Class 11 chapters 9, 10, 11
- 1. 1 Class – XI (Chapters 9, 10,11) Subject: Mathematics 1. Findthe centerand radiusof the circle 2x2 +2y2 -x=0 2. Find the angle between x-axis and the line joining the points (3,-1) and (4,-2) 3. If the sumto n termsof an A.P.if nP+1/2 n(n-1)Q,where Pand Q are constants,findthe commondifference. 4. The line throughthe points(h,3) and(4,1) intersectsthe line 7x-9y-19=0at rightangle.Findthe value of h. 5. Findthe sum to n termsof the series: 1 1×2 + 1 2×3 + 1 3×4 + ⋯ 6. Determine the equation of line through the point (-4, -3) and parallel to x – axis. 7. Findthe equationof the hyperbolawhere foci are (0, ±12) and the lengthof latusrectumis 36. 8. Findthe value of 𝜃 and p if the equationxcos𝜃 +ysin𝜃=pisthe normal form of the line √3x+y+2=0 9. If a( 1 𝑏 + 1 𝑐 ) , b( 1 𝑐 + 1 𝑎 ),c( 1 𝑎 + 1 𝑏 ) are in A.P.prove thata, b, c are in A.P. 10. If S be the sum , Pthe productand R the sum of the reciprocalsof nterms of a G.P. Prove that: ( 𝑺 𝑹 ) 𝒏 = 𝑷 𝟐 . 11. Showthat the product of perpendicularsonthe line 𝒙 𝒂 𝒄𝒐𝒔 𝜽 + 𝒚 𝒃 𝒔𝒊𝒏 𝜽 = 𝟏fromthe points (±√𝒂 𝟐 − 𝒃 𝟐 ,𝟎) is b2 . 12. A rod of length12cm moveswithitsendsalwaystouchingthe coordinate axes.Determine the equationof locusof PointP onrod, whichis3cm fromthe endin contact withx-axis. 13. If p and p' be the perpendicular from the origin upon the straight lines x secθ + y cosecθ = a and x cosθ - y sinθ = a cos 2θ. Prove that 4p2 +p'2 = a2 . 14. A line is such that its segment between the lines 5x-y+4=0 and 3x+4y-4=0 is bisected at the point (1,5). Obtainits equation 15. Referredtoitsprincipal axesasaxesof coordinatesfindthe equationof the hyperbolawhosefoci are at (𝟎, ± √ 𝟏𝟎) and whichpassesthroughthe point(2,3). 16. Findthe equationof anellipse whose axes lie alongx- axisandwhichpassesthrough(4,3) and(6, 2). 17. Findthe equationof the circle whichpassesthroughthe points(7,1), (-2,4) and (5, 5). Findalsothe coordinatesof itscentre and radius. 18. Findthe equationof a line drawnperpendiculartothe line 𝒙 𝟒 + 𝒚 𝟔 = 𝟏throughthe pointwhere it meets the y – axis. 19. Two lines passing through the point (2, 3) intersect each other at an angle of 60o . If slope of one line is 2, find the equation of the other line. 20. If a and b are the rootsof x2 – 3x + p = 0 and c , d are the roots x2 – 12x + q = 0, where a,b, c, d form a G.P.Prove that (q+ p) : (q – p) = 17 : 15. 21. If 𝑎+𝑏𝑥 𝑎−𝑏𝑥 = 𝑏+𝑐𝑥 𝑏−𝑐𝑥 = 𝑐+𝑑𝑥 𝑐−𝑑𝑥 (𝑥 ≠ 0) , then show that a, b, c and d are in G.P. 22. The sum of first three of a G.P. is 16 and the sum of the next three terms is 128. Find the sum of n terms of the G.P. 23. Find the equation of the straight line which passes through the point (2, -3)and the point of intersection of the lines x + y + 4 = 0 and 3x – y – 8 = 0. 24. Prove that the radii of the circles x2 + y2 = 1, x2 + y2 – 2x - 6y - 6 = 0 and x2 + y2 – 4x - 12y - 9 = 0 are in A.P. 25. Find the equation of the circle concentric with the circle 2x2 + 2y2 + 8x + 12y – 39 = 0 and having its area equalto 16π square units. 26. If x = 1 + a + a2 + a3 + ............... ∞,where | 𝑎| < 1 and y = 1+ b + b2 + b3 + ............... ∞,where | 𝑏| < 1 . Prove that 1 + ab + a2 b2 + ............... ∞ = 𝑥𝑦 𝑥+𝑦−1 .