Locus of a variable point P (x,y) is given by \((x^3+ y^3+3xy) = 1\) where \((x,y) ≠ (-1,-1)\) then equation of circle touching the locus of P at (-1,2) and Passing through (1,-2) is given by
(A) \((x^2+ y^2+ 2x+ y - 5) = 0\)
(B) \((x^2+ y^2+ 12x+ 6y - 5) = 0\)
(C) \((x^2+ y^2+ 4x+ 2y - 5) = 0\)
(D) \((x^2+ y^2- 4x- 2y - 5) = 0\)
The sum of the series ..................... up to n terms is
If ax + y – 16 = 0 and x + ay – 6 = 0 represents two adjacent sides of a rhombus whose diagonals intersect at (3,5) then sum of possible value of a is.
Which of the following atom/s has low ionization energy than nitrogen atom?
Select reaction(s) which will favor will forward direction
(D) None of these
Choose correct statements
(A) The Bond dissociation energy of C2 decrease on forming and increases on forming
(B) Formation of from O2 electrons is removed from gerade bonding molecular orbital.
(C) HOMO of F2 is gerade while LUMO of Cl2 is ungerade
(D) In Halogen colour intensity increase F2 to I2
Select an option having incorrect major product?
An equi – convex lens (m = 1.5) is combined with an equi concave lens (m = 1.5). The radii of curvature of all surface is the same. ( Assume the lenses)
(A) The combination behaves like a converging lens in medium of refractive index 1.4 and diverging lens in a Medium of refractive index 1.6
(B) The combination behaves like a converging lens a medium of refractive index 1.2 as well as 1.4
(C) The combination behaves like a diverging lens a medium of refractive index 1.2 as well as 1.6
(D) The combination behaves like a converging lens in medium of refractive index 1.4 and converging lens in a Medium of refractive index 1.6
A mass less inextensible String is wrapped over a cylinder of radius 20cm and mass of 2kg. it is connected to a hanging block of mass 1kg. if surface is smooth, the cylinders reaches a distance l in time t1. If the surface is suffciencently rough, the cylinders reaches the distance l in time t2. Then
In the given circuit the potential difference between a & b is 300 V. the resistors are of 100W each.
A Certain sustained ( not an ideal gas) has a PV graph as a straight line AB when subjected to an adiabatic process. if the same substance goes through goes process A B C, What is the heat given to it?
Electrostatics waves of wave length are incident on a YDSE apparatus. Both slits are same width. Here d = 3mm, D = 2m. Intensity at central maxima is , what is the intensity at a point 1mm a above maxima of order 1?
A Point source and a receiver are stationary. Source sends a wave of frequency 256Hz, which directly reaches to receivers and also after being reflected from a wall. The wall is moving at speed of 1m/s. find beat frequency (in Hz) heard by recciver. Velocity of sound = 321m/s.