If the valence shell electronic configuration for an element is \(\mathrm{ns}^{2} \mathrm{np}^{5}\), this element belongs to the group of:

Consider the Newman projection formulas shown below:

Which of the following statements is correct?

In a CCP lattice of X and Y, X atoms are present at the corners while Y atoms are at face centres. Then, the formula of the compound would be if one of the X atoms from a corner is replaced by Z atoms (also monovalent)?

The state of a thermodynamic system is described by its measurable or macroscopic (bulk) properties. These are:

In the phenomenon of electric discharge through gases at low pressure, the coloured glow in the tube appears as a result of:

Which of the following ligands form a chelate?

From which of the following tertiary butyl alcohol is obtained by the action of methyl magnesium bromide?

\(\mathrm{Fe}^{3+}\) compounds are more stable than \(\mathrm{Fe}^{2+}\) compounds because:

A buffer solution contains \(100~ mL\) of \(0.01 M ~CH _{3} COOH\) and \(200 ~mL\) of \(0.02 M~CH _{3} COONa\). \(700 ~mL\) of water is added to this solution. \(pH\) before and after dilution are: \(\left(p K_{a}=4.74, \log 4 = 0.602\right)\)

In solid state \(\mathrm{N}_{2} \mathrm{O}_{5}\) exists as:

The carbonyl stretching frequency for simple aldehydes, ketones, and carboxylic acids is about \(1710 \mathrm{~cm}^{-1}\), where the carbonyl stretching frequency for esters is about ................... \(\mathrm{cm}^{-1}\):

Adenine is a derivative of __________.

For an ionic crystal of general formula AX and co-ordination number 6, the value of radius ratio will be:

Positive Beilstein shows that:

Calculate the amount of benzoic acid \(\left({C}_{6} {H}_{5} {COOH}\right)\) required for preparing 250 \({mL}\) of \(0.15 {M}\) solution in methanol.

The process of passing of a precipitate into colloidal solution on adding an electrolyte is called:

If a solution prepared by dissolving 1.0 g of polymer of molar mass 185,000 in 450 mL of water at 37°C, calculate the osmotic pressure in Pascal exerted by it?

Alkanes can be prepared from Grignard reagents by reacting with:

Which of the following is a linear molecule?

One gram of charcoal adsorbs \(400 \mathrm{~mL}\) of \(0.5 \mathrm{M}\) acetic acid to form a monolayer, and the molarity of acetic acid reduces to \(0.49 \mathrm{M}\). Calculate the surface area of charcoal adsorbed by each molecule of acetic acid, where the surface area of charcoal is \(3.01 \times 10^{2} \mathrm{~m}^{2} \mathrm{~g}^{-1}\).

Phenol on treatment with \(\mathrm{CO}_2\) in the presence of \(\mathrm{NaOH}\) followed by acidification produces compound \(\mathrm{X}\) as the major product. \(\mathrm{X}\) on treatment with \(\left(\mathrm{CH}_3 \mathrm{CO}\right)_2 \mathrm{O}\) in the presence of catalytic amount of \(\mathrm{H}_2 \mathrm{SO}_4\) produces :

Which of the following contains the same number of atoms as \(20 \mathrm{~g}\) of calcium \(\mathrm{Ca}\)?

Propane cannot be prepared from which reaction?

When hydrogen peroxide is added to an acidified solution of potassium dichromate, a blue colour is produced due to the formation of:

Oxidation state of iron in \(F e(C O)_{4}\) is:

Living cell contains \(60\)-\(75\%\) water. Water present in human body is:

\(3 \mathrm{~g}\) of activated charcoal was added to \(50 \mathrm{~mL}\) of the acetic acid solution \((0.06 \mathrm{~N})\) in a flask. After an hour, it was filtered and the strength of the filtrate was found to be \(0.042 \mathrm{~N}\). The amount of acetic acid adsorbed (per gram of charcoal) is :

The azo-dye \((\mathrm{Y})\) formed in the following reactions is Sulphanilic acid \(+\mathrm{NaNO}_2+\mathrm{CH}_3 \mathrm{COOH} \rightarrow \mathrm{X}\)

Which one of the following species responds to an external magnetic field?

In ___________, a reaction product is itself a catalyst for that reaction leading to positive feedback.

