Mathematics Part-1

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

Conic Sections (Ex – 11.3) In each of the Exercises 1 to 9, find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse. Question 1.x2/36 + y2/16 = 1 Solution:Given equation of ellipse of x2/36 + y2/16 =

Conic Sections (Ex – 11.2) In each of the following Exercises 1 to 6, find the coordinates of the focus, axis of the parabola, the equation of the directrix and the length of the latus rectum. Question 1.y2= 12x Solution:The given equation of parabola is y2 = 12x which is of the form y2 = 4ax.∴ 4a

Conic Sections (Ex – 11.1) In each of the following Exercises 1 to 5, find the equation of the circle with Question 1.center (0, 2) and radius 2 Solution:Here h = 0,k = 2 and r = 2The equation of circle is,(x-h)2 + (y- k)2 = r2∴ (x – 0)2 + (y – 2)2 = (2)2⇒ x2 + y2 + 4