Name the accelerator used to introduce network of crosslink in elastomer.

Which of the following is a property of alkali metals?

The IUPAC name of following compound is:

If $$\mathrm{K}_{\mathrm{b}}$$ denote molal elevation constant of water, then boiling point of an aqueous solution containing $$36 \mathrm{~g}$$ glucose (molar mass $$=180$$ ) per $$\mathrm{dm}^3$$ is:

Which metal halide from following has lowest ionic character ( $$\mathrm{M}=$$ metal atom)?

Which among the following reagents is called as Hinsberg's reagent?

Which among the following amines has highest value of $$\mathrm{pK}_{\mathrm{b}}$$ ?

What is vapour pressure of a solution containing $$1 \mathrm{~mol}$$ of a nonvolatile solute in $$36 \mathrm{~g}$$ of water $$\left(\mathrm{P}_1^0=32 \mathrm{~mm} \mathrm{~Hg}\right)$$ ?

Identify the product obtained when phenol is reacted with dilute nitric acid at low temperature.

For an elementary reaction

$$2 \mathrm{~A}+\mathrm{B} \longrightarrow 3 \mathrm{C}$$

rate of appearance of $$\mathrm{C}$$ is $$1.3 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}$$, the rate of disappearance of $$\mathrm{A}$$ is:

Which among the following alkenes is most stable?

Identify a CORRECT formula for spin only magnetic moment.

Which of the following salts turns red litmus blue in its aqueous solution?

What is the value of increase in internal energy when system does $$8 \mathrm{~J}$$ of work on surrounding by supplying $$40 \mathrm{~J}$$ of heat to it?

Benzonitrile on reduction with stannous chloride in presence of hydrochloric acid followed by acid hydrolysis forms:

Which among the following is TRUE for isobaric process?

Which among the following statements is TRUE about gammexane?

Which of the following is primary allylic alcohol?

Which of following is NOT correct about fructose?

Which among following salts shows decrease in solubility with increase in temperature?

Find the number of faradays of electricity required to produce $$45 \mathrm{~g}$$ of $$\mathrm{Al}$$ from molten $$\mathrm{Al}_2 \mathrm{O}_3$$.

(At. mass of $$\mathrm{Al}=27$$ )

Identify the reagent that confirms the presence of five $$-\mathrm{OH}$$ groups in glucose.

What is the concentration of $$\mathrm{OH}^{-}$$ ion in a solution containing $$0.05 \mathrm{~M} \mathrm{~H}^{+}$$ ions?

Which formula is used to calculate edge length in bcc structure?

Identify the products of following reaction:

What is the volume in $$\mathrm{dm}^3$$ occupied by $$3 \mathrm{~mol}$$ of ammonia gas at STP?

Slope of the graph between $$\log \frac{[\mathrm{A}]_0}{[\mathrm{~A}]_{\mathrm{t}}}$$ (y axis) and time ( $$x$$ axis) for first order reaction is equal to:

What is total number of donor atoms in $$\left[\mathrm{Co}\left(\mathrm{H}_2 \mathrm{O}\right)\left(\mathrm{NH}_3\right)_5\right] \mathrm{I}_3$$ ?

Which from following equations is used to express the angular momentum of an electron in a stationary state?

Which emission transition series is obtained when electron jumps from $$\mathrm{n}_2=\infty$$ to $$\mathrm{n}_1=1$$ ?

What is half life time of a first order reaction if initial conc. of reactant is $$0.01 \mathrm{~mol} \mathrm{~L}^{-1}$$ and rate of reaction is $$0.00352 \mathrm{~mol} \mathrm{~L}^{-1}$$ minute $$^{-1}$$ ?

Which among the following pairs of polymers contains both members as copolymers?

What is atomic mass of an element with $$\mathrm{BCC}$$ structure and density $$10 \mathrm{~g} \mathrm{~cm}^{-3}$$ having edge length $$300 \mathrm{~pm}$$ ?

Oxidation state of manganese in potassium permanganate is:

Which among following complexes is a neutral complex?

Which among the following halogens combines readily with metals to form metal halides with highest ionic character?

Which of the following compounds has highest boiling point?

Identify physisorption from following.

Identify the product of following reaction.

Benzoyl chloride $$\stackrel{\mathrm{H}_2 \mathrm{O}}{\longrightarrow}$$ product

What is IUPAC name of the compound?

