A few electric field lines for a system of two charges Q1 and Q2 fixes at two different points on the x-axis are shown in the figure. These lines suggest that
Let P and Q be distinct points on the parabola y2=2x such that a circle with PQ as diameter passes through the vertex O of the parabola. If P lies in the first quadrant and the area of the triangle ΔOPQ is 32 , then which of the following is (are) the coordinates of P?
Let Pbe a point in the first octant, whose image Qin the plane x+y=3(that is, the line segment PQis perpendicular to the plane x+y=3and the mid-point of PQlies in the plane x+y=3)lies on the z-axis. Let the distance of Pfrom the x-axis be 5. If Ris the image of Pin the xy-plane, then the length of PRis _______.
Let m be the smallest positive integer such that the coefficient of x2 in the expansion of (1+x)2+(1+x)3+(1+x)4+……..+(1+x)49+(1+mx)50 is (3n+1).51C3 for some positive integer n. Then the value of n is
A solution curve of the differential equation (x2+xy+4x+2y+4)(dxdy)−y2=0 passes through the point (1,3) Then the solution curve is
Let f:R0,1 be a continuous function. Then, which of the following function (s) has (have) the value zero at some point in the interval (0,1)? ex−∫0xf(t)sintdt (b) f(x)+∫02πf(t)sintdt(c)x−∫02π−xf(t)costdt (d) x9−f(x)