Which among the following salts forms basic solution when dissolved in water?

Identify the product formed when 2-Bromobutane is heated with aqueous solution of sodium hydroxide.

What is the charge required to convert $2 \mathrm{~mol} \mathrm{KMnO}_4$ to $\mathrm{MnSO}_4$ ?

Find the volume of 56 g dinitrogen at STP

Calculate the vapour pressure of solution if relative lowering of vapour pressure and vapour pressure of pure solvent are 0.018 and 18 mm Hg respectively at 300 K .

Which from following elements in respective oxidation state develops highest spin only magnetic moment?

Which from following polymers is used as wool substitute?

Which from following compounds does NOT contain nitrogen in it?

A container contains $4 \mathrm{~g} \mathrm{H}_2, 4 \mathrm{~g} \mathrm{He}$ and certain amount of 'Ne' at a certain temperature. What is the mass of 'Ne' required so that the partial pressure exerted by 'Ne' is equal to the partial pressure of He ?

Find the EAN of Zn in $\left[\mathrm{Zn}\left(\mathrm{NH}_3\right)_4\right]^{2+}$ ?

If standard reduction potential $\left(\mathrm{E}^{\circ}\right)$ of $\left(\mathrm{Mg}_{(\mathrm{aq})}^{+2} \mid \mathrm{Mg}_{(\mathrm{s})}\right),\left(\mathrm{Ag}_{(\mathrm{aq})}^{+} \mid \mathrm{Ag}_{(\mathrm{s})}\right),\left(\mathrm{Zn}^{+2}{ }_{(\mathrm{aq})} \mid \mathrm{Zn}_{(\mathrm{s})}\right)$ and $\left(\mathrm{Cu}^{+2}{ }_{(\text {aq })} \mid \mathrm{Cu}_{(\text {s })}\right)$ are $-2.37 \mathrm{~V},+0.79 \mathrm{~V},-0.76 \mathrm{~V}$ and +0.34 V respectively. Which of the following reaction is spontaneous?

Which from following statements is NOT true for phenol?

In carbinol system, sec-Butyl alcohol is named as

Calculate the number of unit cells in $1 \mathrm{~cm}^3$ volume of metal if unit cell edge length is $1.25 \times 10^{-8} \mathrm{~cm}$.

Calculate the number of moles of nonvolatile solute dissolved in 0.5 kg solvent if molal elevation constant for solvent is $2 \mathrm{~kg} \mathrm{~K} \mathrm{~mol}^{-1} \left[\Delta \mathrm{T}_{\mathrm{b}}=0.8 \mathrm{~K}\right]$

Which from following is an example of both intensive property and state function?

What is the number of moles of H atoms required for complete reduction of one mole acetonitrile?

Calculate the pH of centimolar solution of monoacidic weak base. Which is $10 \%$ dissociated in its aqueous solution?

$$ \text { Identify ' } A \text { ' in the following reaction. } $$

A $\xrightarrow{\text { Lithium amide }}$ Ethynyl lithium $\xrightarrow{\text { Bromoethane }}$ But - 1 - yne

What is molar conductivity at zero concentration in $\Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ for aluminium sulphate, if molar ionic conductivities at zero concentration of $\mathrm{Al}^{+3}$ and $\mathrm{SO}_4^{-2}$ are $189 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ and $50.1 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ respectively?

Which of the following compounds is an optically inactive compound?

Which of the following reagents is used in the conversion of phenol into picric acid?

Which of the following is an example of second order reaction?

Calculate the total volume occupied by all particles in fcc unit cell if volume of unit cell is $6.4 \times 10^{-23} \mathrm{~cm}^3$

Identify the product formed in the following reaction. $\left(\mathrm{CH}_3 \mathrm{CO}\right)_2 \mathrm{O} \xrightarrow{\mathrm{H}_2 \mathrm{O}}$ Product

What type of glycosidic linkages are present in amylose?

Which of the following is more polar?

