______ metal generally occurs in free state.

Up to which element, the Law of Octaves was found applicable?

\(\mathrm{C}-\mathrm{Cl}\) bond of chlorobenzene in comparison to \(\mathrm{C}-\mathrm{Cl}\) bond of methyl chloride is:

The number of statement's, which are correct with respect to the compression of carbon dioxide from point (a) in the Andrews isotherm from the following is____

A. Carbon dioxide remains as a gas upto point (b)

B. Liquid carbon dioxide appears at point (c)

C. Liquid and gaseous carbon dioxide coexist between points (b) and (c)

D. As the volume decreases from (b) to (c), the amount of liquid decreases

If the wavelength for an electron emitted from \(\mathrm{H}\)-atom is \(3.3 \times 10^{-10} \mathrm{~m}\), then energy absorbed by the electron in its ground state compared to minimum energy required for its escape from the atom, is times. (Nearest integer)

[Given : \(\mathrm{h}=6.626 \times 10^{-34} \mathrm{~J} \mathrm{~s}\) ]

Mass of electron \(=9.1 \times 10^{-31} \mathrm{~kg}\)

Elements of group \(13\) are part of which of the following block of elements?

Ammonium chloride crystallizes in a body centred cubic lattice with edge length of unit cell of 390 pm. If the size of chloride ion is 180 pm, the size of ammonium ion would be:

Choose the correct answer. A thermodynamic state function is a quantity:

The number of electrons, protons and neutrons in a species are equal to \(18\), \(16\) and \(16\) respectively. Assign the proper symbol to the species.

The co-ordination number and oxidation state of \(\mathrm{Cr}\) in \(\mathrm{K}_{3}\left[\mathrm{Cr}\left(\mathrm{C}_{2} \mathrm{O}_{4}\right)_{3}\right]\) are respectively:

\(50 \mathrm{~mL}\) of \(0.2 \mathrm{M}\) ammonia solution is treated with \(25 \mathrm{~mL}\) of \(0.2 \mathrm{MHCl}\). If \(\mathrm{pK}_{\mathrm{b}}\) of ammonia solution is 4.75 , the \(\mathrm{pH}\) of the mixture will be:

Which of the following Aldehydes is also known as formalin?

The electronic configuration of \(\mathrm{Cu}(\mathrm{II})\) is \(3 d^{9}\) whereas that of \(\mathrm{Cu}(\mathrm{I})\) is \(3 d^{10}\). Which of the following is correct?

\(40 \mathrm{~g}\) of glucose (Molar mass \(=180\) ) is mixed with \(200 \mathrm{~mL}\) of water. The freezing point of solution is ___________ K. (Nearest integer)

[Given, \(\mathrm{K}_{\mathrm{f}}=1.86 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\), density of water \(=1.00 \mathrm{gcm}^{-3}\), freezing point of water \(=273.15 \mathrm{~K}]\)

What is the name of the following compound?

\(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{COCl}\)

The \(K_{m}\) value of the enzyme is the value of the substrate concentration at which the reaction reaches to __________.

A \(2.0 \mathrm{~g}\) sample containing \(\mathrm{MnO}_2\) is treated with \(\mathrm{HCl}\) liberating \(\mathrm{Cl}_2\). The \(\mathrm{Cl}_2\) gas is passed into a solution of \(\mathrm{KI}\) and \(60.0 \mathrm{~mL}\) of 0.1 \(\mathrm{MNa}_2 \mathrm{~S}_2 \mathrm{O}_3\) is required to titrate the liberated iodine. The percentage of \(\mathrm{MnO}_2\) in the sample is_________(Nearest integer)

[Atomic masses (in \(\mathrm{u}\) ) \(\mathrm{Mn}=55 ; \mathrm{Cl}=35.5 ; \mathrm{O}=16, \mathrm{I}=127, \mathrm{Na}=23, \mathrm{~K}=39, \mathrm{~S}=32]\)

Which of the following defect, if present, lowers the density of the crystal?

Which is the correct increasing order of electronegativity of halides?