The reduction in atomic size with increase in atomic number is a characteristic of elements of:

_______ group elements are known as chalcogens.

Among the following the state function(s) is (are):

(i) Internal energy

(ii) Irreversible expansion work

(iii) Reversible expansion work

(iv) Molar enthalpy

The IUPAC name of \(CH _{3} COCH \left( CH _{3}\right)_{2}\) is:

The bond length between hybridised carbon atom and other carbon atom is minimum in:

Which of the following is a tridentate ligand?

\(R-C H=C R O^{-}+C H_{2}-N^{+} R_{2} \rightarrow N R_{2}-C H_{2}-C H R-C R O\)

The given reaction in an example of:

A first order reaction has the rate constant, \(\mathrm{k}=4.6 \times 10^{-3} \mathrm{~s}^{-1}\). The number of correct statement/s from the following is/are____________.

Given : \(\log 3=0.48\)

A. Reaction completes in \(1000 \mathrm{~s}\).

B. The reaction has a half-life of \(500 \mathrm{~s}\).

C. The time required for \(10 \%\) completion is 25 times the time required for \(90 \%\) completion.

D. The degree of dissociation is equal to \(\left(1-\mathrm{e}^{-\mathrm{kt}}\right)\).

E. The rate and the rate constant have the same unit.

The product obtained when methylamine \(\left(\mathrm{CH}_{3} \mathrm{NH}_{2}\right)\) is treated with nitrous acid is:

The most non-metallic element among the following is:

Ethyl alcohol is industrially prepared from ethylene by:

The production of dihydrogen obtained from coal gasification can be increased by reacting carbon monoxide of syngas mixture with steam in presence of a catalyst iron-chromium. What is this process called?

An evacuated glass vessel weighs \(40.0 \mathrm{~g}\) when empty, \(135.0 \mathrm{~g}\) when filled with a liquid of density \(0.95 \mathrm{~g} \mathrm{~mL}-1\) and \(40.5 \mathrm{~g}\) when filled with an ideal gas at \(0.82 \mathrm{~atm}\) at \(250 \mathrm{~K}\). The molar mass of the gas in \(\mathrm{gmol}^{-1}\) is :

(Given : \(\mathrm{R}=0.082 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\) )

A rigid nitrogen tank stored inside a laboratory has a pressure of \(30 \mathrm{~atm}\) at \(06: 00 \mathrm{am}\) when the temperature is \(27^{\circ} \mathrm{C}\). At \(03: 00 \mathrm{pm}\), when the temperature is \(45^{\circ}\), the pressure in the tank will be ________ atm. [nearest integer]

Match items of Row I with those of Row II.

Row I :

Row II :

(i) \(\alpha\)-D-(-) Fructofuranose.

(ii) \(\beta\)-D-(-) Fructofuranose

(iii) \(\alpha\)-D-(-) Glucopyranose.

(iv) \(\beta\)-D-(-) Glucopyranose

Correct match is

Two liquids \(\mathrm{A}\) and \(\mathrm{B}\) are mixed at temperature \(\mathrm{T}\) in a certain ratio to form an ideal solution. It is found that the partial pressure of \(\mathrm{A}\), i.e. \(\mathrm{P_{A}}\) is equal to \(\mathrm{P_{B}}\), the pressure of \(\mathrm{B}\) for liquid mixture. What is the total pressure of the liquid mixture in terms of \(\mathrm{P_{A}^{0}}\) and \(\mathrm{P_{B}^{0}}\)?

Which of the following is not a redox reaction?

The other name for branched chain alkanes is _____________.

In a buffer solution containing an equal concentration of \(\mathrm{B}^{-}\)  and HB, the \(\mathrm{K}_{\mathrm{b}}\) for \(\mathrm{B}^{-}\)is \(10^{-10}\). The \(\mathrm{pH}\) of the buffer solution is:

Isomeric amines with molecular formula \(\mathrm{C}_8 \mathrm{H}_{11} \mathrm{~N}\) given the following tests

Isomer \((\mathrm{P}) \Rightarrow\) Can be prepared by Gabriel phthalimide synthesis

Isomer \((\mathrm{Q}) \Rightarrow\) Reacts with Hinsberg's reagent to give solid insoluble in \(\mathrm{NaOH}\)

Isomer \((\mathrm{R}) \Rightarrow\) Reacts with \(\mathrm{HONO}\) followed by \(\beta\)-naphthol in \(\mathrm{NaOH}\) to given red dye.

