2024 Engineering Physics Past Paper PDF - CENTRAL INSTITUTE OF PETROCHEMICALS ENGINEERING & TECHNOLOGY

## CENTRAL INSTITUTE OF PETROCHEMICALS ENGINEERING & TECHNOLOGY ### HEAD OFFICE: GUINDY, CHENNAI - 600 032. ### ACADEMIC CELL #### **FIRST SEMESTER EXAMINATION – JANUARY - 2024** **Duration:** 3 Hours **Course:** DPMT **Subject:** Engineering Physics **Max. Marks:** 60 **Date:** 10.01.2024 **Time...

## CENTRAL INSTITUTE OF PETROCHEMICALS ENGINEERING & TECHNOLOGY ### HEAD OFFICE: GUINDY, CHENNAI - 600 032. ### ACADEMIC CELL #### **FIRST SEMESTER EXAMINATION – JANUARY - 2024** **Duration:** 3 Hours **Course:** DPMT **Subject:** Engineering Physics **Max. Marks:** 60 **Date:** 10.01.2024 **Time:** 02.00 p.m. to 05.00 p.m. **(DO NOT CHANGE SEQUENCE OF QUESTION NUMBER IN ANSWER SCRIPT)** ### PART - A **Answer all questions** 1. 'Parsec' is the unit of - a. Distance - b. Time - c. Angle - d. Mass 2. A train travels 4km due east and then 3km due north and finally come back to the starting point travelling 5km along the south-west direction. What is the net displacement? - a. 12km - b. 5km - c. 0km - d. None of these 3. Oil spreads over water while water does not spread over oil. This is due to the property of - a. Elasticity - b. Viscosity - c. Surface tension - d. Friction 4. In Isothermal process, the quantity which remains constant is_ 5. The state of achieving more number of atoms in the higher energy state than in the lower energy state is known as 6. If the diameter of a wire is doubled keeping its length same, its Young's modulus of elasticity will 7. Dimensional formula of work and energy is same (True/False) 8. Centripetal and centrifugal forces have the same magnitude and the same direction. (True/False) 9. The unit of power of Lens is Diopter. (True/False) 10. O.F.C stands for 11. S.I. Stands for 12. M.K.S. stands for ### PART - B **Answer all questions (Max. 40 words)** 1. Define the Pumping. 2. Write the dimensional formula of - a. Gravitational Constant (G) - b. Surface Tension 3. Define rest and motion. 4. Write the modes of heat transfer. ### PART - C **Answer any six questions (Max. 100 words)** 1. Define elasticity and prove that steel is more elastic than rubber. 2. Derive the expression for the Newton's law of viscosity. 3. Write a short note on Total Internal Reflection and define the critical angle. 4. Temperature of a certain bath gives the same reading on both the centigrade and Fahrenheit scales. Calculate the temperature of the bath. 5. Define the Unit and measurement and write a short note on the system of units. 6. A particle moving in a circle of radius 1.0 meter has its angular velocity increased, in one minute, by 90rad/m. Calculate: - a. Angular acceleration - b. Tangential linear acceleration 7. Explain about streamline and turbulent flow. ### PART - D **Answer any two questions (Max. 300 words)** 1. A projectile is fired with velocity 'u', making an angle θ with the horizontal, prove that the path followed by the projectile is parabolic, and also find the condition to achieve the maximum horizontal range. 2. State the triangle's law of vectors addition and derive the expression for the magnitude and direction of the resultant of two vectors. 3. Write a short note on the construction of LASER and explain about its different applications ## CENTRAL INSTITUTE OF PETROCHEMICALS ENGINEERING & TECHNOLOGY ### HEAD OFFICE: GUINDY, CHENNAI – 600 032. #### **FIRST SEMESTER EXAMINATION – FEBRUARY - 2021** **Duration:** 2 Hours **Course:** DPMT **Subject:** Engineering Physics **Max. Marks:** 60 **Date:** 24.02.2021 **Time:** 10.00 a.m. to 12.00 Noon. **( DO NOT CHANGE SEQUENCE OF QUESTION NUMBER IN ANSWER SCRIPT)** ### PART - A **Answer all questions (Max. 40 words)** 1. What do you mean by streamline flow? 2. What is total internal reflection? 