Exactly \(1 {~g}\) of urea dissolved in \(75 {~g}\) of water gives a solution that boils at \(100.114^{\circ} {C}\) at 760 torr. The molecular weight of urea is \(60.1\). The boiling point elevation constant for water is:

In physisorption adsorbent does not show specificity for any particular gas because:

The rate of a first order reaction is \(1.5 \times 10^{-2} M {~min}^{-1}\) at \(0.5 {M}\) concentration of the reactant. The half-life of the reaction is:

An aqueous solution of hydrochloric acid:

Which of the following is an unsaturated compound?

Which of the following will have a net dipole moment?

Which of the carbonates given below is unstable in air and is kept in the CO₂ atmosphere to avoid decomposition?

The percentage of s- character of the hybrid orbitals in ethane, ethene and ethyne are respectively:

Calgon is used for water treatment. Which of the following statement is not true about Calgon?

\(\mathrm{C}_{2} \mathrm{H}_{6}\) compound has:

In the reaction \(4 \mathrm{Fe}+3 \mathrm{O}_{2} \rightarrow 4 \mathrm{Fe}^{3+}+6 O^{2-}\) which of the following statements is incorrect?

Calculate e.m.f of the following cell at \(298 \mathrm{~K}\) :

\(2 \mathrm{Cr}(\mathrm{s})+3 \mathrm{Fe}^{2+}(0.1 \mathrm{M}) \rightarrow 2 \mathrm{Cr}^{3+}(0.01 \mathrm{M})+3 \mathrm{Fe}(\mathrm{s})\)

Given: \(\mathrm{E}^{\circ}\left(\mathrm{Cr}^{3+} \mid \mathrm{Cr}\right)=-0.74 \mathrm{VE}^{\circ}\left(\mathrm{Fe}^{2+} \mid \mathrm{Fe}\right)=-0.44 \mathrm{~V}\)

The helical structure of protein is stabilized by:

Match the following :

L-isomer of tetrose \(\mathrm{X}\left(\mathrm{C}_4 \mathrm{H}_8 \mathrm{O}_4\right)\) gives positive schiff's test and has two chiral carbons. On acetylation. ' \(\mathrm{X}\) ' yields triacetate. ' \(\mathrm{X}\) ' undergoes following reactions

' \(\mathrm{X}\) ' is

\(1.22 \mathrm{~g}\) of an organic acid is separately dissolved in \(100 \mathrm{~g}\) of benzene \(\left(\mathrm{K}_{\mathrm{b}}=2.6 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}\right)\) and \(100 \mathrm{~g}\) of acetone \(\left(\mathrm{K}_{\mathrm{b}}=1.7 \mathrm{Kkg} \mathrm{mol}^{-1}\right)\). The acid is known to dimerise in benzene but remain as a monomer in acetone. The boiling point of the solution in acetone increases by \(0.17^{\circ} \mathrm{C}\). The increase in boiling point of solution in benzene in \({ }^{\circ} \mathrm{C}\) is \(\mathrm{x} \times 10^{-2}\). The value of \(\mathrm{x}\) is....... (Nearest integer)

[Atomic mass: \(\mathrm{C}=12.0, \mathrm{H}=1.0, \mathrm{O}=16.0\) ]

For a 1^st order reaction, if the concentration is doubled then the rate of reaction becomes:

When \(\mathrm{KMnO}_{4}\) solution is added to oxalic acid solution, the decolourisation is slow in the beginning but becomes instantaneous after some time because:

Which of the following statement is correct?

For the process to occur under adiabatic conditions, the correct conditionis:

Heterolysis of carbon-chlorine bond produces:

A complex has the molecular formula \(\mathrm{Co} .5 \mathrm{NH}_{3} . \mathrm{NO}_{2} . \mathrm{Cl}_{2}\). One mole of this complex produces three moles of ions in an aqueous solution. On reacting this solution with excess of \(\mathrm{AgNO}_{3}\) solution, we get 2 moles of white ppt. The complex is:

Which has a smell of oil of wintergreen?

Which of the following are Lewis acids?

Arrange the following compounds in decreasing order of basicity:

\(\mathrm{I}\). Ethylamine 

\(\mathrm{II}\). \(2\) - amino ethanol 

\(\mathrm{III}\). \(3\) - amino - \(1\) - Propanol

In Mendeleev’s Periodic Table, gaps were left for the elements to be discovered later. Which of the following elements found a place in the Periodic Table later?