Isomer \((\mathrm{P}),(\mathrm{Q})\) and \((\mathrm{R})\) respectively are

Boiling of hard water is helpful in removing the temporary hardness by converting calcium hydrogen carbonate and magnesium hydrogen carbonate to

A sample of \(\mathrm{CaCO}_3\) and \(\mathrm{MgCO}_3\) weighed \(2.21 \mathrm{~g}\) is ignited to constant weight of \(1.152 \mathrm{~g}\). The composition of mixture is :

(Given molar mass in gmol \(^{-1} \left.\mathrm{CaCO}_3: 100, \mathrm{MgCO}_3: 84\right)\)

In an adsorption experiment, a graph between \(\log \left(\frac{x}{m}\right)\) versus \(\log p\) is found to be linear with slope of \(45^{\circ}\). The intercept on \(\log \left(\frac{\mathrm{x}}{\mathrm{m}}\right)\) axis was found to \(0.3010\). The amount of the gas adsorbed per gram of charcoal under the pressure of \(0.5 \mathrm{~atm}\) will be:

A mixture is known to contain \(N O_{ {3}}^-\) and \(N O_{ {2}}^-\). Before performing ring test for \(N O_{ {3}}^-\) the aqueous solution should be made free of \(N O_{ {2}}^-\). This is done by heating aqueous extract with:

The energy of a hydrogen atom in the ground state is \(13.6 \mathrm{eV}\). The energy of \(\mathrm{He}^+\) ion in the first excited state will be:

Trigonal bipyramidal geometry is shown by:

The value of \(\underset{{{x \rightarrow 0}}}{\lim} \frac{\tan ^{2} 3 x}{x^{2}}\) is:

The value of \(\omega^{6}+\omega^{7}+\omega^{5}\) is

Let \(\mathrm{L}\) denote the set of all straight lines in a plane. Let a relation \(\mathrm{R}\) be \(\mathrm{l R m}\) if \(\mathrm{l}\) is perpendicular to \(\mathrm{m \forall l, m \in L}\). Then \(\mathrm{R}\) is:

Let S={1,2,3,...,2022}. Then the probability, that a randomly chosen number n from the set S such that HCF(n,2022)=1, is :

What is the area of the parabola \(x^2=y\) bounded by the line \(y=1\)?

Which one of the following is wrong statement?

Find the principal value of \(\sin ^{-1}\left(\frac{-1}{\sqrt{2}}\right)\).

The value of \(\lim _{x \rightarrow 0} \frac{\cos 4 x-1}{1-\cos x}\) is:

Suppose \(\sin 2 \theta=\cos 3 \theta\), here \(0<\theta<\pi / 2\) then what is the value of \(\cos 2 \theta ?\)

The sum of the first 20 terms of the series \(\sqrt{5}+\sqrt{20}+\sqrt{45}+\sqrt{80}+\ldots\) is

Let the equations of two sides of a triangle be 3x−2y+6=0 and 4x+5y−20=0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is:

How many words can be formed by using all the letters of the word ‘DAUGHTER’ so that the vowels always come together?

The equation of the locus of a point equidistant from the point A(1, 3) and B(-2, 1) is:

If \(A\) and \(B\) are two events such that \(P(A) \neq 0\) and \(P(A) \neq 1\), then \(P\left(\frac{\overline{A}}{\overline{B}}\right)\) is:

Solve the differential equation \(\sin x \frac{d y}{d x}+\frac{y}{\sin x}=x \sin x e^{\cot x}\)

Integrating factor of \(\left(1-x^2\right) \frac{d y}{d x}-x y=1\) is:

Mean of 100 observations is 50 and standard deviation is 10. If 5 is added to each observation, then what will be the new mean and new standard deviation respectively?

What is the value of \(7^{\frac{1}{7}} \times 7^{\frac{1}{7^{2}}} \times 7^{\frac{1}{7^{3}}} \times \ldots\infty\) ?

