
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 ...

*Image* ...

∫dx/sin2x+tan2x ...

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. ...

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???? ...

\hspace{16}\bf{(1)\;\;}$ Total no. of real solution in $\bf{2^x = x^2}$\\\\\\ $\bf{(2)\;\;}$ Total no. of real solution in $\bf{2^x = 1+x^2}$\\\\\\ $\bf{(3)\;\;}$ Total no. of real solution in $\bf{2^x+3^x+4^x+5^x = 10x+4}$\ ...

Find till infinity: 1  n^2 + {n^2(n^21^2)}/(2!)^2  {n^2(n^21^2)(n^22^2)}/(3!)^2................................ to infinity,where n belongs to N. ...

\hspace{16}\bf{(1)\;\; \int\sqrt{a+\sqrt{b+\sqrt{x}}}\; dx}$\\\\\\ $\bf{(2)\;\;\int \sqrt{1+2\sqrt{xx^2}}\;dx}$ ...

If G b the centroid of a triangle ABC n O b any other point then prove that : 1.) AB2+ BC2+ CA2 ≡ 3( GA2+ GB2+ GC2) 2.)OA 2+ OB 2+ OC 2 = GA 2+ GB 2+ GC 2+ 3GO 2 ...

\text{1)Evaluate:} a)\lim_{n\rightarrow \infty}\frac{1}{2n}\log\binom{2n}{n} b)\lim_{n\rightarrow \infty}\left[\frac{1}{a+n}+\frac{1}{2a+n}+\cdots +\frac{1}{na+n}\right] \text{2)Let } a_{1}=1 \text{ and }a_{n}=n(a_{n1}+1)\ \ ...

Find the locus of the intersection of two normals to the ellipse x2/a2 + y2/b2=1 which are perpendicular to each other?????? ...

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????? ...

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+eabdf). ...

The minimum are of triangle formed by any tangent to ellipse x2/a + y2/b =1 with the coordinate axes is : ...

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 x1=0 and xy1=0 respectively.Find the coordinates of B and C and the equations of the sides AB and AC. ...

A box contains coupons labeled 1,2,3,....n. A coupon is picked at random and the number x is noted. The coupon is put back into the box and a new coupon is picked at random. The new number is y. Then the probability that one ...

\hspace{16}(1)\;\; \bf{\int_{\pi}^{\pi}\left(\sum_{k=1}^{2013}\sin (kx)\right)^2dx}$\\\\\\ $(2)\;\; \bf{\int_{\pi}^{\pi}\left(\sum_{k=1}^{2013}\cos (kx)\right)^2dx}$\\\\\\ ...

if x be real,prove that x^2 2xcosA +1 x^2 2xcosB +1 lies between sin^2(A/2)/sin^2(B/2) AND cos^2(A/2)/cos^2(B/2). ...

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 ...

\hspace{16}\bf{(1)\;\; \int\frac{1}{(1+x^4)^{\frac{1}{4}}}dx}$\\\\\\ $\bf{(2)\;\; \int\frac{1}{(1x^4)^{\frac{1}{4}}}dx}$\\\\\\ $\bf{(3)\;\;\int\frac{1}{(1+x^4)}dx}$\\\\\\ $\bf{(4)\;\;\int\frac{1}{(1+x^6)}dx}$ ...

Let H be the orthocentre of an acute angled triangle ABC and O be its circumcenter.Then HA+HB+HC A.is equal to HO B.is equal to 3HO C.is equal to 2HO D.is not a scalar multiple of HO in general ...

Let S={1,2,3,...,n} and A={(a,b)l1≤a,b≤n}=S X S. A subset B of A is said to be a good subset if (x,x) belongs to B for every x belonging to S. Then the number of good subsets of A is A. 1 B. 2n C.2n(n1) D.2n2 The answer ...

a2 + b2=7 a3 + b3=10 find greatest value of a+b ...

a2 + b2=7 a3 + b3=10 find greatest value of a+b ...

(AA)^2=DCBA,where A,B,C & D are distinct digits with B being odd. Find the value of D Is the Value of D a constant or variable? ...

a wire of length 25cm is bent so as to lie along the arc of a circle of did 100cm. the angle subtended at the centre by the arc is....????? a)π b)π/2 3)π/4 d)π/8 plzz...show that how u arrived at that answer.... thanks in ...

\hspace{16}\bf{\prod_{m=1}^{n1}\sin \left(\frac{m\cdot \pi}{n}\right)=} ...

\hspace{16}$Find all real polynomials $\bf{p(x)}$ such that $\bf{p(x)\cdot p(x+1)=p(x^2)\;\forall x\in \mathbb{Z}}$ ...

The maximum value M of 3x+5x9x+15x25x,as x varies over reals,satisfies A.3<M<5 B.9<M<25 C.0<M<2 D.5<M<9 ...

Find the equation of the largest circle with centre (1,0) that can be inscribed in the ellipse x2+4y2=16. ...