What is the structural formula of Haloalkane?

Which amongst the given plots is the correct plot for pressure (p) vs density (d) for an ideal gas?

For the following cell, calculate the emf:

\(\mathrm{Al}\left|\mathrm{Al}^{3+}(0.01 M) \| \mathrm{Fe}^{2+}(0.02 \mathrm{M})\right| \mathrm{Fe}\)

Given : \(E_{\mathrm{Al}^{3+} / \mathrm{Al}}^{\circ}=-1.66 \mathrm{~V}, E_{\mathrm{Fe}^{2+} / \mathrm{Fe}}^{\circ}=-0.44 \mathrm{~V}\)

An empty LPG cylinder weight \(14.8 \mathrm{~kg}\). When full, it weight \(29.0 \mathrm{~kg}\) and shows a pressure of \(3.47 \mathrm{~atm}\). In the course of use at ambient temperature, the mass of the cylinder is reduced to \(23.0 \mathrm{~kg}\). The final pressure inside of the cylinder is________atm. (Nearest integer) (Assume LPG of be an ideal gas)

For \(1 \mathrm{M}\) solution of \(\mathrm{HA}\), the dissociation constant \(\mathrm{K}_{\mathrm{a}}\) in terms of vant Hoff factor (i) can be written as :

Iron is extracted from iron oxide using carbon monoxide as shown. 

iron oxide + carbon monoxide → iron + carbon dioxide 

Which statement is correct?

The heats of adsorption (in kJ/mol) in physisorption or physical adsorption lie in the range of:

The solubility of mercurous chloride in water is given as:

Compound A contains \(8.7 \%\) Hydrogen, \(74 \%\) Carbon and \(17.3 \%\) Nitrogen. The molecular formula of the compound is, Given : Atomic masses of \(\mathrm{C}, \mathrm{H}\) and \(\mathrm{N}\) are 12,1 and \(14 \mathrm{amu}\) respectively.

The molar mass of the compound \(\mathrm{A}\) is \(162 \mathrm{gmol}^{-1}\).

Major products of the following reaction are :

The products obtained on heating LiNO₃ will be:

The element molybdenum (Mo) combines with sulphur (S) to form a compound commonly called molybdenum disulphide which used in specialized lithium batteries. A sample of this compound contains \(1.50 \mathrm{~g}\) of  Mo for each \(1.00 \mathrm{~g}\) of S. If a different sample of the compound contains \(2.50 \mathrm{~g}\) of S, how many grams of Mo does it contain?

Calculate the number of protons, neutrons and electrons in \({ }_{35}^{80} \mathrm{Br}\).

The \({pH}\) of a solution obtained by mixing \(100 {ml}\) of \(0.2 {M} {CH}_{3} {COOH}\) with \(100 {ml}\) of \(0.2 {M} {NaOH}\) would be \(\left(p K_{a C H_{3} C O O H}\right.\) \(=4.74)\)

What is the value of \(\lim _{{x} \rightarrow \infty} \frac{{x}^{3}+3 {x}^{2}+6 {x}+5}{{x}^{3}+2 {x}+6}\)?

A discrete random variable \(x\) has the probability functions as:

If \(y \frac{d y}{d x}=x\left[\frac{y^2}{x^2}+\frac{\phi\left(\frac{y^2}{x^2}\right)}{\phi^{\prime}\left(\frac{y^2}{x^2}\right)}\right], x>0, \phi>0\), and \(y(1)=-1\), then \(\phi\left(\frac{y^2}{4}\right)\) is equal to:

If \(A=\left(\begin{array}{cc}\frac{1}{\sqrt{5}} & \frac{2}{\sqrt{5}} \\ -\frac{2}{\sqrt{5}} & \frac{1}{\sqrt{5}}\end{array}\right), B=\left(\begin{array}{cc}1 & 0 \\ 1 & 1\end{array}\right), \mathrm{i}=\sqrt{-1}\), and \(Q=A^T B A\), then the inverse of the matrix \(\mathrm{AQ}^{2021} \mathrm{~A}^{\mathrm{T}}\) is equal to:

The nth term of the following sequence 25, -125, 625, -3125, …….. is:

What is the area of the region bounded by the curve \(f(x)=1-\frac{x^2}{4}, x \in[-2,2]\) and the \(x\)-axis?

