Which of the following is an alkali metal?

The electrical conductance of unit volume (1 cm$$^3$$) of solution is called as

What is oxidation state of cobalt in a coordination complex if it's EAN is 36 and the value of C.N. is 6 (Given: Atomic number of cobalt = 27).

Which among the following cations will not form coloured compounds? (Atomic number $$\mathrm{Cu}=29, \mathrm{Ti}=22, \mathrm{~V}=23, \mathrm{Mn}=25$$)

Which of the following aldehydes is less reactive towards nucleophilic addition reaction?

Which of the following is an aldohexose?

Cannizzaro reaction is an example of

The solution containing $$3 \mathrm{~g}$$ urea (molar mass 60 ) per $$\mathrm{dm}^3$$ of water and another solution containing $$4.5 \mathrm{~g}$$ of solute $$\mathrm{A}$$ per $$\mathrm{dm}^3$$ boils at same temperature, then what is molar mass of $$\mathrm{A}$$ ?

Which following statement is true for vinylic halide?

What is the formal charge on 'N' atom in

ion?

Identify the product 'B' in the following series of reactions.

$$\mathrm{CH_3COOH+CH_3CH_2OH}$$ $$\stackrel{\mathrm{H}^{+}}{\rightleftharpoons} A \xrightarrow[\mathrm{Ni} / \mathrm{Pd}, \Delta]{\mathrm{H}_2}$$ B

The solubility of sparingly soluble salt $$\mathrm{AB}_2$$ is $$1.0 \times 10^{-4} \mathrm{~mol} \mathrm{~dm}^{-3}$$. What is it's solubility product?

Which element from following in +3 oxidation state forms colourless compounds?

Which among the following compounds contains amino group?

What is IUPAC name of phloroglucinol?

In a first reaction 60% of reactant decomposes in 4.606 min. What is half life of reaction? (k = 0.1989 min$$^{-1}$$)

The density of chromium metal is 7 g cm$$^{-3}$$. If edge length of unit cell is 300 pm, identify the type of unit cell. (At mass Cr = 52)

How many gram of H$$_2$$O are present in 0.25 mol of it?

Identify molecular formula of pyridine from following

Which of the following is a first step in mechanism of heterogenous catalysis?

Which of the following carboxylic acids has lowest boiling point?

For the reaction, $$2 \mathrm{~A}+\mathrm{B} \rightarrow 2 \mathrm{C}$$, rate of disappearance of $$\mathrm{A}$$ is $$0.076 \mathrm{~mol} \mathrm{~s}^{-1}$$. What is the rate of disappearance of $$\mathrm{B}$$ ?

Which of following is an example of cross-linked polymers?

For isochoric process, the first law of thermodynamics can be expressed as

Which of the following alcohols has lowest boiling point?

What is the $$\mathrm{pH}$$ of $$0.005 \mathrm{~M} \mathrm{~H}_2 \mathrm{SO}_4$$ solution?

The solubility product expression for $$\mathrm{Ca}_3\left(\mathrm{PO}_4\right)_2$$ is represented as

Which among the following is NOT a feature of $$\mathrm{S}_{\mathrm{N}} 1$$ mechanism?

An element has $$\mathrm{BCC}$$ structure with edge length of unit cell $$600 \mathrm{~pm}$$. What is the atomic radius of element?

When certain volume of gas expands against a constant external pressure of $$2.40 \times 10^5 \mathrm{~Pa}$$ at 300 $$\mathrm{K}$$ to $$2.2 \times 10^{-3} \mathrm{~m}^3$$. If the work obtained is $$-0.048 \mathrm{~kJ}$$. What is the initial volume of the gas?

Which among the following pairs of electronic effect and it's example is NOT correct?

A certain mass of a gas occupies volume of 250 mL at 2 atm. Calculate the volume of gas if pressure is increased to 2.5 atm at constant temperature.

Vapour pressure of solution and of pure solvent are $$\mathrm{P}_1$$ and $$\mathrm{P}_1{ }^0$$ respectively. If $$\frac{P_1}{P_1^0}$$ is 0.15, find the mole fraction of solute.

