A sample of gas absorbs $$4000 \mathrm{~kJ}$$ of heat and surrounding does $$2000 \mathrm{~J}$$ of work on sample. What is the value of $$\Delta U$$ ?

What is the value of $$\mathrm{C}-\mathrm{O}-\mathrm{H}$$ bond angle in $$\mathrm{CH}_3-\mathrm{OH}$$ ?

What is the molarity of solution containing $$3.2 \mathrm{~g}$$ of $$\mathrm{NaOH}$$ (molar mass $$40 \mathrm{~g} \mathrm{~mol}^{-1}$$) in $$250 \mathrm{~cm}^3$$ of water?

A metallic element crystallises in simple cubic lattice. If edge length of the unit cell is $$3\mathop A\limits^o$$, with density $$8 \mathrm{~g} / \mathrm{cc}$$, what is the number of unit cells in $$100 \mathrm{~g}$$ of the metal?

(Molar mass of metal $$=108 \mathrm{~g} / \mathrm{mol}$$ )

Which among the following compounds belongs to lipids?

Which of the following alcohols needs acidic $$\mathrm{KMnO}_4$$ to convert it into aldehyde or ketone?

What is the bond order of B$$_2$$ molecule?

Which among the following polymers is obtained from styrene and 1-3-butadiene?

What is the oxidation number of As in H$$_3$$AsO$$_3$$ ?

Identify the product '$$A$$' in the following reaction.

$$\text { Aniline } \xrightarrow[\text { Pyridine }]{\left(\mathrm{CH}_3 \mathrm{CO}\right)_2 \mathrm{O}} A$$

Which of the following molecule contain $$50 \%$$ p-character of hybrid orbital in C atom?

The reaction $$2 \mathrm{R}-\mathrm{Cl}+\mathrm{CoF}_2 \longrightarrow 2 \mathrm{R}-\mathrm{F}+\mathrm{CoCl}_2$$ is an example of ............... .

What is the effective atomic number of $$\mathrm{Zn}$$ in $$\left[\mathrm{Zn}\left(\mathrm{NH}_3\right)_4\right] \mathrm{SO}_4$$ ?

Alkyl cynides on reduction by sodium and ethanol give primary amines. This reaction is called as

Which among the following compounds has highest boiling point?

Identify the product obtained, when benzamide is treated with bromine and aqueous sodium hydroxide.

Which among the following methods is not suitable for the preparation of alkyl chlorides?

A solution has an osmotic pressure of '$$x$$' $$\mathrm{kPa}$$ at $$300 \mathrm{~K}$$ having 1 mole of solute in $$10.5 \mathrm{~m}^3$$ of solution. If it's osmotic pressure is reduced to $$\left(\frac{1}{10}\right)$$th of it's initial value, what is the new volume of solution?

Identify the catalyst $$X$$ used in following reaction.

$$\mathrm{CH}_3 \mathrm{CH}_2 \mathrm{Br}+2[\mathrm{H}] \xrightarrow{X} \mathrm{CH}_3-\mathrm{CH}_3+\mathrm{HBr}$$

Which of the following statements is true for carbonyl group?

Mixture of iodine and sodium sulphate is separated by ............... .

If concentration of reactant '$$A$$' is increased by 10 times the rate of reaction becomes 100 times. What is the order of reaction, if rate law is, rate $$=k[A]^x$$ ?

Which among the following is non-poisonous in nature?

A compound has fcc structure. If density of unit cell is $$3.4 \mathrm{~g} \mathrm{~cm}^{-3}$$, what is the edge length of unit cell?

(Molar mass $$=98.99$$)

Identify the element having highest enthalpyot atomisation from following.

What type of inter molecular force is present between magnesium chloride and water?

Xenon crystallises in fcc lattice and the edge length of unit cell is 620 pm. What is the radius of Xe atom?

How many electrons are involved in the reaction, when $$0.40 \mathrm{~F}$$ of electricity is passed through an electrolytic solution?

Which among the following lanthanoids, shows only +3 oxidation state?

Which among the following is used as refrigerants and for air conditioning?

Identify the tetradentate ligand from the following.