3. Define isothermal process. 4. Give the relation between wavelength and frequency. 5. Mention the four uses of lasers in industries. 6. Define Young's modulus and give its unit. 7. What is scalar and vector quantity? 8. What is Newton's law of cooling? 9. Define the surface tension and angle of contact. 10. i) No moving object can be stopped without applying ii) The force of attraction between molecules of different substances ### PART - B **Answer any eight questions (Max. 100 words)** 1. What are rectangular components of a vector? State and explain the triangle law of vector addition. 2. Define and derive the formula for the bulk modulus of elasticity. 3. What is projectile motion? Drive the expression for the range of flight of a projectile. 4. What is dimensional equation? Write the two uses of dimensional analysis with examples. 5. What is surface energy? Explain the relation between surface tension and surface energy. 6. Describe the construction and working principle of the ruby laser. 7. Drive the relation between angular velocity, angular acceleration to the linear velocity and linear acceleration 8. Briefly explain the modes of heat transfer. 9. What is abbreviation of SI? Write down the SI units of all fundamental quantities. 10. What is terminal velocity? Derive the formula for it. ## CENTRAL INSTITUTE OF PETROCHEMICALS ENGINEERING & TECHNOLOGY ### HEAD OFFICE: GUINDY, CHENNAI - 600 032. #### **FIRST SEMESTER EXAMINATION - FEBRUARY - 2022** **Duration:** 3 Hours **Course:** DPMT **Subject:** Engineering Physics **Max. Marks:** 60 **Date:** 16.02.2022 **Time:** 02.00 p.m. to 04.00 p.m **(DO NOT CHANGE SEQUENCE OF QUESTION NUMBER IN ANSWER SCRIPT)** ### PART - A **Answer all questions (Max. 40 words)** 1. State Boyle's law. 2. Define Poisson's ratio. 3. Why rain drop is spherical? 4. Define elasticity. 5. Explain stress. 6. Write dimensional formula of force. 7. What is the difference between scalar quantity and vector quantity? 8. What is centripetal force? 9. Mention the factors on which the time period of a simple pendulum depends upon. 10. Write the full form for: a) LASER b) SI Unit ### PART - B **Answer any eight questions (Max. 100 words)** 1. What are the fundamental units? 2. Explain Newton's law of cooling. 3. What are the Centigrade scale, Fahrenheit scale and Kelvin scale? 4. Find the dimensional equation for a time period of a simple pendulum. 5. Explain different modes of heat transfer with examples. 6. State the assumptions of the kinetic theory of gases. 7. Write a note on optical fiber and explain with an example. 8. Explain total internal reflection and the critical angle. 9. Derive the relationship between angular velocity and linear velocity. 10. What are the main applications of a LASER? ## CENTRAL INSTITUTE OF PLASTICS ENGINEERING & TECHNOLOGY ### HEAD OFFICE: GUINDY, CHENNAI – 600 032. #### **FIRST SEMESTER EXAMINATION – DECEMBER 2019** **Duration:** 3 Hours **Course:** DPMT **Subject:** Engineering Physics **Max. Marks:** 60 **Date:** 24.12.2019 **Time: 02:00 p.m. to 05.00 p.m.