Calculate the $$\mathrm{pH}$$ of $$1.36 \times 10^{-2} \mathrm{M}$$ solution of perchloric acid.

Which of the following formulae is used to determine compressibility factor for measurement of deviation from ideal behaviour?

The molar conductivity of $$0.02 \mathrm{~M} \mathrm{~AgI}$$ at $$298 \mathrm{~K}$$ is $$142.3 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$$. What is its conductivity?

What is IUPAC name of following compound?

Identify a molecule with incomplete octet from following.

What is the number of unit cells present in a cubic pack crystal lattice having 4 atoms per unit cell and weighing $$0.60 \mathrm{~g}$$ (molar mass $$\left.60 \mathrm{~g} \mathrm{~mol}^{-1}\right)$$ ?

Identify 'A' in the following reaction.

Which among the following is CORRECT formula for determination of cell constant?

Identify the catalyst (A) used in following reaction.

$$\mathrm{CO}+\mathrm{H}_2 \mathrm{O} \stackrel{\mathrm{A}}{\rightleftharpoons} \mathrm{CO}_2+\mathrm{H}_2$$

What is value of PV type of work for following reaction at 1 bar?

$$\underset{(200 \mathrm{~mL})}{\mathrm{C}_2 \mathrm{H}_{4(\mathrm{~g})}}+\underset{(150 \mathrm{~mL})}{\mathrm{HCl}_{(\mathrm{g})}} \longrightarrow \mathrm{C}_2 \mathrm{H}_5 \mathrm{Cl}_{(\mathrm{g})}$$

$$\int\limits_0^\pi \frac{d x}{4+3 \cos x}=$$

If $$y=\log _{\sin x} \tan x$$, then $$\left(\frac{\mathrm{d} y}{\mathrm{~d} x}\right)_{x=\frac{\pi}{4}}$$ has the value

$$\lim _\limits{x \rightarrow 2}\left[\frac{1}{x-2}-\frac{2}{x^3-3 x^2+2 x}\right]$$ is equal to

From a lot of 20 baskets, which includes 6 defective baskets, a sample of 2 baskets is drawn at random one by one without replacement. The expected value of number of defective basket is

If the angle between the lines represented by the equation $$x^2+\lambda x y-y^2 \tan ^2 \theta=0$$ is $$2 \theta$$, then the value of $$\lambda$$ is

Number of common tangents to the circles $$x^2+y^2-6 x-14 y+48=0$$ and $$x^2+y^2-6 x=0$$ are

The left-hand derivative of $$\mathrm{f}(x)=[x] \sin (\pi x)$$, at $$x=\mathrm{k}, \mathrm{k}$$ is an integer and [.] is the greatest integer function, is

Let $$\mathrm{f}(x)=\int \frac{\sqrt{x}}{(1+x)^2} \mathrm{~d} x, x \geq 0$$, then $$\mathrm{f}(3)-\mathrm{f}(1)$$ is equal to

Value of $$c$$ satisfying the conditions and conclusions of Rolle's theorem for the function $$\mathrm{f}(x)=x \sqrt{x+6}, x \in[-6,0]$$ is

Three of six vertices of a regular hexagon are chosen at random. The probability that the triangle with these three vertices is equilateral, equals ___________.

If the direction cosines $$l, \mathrm{~m}, \mathrm{n}$$ of two lines are connected by relations $$l-5 \mathrm{~m}+3 \mathrm{n}=0$$ and $$7 l^2+5 \mathrm{~m}^2-3 \mathrm{n}^2=0$$, then value of $$l+\mathrm{m}+\mathrm{n}$$ is

Let $$\mathrm{f}(x)=\log (\sin x), 0 < x < \pi$$ and $$\mathrm{g}(x)=\sin ^{-1}\left(\mathrm{e}^{-x}\right), x \geq 0$$. If $$\alpha$$ is a positive real number such that $$\mathrm{a}=(\mathrm{fog})^{\prime}(\alpha)$$ and $$\mathrm{b}=(\mathrm{fog})(\alpha)$$, then

Five students are to be arranged on a platform such that the boy $$B_1$$ occupies the second position and such that the girl $$G_1$$ is always adjacent to the girl $$G_2$$. Then, the number of such possible arrangements is

