Mathematical Reasoning (Ex – 14.3) Question 1.For each of the following compound statements first, identify the connecting words and then break it into component statements.(i) All rational numbers are real and all real numbers are not complex.(ii) Square of an integer is positive or negative.(iii) The sand heats up quickly in the Sun and does not cool down […]

Mathematical Reasoning (Ex – 14.2) Question 1.Write the negation of the following statements:(i) Chennai is the capital of Tamil Nadu.(ii) √2 is not a complex number.(iii) All triangles are not equilateral triangle.(iv) The number 2 is greater than 7.(v) Every natural number is an integer. Solution:(i) Negation of statement is: Chennai is not the capital of Tamil Nadu.(ii) Negation of statement is: √2 is a

Mathematical Reasoning (Ex – 14.1) Question 1.Which of the following sentences are statements? Give reasons for your answer.(i) There are 35 days in a month.(ii) Mathematics is difficult.(iii) The sum of 5 and 7 is greater than 10.(iv) The square of a number is an even number.(v) The sides of a quadrilateral have equal length.(vi) Answer this question.(vii) The product of (-1)

Limits and Derivatives (Ex – 13.2) Question 1.Find the derivative of x2 – 2 at x = 10. Solution:let f(x) = x2 – 2Differentiating (i) with respect to x, we getf'(x) = 2xAt x = 10, f'(10) = 2(10) = 20. Question 2.Find the derivative of 99x at x = 10. Solution:let f(x) = 99xDifferentiating (i) with respect to

Limits and Derivatives (Ex – 13.1) Evaluate the following limits in Exercises 1 to 22. Question 1. Solution: Question 2. Solution: Question 3. Solution: Question 4. Solution: Question 5. Solution: Question 6. Solution: Question 7. Solution: Question 8. Solution: Question 9. Solution: Question 10. Solution: Question 11. Solution: Question 12. Solution: Question 13. Solution: Question

Introduction to Three Dimensional Geometry (Ex – 12.3) Question 1.Find the coordinates of the point which divides the line segment joining the points (-2, 3, 5) and (1, -4, 6) in the ratio(i) 2 : 3 internally,(ii) 2 : 3 externally Solution:(i) Let P(x, y, z) be any point which divides the line segment joining the points A(-2,

Introduction to Three Dimensional Geometry (Ex – 12.2) Question 1.Find the distance between the following pairs of points:(i) (2, 3, 5) and (4, 3, 1)(ii) (-3, 7, 2) and (2, 4, -1)(iii) (-1, 3, -4) and (1, -3, 4)(iv) (2, -1, 3) and (-2, 1, 3) Solution: Question 2.Show that the points (-2, 3, 5), (1, 2, 3) and

Introduction to Three Dimensional Geometry (Ex – 12.1) Question 1.A point is on the x-axis. What are its y-coordinate and z-coordinate? Solution:The coordinates of any point on the x-axis will be (x, 0, 0). Thus y-coordinate and z-coordinate of the point are zero. Question 2.A point is in the XZ-plane. What can you say about

Conic Sections (Ex – 11.4) In each of the Exercises 1 to 6, find the coordinates of the foci and the vertices, eccentricity and the length of the latus rectum of the hyperbolas. Question 1.x2/16 − y2/9 = 1 Solution:Given equation of hyperbola is Question 2.y2/9 − x2/27 = 1 Solution:Given equation of hyperbola is