** **(DO NOT CHANGE SEQUENCE OF QUESTION NUMBER IN ANSWER SCRIPT)** ### PART - A **Answer all questions** 1. S.I. unit of temperature is - a) Celsius - b) Fahrenheit - c) Reaumur - d) Kelvin 2. Dot product of two vectors is - a) Scalar - b) Neither scalar nor vector - c) Vector - d) All of these 3. The air resistance to the motion of the projectile is taken as - a) Zero - b) One - c) Infinite - d) None of these 4. The potential energy of a body is due to its - a) Position - b) Velocity - c) Internal structure - d) none of these 5. Force divided by area is called - a) Pressure - b) Volume - c) energy - d) none of these 6. The following remains constant in the isothermal process - a) Pressure - b) volume - c) Temperature - d) none of these 7. Unit of force is - a) Newton - b) joule - c) Newton per meter - d) None of these 8. Snell's law relates - a) Light reflection - b) Light refraction - c) Light transmission - d) Light absorption 9. For stimulated emission which of the following is required - a) Excess population - b) Normal population - c) Population inversion - d) none of these 10. The velocity of light in vacuum is - a) 3X10⁸ m/s - b) 3X10⁷ m/s - c) 3X10⁹ m/s - d) None of these 11. SI unit of frequency is - a) Ampere - b) Hertz - c) Volt - d) Meter 12. A quantity which has only magnitude is called - a) Vector quality - b) dimensionless quantity - c) scalar quantity - d) velocity 13. The maximum velocity of flow of liquid flowing in a streamline flow is known as - a) Critical velocity - b) terminal velocity - c) angular velocity - d) None of them 14. The ratio between lateral strain and longitudinal strain is called - a) Young's modulus - b) Modulus of rigidity - c) Poisson's ratio - d) Bulk modulus 15. The attractive force that exists between molecules of the same substance is - a) Adhesive - b) Cohesive - c) Resistance - d) None of these 16. Brick is a good conductor of heat. State True or False 17. The laser is a high intensity source. State True or False. 18. In conduction there is actual movement of molecules State True or False. 19. According to Hook's law stress is directly proportional to strain State True or False. 20. Acceleration is a vector quantity State True or False. **Write full form of the following** 21. LASER 22. S.I. unit. 23. F.P.S 24. O.F.C 25. T.I.R. 26. More no of atoms in excited states is known as 27. The rain drop is spherical is due to. 28. Acceleration is a quantity. 29. Metal is a good 30. The unit of angular velocity is ### PART - B **Answer all questions (Max. 40 words)** 1. Find the relation between angular velocity and linear velocity. 2. Mention the factors on which the time period of a simple pendulum depends upon. 3. Calculate the dimensional formula of the moment of force. 4. Explain stimulated emission of radiation. ### PART - C **Answer any four questions (Max. 100 words)** 1. Define isothermal and adiabatic process. 2. State and explain Lami's theorem. 3. What do you mean by critical and terminal velocity? 4. Define total internal reflection. 5. State and explain the critical angle. ### PART - D **Answer any two questions (Max. 300 words)** 1. What are the advantages and disadvantages of a dimensional analysis? 2. What are the main applications of a laser? 3. State and explain Newton's law of cooling. ## CENTRAL INSTITUTE OF PETROCHEMICALS ENGINEERING & TECHNOLOGY ### HEAD OFFICE: GUINDY, CHENNAI – 600 032. #### **FIRST SEMESTER EXAMINATION – FEBRUARY - 2021** **Duration:** 2 Hours **Course:** DPMT **Subject:** Electrical & Electronics Engineering **Max. Marks:** 60 **Date:** 24.02.2021 **Time:** 10.00 a.m. to 12.00 Noon. **(DO NOT CHANGE SEQUENCE OF QUESTION NUMBER IN ANSWER SCRIPT)** ### PART - A **Answer all questions (Max. 40 words)** 1. What do you mean by streamline flow? 2. What is total internal reflection? 3. Define isothermal process. 4. Give the relation between wavelength and frequency. 