Find the domain of the inverse trigonometric function \(\sin ^{-1}\left(2 x \sqrt{1-x^{2}}\right)\) is:

If \(p\) and \(q\) are the lengths of the perpendiculars from the origin on the lines,

\(\mathrm{xcosec} \alpha-\mathrm{y} \sec \alpha=\mathrm{k} \cot 2 \alpha\) and \(\mathrm{x} \sin \alpha+\mathrm{y} \cos \alpha=\mathrm{k} \sin 2 \alpha\) respectively, then \(\mathrm{k}^2\) is equal to:

Find the area bounded by the curve between \(y=\sin x+\cos x\) in the interval \(0<\mathrm{x}<\frac{\pi}{2}\).

A balloon, which always remains spherical, has a variable diameter \(\frac{3}{2}(4 x +3)\). Find the rate of change of its volume with respect to \(x\).

Let \(y=y(x)\) be the solution of the differential equation \(\frac{d y}{d x}=2(y+2 \sin x-5) x-2 \cos x\) such that, \(y(0)=7\).

Then \(\mathrm{y}(\pi)\) is equal to:

If \({ }^{{n}} {P}_{{r}}=2760,{ }^{{n}} {C}_{{r}}=23\), then the value of \({r}\) is:

If the mean of 10 observations \(x_{1}, x_{2}, x_{3} \ldots x_{10}\) is 20 , then mean of \(x_{1}+2, x_{2}+4, x_{3}+\) \(6, \ldots x_{10}+20\) is:

Find the rate of change of area of the square at the edge length of 12 cm, if the rate of change of edge length of the square is 2 cm/s.

Let \(x(t)=2 \sqrt{2} \cos t \sqrt{\sin 2 t}\) and

\(y(t)=2 \sqrt{2} \sin t \sqrt{\sin 2 t}, t \in\left(0, \frac{\pi}{2}\right)\)

Then \(\frac{1+\left(\frac{\mathrm{dy}}{\mathrm{dx}}\right)^2}{\frac{\mathrm{d}^2 \mathrm{y}}{\mathrm{dx}^2}}\) at \(\mathrm{t}=\frac{\pi}{4}\) is equal to:

A continuous random variable \(X\) has the distribution function \(F(x)=0\) if \(x<1\) \(=k(x-1)^{4}\) if \(13\) The value of \(k\) is:

The objective function of a linear programming problem is _______________.

If \(A=\{2,4,6\}, B=\{4,6,7\}\) and \(C=\{2,7\}\), then \((A-B) \times(B-C)\) is:

If \(\overrightarrow{\mathrm{a}}, \overrightarrow{\mathrm{b}}\) and \(\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}\) are vectors of magnitude \(\alpha\) then the magnitude of the vector  \(|\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}|\) is?

A bag contains \(4\) black, \(5\) yellow and \(6\) green balls. Three balls are drawn at random from the bag. What is the probability that all of them are yellow?

The range of the real-valued function \(f(x)=\sqrt{9-x^{2}}\) is:

Let \(\mathrm{S}_{\mathrm{K}} \frac{1+2+\ldots+\mathrm{K}}{\mathrm{K}}\) and \(\sum_{\mathrm{j}=1}^{\mathrm{n}} \mathrm{S}_{\mathrm{j}}^2=\frac{\mathrm{n}}{\mathrm{A}}\left(\mathrm{Bn}^2+\mathrm{Cn}+\mathrm{D}\right)\), where \(\mathrm{A}, \mathrm{B}, \mathrm{C}, \mathrm{D} \in \mathrm{N}\) and A has least value. Then:

All the pairs \((x, y)\) that satisfy the inequality \(2 \sqrt{\sin ^2 x-2 \sin x+5} \cdot \frac{1}{4 \sin ^2 y} \leq 1\) also satisfy the equation:

Evaluate the integral \(\int_{1}^{4} \frac{\sqrt{x}+3}{\sqrt{x}} d x\).

If \(A=\{2,3,4\}\) and \(B=\{5,6\}\), then how many subsets does \(A \times B\) have?

If \(\mathrm{P}\) and \(\mathrm{Q}\) be two sets such that \(\mathrm{P} \cup \mathrm{Q}=\mathrm{P},\) then \(\mathrm{P} \cap \mathrm{Q}\) will be:

Let \(\mathrm{S}\) be the set of all real roots of the equation, \(3^{\mathrm{x}}\left(3^{\mathrm{x}}-1\right)+2=3^{\mathrm{x}}-1\left|+3^{\mathrm{x}}-2\right|\). Then \(\mathrm{S}:\)

If the mean of 4, 7, 2, 8, 6 and a is 7, then the mean deviation from the median of these observations is:

Find the number of arrangements of letters in the word ASHUTOSH?

If the constraints in a linear programming problem are changed _______________.

The sum of the roots of the equation \(x+1-2 \log _2\left(3+2^x\right)+2 \log _4\left(10-2^{-x}\right)=0\) is:

Let \(A=\left[\begin{array}{cc}1 & 2 \\ -1 & 4\end{array}\right]\). If \(A^{-1}=\alpha I+\beta A, \alpha, \beta \in R, I\) is a \(2 \times 2\) identity matrix, then \(4(\alpha-\beta)\) is equal to :

The differential equation satisfied by the system of parabolas \(y^2=4 a(x+a)\) is:

Find the value of \(\lim _{{x} \rightarrow \infty} \frac{{x}^{4}+3 {x}^{2}+5}{{x}^{4}+{x}^{2}-6}\)

The smallest positive integer \(n\) for which

\(\left(\frac{1-i}{1+i}\right)^{n^{2}}=1\)

where \(i=\sqrt{-1}\), is

For the vectors \(\overrightarrow{\mathrm{a}}=-4 \hat{\mathrm{i}}+2 \hat{\mathrm{j}}, \overrightarrow{\mathrm{b}}=2 \hat{\mathrm{i}}+\hat{\mathrm{j}}\) and \(\overrightarrow{\mathrm{c}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}},\) if \(\overrightarrow{\mathrm{c}}=\mathrm{m} \overrightarrow{\mathrm{a}}+\mathrm{n} \overrightarrow{\mathrm{b}},\) then the value of \(\mathrm{m}+\mathrm{n}\) is:

If \(\tan ^{-1}\left(\frac{1-x}{1+x}\right)=\frac{1}{2} \tan ^{-1} x, x>0\), then \(x\) equals:

Let \(\mathrm{P}\) be a square matrix such that \(\mathrm{P}^2=\mathrm{I}-\mathrm{P}\). For \(\alpha, \beta, \gamma, \delta \in \mathrm{N}\), if \(\mathrm{P}^\alpha+\mathrm{P}^\beta=\gamma \mathrm{I}-29 \mathrm{P}\) and \(\mathrm{P}^\alpha-\mathrm{P}^\beta=\delta \mathrm{I}-13 \mathrm{P}\), then \(\alpha+\beta+\gamma-\delta\) is equal to :

Using the principal of mathematical induction, prove that \(1+\frac{1}{1+2}+\frac{1}{1+2+3}+\ldots+\frac{1}{1+2+3+\ldots+n}=\frac{2 n}{n+1}\) for all:

If \(-2<2 x-1<2\) then the value of \(x\) lies in the interval:

If \(f: R \rightarrow R\) and \(g: R \rightarrow R\) are two mappings defined as \(f(x)=2 x\) and \(g(x)=x^{2}+2\), then the value of \((f+g)(2)\) is:

If \((a, b)\) be the orthocentre of the triangle whose vertices are \((1,2),(2,3)\) and \((3,1)\), and \(I_1=\int_a^b x \sin \left(4 x-x^2\right) d x, I_2=\int_a^b \sin \left(4 x-x^2\right) d x\), then \(36 \frac{I_1}{I_2}\) is equal to :

The slope of the line perpendicular to the line passing through the points \((3,2)\) and \((1,-1)\) is:

If \(\int_0^1 \frac{1}{\sqrt{3+x}+\sqrt{1+x}} d x=a+b \sqrt{2}+c \sqrt{3}\), where \(a, b, c\) are rational numbers, then \(2 a+3 b-4 c\) is equal to :

