Which mineral among the following contains vanadium in it?

Which of the following is least reactive towards $\mathrm{S}_{\mathrm{N}} 1$ reactions?

Which of the following oxyacids of sulphur contain four $\mathrm{S}=\mathrm{O}$ bonds?

What is the unit of viscosity?

Which of the following compounds does not react with bromine in alkaline medium?

Which of the following molecules has a central atom with complete octet?

Which of the following molecular formula represents Marshall's acid?

An element crystallises in fcc type of unit cell. The volume of one unit cell is $24.99 \times 10^{-24} \mathrm{~cm}^3$ and density of the element $7.2 \mathrm{~g} \mathrm{~cm}^{-3}$. Calculate the number of unit cells in 36 g of pure sample of element?

Which of the following reagents is used for the following conversion?

$$\mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CHO} \longrightarrow \mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CH}_2 \mathrm{OH}$$

Identify $A$ in the following reaction.

$$A+\mathrm{CH}_3 \mathrm{MgBr} \xrightarrow{\text { Ether }} \text { complex }\xrightarrow{\mathrm{H}_3 \mathrm{O}^{+}}\left(\mathrm{CH}_3\right)_3 \mathrm{C}-\mathrm{OH}$$

Identify the number of donor groups present in EDTA.

Identify the enzyme $X$ in the following reaction

$\mathrm{H}_2 \mathrm{O}_2(\mathrm{aq}) \xrightarrow{x} \mathrm{H}_2 \mathrm{O}(l)+\frac{1}{2} \mathrm{O}_2(g)$

The Total number of electrons around the carbon atom of methyl free radical are

Identify tranquiliser from the following?

Which reagent among the following is used to confirm presence of aldehydic carbonyl group in glucose?

What is the percentage of unoccupied space in fcc unit cell?

How many hydrogen atoms are surrounding each oxygen atom in structure of ice?

Which of the following is not an example of antiseptic drug?

Which of the following compounds is obtained, when phenol react with bromine water?

What is standard $N \equiv N$ bond enthalpy from following reaction,

$$\begin{aligned} & \mathrm{N}_2(g)+3 \mathrm{H}_2(g) \longrightarrow 2 \mathrm{NH}_3(g) ; \Delta H^{\circ}=-83 \mathrm{~kJ} \\ & \left(\Delta H^{\circ}(\mathrm{H}-\mathrm{H})=435 \mathrm{~kJ} ; \Delta H^{\circ}(\mathrm{N}-\mathrm{H})=389 \mathrm{~kJ}\right) \\ \end{aligned}$$

Which of the following is correct decreasing order of the repulsive interaction of electron pairs in a molecule?

For first order reaction the concentration of reactant decreases from 0.2 to 0.1 M in 100 minutes. What is the rate constant of the reaction?

The end product $C$ of the following reaction is

$$\mathrm{C}_2 \mathrm{H}_5 \mathrm{NH}_2 \xrightarrow{\mathrm{HNO}_2} A \xrightarrow{\mathrm{PCl}_5} B \xrightarrow[\text { Alcohol }]{\mathrm{NH}_3} C$$

Which among the following sets of elements is present in chalcopyrite?

Which of the following pairs of monomers is used for the preparation of dextron?

What is the oxidation number of Mn in MnO$^{2-}_4$ ion?

The vapour pressure of solvent decreases by 10 mm Hg , if mole fraction of non-volatile solute is 0.2 . Calculate vapour pressure of solvent.

Identify ' $B$ ' in the following reaction.

$$\mathrm{C}_2 \mathrm{H}_6 \xrightarrow[\mathrm{AlBr}_3]{\mathrm{Br}_2} A \xrightarrow[\Delta]{\mathrm{CH}_3 \mathrm{COOAg}} B$$

Which of the following is a Stephen reaction?

Which among the following crystal lattices occupies all of the cubic holes by cations?

What is the name of reaction involving replacement of diazonium group by chloride using cuprous (I) salt ?