5. Mention the four uses of lasers in industries. 6. Define Young's modulus and give its unit. 7. What is scalar and vector quantity? 8. What is Newton's law of cooling? 9. Define the surface tension and angle of contact. 10. i) No moving object can be stopped without applying ii) The force of attraction between molecules of different substances ### PART - B **Answer any eight questions (Max. 100 words)** 1. What are rectangular components of a vector? State and explain the triangle law of vector addition. 2. Define and derive the formula for the bulk modulus of elasticity. 3. What is projectile motion? Drive the expression for the range of flight of a projectile. 4. What is dimensional equation? Write the two uses of dimensional analysis with examples. 5. What is surface energy? Explain the relation between surface tension and surface energy. 6. Describe the construction and working principle of the ruby laser. 7. Drive the relation between angular velocity, angular acceleration to the linear velocity and linear acceleration. 8. Briefly explain the modes of heat transfer. 9. What is the abbreviation of SI? Write down the SI units of all fundamental quantities. 10. What is terminal velocity? Derive the formula for it. ## CENTRAL INSTITUTE OF PETROCHEMICALS ENGINEERING & TECHNOLOGY ### HEAD OFFICE: GUINDY, CHENNAI - 600 032. ### ACADEMIC CELL #### **FIRST SEMESTER EXAMINATION – JANUARY - 2023** **Duration:** 3 Hours **Course:** DPMT **Subject:** Workshop Mathematics **Max Marks:** 60 **Date:** 10.01.2023 **Time:** 02.00p.m. to 05.00 pm **(DO NOT CHANGE SEQUENCE OF QUESTION NUMBER IN ANSWER SCRIPT)** ### PART - A **Answer all questions** 1. A quadratic equation ax² + bx + c = 0 has no real roots if - (a) b² - 4ac > 0 - (b) b² - 4ac = 0 - (c) b² - 4ac < 0 - (d) b² ≠ 4ac 2. The equation x² + 1 = 2x³ is a - (a) Linear equation - (b) Quadratic equation - (c) Cubic equation - (d) None of these 3. The quadratic equation x² -4x + 4 = 0 has - (a) Two equal roots - (b) Two real and unequal roots - (c) No real roots - (d) None of these 4. The quadratic formula to find the roots of a quadratic equation ax² + bx + c = 0 is given by: - (a) x = - (b) x = - (c) x = - (d) = 5. 1/√2 is equal to - (a) 1 - (b) 2 - (c) 5 - √2 - (d) None of these 6. Evaluate 10% of 60 + 15% of 80. - (a) 5 - (b) 6 - (c) 15 - (d) 18 7. If n is a positive integer, then the number of terms in the *expansion* of (x + y)^n is: - (a) n - (b) n + 1 - (c) n + 2 - (d) None of these 8. The sum of the binomial coefficients in the expansion of (x + y)^n is - (a) 4 - (b) 8 - (c) 16 - (d) 32 9. 1 cm is equal to - (a) 1 - (b) 0 - (c) n - (d) None of these 10. If the slope of a straight line is 1, then the slope of the line perpendicular to it, is equal to - (a) 1 - (b) -1 - (c) 2 - (d) -2 11. Which of the following equations represent a circle? - (a) x² + y² + 1 = 0 - (b) x² + 2y² + 2x + 2y + 1 = 0 - (c) 2x² + y² + 2x + 2y + 1 = 0 - (d) x² + y² + 2xy + 2y + 1 = 0 12. The center of the circle (x - 2)² + (y + 3)² = 4 is: - (a) (2, 3) - (b) (2, -3) - (c) (-2, 3) - (d) (-2, -3) 13. 180º is equal to ____ radians - (a) 2 - (b)π - (c) π - (d) 2π 14. sin² 90º + cos² 90º = - (a) 1 - (b) -1 - (c) 0 - (d) 2 15. cos (90º + A) is equal to - (a) sin A - (b) -sin A - (c) cos A - (d) -cos A 16. The sum of the roots of a quadratic equation of the form ax^2 + bx + c = 0 is: 17. If the product of the roots of the quadratic equation x² + 8x + k = 0 is 4, the value of k is 18. If the radius of a circle is 5 cm, then the diameter is ____ cm. 19. If two straight lines are perpendicular to each other, then the product of their slopes is equal to 20. (180)º = 21. If two straight lines are parallel, then their slopes are equal (True/False) 22. The maximum number of roots for a quadratic equation is 2 (True/False) 23. A quadratic equation dx² + hx + 4 = 0 has equal roots, then a > 0. (True/False) 24. The diameter divides the circle into two equal parts, each part is called Semicircle (True/False) 25. sin (-A) = sin (A) (True/False) 26. Area of the circle of radius 4 cm. is 27. sin (A + B) = 28. cos (A + B) = 29. 