Which of the following pairs of compounds is isomorphous?

What is internal energy change when $$62 \mathrm{~J}$$ of work is done on the system and $$128 \mathrm{~J}$$ of heat is transferred to surrounding?

Which of the following catalyst/reagent is used to convert $$\mathrm{C} \equiv \mathrm{C}$$ triple bond to $$\mathrm{C}=\mathrm{C}$$ double bond to form cis isomer of alkene?

Which among the following reactions exhibits the reducing property of ozone?

Which of the following is a correct bridged name of deoxyriboseadenosine monophosphate?

What is IUPAC name of the following compound?

Which among following compounds of chlorine possesses Cl atom in highest oxidation state?

According to Raoult's law mole fraction of solute in solution in given by formula

What is maximum number of electrons accommodated in a subshell having azimuthal quantum number, $$\ell$$ = 2 ?

Half-life and rate constant for first order reaction are related by equation,

What is the conductivity of 0.02 M HCl solution if molar conductivity of the solution at 25$$^\circ$$C is 412.3 $$\Omega^{-1}$$ cm$$^{-1}$$ mol$$^{-1}$$ ?

Which among the following is a source of wool?

What is percentage atom economy during conversion of reactant to product if formula weight of reactants is 246 u and of product is 123 u?

What is the charge required for the reduction of moles of Cu$$^{2+}$$ to Cu?

Which of the following amine is weakest base?

Which of following is NOT a redox reaction?

Which among the following is a correct order of increasing field strength of ligands?

The probability that at least one of the events $$E_1$$ and $$E_2$$ occurs is 0.6. If the simultaneous occurrence of $$\mathrm{E}_1$$ and $$\mathrm{E}_2$$ is $$0.2, \mathrm{P}\left(\mathrm{E}_1^{\prime}\right)+\mathrm{P}\left(\mathrm{E}_2^{\prime}\right)=$$

$$\lim _\limits{x \rightarrow 0} \frac{\sqrt{1-\cos x^2}}{1-\cos x}=$$

If $$\mathrm{A}=\left[\begin{array}{cc}\lambda & \mathrm{i} \\ \mathrm{i} & -\lambda\end{array}\right]$$ and $$\mathrm{A}^{-1}$$ does not exist, then $$\lambda=$$ (where $$\mathrm{i}=\sqrt{-1}$$)

The distance 's' in meters covered by a particle in t seconds is given by $$s=2+27 t-t^3$$. The particle will stop after _________ distance.

If the polar co-ordinates of a point are $$\left(2, \frac{\pi^{\mathrm{c}}}{4}\right)$$, then its Cartesian co-ordinates are

$$\int e^x\left(\frac{1+\sin x}{1+\cos x}\right) d x=$$

The negation of '$$\forall x \in N, x^2+x$$ is even number' is

$$\int_\limits2^5 2[\mathrm{x}] \mathrm{dx}=\{\text { where }[\mathrm{x}] \text { denotes the greatest integer function } \leq \mathrm{x}\}$$

$$\int_\limits0^\pi x \sin x \cos ^4 x d x=$$

The equation of the plane which passes through (2, $$-$$3, 1) and is normal to the line joining the points (3, 4, $$-$$1) and (2, $$-$$1, 5) is given by

A committee of 5 is to be formed out of 6 men and 4 ladies. The number of ways this can be done, when at most 2 ladies are included, is

In a triangle ABC with usual notations a = 2, b = 3, then value of $$\frac{\cos 2 \mathrm{~A}}{\mathrm{a}^2}-\frac{\cos 2 \mathrm{~B}}{\mathrm{~b}^2}$$ is

The particular solution of the differential equation $$\left(1+e^{2 x}\right) d y+e^x\left(1+y^2\right) d x=0$$ at $$x=0$$ and y = 1 is

If $$y=1+x e^y$$, then $$\frac{d y}{d x}=$$

Two dice are thrown simultaneously. If X denotes the number of sixes, then the expectation of X is

If $$G(3,-5, r)$$ is the centroid of $$\triangle A B C$$, where $$A \equiv(7,-8,1), B \equiv(p, q, 5), C \equiv(q+1,5 p, 0)$$ are vertices of the triangle $$A B C$$, then the values of $$p, q, r$$ are respectively

The acute angle between the lines $$\left(x^2+y^2\right) \sin \theta+2 x y=0$$ is

For any non-zero vectors $$\bar{a}, \bar{b}, \bar{c}$$, the value of $$\bar{a} \cdot[(\bar{b} \times \bar{c}) \times(\bar{a}+\bar{b}+\bar{c})]$$ is

If the lines $$\frac{2 x-4}{\lambda}=\frac{y-1}{2}=\frac{z-3}{1}$$ and $$\frac{x-1}{1}=\frac{3 y-1}{\lambda}=\frac{z-2}{1}$$ are perpendicular to each other, then $$\lambda=$$

The order and degree of the differential equation $$\sqrt{\frac{d y}{d x}}-4 \frac{d y}{d x}-7 x=0$$ are respectively.

If $$x=e^t(\sin t-\cos t)$$ and $$y=e^t(\sin t+\cos t)$$, then $$\frac{d y}{d x}$$ at $$t=\frac{\pi}{3}$$ is

If the lines represented by $$(k^2+2) x^2+3 x y-6 y^2=0$$ are perpendicular to each other, then the values of $$\mathrm{K}$$ are

If $$\bar{a}=3 \hat{i}+\hat{j}-\hat{k}, \bar{b}=2 \hat{i}-\hat{j}+23 \hat{k}$$ and $$\bar{c}=7 \hat{i}-\hat{j}+23 \hat{k}$$, then which of the following is valid.

For the set of 50 observations, the sum of their squares is 3050 , their arithmetic mean is 6. Hence the standard deviation of these observations is

If $$y=2 x$$ is a chord of circle $$x^2+y^2-10 x=0$$, then the equation of circle with this chord as diameter is

If $$\sin ^2 x+\cos ^2 y=1$$, then $$\frac{d y}{d x}=$$

If $$f(x)=2\{x\}+5 x$$, where $$\{x\}$$ is fractional part function, then $$f(-1.4)$$ is

The curve $$y=a x^3+b x^2+c x+5$$ touches $$X$$-axis at $$P(-2,0)$$ and cuts $$Y$$-axis at a point $$Q$$, where its gradient is 3, then

The area of the region bounded by the curve $$y=2 x-x^2$$ and X-axis is

The equation of a line with slope $$-\frac{1}{\sqrt{2}}$$ and makes an intercept of $$2 \sqrt{2}$$ units on negative direction of $$y$$-axis is

If $$\mathrm{\frac{3+2i}{1+i}=\frac{1}{2}(x+iy)}$$, then x $$-$$ y =

If the angle between the vectors $$\overline{\mathrm{a}}=2 \lambda^2 \hat{\mathrm{i}}+4 \lambda \hat{\mathrm{j}}+\hat{\mathrm{k}}$$ and $$\overline{\mathrm{b}}=7 \hat{\mathrm{i}}-2 \hat{\mathrm{j}}+\lambda \hat{\mathrm{k}}$$ is obtuse, then $$\lambda \in$$

A population P grew at the rate given by the equation $$\frac{dP}{dt}=0.5P$$, then the population will become double in

If $$A=\left[\begin{array}{ccc}1 & 2 & 3 \\ -1 & 1 & 2 \\ 1 & 2 & 4\end{array}\right]$$, and $$A(\operatorname{adj} A)=k I$$, then the value of $$(k+1)^4$$ is

$$\int \cos ^3 x e^{\log (\sin x)^2} d x=$$

The probability distribution of a random variable X is

then Var(X) =

If $$\mathrm{p}$$ : It is raining.

$$\mathrm{q}$$ : Weather is pleasant

then simplified form of the statement "It is not true, if it is raining then weather is not pleasant" is

If $$\mathrm{f}(\mathrm{x})=\mathrm{x}, \quad$$ for $$\mathrm{x} \leq 0$$

$$=0,\quad$$ for $$x>0$$, then the function $$f(x)$$ at $$x=0$$ is

A fair coin is tossed for a fixed number of times. If probability of getting 7 heads is equal to probability of getting 9 heads, then probability of getting 2 heads is

The region represented by the inequalities $$x \geq 6, y \geq 3,2 x+y \geq 10, x \geq 0, y \geq 0$$ is

IF $$A X=B$$, where $$A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right], X=\left[\begin{array}{l}x \\ y \\ z\end{array}\right], B=\left[\begin{array}{l}4 \\ 0 \\ 2\end{array}\right]$$, then $$2 x+y-z=$$

$$\int \frac{d x}{e^x+e^{-x}+2}=$$

The co-ordinates of the points on the line $$\frac{x+2}{1}=\frac{y-1}{2}=\frac{z+1}{-2}$$ at a distance of 12 units from the point A($$-$$2, 1, $$-$$1) are

The value of $$\tan ^{-1} 2+\tan ^{-1} 3$$ is

If $$\bar{a}+\bar{b}, \bar{b}+\bar{c}, \bar{c}+\bar{a}$$ are coterminus edges of a parallelopiped, then its volume is

The differential equation of all parabolas whose axis is $$y$$-axis, is

The minimum value of the function f(x) = x log x is

The general solution of the differential equation $$\frac{d y}{d x}=\tan \left(\frac{y}{x}\right)+\frac{y}{x}$$ is

$$\tan \mathrm{A}+2 \tan 2 \mathrm{~A}+4 \tan 4 \mathrm{~A}+8 \cot 8 \mathrm{~A}=$$

If the vector equation of the plane $$\bar{r}=(2 \hat{i}+\hat{k})+\lambda \hat{i}+\mu(\hat{i}+2 \hat{j}-3 \hat{k})$$ in scalar product form is given by $$\overline{\mathrm{r}} \cdot(3 \hat{\mathrm{j}}+2 \hat{\mathrm{k}})=\alpha$$ then $$\alpha=$$

A current 'I' produces a magnetic flux '$$\phi$$' per turn in a coil of '$$n$$' turns. Self inductance of the coil is '$$L$$'. The relation between them is

A rejector circuit is the resonant circuit in which

A light of wavelength '$$\lambda$$' and intensity '$$\mathrm{I}$$' falls on photosensitive material. If '$$\mathrm{N}$$' photo electrons are emitted, each with kinetic energy 'E', then

The current drawn from the battery in the given network is (Internal resistance of the battery is negligible)

The moment of inertia of a thin uniform rod of mass 'M' and length 'L' about an axis passing through a point at a distance $$\frac{L}{4}$$ from one of its ends and perpendicular to the length of the rod is

A current $$I=10 \sin (100 \pi t)$$ ampere, is passed in a coil which induces a maximum emf $$5 \pi$$ volt in neighbouring coil. The mutual inductance of two coils is

The average density of the earth is [g is acceleration due to gravity]

Two bar magnets '$$\mathrm{P}$$' and '$$\mathrm{Q}$$' are kept in uniform magnetic field '$$\mathrm{B}$$' with magnetic moments '$$\mathrm{M_P}$$' and '$$\mathrm{M_Q}$$' respectively. Magnet 'P' is oscillating with frequency twice that of magnet 'Q'. If the moment of inertia of the magnet 'P' is twice that of magnet 'Q' then

Which one of the following is NOT a correct expression for an ideal gas?

[$$\mathrm{C_p}=$$ Molar specific heat of a gas at constant pressure,

$$\mathrm{C_v}=$$ Molar specific heat of a gas at constant volume,

$$\mathrm{Y}=$$ Ratio of two specific heats of a gas,

$$\mathrm{R}=$$ Universal gas constant]

The molecular masses of helium and oxygen are 4 and 32 respectively. The ratio of r.m.s. speed of helium at 327$$^\circ$$ to r.m.s. speed of oxygen at 27$$^\circ$$ will be

Which one of the following p-V diagram is correct for an isochoric process:

A magnetic dipole of magnetic moment $$\mathrm{M}$$, is freely suspended in a magnetic field of induction B. The minimum and maximum values of potential energy of the dipole, respectively are

In series LCR circuit, at resonance the peak value of current will be [$$\mathrm{E_0}$$ is peak emf, R is resistance, $$\omega \mathrm{L}$$ is inductive reactance and $$\omega \mathrm{C}$$ is capacitive]

A particle is moving along the circular path with constant speed and centripetal acceleration 'a'. If the speed is doubled, the ratio of its acceleration after and before the change is

The displacement of a particle performing S.H.M. is given by $$x=5 \sin (3 t+3)$$, where $$x$$ is in $$\mathrm{cm}$$ and $$t$$ is in second. The maximum acceleration of the particle will be

A cylindrical tube open at both ends has fundamental frequency 'n' in air. The tube is dipped vertically in water so that one-fourth of it is in water. The fundamental frequency of the air column becomes

In the following electrical network, the value of 1 is

The half life of a radioactive substance is 30 minute. The time taken between 40% decay and 85% decay of the same radioactive substance is

Two monochromatic beams of intensities I and 4 I respectively are superposed to form a steady interference pattern. The maximum and minimum intensities in the pattern are

Three charges each of $$+1 \mu \mathrm{C}$$ are placed at the corners of an equilateral triangle. If the repulsive force between any two charges is $$\mathrm{F}$$, then the net force on either charge will be [$$\cos 60^{\circ}=0.5$$]

Velocity of sound waves in air is '$$\mathrm{V}$$' $$\mathrm{m} / \mathrm{s}$$. For a particular sound wave in air, path difference of 'x' $$\mathrm{cm}$$ is equivalent to phase difference $$n \pi$$. The frequency of this wave is

Choose the correct statement. In conductors

For a transistor, the current ratio $$\alpha_{\mathrm{dc}}=\frac{69}{70}$$, the current gain $$\beta_{\mathrm{dc}}$$ is

'n' small drops of same size fall through air with constant velocity $$5 \mathrm{~cm} / \mathrm{s}$$. They coalesce to form a big drop. The terminal velocity of the big drop is

The depth from the surface of the earth of radius $$\mathrm{R}$$, at which acceleration due to gravity will be $$60 \%$$ of the value on the earth surface is

A body of mass 'm' is moving with speed 'V' along a circular path of radius 'r'. Now the speed is reduced to $$\frac{V}{2}$$ and radius is increased to '3r'. For this change, initial centripetal force needs to be

The path difference between two interfering light waves meeting at a point on the screen is $$\left(\frac{57}{2}\right) \lambda$$. The bond obtained at that point is

Pressure inside two soap bubbles are 1.01 atm and 1.03 atm. The ratio between their volumes is (Pressure outside the soap bubble is 1 atmosphere)

The length and diameter of a metal wire used in sonometer is doubled. The fundamental frequency will change from 'n' to

An alternating e.m.f. is $$\mathrm{e}=\mathrm{e}_0 \sin \omega \mathrm{t}$$. In what time the e.m.f. will have half its maximum value, if '$$\mathrm{e}$$' starts from zero? ($$\mathrm{T}=$$ time period, $$\sin 30^{\circ}=0.5$$)

A ray of light is incident on one face of an equilateral glass prism having refractive index $$\sqrt{2}$$. It produces the emergent ray which just. grazes along the adjacent face. The value of angle of incidence is $$\left(\sin 45^{\circ}=\cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)$$

The input a.c. voltage of frequency $$60 \mathrm{~Hz}$$ is applied to half-wave rectifier and also to full-wave rectifier. The output frequency in case of half-wave rectifier and that in case of full wave rectifier is respectively.

Three point masses, each of mass 'm' are kept at the corners of an equilateral triangle of side 'L'. The system rotates about the centre of the triangle without any change in the separation of masses during rotation. The period of rotation is directly proportional to $$\left(\cos 30^{\circ}=\frac{\sqrt{3}}{2}\right)$$

A closed organ pipe and an open organ pipe of same length produce 2 beats per second when they are set into vibrations together in fundamental mode. The length of open pipe is now halved and that of closed pipe is doubled. The number of beats produced per second will be

A rectangular loop $$\mathrm{PQMN}$$ with movable arm $$\mathrm{PQ}$$ of length $$12 \mathrm{~cm}$$ and resistance $$2 \Omega$$ is placed in a uniform magnetic field of $$0.1 \mathrm{~T}$$ acting perpendicular to the plane of the loop as shown in figure. The resistances of the arms MN, NP and MQ are negligible. The current induced in the loop when arm PQ is moved with velocity $$20 \mathrm{~ms}^{-1}$$ is

Assume that for solar radiation, surface temperature of the sun is $$6000 \mathrm{~K}$$. If Wien's constant 'b' is $$2.897 \times 10^{-3} \mathrm{~mK}$$, the value of maximum wavelength will be

The kinetic energy of a light body and a heavy body is same. Which one of them has greater momentum?

Four electric charges $$+\mathrm{q},+\mathrm{q},-\mathrm{q}$$ and $$-\mathrm{q}$$ are placed in order at the corners of a square of side $$2 \mathrm{~L}$$. The electric potential at point midway between the two positive charges is

White light consists of wavelengths from $$480 \mathrm{~nm}$$ to $$672 \mathrm{~nm}$$. What will be the wavelength range when white light is passed through glass of refractive index 1.6?

A metal sphere cools at the rate of $$1.5^{\circ} \mathrm{C} / \mathrm{min}$$ when its temperature is $$80^{\circ} \mathrm{C}$$. At what rate will it cool when its temperature falls to $$50^{\circ} \mathrm{C}$$. [Temperature of surrounding is $$30^{\circ} \mathrm{C}$$]

The ratio of energies of photons produced due to transition of electron of hydrogen atom from its (i) second to first energy level and (ii) highest energy level to second energy level is

The length of the seconds pendulum is lm on earth. If the mass and diameter of the planet is 1.5 times that of the earth, the length of the seconds pendulum on the planet will be nearly

A solenoid 2 m long and 4 cm in diameter has 4 layers of windings of 1000 turns each and carries a current of 5 A. What is the magnetic field at its centre along the axis? [$$\mu_0=4\pi\times10^{-7}$$ Wb/Am]

A particle of charge 'q' and mass 'm' moves in a circular orbit of radius 'r' with angular speed '$$\omega$$'. The ratio of the magnitude of its magnetic moment to that of its angular momentum depends on

A battery is used to charge a parallel plate capacitor till the potential difference between the plates becomes equal to the e.m.f. of the battery. The ratio of the energy stored int he capacitor to the work done by the battery will be

In a photoelectric experiment, a graph of maximum kinetic energy $$(\mathrm{KE}_{\text {max }})$$ against the frequency of incident radiation (v) is plotted. If $$\mathrm{A}$$ and $$\mathrm{B}$$ are the intercepts on the $$\mathrm{X}$$ and $$\mathrm{Y}$$ axis respectively then the Planck's constant is given by

If the work done in blowing a soap bubble of volume '$$\mathrm{V}$$' is '$$\mathrm{W}$$', then the work done in blowing a soap bubble of volume '$$2 \mathrm{~V}$$' will be

A monochromatic ray of light travels through glass slab and water column. The number of waves in glass slab of thickness $$4 \mathrm{~cm}$$ is the same as in water column of height $$5 \mathrm{~cm}$$. If refractive index of glass is $$\frac{5}{3}$$ then refractive index of water is

Capacitors of capacities $$\mathrm{C}_1, \mathrm{C}_2$$ and $$\mathrm{C}_3$$ are connected in series. If the combination is connected to a supply of '$$\mathrm{V}$$' volt, then potential difference across capacitor '$$\mathrm{C}_1$$' is

A monoatomic gas is suddenly compressed to $$(1 / 8)^{\text {th }}$$ of its initial volume adiabatically. The ratio of the final pressure to initial pressure of the gas is $$(\gamma=5 / 3)$$