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Consider the parabola x2 = 4y and circle x2 + (y – 5)2 = r2 (r > 0). Given that the circle touches the parabola at the points P and Q. Let R be the point of intersection of tangents to parabola at P and Q and S be the ce ...
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An unknown cell balances 300 cm of wire in a potentiometer circuit, but the balance length reduces to 280 cm when a resistance of 28 ohm is added in parallel with the cell.A standard cell of emf 1.1V balances 220 cm on the sa ...
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A body moves with speed 20m/sec for 10 sec and then with 30m/sec for some distance. The average speed may be (A) 8m/sec (B) 15m/sec (C) 25m/sec (D) all of these are possible ...
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There are three coplanar parallel lines.If any p points are taken on each of the line,the maximum number of triangles with vertices at these points is a.3p2(p-1) b.3p2(p-1)+1 c.p2(4p-3) d.None of these ...
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A uniform chain of mass m hangs from a light pulley,with unequal lengths of the chain hanging from the two sides of the pulley.The force exerted by the moving chain on the pulley is (a)mg (b)>mg (c)<mg (d)either (b) or ...
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Find the number of integral values of parameter'a'for which three chords of the ellipse x2/2a2 + y2/a2 =1(other than its diameter)passing through the point P(11a,- a2/4 )are bisected by the parabola y2=4ax. ...
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A parabola is drawn touching the axis of x at the origin and having its vertex at a given distance k from the axis.Prove that the axis of the parabola always touches x2=-8k(y-2k). ...
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If the equation ax3+3bx2+3cx+d=0 has two equal roots,show that it must be equal to bc-ad/2(ac-b2) . ...
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C1 and C2 be two concentric circles.The radius of C2 being twice that of C1.From a point P on C2 tangents PA and PB are drawn to C1.Prove that the centroid of the triangle PAB lies on C1. ...
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In a triangle ABC,the coordinates of the vertex A are (4,-1). If the equations of the bisectors of angles B and C are x-1=0 and x-y-1=0 respectively.Find the coordinates of B and C and the equations of the sides AB and AC. ...
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If each pair of the following three equations x2+ax+b=0, x2+cx+d=0, x2+ex+f=0 has exactly one root in common,then show that (a+c+e)2=4(ac+ce+ea-b-d-f). ...
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Let x2/a2 + y2/b2 =1(a>b) be a given ellipse.Suppose an ellipse congruent to the given ellipse is drawn with the same centre and with the same axes such that it touches the given ellipse at the extremities of the major axi ...
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Find the equation of the largest circle with centre (1,0) that can be inscribed in the ellipse x2+4y2=16. ...
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If 'a' is a complex number such that |a|=1.Find the values of a,so that equation az2+z+1=0 has one purely imaginary root. ...
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Explain..why does O3 and NO2 show permanent dipole moment?? ...
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Among H2S,SO2,H2O which one has least bond angle and why? ...
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A small bar starts sliding down an inclined plane forming an an angle α with the horizontal.The friction coefficient depends on the distance x covered as μ=Kx where K is a constant.Find the distance covered by the bar till ...
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*Image* ...
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Two thin similar convex glass pieces are joined together front to front,with its rear portion silvered such that a sharp image is formed 0.2 m for an object at infinity.When the air between the glass pieces is replaced by wat ...
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A sample contains both H3PO4 and HIO3 along with other unknown substances.10 g of sample required 85 ml of 0.15 N NaOH during titration with phenolphthalein as indicator.A separate 10 g sample required 66ml of 0.15 N NaOH dur ...
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10 g sample of zinc was dissolved in 200 ml of 0.1 N KMnO4 solution acidified with H2SO4.The KMnO4 solution was totally discharged.It was found that a gas was produced which when allowed to react with the requisite amount of ...
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1.A square is made by joining four rods each of mass M and length L.Its moment of inertia about an axis,in its plane and passing through one of its corner is (a)6ML2 (b) 4ML2/3 (c) 8ML2/3 (d) 10ML2/3 2.A thin rod of length 4l ...
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Find the locus of the centroid of an equilateral triangle inscribed in the ellipse x2/a2 + y2/b2 =1 (Ans is (a2+3b2)x2/a2 + (3a2+b2)y2/b2 =(a2-b2)2...please give the entire working) ...
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If Cr=nCr,the sum of the series 2[( n/2 )fact)2]/nfact [C02-2C12+3C22-......(-1)n(n+1)2Cn2] where n is even integer,is (a)0 (b)(-1) n/2 .(n+1) (c)(-1)n.(n+2) (d)(-1)n.n (e)none of these Ans is (e)..however..pls provide the so ...
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The circle x2+y2+2kx=0,k belongs to R,touches the parabola y2=4x externally.Then (a)k>0 (b)k<0 (c)k>1 (d)none of these Ans is (a). i have put y2=4x in the eq.of the circle.and in the quad.of x,i put b2=4ac.i got k=-2 ...
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A body floats in complete immersed condition in water as shown as in figure.As the whole system is allowed to slide down freely along the inclined surface,the magnitude of buoyant force *Image* (a)remains unchanged (b)increas ...
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A right angled triangle ABC having right angle at C.Ca=b and CB=a moves such that the angular points A and B slide along x-axis and y-axis respectively.Find the locus of C. ...
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In the periodic table,note that for the main group elements,if the periodic group of the element is even,the monoatomic ion and the oxyanions of the element have charges that are even numbers,while if the periodic group numbe ...
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1)When burnt in air,a 12.0 g mixture of carbon and sulphur yields a mixture of CO2 and SO2,in which the number of moles of SO2 is half that of CO2.The mass of the carbon the mixture contains is (a)4.08g (b)5.14g (c)8.74g (d)1 ...
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1)When burnt in air,a 12.0 g mixture of carbon and sulphur yields a mixture of CO2 and SO2,in which the number of moles of SO2 is half that of CO2.The mass of the carbon the mixture contains is (a)4.08g (b)5.14g (c)8.74g (d)1 ...