Let A be a 3×3 real matrix such that \(\mathrm{A}\left(\begin{array}{l}1 \\ 1 \\ 0\end{array}\right)=\left(\begin{array}{l}1 \\ 1 \\ 1\end{array}\right) ; \mathrm{A}\left(\begin{array}{l}1 \\ 0 \\ 1\end{array}\right)=\left(\begin{array}{c}-1 \\ 0 \\ 1\end{array}\right)\) and \(\mathrm{A}\left(\begin{array}{l}0 \\ 0 \\ 1\end{array}\right)=\left(\begin{array}{l}1 \\ 1 \\ 2\end{array}\right)\) \(\text { If } \mathrm{X}=\left(\mathrm{x}_1, \mathrm{x}_2, \mathrm{x}_3\right)^{\mathrm{T}} \text { and } \mathrm{I} \text { is an identity matrix of order } 3 \text {, then the system }\)

\((A-2 I) X=\left(\begin{array}{l}4 \\ 1 \\ 1\end{array}\right)\)

If \(u_{1}=u_{2}=1\) and \(u_{n+2}=u_{n+1}+u_{n} \cdot n \geq 1\). Then use mathematical induction to show that \(u_{n}=\frac{1}{\sqrt{5}}\left[\left(\frac{1+\sqrt{5}}{2}\right)^{n}-\left(\frac{1-\sqrt{5}}{2}\right)^{n}\right]\) for all \(n>1\).

Find the equation of the normal to the curve \(y=3 x^{2}+1\), which passes through \((2,13)\).

Find the vector equation of the line passing through the point with position vector \(\hat{i}-2 \hat{j}+5 \hat{k}\) and perpendicular to the plane \(\vec{r} \cdot(2 \hat{i}-3 \hat{j}-\hat{k})=0\).

If \(f(x)=\left|\begin{array}{ccc}x^3 & 2 x^2+1 & 1+3 x \\ 3 x^2+2 & 2 x & x^3+6 \\ x^3-x & 4 & x^2-2\end{array}\right|\) for all \(x \in \mathbb{R}\), then \(2 f(0)+f^{\prime}(0)\) is equal to:

If \(\omega\) is a cube root of unity, then a root of the equation is:

\(\left|\begin{array}{ccc}x+1 & \omega & \omega^2 \\ \omega & x+\omega^2 & 1 \\ \omega^2 & 1 & x+\omega\end{array}\right|=0\)

\(P\) and \(Q\) are considering to apply for a job. The probability that \(P\) applies for the job is \(\frac{1}{4}\), the probability that \(P\) applies for the job given that \(Q\) applies for the job is \(\frac{1}{2}\), and the probability that \(Q\) applies for the job given that \(P\) applies for the job is \(\frac{1}{3}\). Then the probability that \(P\) does not apply for the job given that \(Q\) does not apply for the job is:

Let two vertices of a triangle \(\mathrm{ABC}\) be \((2,4,6)\) and \((0,-2,-5)\), and its centroid be \((2,1,-1)\). If the image of the third vertex in the plane \(x+2 y+4 z=11\) is \((\alpha, \beta, \gamma)\), then \(\alpha \beta+\beta \gamma+\gamma \alpha\) is equal to :

\(\text { If } \lim _{n \rightarrow \infty}\left(\sqrt{n^2-n-1}+n \alpha+\beta\right)=0 \text {, then } 8(\alpha+\beta) \text { is equal to: }\)

Find the value of \(x\) and \(y\) such that \(\left[\begin{array}{l}x-y \\ x+y\end{array}\right]=\left[\begin{array}{c}2 \\ 16\end{array}\right]\).

General solution of \(\left(x^2+y^2\right) d x-2 x y d y=0\) is:

The derivative of \(\cos ^{-1}\left(\frac{1}{2 x^{2}-1}\right)\) with respect to \(\sqrt{1-x^{2}}\) is:

The area of the region bounded by the curve \(y=\sqrt{16-x^2}\) and \(x\)-axis is:

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

Consider the function \(f: R \rightarrow\{0,1\}\) such that: 

\(f(x)=\left\{\begin{array}{c}1 \text { if } x \text { is rational } \\ 0 \text { if } x \text { is irrational }\end{array}\right.\). 

Which one of the following is correct?

The maximum value of \(P=x+3 y\) such that \(2 x+y \leq 20, x+2 y \leq\) \(20, x \geq 0, y \geq 0\), is:

The mean and standard deviation of a set of values are 5 and 2 respectively. If 5 is added to each value, then what is the coefficient of variation for the new set of values?

