The temperature at which Celsius and Fahrenheit scales read the same is:
A. 0 degrees
B. 32 degrees
C. -40 degrees
D. 100 degrees
Correct Answer: C C/5 = (F-32)/9. Set C = F = x: x/5 = (x-32)/9 -> 9x = 5x-160 -> x = -40.
Q2. Physics
Transformer works on the principle of:
A. Self induction
B. Mutual induction
C. Electromagnetic induction
D. Both B and C
Correct Answer: B Transformer works on electromagnetic induction via mutual induction between coils.
Q3. Chemistry
Which element has the highest ionization energy?
A. Li
B. Na
C. He
D. Ne
Correct Answer: C Helium has the highest ionization energy due to its full 1s^2 configuration and small atomic size.
Q4. Chemistry
Which of the following shows +R effect?
A. -OH
B. -NO
C. -CN
D. -COOH
Correct Answer: A -OH, -NH, -OR show +R (resonance) effect as they donate electrons. -NO, -CN, -COOH show -R effect.
Q5. Mathematics
If the function f(x) = sin(x) is given, what is the value of x for which f(x) = 1?
A. 0
B. pi/2
C. pi
D. 3pi/2
Correct Answer: B The function f(x) = sin(x) has a value of 1 when x = pi/2. This is because the sine function has a maximum value of 1 at x = pi/2.
Q6. Physics
A car accelerates uniformly from rest to 20 m/s in 10 s. The acceleration is:
A. 1 m/s^2
B. 2 m/s^2
C. 0.5 m/s^2
D. 4 m/s^2
Correct Answer: B a = (v-u)/t = (20-0)/10 = 2 m/s^2.
Q7. 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.
Q8. Physics
A ray of light passes from air into a medium with refractive index 1.5. If the angle of incidence is 30 degrees, what is the angle of refraction?
A. 20 degrees
B. 30 degrees
C. 40 degrees
D. 50 degrees
Correct Answer: A Using Snell's law, n1 sin(theta1) = n2 sin(theta2), we can find the angle of refraction. For air, n1 = 1, and for the medium, n2 = 1.5. Given theta1 = 30 degrees, we have 1*sin(30) = 1.5*sin(theta2), which gives theta2 = 20 degrees.
Q9. 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).
Q10. Mathematics
If sin = 3/5, then cos is:
A. 4/5
B. 4/5
C. 3/5
D. 5/4
Correct Answer: B sin^2 + cos^2 = 1 -> cos^2 = 1 - 9/25 = 16/25 -> cos = 4/5 ( in first quadrant).
Q11. Chemistry
The number of moles in 18 g of HO is:
A. 0.5
B. 1
C. 2
D. 18
Correct Answer: B Molar mass of HO = 18 g/mol. n = 18/18 = 1 mol.
Q12. Physics
The equivalent resistance of three 6 resistors connected in parallel is:
A. 18
B. 6
C. 2
D. 3
Correct Answer: C 1/Rp = 1/6 + 1/6 + 1/6 = 3/6 = 1/2 -> Rp = 2 .
Q13. Mathematics
The solution of 2x + 3 = 7 is:
A. 1
B. 2
C. 3
D. 4
Correct Answer: B 2x = 4 -> x = 2.
Q14. 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.