If $$38.55 \mathrm{~kJ}$$ of heat is absorbed, when 6.0 of $$\mathrm{O}_2$$ react $$\mathrm{CIF}$$ according to reaction.

$$2 \mathrm{CIF}(g)+\mathrm{O}_2(g) \longrightarrow \mathrm{Cl}_2(g)+\mathrm{OF}_2(g)$$

What is the standard enthalpy of reaction?

A first order reaction has rate constant $$1 \times 10^{-2} \mathrm{~s}^{-1}$$. What time will, it take for $$20 \mathrm{~g}$$ or reactant to reduce to $$5 \mathrm{~g}$$ ?

Which of the following salt contain interstitial water molecule in it?

Which of the following is not present in baking powder?

Identify the enzyme that catalyses the reaction of $$\mathrm{CO}_2$$ with water in huma body.

Which among the following pairs of halogen forms the interhalogen compound of the type $$X X^{\prime}{ }_7$$ ?

Which among the following is a biodegradable polymer?

Which among the following ore is concentrated by froth floatation process?

Which of the following is called as mandelonitrile?

Which among the following group-15 elements does not react with concentrated sulphuric acid?

What will be the concentration of $$\mathrm{NaCl}$$ solution, if the molar conductivity and conductivity of $$\mathrm{NaCl}$$ solution is $$124.3 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$$ and $$1.243 \times 10^{-4} \Omega^{-1} \mathrm{~cm}^2$$ respectively?

Which among the following is an example of allylic alcohol?

Which among the following amino acids has lowest molar mass?

Identify the symbol used for water according to Dalton's atomic theory?

An ideal gas expands isothermally and reversibly from $$10 \mathrm{~m}^3$$ to $$20 \mathrm{~m}^3$$ at $$300 \mathrm{~K}$$, performing $$5.187 \mathrm{~kJ}$$ of work on surrounding, calculate number of moles of gas used.

Which among the following type of linkages is present in cellulose?

Zirconium is refined by

If a centimolal aqueous solution of K$$_3$$[Fe(CN)$$_6$$] has degree of dissociation 0.78. What is the value of van't Hoff factor?

Which among the following is antioxident?

In a triangle $$A B C$$ with usual notations, if $$\frac{\cos A}{a}=\frac{\cos B}{b}=\frac{\cos C}{c}$$, then area of triangle $$A B C$$ with $$a=\sqrt{6}$$ is

If $$\frac{x}{\sqrt{1+x}}+\frac{y}{\sqrt{1+y}}=0, x \neq y$$, then $$(1+x)^2 \frac{d y}{d x}=$$

If $$\int \frac{\sin \theta}{\sin 3 \theta} d \theta=\frac{1}{2 k} \log \left|\frac{k+\tan \theta}{k-\tan \theta}\right|+c$$, then $$k=$$

The probability that bomb will miss the target is 0.2. Then, the probability that out of 10 bombs dropped exactly 2 will hit the target is

The polar co-ordinates of the point whose cartesian co-ordinates are $$(-2,-2)$$, are given by

If $$\int \sqrt{x-\frac{1}{x}}\left(\frac{x^2+1}{x^2}\right) d x=\frac{2}{3}\left(x-\frac{1}{x}\right)^k+c$$, then value of $$k$$ is

$$\int_0^a \sqrt{\frac{x}{a-x}} d x=$$

The minimum value of $$Z=5 x+8 y$$ subject to $$x+y \geq 5,0 \leq x \leq 4, y \geq 2, x \geq 0, y \geq 0$$ is

The sum of the cofactors of the elements of second row of the matrix $$\left[\begin{array}{rrr}1 & 3 & 2 \\ -2 & 0 & 1 \\ 5 & 2 & 1\end{array}\right]$$ is

If the foot of perpendicular drawn from the origin to the plane is $$(3,2,1)$$, then the equation of plane is

If $$f(x)=\log (\sin x), x \in\left[\frac{\pi}{6}, \frac{5 \pi}{6}\right]$$, then value of '$$c$$' by applying LMVT is

