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10. To reduce y ax" to a linear form a straight line is obtained by plotting : A. x against y B. x against log y C. log x against logy D.- against - 11.The gradient of the straight line obtained when: + a = 1 is reduced to a linear form is: C.- 1 A. - В. b. D. a a x+b: Pis reduced to form Y = mx + c. the values of m and c are given by: 12. The relation y a' A. m a, c = b B. m Ina, c= InbC. m = -,c = blna D. m Ina, c blna 13 M (1 2) ond N (6 0)

10. To reduce y ax" to a linear form a straight line is obtained by plotting : A. x against y B. x against log y C. log x against logy D.- against - 11.The gradient of the straight line obtained when: + a = 1 is reduced to a linear form is: C.- 1 A. - В. b. D. a a x+b: Pis reduced to form Y = mx + c. the values of m and c are given by: 12. The relation y a' A. m a, c = b B. m Ina, c= InbC. m = -,c = blna D. m Ina, c blna 13 M (1 2) ond N (6 0)

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Solve all Q10, 11, 12 explaining detailly each step

COORDINATE GEOMETRY a) MCQS: 1. Q (a1, b¡) and R(a, b2) are two points on a line segment PR. If Q is the midpoint of PR the coordinates of P are: A. (a – a3, 2b, – b;) B. (*a2 D: C. (2a1 – a3, A1+a2 b1+b2 )C. (2a1 – az. 2b1 - b2) D. (2a2 - a1, 2b - b1) | 2 2. An equation of the line L,is 3x + 4y = 5. Another line L2 passes through the point (1,2) and is perpendicular to Lq. Find the equation of L2 A. 3x – 4y = -2 Find the coordinates of a point which divides the line segment joining the points (4,1) and B. 4x – 3y = -2 C. 4x – 3y = 2 D. 3x – 4y = 2 %3D -- (7.7) in the ratio 2:1 A. (6.5) В. (5.5) C. (5,6) D. (6,3) 4. The coordinates of the point which divides internally the line joining the points (2,4) and (- 3, 9) in the ratio 1:4 are: A. (5, 1) B. (1, 5) C. () D. () -11 -7 -1 13 3 3 2 5. M and N are points with coordinates (2, 6) and (3, 5) respectively. The coordinates of the point which divides the line segment MN externally in ratio 2: 1 are: 8 16 A. (,) B. () 16 8 D. () 6. The tangent of the acute angle between the lines 2x -y = 1 and 4x + 3y = 2 is: 5 11) C. (4, 4) 13 3 3. 2 %3D A. 2 B.-3 C.() D. ) 10 Á. 2 11/ .5. 7. Find the equation of a line through the origin which is inclined at - to the line:2x + 3y-4 = 0 A. x - y= 0 B. x – 5y 0 C. 3y +5x = 0 D. 2x + y= 0 8. The curve y = ax- x cuts the line y = 3x at right angles. The possible values of a are: IT 4 %3D 1 19 A. 4,-3 B. 3, - 3 C. -, 19 D. ww. 3' 3 9. The least distance from the origin to the curve y rx + 5 occurs when x 2. The value of the constant r is: B. - 10. To reduce y = ax" to a linear form a straight line is obtained by plotting: 5 A. --4 C. 2 D. 4 2 A. x against y B. x against log y C. log x against logy D. - against - y 11.The gradient of the straight line obtained when: "+- a 1 is reduced to a linear form is: y 1 A. – 2 12. The relation y = a*Dis reduced to form Y = mx + c. the values of m and c are given by: 1 В. - C.- b. D. - a a a a x+b: A. m = a, c = b B. m Ina, c= InbC. m 13. M (1, -2) and N (6, 8) are two points in the X - y plane. The equation of the locus of the b ,c = blna D. m Ina, c = blna a point P which moves in such a way that MP:NP = 3:2 is: A. x+y + 2x+ 16y- 5 0 C. 3x² + 3:-- x+ 24y – 5 = 0 D. 3x + 3y“ – 20x – 36y + 95 = 0 B. x + y - 10x -- 20y + 45 = 0 64
Transcribed Image Text:COORDINATE GEOMETRY a) MCQS: 1. Q (a1, b¡) and R(a, b2) are two points on a line segment PR. If Q is the midpoint of PR the coordinates of P are: A. (a – a3, 2b, – b;) B. (*a2 D: C. (2a1 – a3, A1+a2 b1+b2 )C. (2a1 – az. 2b1 - b2) D. (2a2 - a1, 2b - b1) | 2 2. An equation of the line L,is 3x + 4y = 5. Another line L2 passes through the point (1,2) and is perpendicular to Lq. Find the equation of L2 A. 3x – 4y = -2 Find the coordinates of a point which divides the line segment joining the points (4,1) and B. 4x – 3y = -2 C. 4x – 3y = 2 D. 3x – 4y = 2 %3D -- (7.7) in the ratio 2:1 A. (6.5) В. (5.5) C. (5,6) D. (6,3) 4. The coordinates of the point which divides internally the line joining the points (2,4) and (- 3, 9) in the ratio 1:4 are: A. (5, 1) B. (1, 5) C. () D. () -11 -7 -1 13 3 3 2 5. M and N are points with coordinates (2, 6) and (3, 5) respectively. The coordinates of the point which divides the line segment MN externally in ratio 2: 1 are: 8 16 A. (,) B. () 16 8 D. () 6. The tangent of the acute angle between the lines 2x -y = 1 and 4x + 3y = 2 is: 5 11) C. (4, 4) 13 3 3. 2 %3D A. 2 B.-3 C.() D. ) 10 Á. 2 11/ .5. 7. Find the equation of a line through the origin which is inclined at - to the line:2x + 3y-4 = 0 A. x - y= 0 B. x – 5y 0 C. 3y +5x = 0 D. 2x + y= 0 8. The curve y = ax- x cuts the line y = 3x at right angles. The possible values of a are: IT 4 %3D 1 19 A. 4,-3 B. 3, - 3 C. -, 19 D. ww. 3' 3 9. The least distance from the origin to the curve y rx + 5 occurs when x 2. The value of the constant r is: B. - 10. To reduce y = ax" to a linear form a straight line is obtained by plotting: 5 A. --4 C. 2 D. 4 2 A. x against y B. x against log y C. log x against logy D. - against - y 11.The gradient of the straight line obtained when: "+- a 1 is reduced to a linear form is: y 1 A. – 2 12. The relation y = a*Dis reduced to form Y = mx + c. the values of m and c are given by: 1 В. - C.- b. D. - a a a a x+b: A. m = a, c = b B. m Ina, c= InbC. m 13. M (1, -2) and N (6, 8) are two points in the X - y plane. The equation of the locus of the b ,c = blna D. m Ina, c = blna a point P which moves in such a way that MP:NP = 3:2 is: A. x+y + 2x+ 16y- 5 0 C. 3x² + 3:-- x+ 24y – 5 = 0 D. 3x + 3y“ – 20x – 36y + 95 = 0 B. x + y - 10x -- 20y + 45 = 0 64
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