A tangent PT is drawn to the circle x2 + y2 = 4 at the point P(√3, 1). If a straight line L which is perpendicular to PT is a tangent to the circle (x- 3)2 + y2 = 1, then a possible equation of L is
If a point P moves so that the distance from (0,2) to P is \(\frac{1}{√2 }\) times the distance of P from (-1,0), then the locus of the point P is
Let d be the distance between the parallel lines 3x - 2y + 5 = 0 and 3x - 2y + 5 + 2√13 = 0. Let L1 = 3x - 2y + k1 = 0 (k1 > 0) and L2 = 3x - 2y + k2 = 0 (k2 > 0) be two lines that are at the distance of \(\frac{4d}{√13}\) and \(\frac{3d}{√13}\) from the line 3x - 2y + 5y = 0. Then the combined equation of the lines L1 = 0 and L2 = 0 is:
5 persons entered a lift cabin in the cellar of a 7-floor building apart from cellar. If each of the independently and with equal probability can leave the cabin at any floor out of the 7 floors beginning with the first, then the probability of all the 5 persons leaving the cabin at different floors is
If sin y = sin 3t and x = sin t, then \(\frac{dy}{dx}\) =
Which of the following does not form a buffer solution?
The ratio of lone pair of electrons to bond pair of electrons in ozone molecule is:
Ziegler-Natta Catalyst is used in the manufacture of
The aromatic compound/species with maximum number of x - electrons is
XeF4 + O2F2 → X + O2 X + H2O → Y +2HF The shape of the molecules of X and Y respectively are:
The following molecule with the structure acts as
The number of electrons with (n+1) values equal to 3,4 and 5 in an element with atomic number (z) 24 are respectively (n = principal quantum number and l = azimuthal quantum number)
Which one of the following has the same number of atoms as are in 6g of H2O
A current of 15.0 amperes is passed through a solution of CrCl2, for 45 minutes. The volume of Cl2 , (in I) obtained at the anode at 1 atm and 273 K is around (IF=96500 Cmol-1, At. wt. of Cl=35.5, R=0.082 L-atmK-1 mol-1)
Consider the following statements about the oxides of halogens A. At room temperature, OF2; is thermally stable B. Order of stability of oxides of halogens is I > Br > Cl C. I2O5 is used in the estimation of CO D. ClO2; is used as a bleaching agent The correct statements are
Arrange the following in the correct order of their reactivity towards nucleophilic addition reactions
The rate of diffusion of a gas A is √5 times more than of gas B. If the molar mass of A is x gmol-1, the molar mass of B ( in g mole-1) is
Among the following the incorrect statement about transition metals is
An alkene X on ozonolysis gives a mixture of Propan-2-one and methanal. What is X?
Match the following : List -I (Atomic number) List II (Group number and period number)
List -I (Atomic number)
List II (Group number and period number)
According to MO theory, the molecule which contain only π-Bonds between the atoms is
The formula of a metal oxide is M0.96 O1. The fractions of metal that exists as M3+and M2+ ions in that oxide are respectively
In which if the following changes there is no change in hybridization of the central atom?
Identify the correct statement about the oxidation states of group 14 elements