The value of $$\sin ^{-1}\left(-\frac{1}{2}\right)+\cos ^{-1}\left(-\frac{\sqrt{3}}{2}\right)$$ is

If $$p \rightarrow(\sim p \vee q)$$ is false, then the truth values of $$p$$ and $$q$$ are respectively

If the equation $$k x y+5 x+3 y+2=0$$ represents a pair of lines, then $$k=$$

If $$(a,-2 a), a>0$$ is the mid-point of a line segment intercepted between the co-ordinate axes, then the equation of the line is

If the vectors $$\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$2 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+m \hat{\mathbf{k}}$$ are coplanar, then $$m=$$

The letters of the word 'LOGARITHM' are arranged at random. The probability that arrangement starts with vowel and end with consonant is

If $$\sqrt{\frac{x}{y}}+\sqrt{\frac{y}{x}}=4$$, then $$\frac{d y}{d x}=$$

If $$x \cos \theta+y \sin \theta=5, x \sin \theta-y \cos \theta=3$$, then the value of $$x^2+y^2=$$

The area of the region bounded by the curve $$y=4 x^3-6 x^2+4 x+1$$ and the lines $$x=1, x=5$$ and $$X$$-axis is

$$\int_\limits2^3 \frac{x}{x^2-1} d x=$$

The angles between the lines $$\mathbf{r}=(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})+\lambda(\hat{\mathbf{i}}+\hat{\mathbf{j}}+2 \hat{\mathbf{k}}) \text { and } \mathbf{r}=(3 \hat{\mathbf{i}}+\hat{\mathbf{k}})+\lambda^{\prime}(2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}), \lambda, \lambda^{\prime} \in \mathbf{R}$$ is

The p.d.f of c.r.v $$X$$ is given by $$f(x)=\frac{x+2}{18}$$, if $$-2

The approximate value of the function $$f(x)=x^3-3 x+5$$ at $$x=1.99$$ is

If for an arithmetic progression, 9 times nineth term is equal to 13 times thirteenth term, then value of twenty second term is

If $$A=\left[\begin{array}{rrr}2 & 0 & -1 \\ 5 & 1 & 0 \\ 0 & 1 & 3\end{array}\right]$$ and $$A^{-1}=\left[\begin{array}{rrr}3 & -1 & 1 \\ \alpha & 6 & -5 \\ \beta & -2 & 2\end{array}\right]$$, then the values of $$\alpha$$ and $$\beta$$ are, respectively.

The differential equation obtained from the function $$y=a(x-a)^2$$ is

In a quadrilateral $$ABCD, M$$ and $$N$$ are the mid-points of the sides $$A B$$ and $$C D$$ respectively. If $$\mathbf{A D}+\mathbf{B C}=t \mathbf{M N}$$, then $$t=$$

If $$f(x)=\log (\sec x+\tan x)$$, then $$f^{\prime}\left(\frac{\pi}{4}\right)=$$

If $$f(x)=\frac{2 x+3}{3 x-2}, x \neq \frac{2}{3}$$, then the function $$f$$ of is

$$\int \cot x \cdot \log [\log (\sin x)] d x=$$

If $$\sin \theta=-\frac{12}{13}, \cos \phi=-\frac{4}{5}$$ and $$\theta, \phi$$ lie in the third quadrant, then $$\tan (\theta-\phi)=$$

The symbolic form of the following circuit is (where $$p, q$$ represents switches $$S_1$$ and $$s_2$$ closed respectively)

The differential equation of all lines perpendicular to the line $$5 x+2 y+7=0$$ is

$$\int_\limits0^{\frac{\pi}{2}} \log \left[\sqrt{\frac{1-\cos 2 x}{1+\cos 2 x}}\right] d x=$$

If $$[\vec{a}\ \vec{b}\ \vec{c}\ ] \neq 0$$, then $$\frac{[\vec{a}\ +\vec{b}\ \vec{b}\ +\vec{c}\ \vec{c}\ +\vec{a}\ ]}{[\vec{b}\ \vec{c}\ \vec{a}\ ]}=$$

The cartesian co-ordinates of the point on the parabola $$y^2=x$$ whose parameter is $$-\frac{4}{3}$$ are