How many moles of gaseous oxygen at one atmosphere is considered for the reaction with element for plotting a graph in Ellingham diagram?

How many Faradays of electricity is required to produce 4.8 g of Mg at cathode in the electrolysis of molten $\mathrm{MgCl}_2$ ? (Molar mass of $\mathrm{Mg}=24 \mathrm{~g} / \mathrm{mol}$ )

Which of the following compound is highly reactive towards HCN?

What is the range of number of carbon atoms in alkanes found in paraffin wax?

Which of the following amines is most basic in nature in aqueous phase?

Which of the following $0-10 \mathrm{~m}$ aqueous solutions will have maximum $\Delta T_f$ value?

If boiling point of urea solution is $100.18^{\circ} \mathrm{C}$ and $K_b$ for water is $0.512 \mathrm{~K} \mathrm{~kg} \mathrm{~mol}^{-1}$, molality of solution is (Boiling point of water $=100^{\circ} \mathrm{C}$)

What is the SI unit for electrochemical equivalent?

Number of electrons involved in the reaction, when 1 Faraday of electricity is passed through an electrolytic solution is

Which carbon atoms of $\alpha-D$ glucopyranose and $\beta$-D-fructofuranose respectively are linked together to form glycosidic linkage in sucrose?

Which of the following compounds reacts with ammonia to form urotropine?

A first order reaction is $25 \%$ completed in 40 minutes. What is the rate constant $k$ for the reaction?

Which among the following is an ambidentate ligand?

What is the formula of hydrolith?

For the reaction,

$$\mathrm{N}_2(g)+3 \mathrm{H}_2(g) \longrightarrow 2 \mathrm{NH}_3(g) ; \Delta H$$

is equal to

What is the highest oxidation state possessed by phosphorus in it's oxyacids?

When 6.0 g of graphite reacts with dihydrogen to give methane gas, 37.4 kJ of heat is liberated. What is standard enthalpy of formation of $\mathrm{CH}_4(\mathrm{~g})$ ?

Which among the following polymers is used for making handles of cooker?

Identify the correct decreasing order of densities of $d$-block elements.

With usual notations, if the angles $A, B, C$ of a $\triangle A B C$ are in $A P$ and $b: c=\sqrt{3}: \sqrt{2}$

$$\int \sin ^{-1} x d x=$$

The integrating factor of the differential equation $x \frac{d y}{d x}+y \log x=x^2$ is

If $\mathbf{a}=3 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}, \mathbf{b}=2 \hat{\mathbf{i}}-\hat{\mathbf{j}}+7 \hat{\mathbf{k}}$ and $\mathbf{c}=7 \hat{\mathbf{i}}-\hat{\mathbf{j}}+23 \hat{\mathbf{k}}$ are three vectors, then which of the following statement is true.

The maximum volume of a right circular cylinder if the sum of its radius and height is 6 m is

If the slopes of the lines given by the equation $a x^2+2 h x y+b y^2=0$ are in the ratio $5: 3$, then the ratio $h^2: a b=$

The equation of a line passing through the point $(7,-4)$ and perpendicular to the line passing through the points $(2,3)$ and $(1,-2)$ is

$\int_\limits0^1 \tan ^{-1}\left(\frac{2 x-1}{1+x-x^2}\right) d x=$

If $f(x)=\frac{1-\sin x+\cos x}{1+\sin x+\cos x}$, for $x \neq \pi$ is continuous at $x=\pi$, then $f(\pi)=$

$\mathbf{a}$ and $\mathbf{b}$ are non-collinear vectors. If $p=(2 x+1) a-b$ and $q=(x-2) a+b$ are collinear vectors, then $x=$

If $A=\left[\begin{array}{ll}4 & 5 \\ 2 & 1\end{array}\right]$ and $A^2-5 A-6 I=0$, then $A^{-1}=$

The quadratic equation whose roots are the numbers having arithmetic mean 34 and geometric mean 16 is

If $x=a \sin t-b \cos t, y=a \cos t+b \sin t$, then $y^3 \frac{d^2 y}{d x^2}+x^2+y^2=$

The area of the triangle formed by the lines joining vertex of the parabola $x^2=12 y$ to the extremities of its latus rectum is

If the sum of the mean and the variance of a binomial distribution for 5 trials is 1.8 , then $p=$

The odds in favour of getting sum multiple of 3 , when pair of dice are thrown is

The rate of disintegration of a radio active element at time $t$ is proportional to its mass, at the time. Then the time during which the original mass of 1.5 gm . Will disintegrate into its mass of 0.5 gm . is proportional to

If $\mathbf{a}, \mathbf{b}, \mathbf{c}$ are non-coplanar vectors and $p=\frac{\mathbf{b} \times \mathbf{c}}{[a b c]}, q=\frac{\mathbf{c} \times \mathbf{a}}{[a b c]}, r=\frac{\mathbf{a} \times \mathbf{b}}{[a b c]}$, then $\mathbf{a} \cdot \mathbf{p}+\mathbf{b} \cdot \mathbf{q}+\mathbf{c} \cdot \mathbf{r}=$

The negation of the statement pattern $\sim p \vee(q \rightarrow \sim r)$ is

The point $P$ lies on the line $A, B$ where $A=(2,4,5)$ and $B \equiv(1,2,3)$. If $z$ co-ordinate of point $P$ is 3 , the its $y$ co-ordinate is

If $R=\{(a, b) / b=a-1, a \in Z, 5 < a < 9$, then the range of $R$ is

$$\int \log x \cdot(\log x+2) d x=$$

The c.d.f, $F(x)$ associated with p.d.f. $f(x)=3\left(1-2 x^2\right)$. If $0< x<1$ is $k\left(x-\frac{2 x^3}{k}\right)$, then value of $k$ is

The range of the function $f(x)=\frac{x-3}{5-x}, x \neq 5$ is

If $y=\sin ^{-1}\left[\frac{\sqrt{1+x}+\sqrt{1-x}}{2}\right]$, then $\frac{d y}{d x}=$

The area of the $\triangle A B C$ is $10 \sqrt{3} \mathrm{~cm}^2$, angle $B$ is $60^{\circ}$ and its perimeter is 20 cm , then $\ell(A C)=$

The equation of the normal to the curve $2 x^2+y^2=12$ at the point $(2,2)$ is

$$\frac{1-\sin \theta+\cos \theta}{1-\sin \theta-\cos \theta}=$$

If $A$ and $B$ are supplementary angles, then $\sin ^2 \frac{A}{2}+\sin ^2 \frac{B}{2}=$

If the equation $3 x^2+10 x y+3 y^2+16 y+k=0$ represents a pair of lines, then the value of kis

If $2 \cos ^2 \theta+3 \cos \theta=2$, then permissible value of $\cos \theta$ is

A line makes angles $\alpha, \beta, \gamma$ with the co-ordinate axes and $\alpha+\beta=90^{\circ}$, then $\gamma=$

The equations of planes parallel to the plane $x+2 y+2 z+8=0$, which are at a distance of 2 units from the point $(1,1,2)$ are

If $X$ is a.r.v. with c.d.f $F(x)$ and its probability distribution is given by

then, $F(1.5)-F(-0.5)=$

$$\int \frac{d x}{x^2+4 x+13}=$$

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

$$\int_\limits0^{\frac{\pi}{2}} \frac{\sqrt[7]{\sin x}}{\sqrt[7]{\sin x}+\sqrt[7]{\cos x}} d x=$$

$\int_\limits0^1\left(1-\frac{x}{1!}+\frac{x^2}{2!}-\frac{x^3}{3!}+\ldots\right.$ upto $\left.\infty\right) e^{2 x} d x=$

The principal solutions of $\cot x=\sqrt{3}$ are

The statement pattern $p \wedge(q \vee \sim p)$ is equivalent to

The LPP to maximize $Z=x+y$, subject to $x+y \leq 1,2 x+2 y \geq 6, x \geq 0, y \geq 0$ has

