The reaction of cyanamide, \(\mathrm{NH}_{2} \mathrm{CN}(\mathrm{s})\) with dioxygen was carried out in a bomb calorimeter and \(\Delta \mathrm{U}\) was found to be \(-742.7 \mathrm{KJ} \mathrm{mol}^{-1}\) at \(298 \mathrm{~K}\). Calculate the enthalpy change for the reaction at \(298 \mathrm{~K}\).

\(\mathrm{N H}_{4} \mathrm{CN}_{(\mathrm{g})}+\frac{3}{2} \mathrm{O}_{2(\mathrm{~g})} \rightarrow \mathrm{N}_{2(\mathrm{~g})}+\mathrm{CO}_{2(\mathrm{~g})}+\mathrm{H}_{2} \mathrm{O}_{(\mathrm{l})}\)

Ethylidene chloride is a/an ___________.

Match List-I with List-II

Choose the correct answer form the options given below.

Which of the following is not a heteroatom?

In a hexagonal closed packing lattice, coordination number of an atom in a unit cell is:

Calculate (a) wavenumber and (b) frequency of yellow radiation having wavelength \(5800 Å\).

In the complex \(K _{2} Fe \left[ Fe ( CN )_{6}\right]\):

Which of the following compounds give(s) positive test with Tollens' reagent?

A. Carboxylic acid

B. Alcohol

C. Alpha hydroxy ketones

D. Aldehydes

A rain in 50% completed om shown and 75% in 4 hours. Find the order of reaction:

Bonds that do not exist in tertiary structure of proteins:

Consider the following reactions :

(i) Glucose + ROH \(\xrightarrow{\text { dry } \mathrm{HCl}}\), Acetal \(\frac{\text { xeq. of }}{\left(\mathrm{CH}_3 \mathrm{CO}_2 \mathrm{O}\right.}\) acetyl derivative

(i) Glucose \(\xrightarrow{\mathrm{Ni} / \mathrm{H}_2} \cdot \mathrm{A} \frac{\text { yeq. of }}{\left(\mathrm{CH}_3 \mathrm{CO}_2 \mathrm{O}\right.} \cdot\) acetyl derivative

(i) Glucose \(+\frac{z \text { eq. of }}{\left(\mathrm{CH}_3 \mathrm{CO}_2 \mathrm{O}\right.} \times\) acetyl derivative

' \(x\) ', 'y' and 'z' in these reactions are respectively.

The boiling points of water, ethanol and diethyl ether are 100°C, 78.5°C and 34.6°C, respectively. The intermolecular forces will be in order.

Toluene reacts with halogen in presence of iron(III) chloride giving ortho and para halo compounds, the reaction is?

Oils are rich in:

A hydrocarbon has molecular formula \(\mathrm{C}_{2} \mathrm{H}_{6}\). Which of the class of hydrocarbons cannot have this formula?

The freezing point of equimolal aqueous solution will be highest for:

Which is the shape of sulfur hexafluoride molecule?

In which of the following conditions, the potential for the following half-cell reaction is maximum?

\(2 \mathrm{H}^{+}+2 e \rightarrow \mathrm{H}_{2}\)

Identify the species in which the metal atom is in \(\mathrm{+6}\) oxidation state.

What are Oxo-Acids?

Generally transition elements form coloured salts due to the presence of unpaired electrons. Which of the following compounds will be coloured in solid state? 

The enthalpy change on freezing of \(1 \mathrm{~mol}\) of water at \(5^{\circ} \mathrm{C}\) to ice at \(-5^{\circ} \mathrm{Cis}\) :

\(\left(\text { Given } \Delta_{\text {fis }} \mathrm{H}=6 \mathrm{~kJ} \mathrm{~mol}^{-1} \text { at } 0^{\circ} \mathrm{C}\right. \text {, } \)

\(\mathrm{C}_{\mathrm{p}}\left(\mathrm{H}_2 \mathrm{O}, 1\right)=75.3 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1} \)

\(\left.\mathrm{C}_{\mathrm{p}}\left(\mathrm{H}_2 \mathrm{O}, \mathrm{s}\right)=36.8 \mathrm{~J} \mathrm{~mol}^{-1} \mathrm{~K}^{-1}\right)\)

How many structural isomers are possible for \(\mathrm{C}_{3} \mathrm{H}_{9} \mathrm{~N}\) ?

Calculate energy of one mole of photons of radiation whose frequency is \(5 \times 10^{14}\) \(\mathrm{Hz}\).

 A system is said to be in thermodynamic equilibrium if the system is in:

Hydrogen gas is not obtained when zinc reacts with:

In which of the preparation process of dihydrogen, the syn gas is produced?