1 + tan² A = 30. sin² A + cos² A = ### PART - B **Answer all questions (Max. 40 words)** 1. Find the value of cos 90º + sin 90º. 2. Determine the value of p for which the quadratic equation x² + 2x + p = 0 has equal roots. 3. Find the intercepts of the line 2x + 4y = 8. 4. If the circumference of a circle is 4π cm, then find the radius of the circle. ### PART - C **Answer any four questions (Max. 100 words)** 1. Find the value of sin (75º). 2. Find the combined equation of the straight lines whose separate equations are x + y + 4 = 0 and x + 2y - 4 = 0. 3. Find the 4th term in the expansion of (x + 2y)⁶. 4. Solve: x² + 6x + 6 = 0 by using the quadratic formula. 5. If the equation of the circle is x² + y² + 4x + 4y + 20 = 0, then find the radius and center of the circle. ### PART - D **Answer any two questions (Max. 300 words)** 1. The area of the circle is 16 square units. If the center of the circle is (1, 2), then find the equation of the circle. 2. Find the middle term in the expansion of (2x + 3y)⁸. 3. If A, B are acute angles such that sin A = 3/5, cos B = 4/5, find cos (A + B). ## CENTRAL INSTITUTE OF PETROCHEMICALS ENGINEERING & TECHNOLOGY ### HEAD OFFICE: GUINDY, CHENNAI – 600 032. ### ACADEMIC CELL #### **FIRST SEMESTER EXAMINATION - FEBRUARY - 2022** **Duration:** 3 Hours **Course:** DPMT **Subject:** Electrical & Electronics Engineering **Max Marks:** 60 **Date:** 17.02.2022 **Time:** 02.00 p.m. to 04.00 p.m. **(DO NOT CHANGE SEQUENCE OF QUESTION NUMBER IN ANSWER SCRIPT)** ### PART - A **Answer all questions (Max. 40 words)** 1. What is intrinsic Semiconductor? 2. Define the terms 'Frequency' & 'Amplitude'. 3. What are the factors affecting the resistance? 4. Why is an auto transformer not used as a distribution transformer? 5. What is transformer ratio? 6. Explain how you will change the direction of rotation of a D.C. Motor. 7. What is core loss? What is its significance in electric machine? 8. State the advantages of bridge rectifier. 9. Define 'Collector' & 'Base'. 10. What is Commutator? ### PART - B **Answer any eight questions (Max. 100 words)** 1. Derive EMF equation of Transformer. 2. Explain working of bridge rectifier with neat and clean diagram. 3. Draw and explain the construction of the D.C Machine. 4. Explain the construction and working of 3 point starter with a clean diagram. 5. Differentiate between N-type & P-type Semiconductor. 6. Differentiate between overhead distribution and underground distribution system. 7. What are the advantages of auto transformer over ordinary transformer? 8. Mention the properties of oil used in transformers and what are the properties of an ideal transformer? 9. Explain Faraday's first law of electromagnetic induction. 10. Differentiate between Series and Parallel Connection of Resistance. ## CENTRAL INSTITUTE OF PETROCHEMICALS ENGINEERING & TECHNOLOGY ### HEAD OFFICE: GUINDY, CHENNAI – 600 032. ### ACADEMIC CELL #### **FIRST SEMESTER EXAMINATION – FEBRUARY - 2021** **Duration:** 2 Hours **Course:** DPMT **Subject:** Electrical & Electronics Engineering **Max. Marks:** 60 **Date:** 25.02.2021 **Time:** 10.00 a.m. to 12.00 Noon. **(DO NOT CHANGE SEQUENCE OF QUESTION NUMBER IN ANSWER SCRIPT)** ### PART - A **Answer all questions (Max. 40 words)** 1. What are the difference between a DC amp and an AC amp, in terms of frequency as well as, flow of electrons? 2. How does mmf and emf generated in magnetic and electrical circuit? 3. Explain the significance of back EMF in dc motor? 4. Write down few application of PT? 5. Explain the difference between NPN and PNP transistor? 6. What are the two types of transformer, depending upon the position of the primary and secondary coils on the core? 7. What is the purpose of a bridge rectifier? 8. Write down two major hazards of electricity and how to prevent it? 9. Explain majority and minority charge carriers in 'n' type semiconductor? 10. Write down the Boolean expression and uses of NOT gate? ### PART - B **Answer any eight questions (Max. 100 words)** 1. Describe the construction of 4-pole dc machine with a diagram? 2. Develop the emf equation of the transformer and from that develop the relation between turns and voltage of the two sides of the winding. 3. Explain Faraday's 1st and 2nd law of electromagnetic induction and give a practical example of electromagnetic induction. 4. How does half wave & full wave rectifier works, explain using input and output waveform? 5. Explain the difference between conductor, insulator and semiconductor on the basis of the energy band. 6. Write down the truth table, Boolean expression, application and symbol of OR gate, XNOR gate, and NAND gate. 7. Describe the types, application and corresponding winding connections of dc motor based on characteristics. 8. Explain using a single line diagram, how power is transferred from generating station to distribution substation? 9. Short Notes on a) MCB b) Servo motor c) Diode d) Uses of Star and Delta connections e) Energy Meter 10. What is the main function of a capacitor in a single phase motor? What are the safety rules in an electrical workshop? ## CENTRAL INSTITUTE OF PETROCHEMICALS ENGINEERING & TECHNOLOGY ### HEAD OFFICE: GUINDY, CHENNAI – 600 032. ### ACADEMIC CELL #### **FIRST SEMESTER EXAMINATION - FEBRUARY - 2022** **Duration:** 3 Hours **Course:** DPMT **Subject:** Environmental Sciences **Max. Marks:** 60 **Date:** 18.02.2022 **Time: 02:00 p.m. to 04.00 p.m.** **(DO NOT CHANGE SEQUENCE OF QUESTION NUMBER IN ANSWER SCRIPT)** ### PART - A **Answer all questions (Max. 40 words)** 1. Why Environmental studies are important for Engineers? 2. What are the components of Environment? 3. What are the functions of Ecosystem? 4. How can we conserve Water Resources? 5. Explain Sustainable Agriculture. 6. Explain Conventional and Non-Conventional energy sources with their example. 7. What are the advantages of Wind Energy? 8. How can we minimize Air Pollution? 9. Explain Thermal Pollution. 10. Explain Disaster Management Cycle. ### PART - B **Answer any eight questions (Max. 100 words)** 1. Write a short note on the importance of environmental Science to our Society. 2. Write a short note on the importance of an Ecosystem. 3. Explain Forest resources & effects of Deforestation. 4. Explain Green Revolution. 5. Write a short note on Solar Energy & its application. 6. Explain the merits & demerits of Nuclear Energy. 7. Write a short note on Global Warming. 8. Explain Ozone-Layer Depletion (Ozone hole). 9. What are the roles of NGOs in Environmental Protection? 