The angle between the line $$r =(\hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}})+\lambda(3 \hat{\mathbf{i}}+\hat{\mathbf{j}})$$ and the plane $$\mathbf{r} \cdot(\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+3 \hat{\mathbf{k}})=8$$ is

The bacteria increases at the rate proportional to the number of bacteria present. If the original number '$$N$$' doubles in $$4 \mathrm{~h}$$, then the number of bacteria in $$12 \mathrm{~h}$$ will be

If $$A=\{x, y, z\}, B=\{1,2\}$$, then the total number of relations from set $$A$$ to set $$B$$ are :

The equation of tangent at $$P(-4,-4)$$ on the curve $$x^2=-4 y$$ is

The rate of decay of certain substance is directly proportional to the amount present at that instant. Initially, there are $$27 \mathrm{~gm}$$ of certain substance and $$3 \mathrm{~h}$$ later it is found that $$8 \mathrm{~gm}$$ are left, then the amount left after one more hour is

The direction cosines of a line which is perpendicular to lines whose direction ratios are $$3,-2,4$$ and $$1,3,-2$$ are

The points of discontinuity of the function

$$\begin{aligned} f(x) & =\frac{1}{x-1}, \text { if } 0 \leq x \leq 2 \\ & =\frac{x+5}{x+3} \text { if } 2< x \leq 4 \end{aligned}$$

in its domain are

If the angle between the lines given by the equation $$x^2-3 x y+\lambda y^2+3 x-5 y+2=0, \lambda \geq 0$$, is $$\tan ^{-1}\left(\frac{1}{3}\right)$$, then $$\lambda=$$

If the p.m.f of a. r.v. $$X$$ is given by

$$P(X=x)=\frac{{ }^5 C_x}{2^5}$$

if $$x=0,1,2, \ldots \ldots . .5=0$$,

0 , otherwise,

then which of the following is not true?

The radius of the circle passing through the points $$(5,7),(2,-2)$$ and $$(-2,0)$$ is

The integrating factor of the differential equation $$\left(1+x^2\right) d t=\left(\tan ^{-1} x-t\right) d x$$ is

In a triangle $$A B C$$, if $$\frac{\sin A-\sin C}{\cos C-\cos A}=\cot B$$, then $$A, B, C$$, are in

If the lines given by $$\frac{x-1}{2 \lambda}=\frac{y-1}{-5}=\frac{z-1}{2}$$ and $$\frac{x+2}{\lambda}=\frac{y+3}{\lambda}=\frac{z+5}{1}$$ are parallel, then the value of $$\lambda$$ is

An ammeter of resistance $$20 \Omega$$ gives full scale deflection, when $$1 \mathrm{~mA}$$ current flows through it. What is the maximum current that can be measured by connecting 4 resistors each of $$16 \Omega$$ in parallel with the ammeter?

An alternating emf of $$0.2 \mathrm{~V}$$ is applied across an L-C-R series circuit having $$R=4 \Omega, C=80 \mu \mathrm{F}$$ and $$L=200 \mathrm{~mH}$$. At resonance the voltage drop across the inductor is

An electron $$(e)$$ is revolving in a circular orbit of radius $$r$$ in hydrogen atom. The angular momentum of the electron is ($$M=$$ magnetic dipole moment associated with it and $$m=$$ mass of electron)

In non-uniform circular motion, the ratio of tangential to radial acceleration is ($$r=$$ radius, $$\alpha=$$ angular acceleration and $$v=$$ linear velocity)

In common emitter amplifier, input resistance is $$1000 \Omega$$, peak value of input signal voltage is $$5 \mathrm{~mV}$$ and $$\beta=60$$. The peak value of output current is

A simple pendulum of length $$L$$ has mass $$m$$ and it oscillates freely with amplitude $$A$$. At extreme position, its potential energy is ($$g=$$ acceleration due to gravity)

The extension in a wire obeying Hooke's law is $$x$$. The speed of sound in the stretched wire is $$v$$. If the extension in the wire is increased to $$4 x$$, then the speed of sound in a wire is

Let force $$F=A \sin (C t)+B \cos (D x)$$, where $$x$$ and $$t$$ are displacement and time, respectively. The dimensions of $$\frac{C}{D}$$ are same as dimensions of

Two vectors of same magnitude have a resultant equal to either of the two vectors. The angle between two vectors is

If there is a change of angular momentum from $$1 \mathrm{j}$$-$$\mathrm{s}$$ to $$4 \mathrm{j}$$-$$\mathrm{s}$$ in $$4 \mathrm{~s}$$, then the torque

For a gas, $$\frac{R}{C_V}=0.4$$, where $$R$$ is universal gas constant and $$C_V$$ is the molar specific heat at constant volume. The gas is made up of molecules, which are

The maximum velocity of the photoelectron emitted by the metal surface is $$v$$. Charge and mass of the photoelectron is denoted by $$e$$ and $$m$$, respectively. The stopping potential in volt is

Energy of the incident photon on the metal surface is $$3 W$$ and then $$5 W$$, where $$W$$ is the work function for that metal. The ratio of velocities of emitted photoelectrons is

Water rises in a capillary tube of radius $$r$$ upto a height $$h$$. The mass of water in a capillary is $$m$$. The mass of water that will rise in a capillary of radius $$\frac{r}{4}$$ will be

Two waves $$Y_1=0.25 \sin 316 t$$ and $$Y_2=0.25 \sin 310 t$$ are propagating along the same direction. The number of beats produced per second are

A small metal sphere of mass $$M$$ and density $$d_1$$ when dropped in a jar filled with liquid moves with terminal velocity after sometime. The viscous force acting on the sphere is ($$d_2=$$ density of liquid and $$g=$$ gravitational acceleration)

The capacitance of a parallel plate capacitor with air as medium is $$3 \mu \mathrm{F}$$. With the introduction of a dielectric medium between the plates, the capacitance becomes $$15 \mu \mathrm{F}$$. The permittivity of the medium in $$\mathrm{SI}$$ unit is $$[\varepsilon_0=8.85 \times 10^{-12} \mathrm{SI}$$ unit]

The mass of earth is 81 times the mass of the moon and the distance between their centres is $$R$$. The distance from the centre of the earth, where gravitational force will be zero is

A coil of $$n$$ turns and resistance $$R \Omega$$ is connected in series with a resistance $$\frac{R}{2}$$. The combination is moved for time $$t$$ second through magnetic flux $$\phi_1$$ to $$\phi_2$$. The induced current in the circuit is

Two identical bar magnets each of magnetic moment $$M$$, separated by some distance are kept perpendicular to each other. The magnetic induction at a point at the same distance $$d$$ from the centre of magnets, is ($$\mu_0=$$ permeability of free space)

A bullet of mass $$m$$ moving with velocity $$v$$ is fired into a wooden block of mass $$M$$, If the bullet remains embedded in the block, the final velocity of the system is

In diffraction experiment, from a single slit, the angular width of the central maxima does not depend upon

A vehicle of mass $$m$$ is moving with momentum $$p$$ on a rough horizontal road. The coefficient of friction between the tyres and the horizontal road is $$\mu$$. The stopping distance is ($$g=$$ acceleration due to gravity)

In Young's double slit experiment green light is incident on the two slits. The interference pattern is observed on a screen. Which one of the following changes would cause the observed fringes to be more closely spaced?

Two identical strings of length $$l$$ and $$2l$$ vibrate with fundamental frequencies $$\mathrm{N} \mathrm{~Hz}$$ and $$1.5 N$$ Hz, respectively. The ratio of tensions for smaller length to large length is

In amplitude modulation,

When a photon enters glass from air, which one of the following quantity does not change?

Two wires $$A$$ and $$B$$ of equal lengths are connected in left and right gap of a meter bridge, null point is obtained at $$40 \mathrm{~cm}$$ from left end. Diameters of the wire $$A$$ and $$B$$ are in that ratio $$3: 1$$. The ratio of specific resistance of $$A$$ to the of $$B$$ is

When a small amount of impurity atoms are added to a semiconductor, then generally its resistivity

When open pipe is closed from one end third overtone of closed pipe is higher in frequency by $$150 \mathrm{~Hz}$$, then second overtone of open pipe. The fundamental frequency of open end pipe will be

A ray of light is incident at an angle $$i$$ on one face of prism of small angle $$A$$ and emerges normally from the other surface. $$\mu$$ is the refractive index of the material of the prism. The angle of incidence is

Two small drops of mercury each of radius $$r$$ coalesce to form a large single drop. The ratio of the total surface energies before and after the change is

A solid cylinder of radius $$r$$ and mass $$M$$ rolls down an inclined plane of height $$h$$. When it reaches the bottom of the plane, then its rotational kinetic energy is ($$g=$$ acceleration due to gravity)

A potentiometer wire is $$4 \mathrm{~m}$$ long and potential difference of $$3 \mathrm{~V}$$ is maintained between the ends. The emf of the cell, which balances against a length of $$100 \mathrm{~cm}$$ of the potentiometer wire is

A charged particle is moving in a uniform magnetic field in a circular path of radius $$R$$. When the energy of the particle becomes three times the original, the new radius will be

The density of a metal at normal pressure $$p$$ is $$\rho$$. When it is subjected to an excess pressure, the density becomes $$\rho^{\prime}$$. If $$K$$ is the bulk modulus of the metal, then the ratio $$\frac{\rho^{\prime}}{\rho}$$ is

For a particle performing SHM when displacement is $$x$$, the potential energy and restoring force acting on it is denoted by $$E$$ and $$F$$, respectively. The relation between $$x, E$$ and $$F$$ is

Surface density of charge on a charged conducting sphere of radius $$R$$ in terms of electric field intensity $$E$$ at a distance $$r$$ in free space is ($$r>R, \varepsilon_0=$$ permittivity of free space)

A body is thrown from the surface of the earth velocity $$\mathrm{v} / \mathrm{s}$$. The maximum height above the earth's surface upto which it will reach is ($$R=$$ radius of earth, $$g=$$ acceleration due to gravity)

Using Bohr's quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule? ($$I=$$ moment of inertia of diatomic molecule and, $$h=$$ Planck's constant)

A monoatomic gas of pressure $$p$$ having volume $$V$$ expands isothermally to a volume $$2V$$ and then adiabatically to a volume $$16 \mathrm{~V}$$. The final pressure of the gas is (ratio of specific heats $$=\frac{5}{3}$$

A particle is moving in a radius $$R$$ with constant speed $$v$$. The magnitude of average acceleration after half revolution is

The magnifying power of a telescope is high, if its objective and eyepiece have respectively

The ratio of speed of an electron in the ground state in the Bohr's first orbit of hydrogen atom to velocity of light $$(c)$$ is ( $$h=$$ Planck's constant, $$\varepsilon_0=$$ permittivity of free space, $$e=$$ charge on electron)

A charge $$q$$ moves with velocity $$v$$ through electric field $$\mathrm{E}$$ as well as magnetic field (B). Then, the force acting on it is

The force acting on the electrons in hydrogen atom (Bohr's theory) is related to the principle quantum number $$n$$ as

A body of mass $$2 \mathrm{~kg}$$ is acted upon by two forces each of magnitude $$1 \mathrm{~N}$$ and inclined at $$60^{\circ}$$ with each other. The acceleration of the body in $$\mathrm{m} / \mathrm{s}$$ is [$$\cos 60^{\circ}=0.5$$]

Two rods of same material and volume having circular cross-section are subjected to tension $$T$$. Within the elastic limit, same force is applied to both the rods. Diameter of the first rod is half of the second rod, then the extensions of first rod to second rod will be in the ratio

An iron rod is placed parallel to magnetic field of intensity $$2000 \mathrm{~A} / \mathrm{m}$$. The magnetic flux through the rod is $$6 \times 10^{-4} \mathrm{~Wb}$$ and its cross-sectional area is $$3 \mathrm{~cm}^2$$. The magnetic permeability of the rod in $$\frac{\mathrm{Wb}}{\mathrm{A}-\mathrm{m}}$$ is

A moving body is covering distances which are proportional to square of the time. Then, the acceleration of the body is