The area of the region bounded by the curve $y=\sin x$ between $x=-\pi$ and $x=\frac{3 \pi}{2}$ is

The equation of a plane containing the point $(1,-1,2)$ and perpendicular to the planes $2 x+3 y-2 z=5$ and $x+2 y-3 z=8$ is

The general solution of the differential equation $\left(1+y^2\right)+\left(x-e^{\tan ^{-1} y}\right) \frac{d y}{d x}=0$ is

The equation of the line passing through $(1,2,3)$ and perpendicular to the lines $x-1=\frac{y+2}{2}=\frac{z+4}{4}$ and $\frac{x-1}{2}=\frac{y-2}{2}=z+3$ is

The cofactors of the elements of the first column of the matrix $A=\left[\begin{array}{ccc}2 & 0 & -1 \\ 3 & 1 & 2 \\ -1 & 1 & 2\end{array}\right]$ are

The equation of the directrix of the parabola $3 x^2=16 y$ is

The order and degree of the differential equation $\left[1+\frac{1}{\left(\frac{d y}{d x}\right)^2}\right]^{\frac{5}{3}}=5 \frac{d^2 y}{d x^2}$ are respectively

If the population grows at the rate of $8 \%$ per year, then the time taken for the population to be doubled, is (Given $\log 2=0.6912$)

The area of the square increases at the rate of $0.5 \mathrm{~cm}^2 / \mathrm{sec}$. The rate at which its perimeter is increasing when the side of the square is 10 cm long, is

A tuning fork $A$ produces 5 beats per second with a tuning fork of frequency 480 Hz . When a little wax is stuck to a prong of fork $A$, the number of beats heard per second becomes 2 . What is the frequency of tuning fork $A$ before the wax is stuck to it ?

Two spherical rain drops reach the surface of the earth with terminal velocities having ratio $16: 9$. The ratio of their surface area is

In system of two particles of masses $m_1$ and $m_2$, the first particle is moved by a distance $d$ towards the centre of mass. To keep the centre of mass unchanged, the second particle will have to be moved by a distance

A graph is plotted between the fringe-width Z and the distance D between the slit and eye-piece, keeping other adjustment same. The correct graph is

(A)

(B)

(C)

(D)

The graph of stopping potential $V_s$ against frequency $v$ of incident radiation is plotted for two different metals $P$ and $Q$ as shown in the graph. $\phi_p$ and $\phi_Q$ are work-functions of $P$ and $Q$ respectively, then

An electron moves in a circular orbit with uniform speed $v$. It produces a magnetic field $B$ at the centre of the circle. The radius of the circle is [ $\mu_0=$ permeability of free space, $e=$ electronic charge]

If the maximum kinetic energy of emitted electrons in photoelectric effect is $3.2 \times 10^{-19} \mathrm{~J}$ and the work-function for metal is $6.63 \times 10^{-19} \mathrm{~J}$, then stopping potential and threshold wavelength respectively are

[Planck's constant, $h=6.63 \times 10^{34} \mathrm{~J}$-s]

[Velocity of light, $c=3 \times 10^8 \frac{\mathrm{~m}}{\mathrm{~s}}$ ]

[Charge on electron $=1.6 \times 10^{-19} \mathrm{C}$ ]

The root mean square velocity of molecules of a gas is $200 \mathrm{~m} / \mathrm{s}$. What will be the root mean square velocity of the molecules, if the molecular weight is doubled and the absolute temperature is halved?

Earth has mass $M_1$ and radius $R_1$. Moon has mass $M_2$ and radius $R_2$. Distance between their centre is $r$. A body of mass $M$ is placed on the line joining them at a distance $\frac{r}{3}$ from centre of the earth. To project the mass $M$ to escape to infinity, the minimum speed required is

Water rises upto a height $h$ in a capillary tube on the surface of the earth. The value of $h$ will increase, if the experimental setup is kept in [ $g=$ acceleration due to gravity]

Van de Graaff generator produces

A carrier wave of peak voltage 16 V is used to transmit a signal. If the modulation index is $75 \%$, the peak voltage of the modulating signal is

The energy levels with transitions for the atom are shown. The transitions corresponding to emission of radiation of maximum and minimum wavelength are respectively

A milliammeter of resistance $40 \Omega$ has a range $0-30 \mathrm{~mA}$. What will be the resistance used in series to convert it into voltmeter of range $0-15 \mathrm{~V}$ ?

A child starts running from rest along a circular track of radius $r$ with constant tangential acceleration a. After time $t$ he feels that slipping of shoes on the ground has started. The coefficient of friction between shoes and the ground is

[g = acceleration due to gravity]

A metal rod has length, cross-sectional area and Young's modulus as $L, A$ and $Y$, respectively. If the elongation in the rod produced is I, then work done is proportional to

Two cells having unknown emfs $E_1$ and $E_2$ $\left(E_1>E_2\right)$ are connected in potentiometer circuit, so as to assist each other. The null point obtained is at 490 cm from the higher potential end. When cell $E_2$ is connected, so as to oppose cell $E_1$, the null point is obtained at 90 cm from the same end. The ratio of the emfs of two cells $\left(\frac{E_1}{E_2}\right)$ is

Three points masses, each of mass $m$ are placed at the corners of an equilateral triangle of side $\ell$. The moment of inertia of the system about an axis passing through one of the vertices and parallel to the side joining other two vertices, will be

Using Bohr's model, the orbital period of electron in hydrogen atom in $n$th orbit is ( $\varepsilon_0=$ permittivity of free space, $h=$ Planck's constant, $m=$ mass of electron and $\theta=$ electronic charge)

Let $\sigma$ and $b$ be Stefan's constant and Wien's constant respectively, then dimensions of $\sigma b$ are

At the poles, a stretched wire of a given length vibrates in unison with a tuning fork. At the equator, for same setting to produce resonance with same fork, the vibrating length of wire

A steel wire of length / has a magnetic moment $M$. It is then bent into a semicircular arc. The new magnetic moment is

The angle subtended by the vector $A=4 \hat{\mathbf{i}}+3 \hat{\mathbf{j}}+12 \hat{\mathbf{k}}$ with the $X$-axis is

$N$ number of balls of mass $m \mathrm{~kg}$ moving along positive direction of $X$ - axis, strike a wall per second and return elastically. The velocity of each ball is $u \mathrm{~m} / \mathrm{s}$. The force exerted on the wall by the balls in newton, is

Metal rings $P$ and $Q$ are lying in the same plane, where current I is increasing steadily. The induced current in metal rings is shown correctly in figure

A 10 m long wire of resistance $20 \Omega$ is connected in series with a battery of emf 3 V and a resistance of $10 \Omega$. The potential gradient along the wire in $\mathrm{V} / \mathrm{m}$ is

A domain in a ferromagnetic substance is in the form of a cube of side $1 \mu \mathrm{~m}$. If it contains $8 \times 10^{10}$ atoms and each atomic dipole has a dipole moment of $9 \times 10^{-24} \mathrm{Am}^2$, then the magnetisation of the domain is

If the surface tension of a soap solution is $3 \times 10^{-2} \mathrm{~N} / \mathrm{m}$ then the work done in forming a soap film of $20 \mathrm{~cm} \times 5 \mathrm{~cm}$ will be

The compressibility of water is $5 \times 10^{-10} \mathrm{~m}^2 / \mathrm{N}$. Pressure of $15 \times 10^6 \mathrm{~Pa}$ is applied on 100 mL volume of water. The change in the volume of water is

Two bodies $A$ and $B$ of equal mass are suspended from two separate massles springs of force constant $k_1$ and $k_2$, respectively. The bodies oscillate vertically such that their maximum velocities are equal. The ratio of the amplitudes of body $A$ to that of body $B$ is