A solid has a ‘BCC’ structure. If the distance of nearest approach between two atoms is 1.73Å, the edge length of the cell is:

The oxidation number of \(\mathrm{Cr}\) in \(\mathrm{Cr} O_{5}\) which has the following structure, is:

Shortest \(\mathrm{C-C}\) bond length is present in ___________.

The correct order of melting point of dichlorobenzenes is

If we assume that one-sixth the mass of an atom of \({ }^{12} C\) isotope is taken as the reference, the mass of one molecule of oxygen will:

Which of the following theory is not related to the chemical kinetics?

Which of the following statement is not correct?

In the upper layers of atmosphere ozone is formed:

In a process, \(701 \mathrm{~J}\) of heat is absorbed by a system and \(394 \mathrm{~J}\) of work is done by the system. What is the change in internal energy for the process?

The hydrocarbon in which all the \(4\) valencies of carbon are fully occupied is called as __________.

Chlorine atom in \(\mathrm{CH}_{3} \mathrm{CH}_{2} \mathrm{Cl}\) is attached to:

A current of \(2\) amp when passed for \(5\) hours through a molten salt deposits \(22.2 \mathrm{~g}\) of metal of atomic mass \(177\). The oxidation state of the metal in the metal salt is:

According to Werner's theory of coordination compounds:

Which pair of oxides is acidic in nature?

Carbon belongs to the second period and Group 14. Silicon belongs to the third period and Group 14. If atomic number of carbon is 6, the atomic number of silicon is:

Ozonolysis of an organic compound gives formaldehyde as one of the products. This confirms the presence of:

In the above conversion the correct sequence of reagents to be added is :

Electrolysis of dilute aqueous \(NaCl\) solution was carried out by passing \(10\) milli ampere current. The time required to liberate \(0.01\) mol of \(H_{2}\) gas at the cathode is: (\(1\) Faraday \(=96500 Cmol ^{-1}\))

Two flasks I and II shown below are connected by a valve of negligible volume.

When the valve is opened, the final pressure of the system in bar is \(x \times 10^{-2}\). The value of \(x\) is _________(Integer answer)

[Assume, Ideal gas, \(1 \mathrm{bar}=10^5 \mathrm{~Pa}\), molar mass of \(\left.\mathrm{N}_2=28.0 \mathrm{gmol}^{-1} ; \mathrm{R}=8.31 \mathrm{Jmol}^{-1} \mathrm{~K}^{-1}\right]\)

Which of the following are arranged in an increasing order of their bond strength?

Calculate the 'spin only' magnetic moment of \({M}^{2+}{ }_{\text {(aq) }}\) ion \(({Z}=27 )\).

Techniques like titration, precipitation, spectroscopy, chromatography, etc. commonly used in ___________________.

In which condition, adsorption will not take place?

When pressure on piece of ice is increases, its melting point __________.

Assertion: Among the carbon allotropes, diamond is an insulator, whereas, graphite is a good conductor of electricity.

Reason: Hybridization of carbon in diamond and graphite are \(\mathrm{sp}^3\) and \(\mathrm{sp}^2\), respectively.

Which compound would give 5 - keto -2 - methylhexanal upon ozonolysis?

\(100 \mathrm{~g}\) of propane is completely reacted with \(1000 \mathrm{~g}\) of oxygen. The mole fraction of carbon dioxide in the resulting mixture is \(x \times 10^{-2}\). The value of \(x\) is_____________(Nearest integer)

[Atomic weight : \(\mathrm{H}=1.008, \mathrm{C}=12.00, \mathrm{O}=16.00\) ]

If \(\mathrm{NaCl}\) is doped with \(10^{-3} \mathrm{~mol} \%\) of \( \mathrm{FeCl}_{3}\), then the number of unoccupied of octahedral voids per mol of \(\mathrm{NaCl}\) is:

Which of the following 0.10m aqueous solution will have the lowest freezing point?

Gallium remains liquid up to __________ Kelvin.

Using \(MO\) theory, predict which of the following species has the shortest bond length?

Find the value of \(k\) if \(\underset{{{x \rightarrow 0}}}{\lim}\frac{-3 x^{2}-7 x+8}{7 x^{2}+2 x+2}=k\)

Let \(f: R \rightarrow R\) be defined as \(f(x)=x^{4}\). Choose the correct answer.

If (x) is an odd periodic function with period 2, then f(4) equal to:

Feasible region (shaded) for a LPP is shown in Fig., Maximise \(Z=5 x+7 y\). Find the maximum value of \(Z\).

Find the area of the region (in sq. units) bounded by the curve \(y=e^{-2 x}\) and \(x\)-axis for \(x \in(-1,1)\).

The number of solutions of the equation \(x^{3}+2 x^{2}+5 x+2 \cos x=0\) in \([0,2 \pi]\) are:

The line passing through the points (1, 2, -1) and (3, -1, 2) meets the yz-plane at which one of the following points?

