Correct Answer: B a = 2, d = 3, T = 2 + (n-1)3 = 3n - 1.
Q2. Mathematics
The number of permutations of 3 objects taken 2 at a time is:
A. 3
B. 6
C. 9
D. 2
Correct Answer: B P = 3!/(3-2)! = 6.
Q3. Mathematics
The value of sin^230 degrees + cos^230 degrees is:
A. 0
B. 1/2
C. 1
D. 3/4
Correct Answer: C sin^2 + cos^2 = 1 (identity).
Q4. 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.
Q5. 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).
Q6. Mathematics
The equation of line with slope 2 passing through (1, 3) is:
A. y = 2x + 1
B. y = 2x + 1
C. y = 2x - 1
D. y = x + 2
Correct Answer: B Point-slope form: y - 3 = 2(x - 1) -> y = 2x + 1.
Q7. Chemistry
What is the pH of a 0.1 M solution of NaOH?
A. 1
B. 12
C. 13
D. 14
Correct Answer: C NaOH is a strong base, so it completely dissociates in water to give OH- ions. The concentration of OH- ions is equal to the concentration of NaOH, which is 0.1 M. Using the equation pOH = -log[OH-], we get pOH = -log(0.1) = 1. Then, pH + pOH = 14, so pH = 14 - pOH = 14 - 1 = 13.
If the equation x^2 + 2x + 1 = 0 has two equal roots, what is the value of the discriminant?
A. 0
B. 1
C. 2
D. 4
Correct Answer: A The discriminant of a quadratic equation ax^2 + bx + c = 0 is given by b^2 - 4ac. For the given equation x^2 + 2x + 1 = 0, a = 1, b = 2, and c = 1. The discriminant is 2^2 - 4*1*1 = 0.
Q11. Chemistry
The IUPAC name of CHCHCH(CH)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.
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 = sqrt(2GM/R). For new planet: v_e' = sqrt(2G.4M/2R) = sqrt(2.2GM/R) = sqrt2.sqrt(2GM/R) = sqrt2 x 11.2 = 15.84 km/s.
Q13. Chemistry
Atomic number of oxygen is:
A. 6
B. 7
C. 8
D. 16
Correct Answer: C Oxygen has atomic number 8 (configuration 1s^22s^22p).
Q14. Physics
Young's modulus is defined for which type of deformation?
A. Shear
B. Longitudinal strain
C. Volume strain
D. Torsion
Correct Answer: B Y = stress/strain for longitudinal (tensile/compressive) deformation.
Q15. Physics
A Carnot engine operates between two reservoirs at temperatures 500 K and 300 K. What is the efficiency of the engine?
A. 0.2
B. 0.4
C. 0.6
D. 0.8
Correct Answer: B The efficiency of a Carnot engine is given by the equation eta = 1 - (T2/T1), where T1 and T2 are the temperatures of the two reservoirs. For the given temperatures, eta = 1 - (300/500) = 1 - 0.6 = 0.4.