Two capacitors of capacities $2 \mu \mathrm{~F}$ and $4 \mu \mathrm{~F}$ are connected in parallel. A third capacitor of $6 \mu \mathrm{~F}$ capacity is connected in series with this combination. A battery of 12 V is connected across this combination. The charge on $2 \mu \mathrm{~F}$ capacitor is

The escape velocity of a body from any planet, whose mass is six times the mass of earth and radius is twice the radius of earth will (v$_e$ = escape velocity of a body from the earth's surface)

A ray of light is incident at an angle $i$ on one face of a thin angled prism. The ray emerges normally from the other face. Refractive inder of the glass prims is $n$ and angle of prism is $A$. The value of $i$ is

What is the angle between resultant of $A+B$ and $\mathbf{A} \times \mathbf{B}$.

A rope is wound around a solid cylinder of mass 1 kg and radius 0.4 m . What is the angular acceleration of cylinder, if the rope is pulled with a force of 25 N ? (Cylinder is rotating about its own axis.)

A transistor having $\alpha=0.8$ is connected in common emitter configuration. When the base current changes by 6 mA , then the change in collector current is

A uniform metal wire has length $L$, mass $M$ and density $\rho$. It is under tension $T$ and $v$ is the speed of transverse wave along the wire. The area of cross-section of the wire is

An object is clearly seen through an astronomical telescope of length 50 cm . The focal lengths of its objective and eye-piece respectively, can be

A bob of a simple pendulum has mass $m$ and is oscillating with an amplitude $a$. If the length of the pendulum is $L$, then the maximum tension in the string is $\left[\cos 0^{\circ}=1\right.$, $g=$ acceleration due to gravity]

The Brewster's angle for the glass-air interface is $(54.74)^{\circ}$. If a ray of light passing from air to glass strickes at an angle of incidence $45^{\circ}$, then the angle of refraction is

$$\left[\tan (54.74)^{\circ}=\sqrt{2}, \sin 45=\frac{1}{\sqrt{2}}\right]$$

For a paramagnetic substance, the magnetic susceptibility is

Let $x=\pi R\left(\frac{P^2-Q^2}{2}\right)$, where $P, Q$ and $R$ are lengths. The physical quantity $x$ is

The fundamental frequency of a closed pipe is 400 Hz . If $\frac{1}{3}$ rd pipe is filled with water, then the frequency of 2nd harmonic of the pipe will be (neglect and correction)

An AC circuit contains resistance of $12 \Omega$ and inductive reactance $5 \Omega$. The phase angle between current and potential difference will be

In an intrinsic semiconductor, at an ordinary temperature, the correct relation between the number of electrons per unit volume $n_e$ and number of holes per unit volume $n_h$.

By increasing the aperture of the objective lens, wavelength of light, focal length of the objective lens and the resolving power of an astronomical telescope respectively

Two galvanometers $A$ and $B$ require currents of 4 mA and 7 mA , respectively to produce the same deflection of 20 divisions. If $S_A$ and $S_B$ are their sensitivities respectively, then

Two circular loop $A$ and $B$ of radii $R$ and $N R$ respectively are made from a uniform wire. Moment of inertia of $B$ about its axis is 3 times that of $A$ about its axis. The value of $N$ is

A body is moving along a circular track of radius 100 m with velocity $20 \mathrm{~m} / \mathrm{s}$. Its tangential acceleration is $3 \mathrm{~m} / \mathrm{s}^2$, then its resultant acceleration will be

A body of mass 64 g is made to oscillate turn by turn on two different springs $A$ and $B$. Spring $A$ and $B$ has force constant $4 \frac{\mathrm{~N}}{\mathrm{~m}}$ and $16 \frac{\mathrm{~N}}{\mathrm{~m}}$ respectively. If $T_1$ and $T_2$ are period of oscillations of springs $A$ and $B$ respectively, then $\frac{T_1+T_2}{T_1-T_2}$ will be