Let \(a_1, a_2, a_3, \ldots, a_n\) be \(n\) positive consecutive terms of an arithmetic progression. If \(d>0\) is its common difference, then :

\(\lim _{n \rightarrow \infty} \sqrt{\frac{d}{n}}\left(\frac{1}{\sqrt{a_1}+\sqrt{a_2}}+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+\ldots \ldots .+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_n}}\right) \text { is }\)

If \(2 \tan ^2 \theta-5 \sec \theta=1\) has exactly 7 solutions in the interval \(\left[0, \frac{n \pi}{2}\right]\), for the least value of \(n \in N\) then \(\sum_{k=1}^n \frac{k}{2^k}\) is equal to:

If the mirror image of the point \((2,4,7)\) in the plane \(3 x-y+4 z=2\) is \((\mathrm{a}, \mathrm{b}, \mathrm{c})\), then \(2 \mathrm{a}+\mathrm{b}+2 \mathrm{c}\) is equal to:

If \(A=\left[\begin{array}{ccc}3 & 4 & 9 \\ 11 & 6 & 7 \\ 8 & 9 & 5\end{array}\right]\) and \(|2 \mathrm{~A}|=\mathrm{k}\) then find the value of \(\mathrm{k}\)?

The optimal value of the objective function is attained at the points ________________.

If \(P\) and \(Q\) are two sets, then \((P-Q) \cup(Q-P) \cup(P \cap Q)\) will be:

An integer is chosen at random from the integers \(1,2,3, \ldots, 50\). The probability that the chosen integer is a multiple of atleast one of 4, 6 and 7 is:

Let \(A=\left[\begin{array}{llc}2 & 1 & 2 \\ 6 & 2 & 11 \\ 3 & 3 & 2\end{array}\right]\) and \(P=\left[\begin{array}{lll}1 & 2 & 0 \\ 5 & 0 & 2 \\ 7 & 1 & 5\end{array}\right]\). The sum of the prime factors of \(\left|\mathrm{P}^{-1} \mathrm{AP}-2 \mathrm{I}\right|\) is equal to:

Let \(\mathrm{f}:[-1,3] \rightarrow R\) be defined as

\(f(x)=\left\{\begin{array}{cc}|x|+[x], & -1 \leq x<1 \\ x+|x|, & 1 \leq x<2 \\ x+[x], & 2 \leq x \leq 3\end{array}\right.\)

where \([t]\) denotes the greatest integer less than or equal to \(t\). Then, \(f\) is discontinuous at:

Let \(\lambda \in \mathbb{R}, \vec{a}=\lambda \hat{i}+2 \hat{j}-3 \hat{k}, \vec{b}=\hat{i}-\lambda \hat{j}+2 \hat{k}\).

If \(\vec{a}+\vec{b}) \times(\vec{a} \times \vec{b} \times(\vec{a}-\vec{b})=8 \hat{i}-40 \hat{j}-24 \hat{k}\), then \(|\lambda(\vec{a}+\vec{b}) \times(\vec{a}-\vec{b})|^2\) is equal to:

If \(\vec{a}, \vec{b}, \vec{c}\) are three non-zero vectors and \(\hat{n}\) is a unit vector perpendicular to \(\overrightarrow{\mathrm{c}}\) such that \(\overrightarrow{\mathrm{a}}=\alpha \overrightarrow{\mathrm{b}}-\hat{\mathrm{n}},(\alpha \neq 0)\) and \(\overrightarrow{\mathrm{b}} \cdot \overrightarrow{\mathrm{c}}=12\), then \(|\overrightarrow{\mathrm{c}} \times(\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}})|\) is equal to:

Using the principle of mathematical induction, prove that \(1 \times 3+2 \times 3^{2}+3 \times 3^{3}+\ldots+n \times 3^{n}=\frac{(2 n-1) 3^{n+1}+3}{4}\) for all:

If \(4 x+3<6 x+7\), then \(x\) belongs to the interval

Evaluate the expression: \(\sqrt{\frac{1+\cos \theta}{1-\cos \theta}}=?\)

\(\text { If } A=\{x \in R:|x|<2\} \text { and } B=\{x \in R:|x-2| \geq 3\} \text {; then : }\)