Objective Questions (Multiple Choice)
1. What is the value of \( \sin(90^\circ) \)?
a) 0
b) 1
c) 0.5
d) -1
2. The derivative of \( x^3 \) with respect to \( x \) is:
a) \( 3x^2 \)
b) \( 2x^3 \)
c) \( x^2 \)
d) \( 3x \)
3. Which of the following is the SI unit of force?
a) Joule
b) Newton
c) Pascal
d) Watt
4. The quadratic equation \( x^2 - 5x + 6 = 0 \) has roots:
a) 2 and 3
b) -2 and -3
c) 1 and 6
d) -1 and -6
5. The value of \( \log_{10}(100) \) is:
a) 1
b) 2
c) 10
d) 100
6. The magnitude of the vector \( \mathbf{A} = 3\mathbf{i} + 4\mathbf{j} \) is:
a) 5
b) 7
c) 12
d) 25
7. Which of the following is the formula for work done?
a) \( \text{Force} \times \text{Distance} \)
b) \( \text{Mass} \times \text{Acceleration} \)
c) \( \text{Force} / \text{Area} \)
d) \( \text{Mass} / \text{Volume} \)
8. The SI unit of electric current is:
a) Volt
b) Ampere
c) Ohm
d) Coulomb
9. The value of \( \cos(60^\circ) \) is:
a) 0.5
b) 1
c) 0
d) -1
10. The integral of \( 2x \) with respect to \( x \) is:
a) \( x^2 + C \)
b) \( 2x^2 + C \)
c) \( x + C \)
d) \( 2 + C \)
11. The SI unit of energy is __________.
12. The value of \( \tan(45^\circ) \) is __________.
13. The formula for density is __________ divided by volume.
14. The derivative of \( \sin(x) \) with respect to \( x \) is __________.
15. The quadratic formula is given by \( x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a} \). For the equation \( x^2 - 4x + 3 = 0 \), the roots are __________ and __________.
16. The SI unit of power is __________.
17. The force acting on a body of mass 5 kg with an acceleration of 2 m/s² is __________ N.
18. The value of \( \pi \) is approximately __________.
19. The integral of \( 3x^2 \) with respect to \( x \) is __________.
20. The formula for the area of a circle is __________.
21. The SI unit of pressure is __________.
22. The value of \( \sin(30^\circ) \) is __________.
23. The formula for momentum is __________ multiplied by velocity.
24. The derivative of \( e^x \) with respect to \( x \) is __________.
25. The SI unit of frequency is __________.
26. The force exerted by a spring is given by __________ Law.
27. The value of \( \log_{2}(8) \) is __________.
28. The formula for the circumference of a circle is __________.
29. The integral of \( \cos(x) \) with respect to \( x \) is __________.
30. The SI unit of electric charge is __________.
Essay Questions
1a. Explain the difference between scalar and vector quantities, giving two examples of each.
1b. Derive the equation of motion \( v = u + at \), where \( v \) is final velocity, \( u \) is initial velocity, \( a \) is acceleration, and \( t \) is time.
1c. State and explain Newton's Second Law of Motion. Provide an example to illustrate its application.
2a. Solve the quadratic equation \( 2x^2 - 5x - 3 = 0 \) using the quadratic formula.
2b. Define specific heat capacity and explain its significance in thermodynamics.
2c. Discuss the concept of work-energy theorem and derive the formula for kinetic energy.
3a. Explain the concept of electric potential difference and its relationship with electric current.
3b. Describe the process of solving a system of linear equations using the substitution method.
3c. Define magnetic flux and explain Faraday's Law of Electromagnetic Induction.
4a. Discuss the importance of dimensional analysis in physics and provide an example.
4b. Explain the concept of projectile motion and derive the equation for the maximum height reached by a projectile.
4c. Discuss the concept of simple harmonic motion and derive the formula for the period of a simple pendulum.
5a. Define the term "resistance" in electricity and explain how it is calculated using Ohm's Law.
5b.. Explain the concept of conservation of momentum and provide an example of its application in collisions.
5c. Discuss the concept of gravitational potential energy and derive the formula for it.
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