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1. If the normal to the curve y= f(x) at x=0 be given by the equation 3x - y + 3 = 0 ,then the value of lim x→0 [x2/{ f(x2) 5 f(4x2) + 4f(7x2)}-1 ] is ???? 2.The tangent to the graph of the function y=f(x) at the point with ...
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If PQ is a double ordinate of the Hyperbola x2/a2 - y2/b2 = 1 such that OPQ is an equilateral triangle ,O being the centre of the hyperbola..Then the range of eccentricity 'e' of the hyperbola is???? ...
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A thin slice is cut out of glass cylinder along a plane parallel to its axis ..The slice is placed on a flat plate (just as a bowl is placed on a table)..the observed interference fringes from this combination shall be??????? ...
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Consider a usual set-up of Young's Double Slit Experiment with slits of equal intensity. Take 'O' as origin and Y-axis as the screen..If the average intensity between y1 = -(λ.D)/(4d) and y2 = +(λ.D)/(4d) equals 'n' times t ...
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A point source 'S' is placed at a height 'h' from the bottom of a vessel of height 'H'(where h is greater than H)..The vessel is polished at the base ..Water is gradually filled in the vessel at a constant rate of α m3/s. Th ...
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Two thin convex lenses of focal lengths f1 and f2 are separated by a horizontal distance 'd' ( where f1 and f2 are greater than 'd') and their centres are displaced by a vertical separation 'δ'...Taking the origin of co-ordi ...
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Find the locus of the intersection of two normals to the ellipse x2/a2 + y2/b2=1 which are perpendicular to each other?????? ...
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The minimum distance of the centre of the ellipse x2/16 + y2/9 = 1 from the chord of contact of mutually perpendicular tangents of the ellipse is????? ...
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ABC is an equilateral triangle such that the vertices B and C lie in two parallel lines at a distance 6.if A lies between the parallel lines at a distance 4 from one of them then find the length of the side of the equilateral ...
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The long straight wire carrying a constant current 'i' is placed distance 'd' above a metal bar of length 'l' which is moving at constant velocity V in the horizontal direction .Calculate the E.M.F induced in the bar? ...
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Prove that the lines joining the middle points of opposite sides of a quadrilateral and the line joining the middle points of its diagonals meet in a point and bisect one another.. ...
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A,B,C,D....... are 'n' points in a plane whose coordinates are (x1,y1),(x2,y2),(x3,y3)..........AB is bisected in the point G1..G1C is divided at G2 in the ratio 1:2 ..G2D is divided at G3 in the ratio 1:3..G3E at G4 in the r ...
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Limn→ ∞ [ n2 . ∫ ( tan-1 nx)/( sin-1 nx) dx Integration upper limit:- ( 1/n ) Integration lower limit:- { (1+ n ) / n } ...
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41. The value of ∫ {x .tanx . secx }/(tanx-x)2 In the answer key answer is given as A...whereas i think it should be B???????????? ...
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1. Why does 2-dimethyl sulphonium butane in a base( ethoxide in ethanol) produces 74% 1-butene (hofmann) and 26% 2-butene (Saytzeff) ?????????????? 2. Why does 2- trimethyl ammonium butane in base(hydroxide in water) produces ...
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1. ∫ (cos 5x +cos 4x) / (1- 2 cos 3x ) dx 2. ∫ ( cos3 x ) . x. elog(sin x) .dx 3. ∫ ( x + ( x 2 ) + 2. x1/6 ) / [ x. { 1+ x } ] ...
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*Image* ...
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∫ x.tan x . dx ...
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*Image* ...
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*Image* Find the foce of attraction between the 2 charges??????? ...
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Given:- k = lim (x→ ∞) [ Σ(k=1 to k=1000){ x + k} m ] / [ x m + 10 1000 ] where m > 101. ...
