemistry
The most abundant element in Earth's crust is:
A. Iron
B. Oxygen
C. Silicon
D. Aluminum
Correct Answer: B
Oxygen (~46.6%) is the most abundant element in Earth's crust.
Q12. Physics
The escape velocity of a body from Earth is 11.2 km/s. What is the escape velocity from a planet having mass 4 times and radius twice that of Earth?
A. 22.4 km/s
B. 5.6 km/s
C. 15.8 km/s
D. 11.2 km/s
Correct Answer: C
v_e = √(2GM/R). For new planet: v_e' = √(2G·4M/2R) = √(2·2GM/R) = √2·√(2GM/R) = √2 × 11.2 = 15.84 km/s.
Q13. Physics
SI unit of resistance is:
A. Volt
B. Ampere
C. Coulomb
D. Ohm
Correct Answer: D
Resistance is measured in Ohms (Ω).
Q14. Physics
A particle is moving with velocity v = 2t² + 3t. Find its acceleration at t = 2s.
A. 11 m/s²
B. 10 m/s²
C. 8 m/s²
D. 14 m/s²
Correct Answer: A
a = dv/dt = d(2t² + 3t)/dt = 4t + 3. At t = 2: a = 4(2) + 3 = 11 m/s².
Q15. Mathematics
The mode of 1, 2, 2, 3, 3, 3, 4 is:
Correct Answer: B
3 appears 3 times (highest frequency).
Q16. Mathematics
If sin θ = 3/5, then cos θ is:
Correct Answer: B
sin²θ + cos²θ = 1 → cos²θ = 1 - 9/25 = 16/25 → cos θ = 4/5 (θ in first quadrant).
Q17. Physics
A capacitor of 10 µF is charged to 100 V. The energy stored is:
A. 0.05 J
B. 0.05 J
C. 0.5 J
D. 5 J
Correct Answer: B
E = ½CV² = ½ × 10×10â»â¶ × 100² = 0.05 J.
Q18. Physics
A body of mass 1 kg has weight approximately:
A. 1 N
B. 10 N
C. 100 N
D. 0.1 N
Correct Answer: B
W = mg = 1 × 10 = 10 N (approx).
Q19. Chemistry
The number of moles in 18 g of Hâ‚‚O is:
Correct Answer: B
Molar mass of Hâ‚‚O = 18 g/mol. n = 18/18 = 1 mol.
Q20. Mathematics
The slope of line passing through (1,2) and (3,6) is:
Correct Answer: B
m = (6-2)/(3-1) = 4/2 = 2.
Q21. Mathematics
The value of i² (where i = √-1) is:
Correct Answer: B
i² = -1 (fundamental property of imaginary numbers).
Q22. Chemistry
The IUPAC name of CH₃CH₂CH(CH₃)COOH is:
A. 2-Methylbutanoic acid
B. 2-Methylbutanoic acid
C. 3-Methylbutanoic acid
D. Pentanoic acid
Correct Answer: B
Longest chain has 4 C with COOH at C1 and methyl at C2 → 2-Methylbutanoic acid.
Q23. Physics
First law of thermodynamics is based on:
A. Conservation of momentum
B. Conservation of energy
C. Conservation of mass
D. Conservation of charge
Correct Answer: B
ΔU = Q - W. First law is the law of conservation of energy for thermodynamic systems.
Q24. Chemistry
The oxidation state of Mn in KMnOâ‚„ is:
Correct Answer: C
K(+1) + Mn + 4O(-2) = 0 → +1 + Mn -8 = 0 → Mn = +7.
Q25. Mathematics
The quadratic equation whose roots are 1 and 2 is:
A. x² - 3x + 2 = 0
B. x² - 3x + 2 = 0
C. x² + 3x + 2 = 0
D. x² - x + 2 = 0
Correct Answer: B
Sum = 3, Product = 2 → x² - 3x + 2 = 0.
Q26. Chemistry
Which of the following is an aromatic compound?
A. Cyclohexane
B. Benzene
C. Cyclohexene
D. 1,3-Butadiene
Correct Answer: B
Benzene follows Hückel's rule (4n+2 π electrons, n=1) and is planar with delocalized electrons.
Q27. Mathematics
If f(x) = 2x + 1, find f(3):
Correct Answer: C
f(3) = 2(3) + 1 = 7.
Q28. Chemistry
The functional group in alcohol is:
A. -CHO
B. -COOH
C. -OH
D. -NHâ‚‚
Correct Answer: C
Alcohols contain the hydroxyl (-OH) functional group.
Q29. Mathematics
The sum of first n odd natural numbers is:
A. n
B. 2n
C. n²
D. n(n+1)/2
Correct Answer: C
1 + 3 + 5 + ... + (2n-1) = n².
Q30. Mathematics
If sin A = 1/2, then the value of A (acute) is:
A. 30°
B. 30°
C. 60°
D. 90°
Correct Answer: B
sin 30° = 1/2.