Find the value of \(x\) for the equation \(2 \tan ^{-1}(\cos x)=\tan ^{-1}(2 \operatorname{cosec} x) ?\)

Form the differential equation for the family of circle with center \((0,0)\) and radius \(r\), where \(r\) is any constant.

Calculate the area under the curve \(y=2 \sqrt{x}\) and included between the lines \(x=0, x=4\).

Evaluate:

\(\frac{\cos x-\sin x+1}{\cos x+\sin x-1}\)

Let \(\vec{\alpha}=3 \hat{i}+\hat{j}\) and \(\vec{\beta}=2 \hat{i}-\hat{j}+3 \hat{k}\). If \(\vec{\beta}=\vec{\beta}_1-\vec{\beta}_2\), where \(\vec{\beta}_1\) is parallel to \(\vec{\alpha}\) and \(\vec{\beta}_2\) is perpendicular to \(\vec{\alpha}\), then \(\vec{\beta}_1 \times \vec{\beta}_2\) is equal to:

How many different words can be formed by using all the letters of the word, ALLAHABAD if both L's do not come together? 

What is the product of the perpendiculars drawn from the points \(\left(\pm \sqrt{a^{2}-b^{2}}, 0\right)\) upon the line \(b x \cos \alpha+\) ay \(\sin \alpha=a b\)?

A basket contains \(6\) blue, \(2\) red, \(4\) green and \(3\) yellow balls. If \(5\) balls are picked up at random, what is the probability that at least one is blue?

The feasible solution for a LPP is shown in Figure. Let \(\mathrm{Z}=3 {x}-4 {y}\) be the Objective function, Maximum of \(\mathrm{Z}\) occurs at:

If \(A=\{2,3\}, B=\{4,5\}, C=\{5,6\}\), then what is the number of elements in \(A \times(B \cap C) ?\)

What is \(\lim _{x \rightarrow 0} \frac{\sin x \log (1-x)}{x^{2}}\) equal to?

\(|\overrightarrow{\mathrm{a}}+\overrightarrow{\mathrm{b}}|=|\overrightarrow{\mathrm{a}}-\overrightarrow{\mathrm{b}}|,\) then which one of the following is correct?

If \(A B^{T}\) is defined as a square matrix then what is the order of the matrix \(B\), where matrix \(A\) has order \(2 \times 3\)?

The relation between, AM, GM and HM is:

A fair die with faces \(\{1,2,3,4,5,6\}\) is thrown repeatedly till \(3\) is observed for the first time. Let \(X\) denote the number of times the die is thrown. The expected value of \(X\) is:

Find the interval in which the function \(f(x)=\log (1+x)-\frac{x}{(1+x)}\) is decreasing?

If \(A=\left[\begin{array}{ccc}1 & 2 & 2 \\ 2 & 1 & -2 \\ a & 2 & b\end{array}\right]\) is a matrix satisfying the equation \(A A^T=9 I\), where I is \(3 \times 3\) identity matrix, then the ordered pair \((a, b)\) is equal to:

If \(\mathrm{P}(\mathrm{n})\) be the statement that \(\mathrm{n}^{2}-\mathrm{n}+41\) is prime, then which of the following is not true?

The interval in which the function \(f(x)=2 x^{3}-15 x^{2}+36 x+12\) is increasing in:

If three distinct numbers \(a, b, c\) are in G.P. and the equations \(\mathrm{ax}^2+2 \mathrm{bx}+\mathrm{c}=0\) and \(\mathrm{dx}^2+2 \mathrm{ex}+\mathrm{f}=0\) have a common root, then which one of the following statements is correct?

The feasible region of an LPP is shown in the figure. If \(z=3 x+9 y\), then the minimum value of \({z}\) occurs at:

Find the value of \(\left|\begin{array}{ccc}1 & 1 & 1 \\ a & b & c \\ a^{3} & b^{3} & c^{3}\end{array}\right|\).

What is the probability of solving a given problem if three students \((A, B\) and \(C)\), try it independently, with respective probabilities \(\frac{4}{7}, \frac{3}{8}\) and \(\frac{1}{2}\)?

If \(A=\left[\begin{array}{ccc}1 & 2 & x \\ 3 & -1 & 2\end{array}\right]\) and \(B=\left[\begin{array}{l}y \\ x \\ 1\end{array}\right]\) be such that \(A B=\left[\begin{array}{l}6 \\ 8\end{array}\right]\),then:

If \(A=\left[\begin{array}{cc}\sin \alpha & -\cos \alpha \\ \cos \alpha & \sin \alpha\end{array}\right]\), then for what value of \(\alpha, A\) is an identity matrix?

The differential equation of the family of curves \(y=c_1 e^x+c_2 e^{-x}\) is:

Find the value of \(k\) if \(\underset{{{x \rightarrow 7}}}{\lim} g(x)=k\) where \(g(x)=\sqrt{8 x-7}\) 

Find the multiplicative inverse of 4 - 3i ?

The total number of subsets of a finite set A has 56 more elements than the total number of subsets of another finite set B. What is the number of elements in set A?

Find the mode of the following data

Find the angle between the line \(\frac{x-1}{3}=\frac{y+1}{-1}=\frac{z-3}{2}\) and the plane \(3 x+4 y+z+5=0\).

Find the values of \(k\) for which the length of the perpendicular from the point \((4,1)\) on the line \(3 x-4 y+k=0\) is 2 units?

The number of ways in which 5 boys and 4 girls to sit around a table, so that, all the boys sit together is:

If \(|x|<-5\) then the value of \(x\) lies in the interval:

The tangent to the curve \(y^{2}=16 x\) and touches the curve at a point (1,4). Find the distance of origin from the tangent.

Find the value of \(\cos ^{-1}\left(4 x^3-3 x\right), x \in[-1,1]\).

Find the value of \(\int \frac{\mathrm{dx}}{1+\mathrm{e}^{-\mathrm{x}}}\), where \(c\) is the constant of integration.

If a curve \(y=f(x)\) passes through the point \((1,2)\) and satisfies \(x \frac{d y}{d x}+y=b x^4\), then for what value of \(b, \int_1^2 f(x) d x=\frac{62}{5} ?\)

A pack of cards has one card missing. Two cards are drawn randomly and are found to be spades. The probability that the missing card is not a spade, is:

Let \(\vec{a}=\hat{i}+\hat{j}+\hat{k}, \vec{c}=\hat{j}-\hat{k}\) and a vector \(\vec{b}\) be such that \(\vec{a} \times \vec{b}=\vec{c}\) and \(\overrightarrow{\mathrm{a}} \cdot \overrightarrow{\mathrm{b}}=3\). Then \(|\overrightarrow{\mathrm{b}}|\) equals?

One of the roots of \(\left|\begin{array}{ccc}x+a & b & c \\ a & x+b & c \\ a & b & x+c\end{array}\right|=0\) is

Solve: \(\frac{-1}{(|x|-2)} \geq 1\) where x ∈ R, x ≠ ±2

What is the area of the rectangle having vertices \(\mathrm{A}, \mathrm{B}, \mathrm{C}\) and \(\mathrm{D}\) with position vectors \(-\hat{\mathrm{i}}+\frac{1}{2} \hat{\mathrm{j}}+4 \hat{\mathrm{k}}, \hat{\mathrm{i}}+\frac{1}{2} \hat{\mathrm{j}}+4 \hat{\mathrm{k}}, \hat{\mathrm{i}}-\frac{1}{2} \hat{\mathrm{j}}+4 \hat{\mathrm{k}}\) and \(-\hat{\mathrm{i}}-\frac{1}{2} \hat{\mathrm{j}}+4 \hat{\mathrm{k}}\)?

Evaluate the integral \(\int_{2}^{3} \frac{\cos x-\sin x}{4} dx\).

If \(2 \sin ^{2} A+3 \cos ^{2} A=2\), find the value of \((\tan A-\cot A)^{2}\) where, \(\sin A>0\)

A sequence \(a_{1}, a_{2}, a_{3} \ldots\) is defined by letting \(a_{1}=3\) and \(a_{k}=7 a_{k-1}\) for all natural numbers \(k \geq 2\). Show that a_n \(=3.7^{\mathrm{n}-1}\) for all:

If the position vectors of the vertices \(A, B\) and \(C\) of a \(\triangle A B C\) are respectively \(4 \hat{i}+7 \hat{j}+8 \hat{k}, 2 \hat{i}+3 \hat{j}+4 \hat{k}\) and \(2 \hat{i}+5 \hat{j}+7 \hat{k}\), then the position vector of the point, where the bisector of \(\angle \mathrm{A}\) meets \(\mathrm{BC}\) is:

Find the value of \(\lim _{x \rightarrow 0} \frac{\sqrt[p]{1+x}-1}{x}\), where \(p\) is a positive integer.

If \(\frac{e^{x}}{1-x}=B_{0}+B_{1} x+B_{2} x^{2}+\ldots+B_{n} x^{n}+\ldots\), then the value of \(B_{n}-B_{n-1}\) is:

Find the equation of the line which makes an angle of \(30^{\circ}\) with the positive direction of the \(x\) -axis and cuts off an intercept of 4 units with the negative direction of the \(y\) axis?

If \(\vec{a}, \vec{b}\), and \(\vec{c}\) are unit vectors such that \(\vec{a}+2 \vec{b}+2 \vec{c}=\overrightarrow{0}\), then \(|\vec{a} \times \vec{c}|\) is equal to: