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Question 1.Find the equation of a circle with(i) centre at origin and radius 4.(ii) centre at (-3, -2) and radius 6.(iii) centre at (2, -3) and radius 5.(iv) centre at (-3, -3) passing through point (-3, -6).Solution:(i) The equation of a circle with centre at origin and radius ‘r’ is given by (iv) Centre of … Read more

(I) Select the correct option from the given alternatives. Question 1.If A is (5, -3) and B is a point on the X-axis such that the slope of line AB is -2, then B ≡ Question 2. Question 3.If A(1, -2), B(-2, 3) and C(2, -5) are the vertices of ΔABC, then the equation of … Read more

Question 1.Find the slope, x-intercept, y-intercept of each of the following lines, i. 2x + 3y-6 = 0 ii. 3x-y-9 = 0 iii. x + 2y = 0Solution:i. Given equation of the line is 2x + 3y – 6 = 0.Comparing this equation with ax + by + c = 0,we geta = 2, b … Read more

Question 1.Write the equation of the line:i. parallel to the X-axis and at a distance of 5 units from it and above it.ii. parallel to the Y-axis and at a distance of 5 units from it and to the left of it.iii. parallel to the X-axis and at a distance of 4 units from the … Read more

Question 1.Find the slope of each of the lines which passes through the following points:i. A(2, -1), B(4,3)ii. C(- 2,3), D(5, 7)iii. E(2,3), F(2, – 1)iv. G(7,1), H(- 3,1)Solution:i. Here, A = (2, -1) andB = (4, 3) Alternate Method:Points E and F have same x co-ordinates i.e. 2.Points E and F lie on a … Read more

Question 1.If A(1, 3) and B(2, 1) are points, find the equation of the locus of point P such that PA = PB.Solution:Let P(x, y) be any point on the required locus.Given, A(1, 3), B(2, 1) andPA = PB -2x – 6y + 10 = -4x – 2y + 5∴ 2x – 4y + 5 … Read more

(I) Select the correct option from the given alternatives. Question 1. Hint: Question 2. (a) Exactly one is defined(b) Exactly two are defined(c) Exactly three are defined(d) all four are definedAnswer:(c) Exactly three are definedHint: Question 3.If A and B are square matrices of equal order, then which one is correct among the following?(a) A … Read more

I. Select the correct option from the given alternatives. Question 1. Question 2.(a) k = -3(b) k = -1(c) k = 1(d) k = 3Answer:(b) k = -1Hint: Question 3. Answer:(b) D is independent of φ Question 4.The value of a for which the system of equations x + (a + 1)y + (a + … Read more

Question 1. Question 2.∴  = -A and A = –∴ A and AT both are skew-symmetric matrices. Question 3. Solution:From (i) and (ii), we get(2A = 2 Question 4. Solution:From (i) and (ii), we get(3A = 3 Question 5. Solution: Question 6. Solution:From (i) and (ii), we get[Note: The question has been modified.] From (i) and (ii), we … Read more

Question 1.Evaluate: Question 2. Solution:From (i) and (ii), we getAB ≠ BA Question 3. answer.Solution:From (i) and (ii), we getAB ≠ BA Question 4.Show that AB = BA, where Solution:From (i) and (ii), we getAB = BA From (i) and (ii), we getAB = BA[Note: The question has been modified.] Question 5. Solution:From (i) and … Read more