At the point `P(a , a^n)` on the graph of `y=x^n ,(n in N),` in the first quadrant, a normal is drawn. The normal intersects the `y-a xi s` at the point `(0, b)dot` If `("lim")_(avec0)b=1/2,` then `n` equals 1 (b) 3 (c) 2 (d) 4

At the point P(a,a^n) on the graph of y=x^n(ninN) in the first quadrant a normal is drawn . The normal Intersects the y-axis at the point (0,b). If lim_(a-0)b=1/2, then n equals

("lim")_(ntooo)1/(1+nsin^2n x) is equal to (a) -1 (b) 0 (c) 1 (d) oo

P(t_1) and Q(t_2) are the point t_1a n dt_2 on the parabola y^2=4a x . The normals at Pa n dQ meet on the parabola. Show that the middle point P Q lies on the parabola y^2=2a(x+2a)dot

A line is drawn form A(-2,0) to intersect the curve y^2=4x at Pa n dQ in the first quadrant such that 1/(A P)+1/(A Q) sqrt(3) (b) sqrt(2) (d) >1/(sqrt(3))

In a geometric series, the first term is a and common ratio is rdot If S_n denotes the sum of the terms and U_n=sum_(n=1)^n S_n ,then r S_n+(1-r)U_n equals a. 0 b. n c. n a d. n a r

Straight lines are drawn by joining m points on a straight line of n points on another line. Then excluding the given points, the number of point of intersections of the lines drawn is (no tow lines drawn are parallel and no these lines are concurrent). a. 4m n(m-1)(n-1) b. 1/2m n(m-1)(n-1) c. 1/2m^2n^2 d. 1/4m^2n^2

The n t h derivative of the function f(x)=1/(1-x^2)[w h e r ex in (-1,1)] at the point x=0 where n is even is (a) 0 (b) n ! (c) n^n C_2 (d) 2^n C_2

A tangent at a point on the circle x^2+y^2=a^2 intersects a concentric circle C at two points Pa n dQ . The tangents to the circle X at Pa n dQ meet at a point on the circle x^2+y^2=b^2dot Then the equation of the circle is (a) x^2+y^2=a b (b) x^2+y^2=(a-b)^2 (c) x^2+y^2=(a+b)^2 (d) x^2+y^2=a^2+b^2

If y=a x^(n)+b x^(-n) ,then x^2(d^2y)/(dx^2) is equal to

If the sub-normal at any point on y=a^(1-n)x^n is of constant length, then find the value of ndot