If the volume of the parallelopiped is $$158 \mathrm{~cu}$$. units whose coterminus edges are given by the vectors $$\bar{a}=(\hat{i}+\hat{j}+n \hat{k}), \bar{b}=2 \hat{i}+4 \hat{j}-n \hat{k}$$ and $$\bar{c}=\hat{i}+n \hat{j}+3 \hat{k}$$, where $$n \geq 0$$, then the value of $$n$$ is

Let $$\mathrm{f}(x)$$ be positive for all real $$x$$. If $$\mathrm{I}_1=\int_\limits{1-\mathrm{h}}^{\mathrm{h}} x \mathrm{f}(x(1-x)) \mathrm{d} x$$ and $$\mathrm{I}_2=\int_\limits{1-\mathrm{h}}^{\mathrm{h}} \mathrm{f}(x(1-x)) \mathrm{d} x$$, where $$(2 h-1)>0$$, then $$\frac{I_1}{I_2}$$ is

The mirror image of the point $$(1,2,3)$$ in a plane is $$\left(-\frac{7}{3},-\frac{4}{3},-\frac{1}{3}\right)$$. Thus, the point _________ lies on this plane.

If $$\alpha=3 \sin ^{-1} \frac{6}{11}$$ and $$\beta=3 \cos ^{-1}\left(\frac{4}{9}\right)$$, where the inverse trigonometric functions take only the principal values, then the correct option is

$$\text { The value of } \sec ^2\left(\tan ^{-1} 2\right)+\operatorname{cosec}^2\left(\cot ^{-1} 3\right) \text { is }$$

The value of $$\tan \left(\frac{\pi}{8}\right)$$ is _________.

A plane is parallel to two lines, whose direction ratios are $$1,0,-1$$ and $$-1,1,0$$ and it contains the point $$(1,1,1)$$. If it cuts co-ordinate axes $$(\mathrm{X}, \mathrm{Y}, \mathrm{Z}$$ - axes resp.) at $$\mathrm{A}, \mathrm{B}, \mathrm{C}$$, then the volume of the tetrahedron $$\mathrm{OABC}$$ is _________ cu. units.

The domain of the function given by $$2^x+2^y=2$$ is

If $$\mathrm{f}(x)=x \mathrm{e}^{x(1-x)}, x \in \mathrm{R}$$, then $$\mathrm{f}(x)$$ is

The solution of the differential equation $$\frac{\mathrm{d} y}{\mathrm{~d} x}=\frac{1+y^2}{1+x^2}$$ is

If $$\bar{a}, \bar{b}, \bar{c}$$ are three vectors such that $$\overline{\mathrm{a}} \cdot(\overline{\mathrm{b}}+\overline{\mathrm{c}})+\overline{\mathrm{b}} \cdot(\overline{\mathrm{c}}+\overline{\mathrm{a}})+\overline{\mathrm{c}} \cdot(\overline{\mathrm{a}}+\overline{\mathrm{b}})=0 \quad$$ and $$\quad|\overline{\mathrm{a}}|=1$$, $$|\bar{b}|=8$$ and $$|\bar{c}|=4$$, then $$|\bar{a}+\bar{b}+\bar{c}|$$ has the value _________.

Let $$\bar{a}=2 \hat{i}+\hat{j}-2 \hat{k}$$ and $$\bar{b}=\hat{i}+\hat{j}$$. If $$\bar{c}$$ is a vector such that $$\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}=|\overline{\mathrm{c}}|,|\overline{\mathrm{c}}-\overline{\mathrm{a}}|=2 \sqrt{2}$$ and the angle between $$(\bar{a} \times \bar{b})$$ and $$\bar{c}$$ is $$\frac{\pi}{6}$$, then $$|(\bar{a} \times \bar{b}) \times \bar{c}|$$ is

$$\int_\limits{-1}^3\left(\cot ^{-1}\left(\frac{x}{x^2+1}\right)+\cot ^{-1}\left(\frac{x^2+1}{x}\right)\right) \mathrm{d} x=$$

If $$P=\left[\begin{array}{lll}1 & \alpha & 3 \\ 1 & 3 & 3 \\ 2 & 4 & 4\end{array}\right]$$ is the adjoint of a $$3 \times 3$$ matrix $$A$$ and $$|A|=4$$, then value of $$\alpha$$ is

If $$\mathrm{f}(x)=\left\{\begin{array}{ll}\frac{\sqrt{1+\mathrm{m} x}-\sqrt{1-\mathrm{m} x}}{x}, & -1 \leq x < 0 \\ \frac{2 x+1}{x-2} & , 0 \leq x \leq 1\end{array}\right.$$ is continuous in the interval $$[-1,1]$$, then $$\mathrm{m}$$ is equal to

The area of the region bounded by the parabola $$y=x^2$$ and the curve $$y=|x|$$ is

Derivative of $$\tan ^{-1}\left(\frac{\sqrt{1+x^2}-\sqrt{1-x^2}}{\sqrt{1+x^2}+\sqrt{1-x^2}}\right)$$ w.r.t. $$\cos ^{-1} x^2$$ is

A binomial random variable $$\mathrm{X}$$ satisfies $$9. p(X=4)=p(X=2)$$ when $$n=6$$. Then $$p$$ is equal to

If in $$\triangle \mathrm{ABC}$$, with usual notations, $$a \cdot \cos ^2 \frac{C}{2}+c \cos ^2 \frac{A}{2}=\frac{3 b}{2}$$, then

The lines $$\frac{x-1}{3}=\frac{y+1}{2}=\frac{z-1}{5} \quad$$ and $$\frac{x+2}{4}=\frac{y-1}{3}=\frac{z+1}{2}$$

A curve passes through the point $$\left(1, \frac{\pi}{6}\right)$$. Let the slope of the curve at each point $$(x, y)$$ be $$\frac{y}{x}+\sec \left(\frac{y}{x}\right), x>0$$, then, the equation of the curve is

For the following shaded area, the linear constraints except $$x,y \ge 0$$ are

Let $$\omega \neq 1$$ be a cube root of unity and $$S$$ be the set of all non-singular matrices of the form $$\left[\begin{array}{ccc}1 & a & b \\ \omega & 1 & c \\ \omega^2 & \omega & 1\end{array}\right]$$ where each of $$a, b$$ and $$c$$ is either $$\omega$$ or $$\omega^2$$, then the number of distinct matrices in the set $$\mathrm{S}$$ is

The value of $$2 \tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{7}$$

$$\int \frac{\mathrm{e}^x(1+x)}{\cos ^2\left(\mathrm{e}^x \cdot x\right)} \mathrm{d} x=$$

In a triangle $$\mathrm{ABC}$$, with usual notations, if $$\mathrm{m} \angle \mathrm{A}=60^{\circ}, \mathrm{b}=8, \mathrm{a}=6$$ and $$\mathrm{B}=\sin ^{-1} x$$, then $$x$$ has the value

If variance of $$x_1, x_2 \ldots \ldots, x_n$$ is $$\sigma_x^2$$, then the variance of $$\lambda x_1, \lambda x_2, \ldots \ldots, \lambda x_{\mathrm{n}}(\lambda \neq 0)$$ is

If $$\quad \overline{\mathrm{a}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}, \quad \overline{\mathrm{b}}=2 \hat{\mathrm{j}}-\hat{\mathrm{k}} \quad$$ and $$\quad \overline{\mathrm{r}} \times \overline{\mathrm{a}}=\overline{\mathrm{b}} \times \overline{\mathrm{a}}, \overline{\mathrm{r}} \times \overline{\mathrm{b}}=\overline{\mathrm{a}} \times \overline{\mathrm{b}}$$, then the value $$\frac{\overline{\mathrm{r}}}{|\overline{\mathrm{r}}|}$$ is

If $$\mathrm{z}=x+\mathrm{i} y$$ and $$\mathrm{z}^{1 / 3}=\mathrm{p}+\mathrm{iq}$$, where $$x, y, \mathrm{p}, \mathrm{q} \in \mathrm{R}$$ and $$\mathrm{i}=\sqrt{-1}$$, then value of $$\left(\frac{x}{\mathrm{p}}+\frac{y}{\mathrm{q}}\right)$$ is

If $$\int \frac{\mathrm{d} x}{x \sqrt{1-x^3}}=\mathrm{k} \log \left(\frac{\sqrt{1-x^3}-1}{\sqrt{1-x^3}+1}\right)+\mathrm{c}$$, (where $$\mathrm{c}$$ is a constant of integration), then value of $$\mathrm{k}$$ is

The statement pattern $$\mathrm{p} \rightarrow \sim(\mathrm{p} \wedge \sim \mathrm{q})$$ is equivalent to

$$\mathrm{a}$$ and $$\mathrm{b}$$ are the intercepts made by a line on the co-ordinate axes. If $$3 \mathrm{a}=\mathrm{b}$$ and the line passes through $$(1,3)$$, then the equation of the line is

Let $$\bar{a}, \bar{b}$$ and $$\bar{c}$$ be three unit vectors such that $$\bar{a} \times(\bar{b} \times \bar{c})=\frac{\sqrt{3}}{2}(\bar{b}+\bar{c})$$. If $$\bar{b}$$ is not parallel to $$\bar{c}$$, then the angle between $$\bar{a}$$ and $$\bar{b}$$ is

The vector equation of the line $$2 x+4=3 y+1=6 z-3$$ is

If $$\overline{\mathrm{a}}$$ and $$\overline{\mathrm{b}}$$ are two unit vectors such that $$\overline{\mathrm{a}}+2 \overline{\mathrm{b}}$$ and $$5 \bar{a}-4 \bar{b}$$ are perpendicular to each other, then the angle between $$\bar{a}$$ and $$\bar{b}$$ is

$$\int \frac{\log (\cot x)}{\sin 2 x} d x=$$

$$\text { If } y=\sqrt{\frac{1-\sin ^{-1}(x)}{1+\sin ^{-1}(x)}} \text {, then } \frac{\mathrm{d} y}{\mathrm{~d} x} \text { at } x=0 \text { and } y=1 \text { is }$$

A coil of radius '$$r$$' is placed on another coil (whose radius is $$\mathrm{R}$$ and current flowing through it is changing) so that their centres coincide $$(\mathrm{R} \gg \mathrm{r})$$. If both the coils are coplanar then the mutual inductance between them is ( $$\mu_0=$$ permeability of free space)

Two capillary tubes of the same diameter are kept vertically in two different liquids whose densities are in the ratio $$4: 3$$. The rise of liquid in two capillaries is '$$h_1$$' and '$$h_2$$' respectively. If the surface tensions of liquids are in the ratio $$6: 5$$, the ratio of heights $$\left(\frac{h_1}{h_2}\right)$$ is

(Assume that their angles of contact are same)

Two spherical black bodies of radii '$$r_1$$' and '$$r_2$$' at temperature '$$\mathrm{T}_1$$' and '$$\mathrm{T}_2$$' respectively radiate power in the ratio $$1: 2$$ Then $$r_1: r_2$$ is

For a particle executing S.H.M., its potential energy is 8 times its kinetic energy at certain displacement '$$x$$' from the mean position. If '$$A$$' is the amplitude of S.H.M the value of '$$x$$' is

The maximum kinetic energies of photoelectrons emitted are $$\mathrm{K}_1$$ and $$\mathrm{K}_2$$ when lights of wavelengths $$\lambda_1$$ and $$\lambda_2$$ are incident on a metallic surface. If $$\lambda_1=3 \lambda_2$$ then

A particle moves along a circular path with decreasing speed. Hence

Identify the correct circuit diagrams for the normal operation from the following.

With the gradual increase in frequency of an a. c. source, the impedance of an LCR series circuit

In energy band diagram of insulators, a band gap and the conduction band is respectively

Two positively charged identical spheres separated by a distance 'd' exert some force (F) on each other when they are kept in air. If both the spheres are immersed in a liquid of dielectric constant 5 , the force experienced by each is (All other parameters are unchanged.)

A string fixed at both the ends forms standing wave with node separation of $$5 \mathrm{~cm}$$. If the velocity of the wave on the string is $$2 \mathrm{~m} / \mathrm{s}$$, then the frequency of vibration of the string is

A ball of mass '$$\mathrm{m}$$' is attached to the free end of a string of length '$$l$$'. The ball is moving in horizontal circular path about the vertical axis as shown in the diagram.

The angular velocity '$$\omega$$' of the ball will be [ $$\mathrm{T}=$$ Tension in the string.]

Radius of gyration of a thin uniform circular disc about the axis passing through its centre and perpendicular to its plane is $$\mathrm{K}_{\mathrm{c}}$$. Radius of gyration of the same disc about a diameter of the disc is $$K_d$$. The ratio $$K_c: K_d$$ is

When a current of $$1 \mathrm{~A}$$ is passed through a coil of 100 turns, the flux associated with it is $$2.5 \times 10^{-5} \mathrm{~Wb} /$$ turn. The self inductance of the coil in millihenry is

A spherical liquid drop of radius $$\mathrm{R}$$ is divided into 8 equal droplets. If surface tension is $$\mathrm{S}$$, then the work done in this process will be

The rate of flow of heat through a metal rod with temperature difference $$40^{\circ} \mathrm{C}$$ is $$1600 \mathrm{~cal} / \mathrm{s}$$. The thermal resistance of metal rod in $${ }^{\circ} \mathrm{C} \mathrm{s} / \mathrm{cal}$$ is

Two charges of equal magnitude '$$q$$' are placed in air at a distance '$$2 r$$' apart and third charge '$$-2 \mathrm{q}$$' is placed at mid point. The potential energy of the system is $$\left(\varepsilon_0=\right.$$ permittivity of free space)

The size of the real image produced by a convex lens of focal length $$F$$ is '$$m$$' times the size of the object. The image distance from the lens is

A double slit experiment is immersed in water of refractive index 1.33. The slit separation is $$1 \mathrm{~mm}$$, distance between slit and screen is $$1.33 \mathrm{~m}$$ The slits are illuminated by a light of wavelength $$6300 \mathop A\limits^o$$. The fringe width is

Potential difference between the points P and Q is nearly

An electron in the hydrogen atom jumps from the first excited state to the ground state. What will be the percentage change in the speed of electron?

In series LCR circuit, the voltage across the inductance and the capacitance are not

If the temperature of a hot body is increased by $$50 \%$$, then the increase in the quantity of emitted heat radiation will be approximately

The second overtone of an open pipe has the same frequency as the first overtone of a closed pipe of length '$$L$$'. The length of the open pipe will be

The radius of earth is $$6400 \mathrm{~km}$$ and acceleration due to gravity $$\mathrm{g}=10 \mathrm{~ms}^{-2}$$. For the weight of body of mass $$5 \mathrm{~kg}$$ to be zero on equator, rotational velocity of the earth must be (in $$\mathrm{rad} / \mathrm{s}$$ )

A car sounding a horn of frequency $$1000 \mathrm{~Hz}$$ passes a stationary observer. The ratio of frequencies of the horn noted by the observer before and after passing the car is $$11: 9$$. If the speed of sound is '$$v$$', the speed of the car is

The time period of a simple pendulum inside a stationary lift is '$$T$$'. When the lift starts accelerating upwards with an acceleration $$\left(\frac{\mathrm{g}}{3}\right)$$, the time period of the pendulum will be

The mutual inductance of a pair of coils, each of '$$N$$' turns, is '$$M$$' henry. If a current of '$$I$$' ampere in one of the coils is brought to zero in '$$t$$' second, the e. m. f. induced per turn in the other coil in volt is

To manufacture a solenoid of length $$1 \mathrm{~m}$$ and inductance $$1 \mathrm{~mH}$$, the length of thin wire required is

(cross - sectional diameter of a solenoid is considerably less than the length)

In a radioactive disintegration, the ratio of initial number of atoms to the number of atoms present at time $$t=\frac{1}{2 \lambda}$$ is [$$\lambda=$$ decay constant]

A bullet is fired on a target with velocity '$$\mathrm{V}$$'. Its velocity decreases from '$$\mathrm{V}$$' to '$$\mathrm{V} / 2$$' when it penetrates $$30 \mathrm{~cm}$$ in a target. Through what thickness it will penetrate further in the target before coming to rest?

In the experiment of diffraction due to a single slit, if the slit width is decreased, the width of the central maximum

A cylindrical magnetic rod has length $$5 \mathrm{~cm}$$ and diameter $$1 \mathrm{~cm}$$. It has uniform magnetization $$5.3 \times 10^3 \mathrm{~A} / \mathrm{m}^3$$. Its net magnetic dipole moment is nearly

In biprism experiment, if $$5^{\text {th }}$$ bright band with wavelength $$\lambda_1^{\prime}$$ coincides with $$6^{\text {th }}$$ dark band with wavelength $$\lambda_2{ }^{\prime}$$ then the ratio $$\left(\frac{\lambda_2}{\lambda_1}\right)$$ is

