www.sakshieducation.com SR. INTER MATHEMATICS-IIB SECTION - I Answer the following questions:- 10 x 2 = 20M 1) If the length of the tangent from (2,5) to the circle x 2 2) Obtain the parametric equation of the circle x 3 3) Show that the angle between the circles x 2 4) If 1 x log x log log x 7) Evaluate e x 8) Find 2 0 1 x dx cos7 x sin 2 x dx 9) 0 3 4 8 x , find the coordinates of the other dy dx 3 6 5 6y ak SECTION - II Answer any five of the following questions:5 x 4 = 20M 2 2 If the abscissa of points A,B are the roots of the equation x 2ax b 0 and ordinates of A,B are the roots of y 2 2 py q 2 0 , then find the equation of a circle for which AB is a diameter . Show that the circles x 2 y 2 8 x 2 y 8 0 and x 2 y 2 2 x 6 y 6 0 touch each other and find the point of contact Find the length of major axis, minor axis, latus rectum, eccentricity, coordinates of center, foci and the equation of directorix of the ellipse 4 x 2 y 2 8 x 2 y 1 0 If P is a point of the ellipse w 14) 37 , then find k. 8 . ax ay is . 0 is 2 .s 13) dx on 1, d2y Find order and degree of dx 2 w 12) y2 1 x log x dx x 2 II) 11) a2 , x2 1 , 2 is one extremity of a focal chord of the parabola y 2 2 extremity. Define rectangular hyperbola and find its eccentricity 6) 10) y 4 2 sh ie du ca t 5) y2 2 y 2 5x 4 y k io n. co m I) x a2 y2 b2 1, whose foci S and S ' then show that SP S ' P 2a w (constant) 15) 16) 17) Find the equations of the tangents to the hyperbola 3x 2 4 y 2 12 which are Perpendicular to the line y=x-7 Find the area enclosed between the curves y 2 dy Solve y sec x tan x dx 4 x and x 2 4y www.sakshieducation.com www.sakshieducation.com 20) 21) SECTION – III Answer any five of the following questions: 5 x 7 = 35 M Find the value of ‘C’ if the points (2,0), (0,1), (4,5) and (0,C) are concylic Find the equation of a circle which passes through the points (4,1), (6,5) and having centre on 4 x 3 y 24 0 Derive the equation of parabola y 2 4ax in standard form 2sin x 3cos x 4 Evaluate dx 3sin x 4cos x 5 22) Obtain reduction formula for I n 23) Show that x dx log sin x cos x 2 2 Solve 2 x y 3 dx 2 y x 1 dy 0 2 , and also evaluate 2 1 w w w .s ak sh ie du ca t 24) 2 sin n x.dx n io n. co m III) 18) 19) www.sakshieducation.com sin 6 x.dx