In context of the lanthanoids, which of the following statements is not correct?

The outer electron configuration of $$Gd$$ (Atomic No. $$64$$) is :

The structure of IF7 is :

The hybridization of orbitals of N atom in $$N{O}_3^{-}$$, $$N{O}_2^{+}$$ and $$N{H}_4^{+}$$ are respectively :

Among the following the maximum covalent character is shown by the compound :

The presence or absence of hydroxyl group on which carbon atom of sugar differentiates RNA and DNA ?

Let \cos \left( {\alpha + \beta } \right) = {4 \over 5} and \sin \,\,\,\left( {\alpha - \beta } \right) = {5 \over {13}}, where 0 \le \alpha ,\,\beta \le {\pi \over 4}. Then $$tan2\alpha$$ =

Let $$A$$ be a $$2\times 2$$ matrix with non-zero entries and let $$A^2=I,$$ where $$I$$ is $$2\times 2$$ identity matrix. Define $$Tr$$$$(A)=$$ sum of diagonal elements of $$A$$ and $$\left|A\right|=$$ determinant of matrix $$A$$. Statement- 1: $$Tr$$$$(A)=0$$. Statement- 2: $$\left|A\right|=1$$ .

Consider the system of linear equations; $\matrix{ {{x_1} + 2{x_2} + {x_3} = 3} \cr {2{x_1} + 3{x_2} + {x_3} = 3} \cr {3{x_1} + 5{x_2} + 2{x_3} = 1} \cr }$ The system has :

The number of $$3\times 3$$ non-singular matrices, with four entries as $$1$$ and all other entries as $$0$$, is :

Four numbers are chosen at random (without replacement) from the set $$\left\{1,2,3,....20\right\}.$$ Statement - 1: The probability that the chosen numbers when arranged in some order will form an AP is {1 \over {85}}. Statement - 2: If the four chosen numbers form an AP, then the set of all possible values of common difference is $$\left(\pm 1,\pm 2,\pm 3,\pm 4,\pm 5\right).$$

An urn contains nine balls of which three are red, four are blue and two are green. Three balls are drawn at random without replacement from the urn. The probability that the three balls have different colours is :

Let $$f:\left(-1,1\right)\to R$$ be a differentiable function with $$f\left(0\right)=-1$$ and $$f^{\prime }\left(0\right)=1$$. Let $$g\left(x\right)={\left[f\left(2f\left(x\right)+2\right)\right]}^2$$. Then $$g^{\prime }\left(0\right)=$$

Solution of the differential equation \cos x\,dy = y\left( {\sin x - y} \right)dx,\,\,0 < x <{\pi \over 2} is :

The line $$L$$ given by {x \over 5} + {y \over b} = 1 passes through the point $$\left(13,32\right)$$. The line K is parrallel to $$L$$ and has the equation {x \over c} + {y \over 3} = 1. Then the distance between $$L$$ and $$K$$ is :

Let $$s_1=\sum _{j=1}^{10}j\left(j-1\right){}^{10}{C}_j$$, $$s_2=\sum _{j=1}^{10}j.{}^{10}{C}_j$$ and $$s_3=\sum _{j=1}^{10}{j}^2.{}^{10}{C}_j.$$ Statement-1 : $$S_3=55\times 2^9$$. Statement-2 : $$S_1=90\times 2^8$$ and $$S_2=10\times 2^8$$.

If two tangents drawn from a point $$P$$ to the parabola $$y^2=4x$$ are at right angles, then the locus of $$P$$ is

Let $$p(x)$$ be a function defined on $$R$$ such that $$p^{\prime }(x)=p^{\prime }(1-x),$$ for all $$x\in \left[0,1\right],p\left(0\right)=1$$ and $$p(1)=41.$$ Then $$\underset{0}{\overset{1}{\int }}p\left(x\right)dx$$ equals :

The number of complex numbers z such that $$\left|z-1\right|=\left|z+1\right|=\left|z-i\right|$$ equals :

The circle $$x^2+y^2=4x+8y+5$$ intersects the line $$3x-4y=m$$ at two distinct points if :