If \(A\) is an invertible matrix of order 3 and the determinant of \(A\) is 9, then the determinant of \(A^{-1}\) is :

Angle between tangents to the curve \(y=x^2-5 x+6\) at the points \((2,0)\) and \((3,0)\) is :

Match List-I with List-II

List-I	List-II
(A) \(f ( x )=| x |\)	(I) Not differentiable at \(x=-2\) only
(B) \(f(x)=|x+2|\)	(II) Not differentiable at \(x=0\) only
(C) \(f(x)=\left|x^2-4\right|\)	(III) Not differentiable at \(x=2\) only
(D) \(f(x)=|x-2|\)	(IV) Not differentiable at \(x=2,-2\) only

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Which of the following statement(s) is/are TRUE?
(A) Skew symmetric matrix of even order is always symmetric
(B) Skew symmetric matrix of odd order is non-singular
(C) Skew symmetric matrix of odd order is singular
(D) Skew symmetric matrix is always square matrix
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If \(\theta\) is the angle between two unit vectors \(\hat{a}\) and \(\hat{b}\) then \(|\hat{a}-\hat{b}|=\)

If \(\vec{a}, \vec{b}\) and \(\vec{c}\) are three vectors such that \(\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0},|\vec{a}|=7,|\vec{b}|=3\) and \(|\vec{c}|=5\), then angle between \(\vec{b}\) and \(\vec{c}\) is

If \(\mathbb{Z}\) and \(\mathbb{R}\) set of integers and set of real numbers respectively, then match List I with List II.

List - I	List - II
(A) \(5 x-3<3 x+1, x \in \mathbb{Z}\)	(I) \(x \in(-\infty,-3)\)
(B) \(3 x+17 \leq 2(1-x), x \in \mathbb{R}\)	(II) \(x \in(-\infty,-1)\)
(C) \(13 x+17<2(1-x), x \in \mathbb{R}\)	(III) \(\{\ldots,-4,-3, \ldots, 0,1\}\)
(D) \(\frac{2 x+3}{5}-2>\frac{3(x-2)}{5}, x \in \mathbb{Z}\)	(IV) \(\{\ldots,-4,-3,-2\}\)

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Identify the equation representing logistic growth of a population.

Read the passage carefully and answer the Questions
Werner in 1898, propounded his theory of coordination compounds. In coordination compounds metals show two types of linkages (valences)-primary and secondary. The primary valences are normally ionisable and are satisfied by negative ions. The secondary valences are non-ionisable. These are satisfied by neutral molecules or negative ions. The secondary valence is equal to the coordination number and is fixed for a metal. The ions or group bound by the secondary linkages to the metal have characteristic spatial arrangements corresponding to the different coordination numbers. Both double salts as well as complexes are formed by the combination of two or more stable compounds in stoichiometric ratio. However, they differ in the fact that double salts such as carnallite, Mohr's salt, potash alum etc. dissociate into simple ions completely when dissolved in water. But complex ions do not dissociate completely into simple ions.
When \(1 mol CrCl _3 \cdot 6 H _2 O\) is treated with excess of \(AgNO _3, 3 mol\) of AgCl are obtained. The formula of the complex is:

Nowadays, biofertilisers are available in the market. Select the correct statements regarding biofertilisers given below:
(A) Biofertilisers increase the soil fertility.
(B) Biofertilisers kill the pathogenic microbes
(C) Biofertilisers increase the iron content in the soil
(D) Biofertilisers increase the crop production.
(E) Excess use of biofertilisers causes water and soil pollution.
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Monochromatic lights of wavelengths \(6 2 0 ~ n m\) and \(6 2 6 ~ n m\), respectively are used to study diffraction at a single slit of aperture \(0 . 7 ~ m m\). The distance between the slit and the screen is 1.8 m . The separation between the positions of the first maxima of the diffraction pattern obtained in the two cases is

Arrange the following compounds towards increasing \(S_{N}2\) reaction?
(A) n-Butyl bromide
(B) Isobutyl bromide
(C) Tertiary butyl bromide
(D) Sec-Butyl bromide
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The relation R in the set \(\mathbb{R}\) of real numbers defined as \(R = \{(a, b) : a \le b^2\}\) is: