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Sections: PhysicsChemistryMathematics
Q1. Mathematics
Find the derivative of f(x) = sin(x^2).
A. cos(x^2)
B. 2x cos(x)
C. 2x cos(x^2)
D. x^2 cos(x^2)
Correct Answer: C
Using chain rule: d/dx[sin(x^2)] = cos(x^2) . d/dx(x^2) = 2x cos(x^2).
Q2. Chemistry
Which gas is known as "Laughing Gas"?
Correct Answer: B
Nitrous oxide (NO) is called laughing gas due to its euphoric effects when inhaled.
Q3. 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.
Q4. Chemistry
The number of valence electrons in carbon is:
Correct Answer: C
Carbon (Z=6) has electronic configuration 2,4 -> 4 valence electrons.
Q5. Chemistry
The pH of 10 M HCl solution is:
Correct Answer: B
[H] = 10 M. pH = -log[H] = -log(10) = 3.
Q6. Mathematics
The number of permutations of 3 objects taken 2 at a time is:
Correct Answer: B
P = 3!/(3-2)! = 6.
Q7. Physics
The photon energy of light with wavelength 500 nm is (h = 6.63 x 10 Js):
A. 2.48 x 10 J
B. 3.98 x 10 J
C. 1.99 x 10 J
D. 4.97 x 10 J
Correct Answer: B
E = hc/ = (6.63x10 x 3x10)/(500x10) = 3.98x10 J.
Q8. Physics
A capacitor of 10 F 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 = 1/2CV^2 = 1/2 x 10x10 x 100^2 = 0.05 J.
Q9. Chemistry
Shape of water molecule is:
A. Linear
B. Trigonal planar
C. Bent/V-shaped
D. Tetrahedral
Correct Answer: C
Water has 2 bond pairs + 2 lone pairs -> bent shape with ~104.5 degrees bond angle.
Q10. Mathematics
The sum of first 10 natural numbers is:
Correct Answer: B
Sum = n(n+1)/2 = 10x11/2 = 55.
Q11. Mathematics
The quadratic equation whose roots are 1 and 2 is:
A. x^2 - 3x + 2 = 0
B. x^2 - 3x + 2 = 0
C. x^2 + 3x + 2 = 0
D. x^2 - x + 2 = 0
Correct Answer: B
Sum = 3, Product = 2 -> x^2 - 3x + 2 = 0.
Q12. Chemistry
The chemical name of common salt is:
A. Sodium nitrate
B. Sodium chloride
C. Sodium carbonate
D. Sodium hydroxide
Correct Answer: B
Common salt is NaCl - Sodium chloride.
Q13. Chemistry
Which of the following is an aromatic compound?
A. Cyclohexane
B. Benzene
C. Cyclohexene
D. 1,3-Butadiene
Correct Answer: B
Benzene follows Hckel's rule (4n+2 pi electrons, n=1) and is planar with delocalized electrons.
Q14. Physics
In SHM, the acceleration is maximum at:
A. Mean position
B. Equilibrium position
C. Extreme position
D. Same everywhere
Correct Answer: C
a = -^2x. Acceleration is maximum at extreme positions (x = A) and zero at mean position.
Q15. Mathematics
The value of i^2 (where i = sqrt-1) is:
Correct Answer: B
i^2 = -1 (fundamental property of imaginary numbers).