A body of mass '$$\mathrm{m}$$' kg starts falling from a distance 3R above earth's surface. When it reaches a distance '$$R$$' above the surface of the earth of radius '$$R$$' and Mass '$$M$$', then its kinetic energy is

In the case of NAND gate, if A and B are the inputs and $$\mathrm{Y}$$ is the output then

A monoatomic gas at pressure '$$\mathrm{P}$$', having volume '$$\mathrm{V}$$' expands isothermally to a volume '$$2 \mathrm{~V}$$' and then adiabatically to a volume '$$16 \mathrm{~V}$$'. The final pressure of the gas is (Take $$\gamma=5 / 3$$ )

In potentiometer experiments, two cells of e. m. f. '$$E_1$$' and '$$E_2$$' are connected in series $$\left(E_1>E_2\right)$$, the balancing length is $$64 \mathrm{~cm}$$ of the wire. If the polarity of $$E_2$$ is reversed, the balancing length becomes $$32 \mathrm{~cm}$$. The ratio $$\mathrm{E}_1 / \mathrm{E}_2$$ is

A diatomic gas $$\left(\gamma=\frac{7}{5}\right)$$ is compressed adiabatically to volume $$\frac{V_i}{32}$$ where $$V_i$$ is its initial volume. The initial temperature of the gas is $$T_i$$ in Kelvin and the final temperature is '$$x T_i$$'. The value of '$$x$$' is

A disc has mass $$M$$ and radius $$R$$. How much tangential force should be applied to the rim of the disc, so as to rotate with angular velocity '$$\omega$$' in time $$\mathrm{t}$$ ?

An electron moving with velocity $$1.6 \times 10^7 \mathrm{~m} / \mathrm{s}$$ has wavelength of $$0.4 \mathop A\limits^o$$. The required accelerating voltage for the electron motion is [charge on electron $$=1.6 \times 10^{-19} \mathrm{C}$$, mass of electron $$=9 \times 10^{-31} \mathrm{~kg}$$ ]

The prism has refracting angle '$$\mathrm{A}$$'. The second refracting surface of the prism is silvered. Light ray falling on first refracting surface with angle of incidence '$$2 \mathrm{~A}$$', reaches the second surface and returns back through the same path due to reflection at the silvered surface. The refractive index of the material of the prism is

Two parallel wires of equal lengths are separated by a distance of $$3 \mathrm{~m}$$ from each other. The currents flowing through $$1^{\text {st }}$$ and $$2^{\text {nd }}$$ wire is $$3 \mathrm{~A}$$ and 4.5 A respectively in opposite directions. The resultant magnetic field at mid point between the wires $$\left(\mu_0=\right.$$ permeability of free space)

Three point charges $$+\mathrm{q},+2 \mathrm{q}$$ and $$+\mathrm{Q}$$ are placed at the three vertices of an equilateral triangle. If the potential energy of the system of three charges is zero, the value of $$Q$$ in terms of $$q$$ is

If a gas is compressed isothermally then the r.m.s. velocity of the molecules

The bob of a simple pendulum of length '$$L$$' has a mass '$$\mathrm{m}$$' and charge '$$\mathrm{q}$$'. The pendulum is suspended between the plates of a charged parallel plate capacitor. The direction of electric field is shown in figure. The period of oscillations of the simple pendulum is (acceleration due to gravity $$\mathrm{g}>\mathrm{qE} / \mathrm{m}$$ )

An electron is projected along the axis of circular conductor carrying current I. Electron will experience

Two identical capacitors have the same capacitance '$$C$$'. One of them is charged to a potential $$V_1$$ and the other to $$V_2$$. The negative ends of the capacitors are connected together. When the positive ends are also connected, the decrease in energy of the combined system is

A transverse wave $$\mathrm{Y}=2 \sin (0.01 \mathrm{x}+30 \mathrm{t})$$ moves on a stretched string from one end to another end in 0.5 second. If $$x$$ and $$y$$ are in $$\mathrm{cm}$$ and $$t$$ in second, then the length of the string is

A body of density '$$\rho$$' is dropped from rest at a height '$$h$$' into a lake of density '$$\sigma' (\sigma>\rho)$$. The maximum depth to which the body sinks before returning to float on the surface is (neglect air dissipative forces)