Two dice A and B are rolled. Let numbers obtained on A and B be α and β respectively. If the variance of α−β is $\frac{p}{q}$, where p and q are co-prime, then the sum of the positive divisior of p is equal to:

A passenger wants to travel from Delhi to Mangalore by train. There is no direct train from Delhi to Mangalore, but there are trains from Delhi to Mumbai and from Mumbai to Mangalore. Actually, there are four trains from Delhi to Mumbai and three trains from Mumbai to Bangalore. In how many ways can he travel from Delhi to Mangalore?

If \(\omega\) is a cube root of unity, then the value of \(\left(1-\omega+\omega^{2}\right)\left(1+\omega-\omega^{2}\right)\) is:

If \(\sin ^{-1} x+\sin ^{-1} y=\frac{5 \pi}{6}\), then what is the value of \(\cos ^{-1} x+\cos ^{-1} y\)?

An organization awarded 48 medals in event ' A ', 25 in event ' B' and 18 in event ' C '. If these medals went to total 60 men and only five men got medals in all the three events, then, how many received medals in exactly two of three events ?

Evaluate the integral \(\int_{0}^{1} \frac{e^{x}}{1+e^{2 x}} d x\).

If given constraints are \(5 x+4 y \geq 2, x \leq 6, y \leq 7\), then the maximum value of the function \(z=x+2 y\) is:

In a group of 100 persons 75 speak English and 40 speak Hindi. Each person speaks at least one of the two languages. If the number of persons, who speak only English is α and the number of persons who speak only Hindi is β, then the eccentricity of the ellipse 25( β²x²+α²y² )=α²β² is :

Let \(\vec{a}=2 \hat{i}-7 \hat{j}+5 \hat{k}, \vec{b}=\hat{i}+\hat{k}\) and \(\vec{c}=\hat{i}+2 \hat{j}-3 \hat{k}\) be three given vectors. If \(\vec{r}\) is a vector such that \(\vec{r} \times \vec{a}=\vec{c} \times \vec{a}\) and \(\vec{r} \cdot \vec{b}=0\), then \(\mid \vec{r}|\) is equal to :

A unit vector which is perpendicular to the vector \(2 \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}\) and is coplanar with the vectors \(\hat{i}+\hat{j}-\hat{k}\) and \(2 \hat{i}+2 \hat{j}-\hat{k}\) is:

Solve the linear inequality: 

\(\frac{x}{4}<\frac{(5 x-2)}{3}-\frac{(7 x-3)}{5}\)

Find the vector equation of the line that passes through the points \(A(1,0,2)\) and \(B(3,9,6)\).

\(\frac{\sin 7 x+6 \sin 5 x+17 \sin 3 x+12 \sin x}{\sin 6 x+5 \sin 4 x+12 \sin 2 x}\) equals:

Let \(A=\left[\begin{array}{cc}\frac{1}{\sqrt{10}} & \frac{3}{\sqrt{10}} \\ \frac{-3}{\sqrt{10}} & \frac{1}{\sqrt{10}}\end{array}\right]\) and \(B=\left[\begin{array}{cc}1 & -i \\ 0 & 1\end{array}\right]\), where \(i=\sqrt{-1}\). If \(M=A^T B A\), then the inverse of the matrix \(A M^{2023} A^T\) is:

Let two vertices of a triangle \(\mathrm{ABC}\) be \((2,4,6)\) and \((0,-2,-5)\), and its centroid be \((2,1,-1)\). If the image of the third vertex in the plane \(x+2 y+4 z=11\) is \((\alpha, \beta, \gamma)\), then \(\alpha \beta+\beta \gamma+\gamma \alpha\) is equal to :

Let \(p(n)=x\left(x^{n-1}-n \cdot a^{n-1}+a^{n}(n-1)\right)\) is divisible by \((x-a)^{2}\) for:

If \(A=\left[\begin{array}{cc}4 & x+2 \\ 2 x-3 & x+1\end{array}\right]\) is symmetric, then what is \(x\) equal to:

If \(f(x)=\frac{\sin \left(e^{x-2}-1\right)}{\log (x-1)}, x \neq 2\) and \(f(x)=k\). Then, the value of k for which f will be continuous at x = 2 is:

If the planes \(2 x-y-3 z-7=0\) and \(4 x-2 y+5 k z+9=0\) are parallel, then \(5 k+7\) is: