COMEDK 2023 EVENING SHIFT

$$ \text { If } f(x)=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^x}\right) \text { then } f^{\prime}(0) \text { is equal to } $$

The scalar components of a unit vector which is perpendicular to each of the vectors $$\hat{\imath}+2 \hat{\jmath}-\hat{k}$$ and $$3 \hat{\imath}-\hat{\jmath}+2 \hat{k}$$ are

What would be the van't Hoff factor for a solution prepared by dissolving $$3.42 \mathrm{~g}$$ of $$\mathrm{CaCl}_2$$ in $$2500 \mathrm{~ml}$$ of water having an Osmotic pressure equal to $$0.75 \mathrm{~atm}$$. at $$27^{\circ} \mathrm{C}$$ ? Molar mass of $$\mathrm{CaCl}_2=111 \mathrm{~amu}$$.

$$ \text { Let } f(x)=\cos ^{-1}(3 x-1) \text {, then domain of } f(x) \text { is equal to } $$

Choose the incorrect statement.

The nucleus of a helium atom travels along the inside of a straight hollow tube $$4 \mathrm{~m}$$ long which forms part of a particle accelerator. If one assumes uniform acceleration, how long is the particle in the tube if it enters at a speed of $$2000 \mathrm{~m} / \mathrm{s}$$ and leaves at $$8000 \mathrm{~m} / \mathrm{s}$$

The particular solution of $$e^{\frac{d y}{d x}}=2 x+1$$ given that $$y=1$$ when $$x=0$$ is

A tentative explanation of observations without assuming that it is true is called

A drone is flying due west, a little above the train, with a speed of $$10 \mathrm{~m} / \mathrm{s}$$. A 270 meter long train is moving due east at a speed of $$20 \mathrm{~m} / \mathrm{s}$$. The time taken by the drone to cross the train is

If the resultant of all external forces acting on a system of particles is zero, then from an inertial frame one can surely say that

The time dependence of a physical quantity P is give by $$\mathrm{P=P}_0 \exp \left(-\alpha t^2\right)$$ where $$\alpha$$ is a constant and $$t$$ is time. The constant $$\alpha$$ will

A wheel is free to rotate about a horizontal axis through O. A force of $$200 \mathrm{~N}$$ is applied at a point $$\mathrm{P} 2 \mathrm{~cm}$$ from the center $$\mathrm{O}$$. OP makes an angle of $$55^{\circ}$$ with $$\mathrm{x}$$ axis and the force is in the plane of the wheel making an angle of $$25^{\circ}$$ with the horizontal axis. What is the torque?

A neutron makes a head on elastic collision with a lead nucleus. The ratio of nuclear mass to neutron mass is 206 . The fractional change in kinetic energy of a neutron is

A hockey player hits the ball at an angle of $$37^{\circ}$$ from the horizontal with an initial speed of $$40 \mathrm{~m} / \mathrm{s}$$ (a right angled triangle with one of the angle is $$37^{\circ}$$ and their sides in the ratio of $$6: 8: 10$$). Assume that the ball is in a vertical plane. The time at which the ball reaches the highest point of its path is

If reaction is $$\mathrm{R}$$ and coefficient of friction is $$\mu$$, what is work done against friction in moving a body by distance $$\mathrm{d}$$ ?

A man grows into a giant such that his height increases to 8 times his original height. Assuming that his density remains same, the stress in the leg will change by a factor of

$$\mathrm{F}_{\mathrm{A}}, \mathrm{F}_{\mathrm{B}}$$ and $$\mathrm{F}_{\mathrm{C}}$$ are three forces acting at point $$\mathrm{P}$$ as shown in figure. The whole system is in equilibrium state. The magnitude of $$\mathrm{F}_{\mathrm{A}}$$ is

A spring of force constant $$k$$ is cut into lengths of ratio $$1:3:4$$. They are connected in series and the new force constant is $$\mathrm{k}$$'. Then they are connected in parallel and force constant is $$\mathrm{k}$$''. Then $$\mathrm{k}^{\prime}: \mathrm{k}^{\prime \prime}$$ is

Water from a tap of cross-sectional area $$1 \mathrm{~cm}^2$$, falls vertically downwards at $$2 \mathrm{~m} / \mathrm{s}$$. The cross sectional area of the stream, $$20 \mathrm{~cm}$$ below the tap is (assume that pressure is constant throughout and the flow is streamlined; $$\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$$

In an adiabatic expansion of air, the volume is increased by $$6.2 \%$$. The percentage change in pressure is $$(\gamma=1.4)$$

If the ratio of specific heat of a gas at constant pressure to that at constant volume is $$\gamma$$, the change in internal energy of a mass of a gas when the volume changes from $$\mathrm{V}$$ to $$3 \mathrm{~V}$$ at constant pressure is

The molecules of a given mass of a gas have root mean square speed of $$120 \mathrm{~m} / \mathrm{s}$$ at $$88^{\circ} \mathrm{C}$$ and 1 atmospheric pressure. The root mean square speed of the molecules at $$127^{\circ} \mathrm{C}$$ and 2 atmospheric pressure is

Two black bodies $$\mathrm{P}$$ and $$\mathrm{Q}$$ have equal surface areas and are kept at temperatures $$127^{\circ} \mathrm{C}$$ and $$27^{\circ} \mathrm{C}$$ respectively. The ratio of thermal power radiated by A to that by B is

A light having wavelength $$6400^{\circ} \mathrm{A}$$ is incident normally on a slit of width $$2 \mathrm{~mm}$$. Then the linear width of the central maximum on the screen kept $$2 \mathrm{~m}$$ from the slit is :

Two open organ pipes A and B of length $$22 \mathrm{~cm}$$ and $$22.5 \mathrm{~cm}$$ respectively produce 2 beats per sec when sounded together. The frequency of the shorter pipe is

The acceleration due to gravity at a height of $$7 \mathrm{~km}$$ above the earth is the same as at a depth d below the surface of the earth. Then d is

A person has a normal near point $$25 \mathrm{~cm}$$. What is the magnifying power of the simple microscope he used, if the focal length of the convex lens used is $$10 \mathrm{~cm}$$ and the final image is formed at the least distance of distinct vision?

An uniform sphere of mass $$M$$ and radius $$R$$ exerts a force of $$F$$ on a small mass $$m$$ placed at a distance of 3R from the centre of the sphere. A spherical portion of diameter $$R$$ is cut from the sphere as shown in the fig. The force of attraction between the remaining part of the disc and the mass $$\mathrm{m}$$ is

In the young's double slit experiment the fringe width of the interference pattern is found to be $$3.2 \times 10^{-4} \mathrm{~m}$$, when the light of wave length $$6400^{\circ} \mathrm{A}$$ is used. What will be change in fringe width if the light is replaced with a light of wave length $$4800^{\circ} \mathrm{A}$$

The critical angle of a medium having the refractive index $$\sqrt2$$ is :

When angle of incidence on one face of the equilateral glass prism is $$3 / 4^{\text {th }}$$ of the angle of prism, the ray of light undergoes minimum deviation. If the velocity of light in vacuum is '$$c$$' then the velocity of light in the glass is :

What will be change in wave length, if a light of wave length $$600 \mathrm{~nm}$$ travels from air enters a medium of refractive index 1.5 and continues its journey through that medium?

A spherical metal ball of density '$$\rho$$' and radius '$$r$$' is immersed in a liquid of density '$$\sigma$$'. When an electric field is applied in the upward direction the metal ball remains just suspended in the liquid. Then the expression for the charge on the metal ball is :

Two point charges $$20 \mu \mathrm{C}$$ and $$-10 \mu \mathrm{C}$$ are separated by a distance of $$1 \mathrm{~m}$$ in air. At what point on the line joining the two charges, the electric potential is zero.

A lens of power $$+1 \mathrm{D}$$ is made in contact with another lens of power $$-2 \mathrm{D}$$ the combination will then act as a:

An electron and a proton having mass $$m_e$$ and $$m_p$$ respectively, initially at rest, move through the same distance '$$s$$' in a uniform electric field '$$E$$'. If the time taken by them to cover that distance is $$t_e$$ and $$t_p$$ respectively, then $$t_e / t_p$$ is equal to:

The electric flux from cube of side $$1 \mathrm{~m}$$ is '$$\Phi$$' When the side of the cube is made $$3 \mathrm{~m}$$ and the charge enclosed by the cube is made one third of the original value, then the flux from the bigger cube will be :

The force between two electric point charges at rest in air is $$F_1$$ When the same arrangement is kept inside water, the force between them is $$F_2$$. Which of the following statement is correct?

A resistor of wire $$24 \mathrm{~cm}$$ length and resistance $$8 \Omega$$ is stretched in to a uniform wire of $$48 \mathrm{~cm}$$ length, then the new resistance will be :

The SI unit of electrical conductivity is :

PQRS is square of side $$1 \mathrm{~m}$$. A charge of $$100 \mu \mathrm{C}$$ is placed at the centre of the square. Then the work done to take $$3 \mu \mathrm{C}$$ charge from the corner $$\mathrm{P}$$ to the corner $$\mathrm{R}$$.

A magnetic field does not interact with:

A battery is made of 12 cells having emf $$5 \mathrm{~V}$$ each. If three cells are unknowingly connected wrong, the resultant emf of the battery will be:

In the figure, first the capacitors are fully charged by closing the key $$\mathrm{K}$$. Then after opening the Key a dielectric material with dielectric constant 2 is filled in the space between the plates of both the capacitor. At this state the ratio of the Charge on the capacitor $$C_1$$ to that of $$C_2$$ is:

A metallic rod of $$10 \mathrm{~cm}$$ is rotated with a frequency 100 revolution per second about an axis perpendicular to its length and passing through its one end in uniform transverse magnetic field of strength $$1 \mathrm{~T}$$. The emf developed across its ends is:

The current drawn by the primary coil of an ideal transformer, which steps up $$22 \mathrm{~V}$$ into $$220 \mathrm{~V}$$, to operate a device having a load resistance $$110 \Omega$$ is:

The current passing through the 100$$\Omega$$ resistor in the given electrical circuit is :

The radius of the current carrying circular coil is doubled keeping the current passing through it the same. Then the ratio of the magnetic field produced at the centre of the coil before the doubling of the radius to the magnetic field after doubling of the radius.

$$220 \mathrm{~V}$$ ac is more dangerous than $$220 \mathrm{~V}$$ dc Why?

The magnetic permeability '$$\mu$$' a of a paramagnetic substance is :

One volt induced emf is produced in the secondary coil when the current through the primary coil is changed from $$3 \mathrm{~A}$$ to $$1 \mathrm{~A}$$ in 100 milliseconds. the mutual inductance of the two coil is:

Find the pole strength of a magnet of length $$2 \mathrm{~cm}$$, if the magnetic field strength $B$ at distance $$10 \mathrm{~cm}$$ from the centre of a magnet on the axial line of the magnet is $$10^{-4} \mathrm{~T}$$.

A circular loop of area $$0.04 \mathrm{~m}^2$$ carrying a current of $$10 \mathrm{~A}$$ is held with its plane perpendicular to a magnetic field induction $$0.4 \mathrm{~T}$$ Then the torque acting on the circular loop is :

A particle at rest decays in to two particles of mass $$m_1$$ and $$m_2$$ and move with velocities $$v_1$$ and $$v_2$$. The ratio of their de Broglie wave length $$\frac{\lambda_1}{\lambda_2}$$ is:

What should be the inductance of an inductor connected to $$200 \mathrm{~V}, 50 \mathrm{~Hz}$$ source so that the maximum current of $$\sqrt{2}$$ A flows through it?

In the given circuit the diode $$D_1$$ and $$D_2$$ have the forward resistance $$25 \Omega$$ and infinite backward resistance. When they are connected to the source as shown, the current passing through the $$175 \Omega$$ resistor is:

The reverse current in the semiconductor diode changes from $$20 \mu \mathrm{A}$$ to $$40 \mu \mathrm{A}$$ when the reverse potential is changed from $$10 \mathrm{~V}$$ to $$15 \mathrm{~V}$$, then the reverse resistance of the junction diode will be :

What feature of the infrared waves make it useful for the haze photography?

The energy gap between valance band and the conduction band for a given material is $$6 \mathrm{~eV}$$, then the material is :

The mass number of two nuclei $$\mathrm{P}$$ and $$\mathrm{Q}$$ are 27 and 125 respectively. The ratio of their radii $$R_P: R_Q$$ is given by:

Which of the following statement is true when a gamma decay occurs from the nucleus of an atom?

In a nuclear reaction 2 deuteron nuclei combine to form a helium nucleus. The energy released in $$\mathrm{MeV}$$ will be: (Given mass of deuteron $$=2.01355 \mathrm{~amu}$$. and mass of helium nucleus $$=4.0028 \mathrm{~amu}$$.

In the photoelectric experiment, the frequency of the incident radiation is doubled. What will be its effect on the photoelectric current?

In the head-on collision of two alpha particles $$\alpha_1$$ and $$\alpha_2$$ with the gold nucleus, the closest approaches are 31.4 fermi and 94.2 fermi respectively. Then the ratio of the energy possessed by the alpha particles $$\alpha_2 / \alpha_1$$ is:

The ground state energy of hydrogen atom is $$-13.6 \mathrm{~eV}$$. If the electron jumps from the $$3^{\text {rd }}$$ excited state to the ground state then the energy of the radiation emitted will be:

$$5.8 \mathrm{~g}$$ of a gas maintained at $$95^{\circ} \mathrm{C}$$ occupies the same volume as $$0.368 \mathrm{~g}$$ of hydrogen gas maintained at a temperature of $$17^{\circ} \mathrm{C}$$ and pressure being the same atmospheric pressure for both the gases. What is the molecular mass of the unknown gas?

A proton having mass equal to $$1.66 \times 10^{-27} \mathrm{~kg}$$ is accelerated to one tenth of the velocity of light. If its velocity can be measured to an accuracy of $$\pm 2 \%$$, what would be the uncertainty in its position?

A Gas taken in a closed vessel is heated from $$54^{\circ} \mathrm{C}$$ to $$1254^{\circ} \mathrm{C}$$. The pressure of the gas becomes ___________ times its original pressure $$\mathrm{P_1}$$

$$\mathrm{Mg}(\mathrm{OH})_2$$ is used as an antacid. If a person, suffering from acidity, produces $$2.5 \mathrm{~L}$$ of Gastric juice in a day, approximately how many antacid tablets, each containing $$600 \mathrm{~mg}$$ of $$\mathrm{Mg}(\mathrm{OH})_2$$, will be required to completely neutralise the whole $$\mathrm{HCl}$$ produced in the stomach in one day? (Gastric juice contains $$3.0 \mathrm{~g}$$ of $$\mathrm{HCl}$$ per L). (Atomic masses: $$\mathrm{Mg}=24 \mathrm{~g} / \mathrm{mol}, \mathrm{O}=16 \mathrm{~g} / \mathrm{mol}$$ & $$\mathrm{H}=1 \mathrm{~g} / \mathrm{mol}$$.)

The energy of an electron in the ground state of Hydrogen atom is $$-2.18 \times 10^{-18} \mathrm{~J}$$. What would be the energy associated with the second excited state of $$\mathrm{Li}$$ ?

Gaseous Nitrous oxide decomposes at $$298 \mathrm{~K}$$ to form Nitrogen gas and Oxygen gas. The $$\Delta \mathbf{H}$$ for the reaction at $$1.0 \mathrm{~atm}$$ pressure and $$298 \mathrm{~K}$$ is $$\mathbf{- 1 6 3 . 1 5} \mathbf{~ k J}$$. Calculate Internal energy change for the decomposition of $$100 \mathrm{~g}$$ of Nitrous oxide gas under the same conditions of temperature and pressure.

What is the mole fraction of solute in a $$5 \mathrm{~m}$$ aqueous solution?

If the depression in freezing point of an aqueous solution containing a solute, which is neither dissociated nor associated, is $$\mathbf{a} \mathrm{K}$$ with $$\mathrm{K}_{\mathrm{f}}=\mathbf{b ~ K ~ k g ~ m o l}{ }^{-1}$$, what would be the elevation in boiling point $$(\mathrm{X})$$ for this solution if its $$\mathrm{K}_{\mathrm{b}}=\mathbf{\mathrm { ~K } \mathrm { ~K } \mathrm { ~kg } \mathrm { ~mol }}{ }^{-1}$$ ?

$$\mathrm{X}$$ is an electrolyte with a concentration of $$0.04 \mathrm{M}$$ whose formula is of the type $$\mathrm{X}_2 \mathrm{~A}$$. $$\mathrm{Y}$$ is a non-electrolyte solution with a concentration of $$0.2 \mathrm{M}$$ and has an osmotic pressure equal to $$\mathrm{P}_2$$ at room temperature. What is the relationship between the Osmotic pressure $$\pi$$ of $$\mathrm{X}$$ and $$\mathrm{P}_2$$ ?

Choose the incorrect statement:

The equilibrium constants for the reactions $$a, b$$, and $$c$$ are as given:

a) $$\mathrm{N}_2+3 \mathrm{H}_2=2 \mathrm{NH}_3: \mathbf{K}_1$$

b) $$\mathrm{N}_2+\mathrm{O}_2=2 \mathrm{NO}: \mathrm{K}_2$$

c) $$2 \mathrm{H}_2+\mathrm{O}_2=2 \mathrm{H}_2 \mathrm{O}: \mathbf{K}_3$$

What would be the Equilibrium constant for the reaction:

$$4 \mathrm{NH}_3+5 \mathrm{O}_2=4 \mathrm{NO}+6 \mathrm{H}_2 \mathrm{O} ; \mathbf{K}_{\mathbf{x}}$$

What would be the volume of water required to dissolve $$0.2 \mathrm{~g}$$ of $$\mathrm{PbCl}_2$$ of molar mass $$278 \mathrm{~g} / \mathrm{mol}$$ to prepare a saturated solution of the salt? $$(\mathrm{K}_{\mathrm{SP}}$$ of $$\mathrm{PbCl}_2=3.2 \times 10^{-8})$$

In neutral medium $$\mathrm{KMnO}_4$$ oxidises $$\mathrm{MnSO}_4$$ to _________

In the given Redox equation, identify the stoichiometric coefficients $$\mathrm{w}, \mathrm{x}, \mathrm{y}$$ and $$\mathrm{z}$$.

$$\mathrm{ClO}_3^{-1}+\mathrm{w} \mathrm{Cl}^{-1}+\mathrm{xH}^{+} \rightarrow \mathrm{y} \mathrm{H}_2 \mathrm{O}+\mathrm{zCl}_2$$

Identify the catalyst used in the reaction between Iodide and persulphate ions.

$$2 \mathrm{I}^{-}+\mathrm{S}_2 \mathrm{O}_8{ }^{2-} \rightarrow \mathrm{I}_2+2 \mathrm{SO}_4{ }^{2-}$$

When Lead Storage battery is in the process of getting charged which one of the following reactions takes place?

The Molar conductivity of $$0.05 \mathrm{M}$$ solution of $$\mathrm{MgCl}_2$$ is $$194.5 \mathrm{~ohm}^{-1} \mathrm{~cm}^2$$ per mole at room temperature. A Conductivity cell with electrodes having $$3.0 \mathrm{~cm}^2$$ surface area and $$1.0 \mathrm{~cm}$$ apart is filled with the solution of $$\mathrm{MgCl}_2$$. What would be the resistance offered by the conductivity cell?

If electrolysis of water is carried out for a time duration of 2 hours, how much electric current in amperes would be required to liberate $$100 \mathrm{~ml}$$ of $$\mathrm{O}_2$$ gas measured under standard conditions of temperature and pressure?

The rate constant for a First order reaction at $$560 \mathrm{~K}$$ is $$1.5 \times 10^{-6}$$ per second. If the reaction is allowed to take place for 20 hours, what percentage of the initial concentration would have converted to products?

Given below are graphs showing the variation in velocity constant with temperature on Kelvin scale. Identify the graph which represents Arrhenius equation.

Match the details given in Column I with those given in Column II

The reaction taking place in a galvanic cell is as given

$$\mathrm{A}(\mathrm{s})+\mathrm{B}^{2+}\left(\mathbf{1} \mathbf{1} \mathbf{1 0} \mathbf{0}^{-\mathrm{M}} \mathbf{M}\right) \rightarrow \mathrm{B}_{(\mathrm{s})}+\mathrm{A}^{2+}(0.1 \mathrm{M}).$$

The emf of the cell is $$+2.651 \mathrm{~V}$$. If the standard emf of the cell is $$+2.71 \mathrm{~V}$$, what is the value of $$\mathrm{X}$$ ?

Match the items in Column I with their description in Column II

A first order reaction proceeds to $$90 \%$$ completion. What will be the approximate time taken for $$90 \%$$ completion in relation to $$t_{1 / 2}$$ of the reaction?

Para and ortho hydrogen differ in:

For a reaction of the type, $$2 \mathrm{X}+\mathrm{Y} \rightarrow \mathrm{A}+\mathrm{B}$$, the following is the data collected:

What is the overall order of the reaction?

Arrange the following in the decreasing order of their Dipole moments.

a. Chlorobenzene

b. 1,2-Dichlorobenzene

c. 1,3-Dichlorobenzene

d. 1,4-Dichlorobenzene.

Find the correct matches of the substances, given in Column I, from their characteristic properties given in Column II.

In the following question, Assertion (A) is given followed by a statement of Reason (R). Choose the correct answer.

Assertion (A): $$\pi\left(2 p_x\right), \pi\left(2 p_y\right), \pi^*\left(2 p_x\right), \pi^*\left(2 p_y\right)$$ molecular orbitals have one nodal plane each.

Reason $$(\mathrm{R})$$ : All the molecular orbitals formed by the sideways overlapping have one nodal plane.

Identify the correct statement describing the characteristics of $$\mathrm{C}_2$$ molecule.

Match the following characteristics of transition metals given in Column I with the examples listed in Column II

Which one of the following is an incorrect statement pertaining to the properties of Coordination compounds?

Which one of the following Coordination entities exhibits Facial and Meridional isomerism?

Identify the correct IUPAC name of $$[\mathrm{CoCl}_2(\mathrm{NO}_2)(\mathrm{NH}_3)_3]$$

Identify the incorrect statement.

The group number of the element in the periodic table with the electronic configuration $$(\mathrm{n}-1) \mathrm{d}^2 \mathrm{~ns}^2$$. For $$n=4$$ is:

Structures of 3 Monosaccharides are given below. Two of them are Anomers. Identify the two Anomers.

Select the strongest base from the given compounds:

[A] p- $$\mathrm{NO}_2-\mathrm{C}_6 \mathrm{H}_4 \mathrm{NH}_2$$

[B] $$\mathrm{C}_6 \mathrm{H}_5-\mathrm{CH}_2-\mathrm{NH}_2$$

[C] $$\mathrm{m}-\mathrm{NO}_2-\mathrm{C}_6 \mathrm{H}_4 \mathrm{NH}_2$$

[D] $$\mathrm{C}_6 \mathrm{H}_5 \mathrm{NH}_2$$

Which of the following will show geometrical isomerism?

Identify the compounds A, B, C and D.

$$ \text { 1,2,2,2-tetrachloroethane } \xrightarrow[\Delta]{\mathrm{Zn}}[\mathrm{A}] $$

[A] $$ \xrightarrow[675 \mathrm{~K}]{\text { Fe tube }} $$ [B] $$ \xrightarrow[\text { Conc. } \mathrm{H}_2 \mathrm{SO}_4]{\text { Conc. } \mathrm{HNO}_3} $$ [C] $$ \xrightarrow[\text { Anhydrous } \mathrm{AlCl}_3]{\mathrm{Cl} /}$$ [D]

The reactions taking place with $$\mathrm{2- Phenyl-2-bromopropane}$$ as the starting material is shown below. Identify [A] and [B] formed in the reaction.

$$ \mathrm{C}_6 \mathrm{H}_5-\mathrm{C}\left(\mathrm{CH}_3\right)_2^{-} \mathrm{Br} \xrightarrow[\Delta]{\text { KOH Alcoholic }}[\mathrm{A}] $$

$$ [\mathrm{A}]+\mathrm{HBr} \xrightarrow{\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CO})_2 \mathrm{O}\right.}[\mathrm{B}]$$

Which one of the following statements is correct?

Which one of the following will undergo Nucleophilic substitution, by $$\mathrm{S}_{\mathrm{N}}{ }^1$$ mechanism, fastest?

Which one of the following compounds would not undergo Aldol condensation?

Choose the incorrect statement.

From among the following, identify the compound which forms two moles of a ketone on ozonolysis.

[A] 2,3-Dimethylbutane.

[B] 3-Methyl-1-pentene.

[C] 2,3-Dimethyl-2-butene.

[D] 2-Methyl-2-pentane.

Identify the starting compound from the following data:

$$\mathrm{C}_6 \mathrm{H}_{14} \mathrm{O}(\mathrm{X})$$ on reaction with $$\mathrm{HI}$$ yields a haloalkane (A) and an alcohol (B). Compound (A) on reaction with aqueous $$\mathrm{NaOH}$$ gives an alcohol (C). Compounds (B) and (C) on reaction with $$\mathrm{CrO}_3$$ in anhydrous medium yields Butanone and Ethanal respectively.

Choose the correct order of increasing acidic strength of the following compounds.

Which one of the following correctly represents the decreasing order of acidic nature of the given carboxylic acids:

[A] 2-Hydroxybenzoic acid

[B] Benzoic acid

[C] 3-Hydroxybenzoic acid

[D] 4- Hydroxybenzoic acid

What would be the products obtained when a mixture of p-Methoxy benzaldehyde and Methanal are heated with $$50 \%$$ concentrated Caustic soda solution?

One among the 4 Vitamins belonging to $$\mathrm{B}$$ Complex, can be stored in our body. Identify the Vitamin.

Which one of the following will give a positive result when it is warmed with Chloroform and alcoholic solution of $$\mathrm{KOH}$$ ?

Choose the incorrect statement regarding Cellulose.

What would be the final product [$$\mathbf{X}$$] formed when p-Toluidine undergoes the following series of reactions?

$$\begin{aligned} & \text { P-Toluidine } \xrightarrow[\text { Pyridine }]{\left\{\mathrm{CH}_2, \mathrm{CO}_2 \mathrm{O}\right.}[\mathrm{P}] \\ & {[\mathrm{P}] \xrightarrow{\mathrm{Br}_2 / \mathrm{CH}_3 \mathrm{COOH}}[\mathrm{O}]} \\ & {[\mathrm{Q}] \xrightarrow[\Delta]{\text { dilнG }}[\mathrm{R}]} \\ & {\mathrm{[R]} \xrightarrow[0^{\circ} \mathrm{C}]{\mathrm{Nan}_2 / \mathrm{HCl}}\mathrm{[S]}} \\ & {[\mathrm{S}] \xrightarrow{\mathrm{H}_2 \mathrm{PO}_2}[\mathrm{X}]} \\ \end{aligned}$$

If three numbers $$a, b, c$$ constitute both an A.P and G.P, then

Which of the following is a singleton set?

Let $$X$$ and $$Y$$ be the set of all positive divisors of 400 and 1000 respectively (including 1 and the number). Then $$n(X \cap Y)$$ is equal to

If the conjugate of $$(x+i y)(1-2 i)$$ be $$1+i$$, then

Le $$x$$ be the arithmetic mean and $$y, z$$ be the two geometric means between any two positive numbers, then $$\frac{y^3+z^3}{x y z}=$$ -----------

In the set $$\mathrm{W}$$ of whole numbers an equivalence relation $$\mathrm{R}$$ is defined as follows $$\mathrm{aRb}$$ iff both $$\mathrm{a}$$ & $$\mathrm{~b}$$ leave the same reminder when divided by 5. The equivalence class of 1 is given by.

In a 12 storey house, 10 people enter a lift cabin. It is known that they will leave the lift in pre-decided groups of 2, 3 & 5 people at different storeys. The number of ways they can do so if the lift does not stop up to the second storey is

How many factors of $$2^5 \times 3^6 \times 5^2$$ are perfect squares?

A candidate is required to answer 7 questions out of 12 questions which are divided into two groups each containing 6 questions. He is not permitted to attempt more than 5 questions from either group. The number of ways in which he can choose the 7 question is

Match the Coordination compounds given in Column I with their characteristic features listed in Column II.

Bag A contains 3 white and 2 red balls. Bag B contains only 1 white ball. A fair coin is tossed. If head appears then 1 ball is drawn at random from bag A and put into bag B. However if tail appears then 2 balls are drawn at random from bag A and put into bag B. Now one ball is drawn at random from bag B. Given that the drawn ball from B is white, the probability that head appeared on the coin is

A die is thrown twice and the sum of numbers appearing is observed to be 8 . What is the conditional probability that the number 5 has appeared atleast once?

If the direction ratios of two lines are given by $$3 l m-4 l n+m n=0$$ and $$l+2 m+3 n=0$$, then the angle between the lines is

$$ \text { If } P(B)=\frac{3}{5} \quad P(A / B)=\frac{1}{2} \text { and } P(A \cup B)=\frac{4}{5} \text { then } P(A \cup B)^{\prime}+P\left(A^{\prime} \cup B\right)= $$

$$ \text { If } \vec{a} \text { and } \vec{b} \text { are unit vectors, then the angle between } \vec{a} \text { and } \vec{b} \text { for which } a-\sqrt{2} \vec{b} \text { is a unit vector is } $$

$$ \mathrm{P} \text { is a point on the line segment joining the points }(3,2,-1) \text { and }(6,2,-2) \text {. If the } x \text { co ordinate of } \mathrm{P} \text { is } 5 \text {, then its } \mathrm{y} \text { coordinate is } $$

18 Points are indicated on the perimeter of a triangle $$\mathrm{ABC}$$ as shown below. If three points are chosen then probability that it will from a triangle is

The probability distribution of a discrete random variable X is given as

$$ \text { Then the value of } A \text { if } E(X)=2.94 \text { is } $$

The distance of the point $$(2,3,4)$$ from the line $$1-x=\frac{y}{2}=\frac{1}{3}(1+z)$$ is

The coordinates of the vertices of the triangle are $$A(-2,3,6), B(-4,4,9)$$ and $$C(0,5,8)$$. The direction cosines of the median $$\mathrm{BE}$$ are

If $$\left[\begin{array}{ccc}2+x & 3 & 4 \\ 1 & -1 & 2 \\ x & 1 & -5\end{array}\right]$$ is a singular matrix, then $$x$$ is

$$A$$ and $$B$$ are invertible matrices of the same order such that $$\left|(A B)^{-1}\right|=8$$ if $$|A|=2$$ then $$|B|$$ is

$$ \text { If } A=\left(\begin{array}{ll} 1 & 2 \\ 0 & 1 \end{array}\right) \quad P=\left(\begin{array}{cc} \cos \theta & \sin \theta \\ -\sin \theta & \cos \theta \end{array}\right) \quad Q=P^T A P, \quad \text { then } P Q^{2014} P^T \text { is equal to } $$

If the position vector of a point $$A$$ is $$\vec{a}+2 \vec{b}$$ and $$\vec{a}$$ divides $$A B$$ in the ratio $$2: 3$$, then the position vector of $$B$$ is

Solution of $$x-y+z=4 ; x-2 y+2 z=9$$ and $$2 x+y+3 z=1$$ is

Consider the first 10 natural numbers. If we multiply each number by $$-$$1 and add 1 to each number, the variance of the numbers so obtained is

The minimum value of $$Z=3 x+5 y$$, given subject to the constraints $$x+y \geq 2, x+3 y \geq 3, x, y \geq 0$$ is

If $$2 A+3 B=\left[\begin{array}{ccc}2 & -1 & 4 \\ 3 & 2 & 5\end{array}\right]$$ and $$A+2 B=\left[\begin{array}{lll}5 & 0 & 3 \\ 1 & 6 & 2\end{array}\right]$$ then $$B=$$

$$ \cos ^6 A-\sin ^6 A \text { is equal to } $$

$$ \text { If } \operatorname{cosec}(90+A)+x \cos A \cot (90+A)=\sin (90+A) \text { then the value of } x \text { is } $$

A triangular park is enclosed on two sides by a fence and on the third side by a straight river bank. The two sides having fence are of same length $$x$$. The maximum area enclosed by the park is

In a $$\triangle A B C$$, if coordinates of point $$A$$ is $$(1,2)$$ and equation of the medians through $$B$$ and $$C$$ are $$x+y=5$$ and $$x=4$$ respectively, then the coordinates of $$B$$ is

If the length of the major axis of an ellipse is 3 times the length of the minor axis, then its eccentricity is

$$ \text { The value of } \sin ^{-1}\left[\cos \left(39 \frac{\pi}{5}\right)\right] \text { is } $$

The distance between the foci of a hyperbola is 16 and its eccentricity is $$\sqrt{2}$$. Then its equation is

If $$\cos \alpha=k \cos \beta$$ then $$\cot \left(\frac{\alpha+\beta}{2}\right)$$ is equal to

$$ \lim _\limits{x \rightarrow 0} \frac{a^x-b^x}{x} \text { is equal to } $$

The range of $$x$$ which satisfy the inequation : $$-5 \leq \frac{2-3 x}{4} \leq 9$$ is

$$ \text { The function defined by } f(x)=\left\{\begin{array}{cc} \frac{\sin x}{x}+\cos x & x>0 \\ -5 k & x=0 \\ \frac{4(1-\sqrt{1-x})}{x} & x<0 \end{array} \quad \text { is continous at } x=0, \quad \text { then } k\right. \text { equals } $$

What can be said regarding a line if its slope is negative?

The centre of the circle passing through $$(0,0)$$ and $$(1,0)$$ and touching the circle $$x^2+y^2=9$$ is

The ratio in which the line $$3 x+4 y+2=0$$ divides the distance between the lines $$3 x+4 y+5=0$$ and $$3 x+4 y-5=0$$ is

If the volume of a sphere is increasing at a constant rate, then the rate at which its radius is increasing is

$$ \int \frac{\cos 4 x+1}{\cot x-\tan x} d x= $$

The function $$f(x)=\frac{x}{2}+\frac{2}{x}$$ has a local minimum at

$$ f(x)=2 x-\tan ^{-1} x-\log (x+\sqrt{x^2+1}) \text { is monotonically increasing, when } $$

If $$f(x)=\frac{(x+1)^7 \sqrt{1+x^2}}{\left(x^2-x+1\right)^6}$$ then the value of $$f^{\prime}(0)$$ is equal to

The altitude of a cone is $$20 \mathrm{~cm}$$ and its semi vertical angle is $$30^{\circ}$$. If the semi vertical angle is increasing at the rate of $$2^0$$ per second, then the radius of the base is increasing at the rate of

$$ \int e^x\left(1+\tan x+\tan ^2 x\right) d x \text { is equal to } $$

$$\int x^x(1+\log x) d x$$ is equal to

The area bounded by the curve $$y^2=4 a^2(x-1)$$ and the lines $$x=1, y=4 a$$ is

$$ \int_0^2\left|x^2+2 x-3\right| d x \text { is equal to } $$

The area of the upper half of the circle whose equation is $$(x-1)^2+y^2=1$$ is given by

$$ \int \sqrt{\operatorname{cosec} x-1} d x= $$

The conversion of Propyne to Benzene can be brought out in 4 steps.

Choose the reagents to be used, in the proper sequential order, to bring out the conversion.

Reagents provided: alc. $$\mathrm{KOH}, \mathrm{H}_2 / \mathrm{Pd}, \mathrm{Na} /$$ dry ether, $$\mathrm{HBr}, \mathrm{HBr} /\left(\mathrm{C}_6 \mathrm{H}_5 \mathrm{CO}\right)_2 \mathrm{O}_2$$, Soda-lime, $$\mathrm{Cr}_2 \mathrm{O}_3$$ (high T and P), Conc. $$\mathrm{H}_2 \mathrm{SO}_4$$

Identify the reagents $$\mathrm{X}, \mathrm{Y}$$ and $$\mathrm{Z}$$ used to bring out the following reactions.

The solution of the differential equation $$\frac{d y}{d x}+y \cos x=\frac{1}{2} \sin 2 x$$

Identify the final product formed during the course of the given reactions.

Pentan-2-one $$\xrightarrow{\mathrm{NaCN} / \mathrm{HCl}}[\mathrm{X}]$$

$$[\mathrm{X}] \xrightarrow[95 \% \mathrm{H}_3 \mathrm{PO}_4]{\Delta \text { with }}[Y]$$

The sum of the degree and order of the following differential equation $$\left[1-\left(\frac{d y}{d x}\right)^2\right]^{\frac{3}{2}}=k x \frac{d^2 y}{d x^2}$$

The general solution of the differential equation $$\left(1+y^2\right) d x=\left(\tan ^{-1} y-x\right) d y$$