10. Explain Air (Prevention and Control of pollution) Act, 1981. ## CENTRAL INSTITUTE OF PLASTICS ENGINEERING & TECHNOLOGY ### HEAD OFFICE: GUINDY, CHENNAI – 600 032. ### ACADEMIC CELL #### **FIRST SEMESTER EXAMINATION-JANUARY - 2023** **Duration:** 3 Hours **Course:** DPMT **Subject:** Workshop Mathematics **Max. Marks:** 60 **Date:** 23.12.2019 **Time:** 02.00 p.m. to 05.00 p.m. ( **DO NOT CHANGE SEQUENCE OF QUESTION NUMBER IN ANSWER SCRIPT**) ### PART - A **Answer all questions** 1. If b² - 4ac = 0, then the roots of ax² + bx + c = 0 are - (a) equal - (b) imaginary - (c) irrational - (d) rational 2. If roots of x² - 5x + a = 0 are equal, then a = - (a) 25/5 - (b) ±25/4 - (c) 25/4 - (d) None of Above 3. If Sin A = ½, Cos A = √3/2, then Sin 2A = - (a) √3 / 2 - (b) 4 - (c) 1 - (d) None of These 4. Find the value of Cos A – Sin A - (a) √3 / 2 - (b) Cos A - (c) Sin A - (d) Cos 2A 5. Cot (90º + θ) = - (a) Sec θ - (b) –Tan θ - (c) Cosec θ - (d) Cot θ 6. Find ⁴C₂ = - (a) 6 - (b) 5 - (c) 4 - (d) 3 7. The sum of the coefficients in the expansion of (1 - x)¹⁰ is - (a) 0 - (b) 1 - (c) 100 - (d) 1024 8. If the two straight lines are parallel. Then their slopes are: - (a) equal - (b) not equal - (c) zero - (d) None of these 9. Write slope-point formula having slope *m* and passing through (x₁, y₁) is - (a) y - y₁ = m (x - x₁) - (b) y - y₁ = (x - x₁) - (c) y + y₁ = m (x + x₁) - (d) None of these 10. If θ is the angle between the pair of straight lines ax² + 2hxy + by² + 2gx + 2fy + c = 0 then θ = - (a) tan⁻¹ - (b) tan⁻¹ - (c) tan⁻¹ - (d) None of these 11. The equation of the straight line perpendicular to the straight line 3x - 2y + 9 = 0 is of the form: - (a) 2x + 3y + k = 0 - (b) 3x + 2y + k = 0 - (c) 2x - 3y + k = 0 - (d) None of these 12. Find the center and radius of circle x² + y² + 2x - 4y + 3 = 0 - (a) (2, 2) & √3 - (b) (-1, 2) & √2 - (c) (1, 2) & 2 - (d) (2, -3) & √3 13. Find the equation of the circle if center C(0, 0) and r = 4 is - (a) x² + y² = 25 - (b) x² - y² = 16 - (c) x² + y² = 16 - (d) x² - y² = 9 14. If 2x + 3y = 0 and 3x - 2y = 0 are the equations of two diameters of a circle, then its center is: - (a) (1, -2) - (b) (2, 3) - (c) (0, 0) - (d) (-3, -2) 15. If the radius of a circle is 4cms, then the diameter is ____ cms. - (a) 2 - (b) 6 - (c) 8 - (d) 10 16. The sum of the roots of the quadratic equation x² - 6 = 0 is 17. If b² - 4ac < 0, then the roots of ax² + bx + c = 0 are 18. Write ¾ into degrees 19. Cos (A + B) = 20. If the slope of a straight line is 2/3, then the slope of the line perpendicular to it, is. 21. Sum of the binomial coefficients is 2^n (Say True or False) 22. If is equal to -1 (Say True or False) 23. Equation of two parallel straight lines differ by Constant term. (Say True or False) 24. The length of the diameter of the circle x² + y² - 6x -8y = 0 is 5 (Say True or False) 25. In formula 2πr, 'r' is considered as area. (Say True or False) 26. Write tan (A + B) = 27. Diameter of the circle = 28. Area of the circle = 29. Sin A = 30. Write π = ### PART - B **Answer all questions (Max. 40 words)** 1. If tan A = 3 and tan B = ½, prove that A - B = 2. Find the sum and product of the slope of the lines represented by 6x² - 5xy + y² = 0 3. Expand (7x - 4y)⁴ using binomial theorem 4. Define circle. ### PART - C **Answer any four questions (Max. 100 words)** 1. Prove that cos A + cos (120º +A) + cos (120º - A) = 0. 2. Find the equation of the circle if (2, -3) and (3, 1) are the extremities of a diameter. 3. Solve: 3x² - 10x - 4 = 0 using the Quadratic Formula. 4. Find the angle between the straight lines x² + 4xy + 3y² = 0. 5. If sin A = 1/3, sin B = 1/4 find sin (A + B), where A and B are acute. ### PART - D **Answer any two questions (Max. 300 words)** 1. Find the equation of the circle passing through the points (