When 2-methylbut-2-ene is treated with hydrogen chloride, the major product formed is

Which colour is developed to the solution when alkaline earth metals are dissolved in liquid ammonia?

Which of the following house hold plastic material is used to prepare drinking straws?

What is the time required for $99 \%$ completion of a first order reaction if rate constant is $23.03 \mathrm{~min}^{-1}$ ?

Identify the product formed in the following reaction. $\mathrm{C}_6 \mathrm{H}_5-\mathrm{CH}_2-\mathrm{CH}_3 \xrightarrow[\text { ii) } \mathrm{H}_3 \mathrm{O}^{+}]{\text {i) alk. } \mathrm{KMnO}_4}$ Product

Arrange the following equimolar solutions according to increasing order of osmotic pressure [Assume complete ionisation]

i) KCl

ii) $\mathrm{BaCl}_2$

iii) $\mathrm{AlCl}_3$

iv) $\mathrm{Al}_2\left(\mathrm{SO}_4\right)_3$

Which from following is useful to extract analgesic and antimicrobial compounds?

Which element from following has smallest ionic size in +3 state?

Identify the monomers used in preparation of Nylon 2- nylon 6

Identify the correct increasing order of field strength of ligands from following.

A monobasic weak acid dissociates $2 \%$ in its 0.002 M solution. Calculate the dissociation constant of weak acid.

Which of the following pair of compounds consists equal number of lone pair of electrons in the valence shell of central atom?

Which of the following is an acidic oxide?

What is oxidation number of sulphur in $\mathrm{SO}_3$ ?

Which from following substances is classified as macromolecular colloid?

What is the total number of unit cells shared by each corner particle of bcc unit cell?

Which of the following is used as reagent in Etard reaction?

For a certain reaction, $\Delta \mathrm{H}=-210 \mathrm{~kJ}$ and $\Delta \mathrm{S}=-150 \mathrm{~kJ} \mathrm{~K}^{-1}$ Find the temperature so that $\Delta \mathrm{G}=0$.

Which of the following elements contains maximum number of unpaired electrons?

Which from following amines on heating with chloroform and ethanolic potassium hydroxide produces foul smell?

What is the total number of carbon atoms present in a sugar molecule of RNA nucleotide?

If a circle with centre at $(-1,1)$ touches the line $x+2 y+4=0$ then the co-ordinates of the point of contact are

A doctor assumes that patient has one of three diseases $\mathrm{d} 1, \mathrm{~d} 2$ or d 3 . Before any test he assumes an equal probability for each disease. He carries out a test that will be positive with probability 0.7 if the patient has disease $\mathrm{d} 1,0.5$ if the patient has disease d 2 and 0.8 if the patient has disease d3. Given that the outcome of the test was positive then probability that patient has disease d2 is

A particle P starts from the point $\mathrm{Z}_0=1+2 \mathrm{i}$ where $\mathrm{i}=\sqrt{-1}$. It moves first horizontally away from the origin by 5 units and then vertically upwards parallel to positive Y -axis by 3 units to reach a point $Z_1$. From $Z_1$ the particle moves $\sqrt{2}$ units in the direction of vector $\hat{\mathrm{i}}+\hat{\mathrm{j}}$ and then it moves through an angle $\frac{\pi}{2}$ in anticlockwise direction on a circle with centre at origin to reach at point $Z_2$, then $Z_2=$

$$ \mathop {\lim }\limits_{x \to 0} \frac{63^x-9^x-7^x+1}{\sqrt{2}-\sqrt{1+\cos x}}=\ldots \ldots $$

Consider the following three statements

(A) If $3+2=7$ then $4+3=8$.

(B) If $5+2=7$ then earth is flat.

(C) If both (A) and (B) are true then $5+6=11$. Which of the following statements is correct?

If $\mathrm{A}=\left[\begin{array}{cc}5 \mathrm{a} & -\mathrm{b} \\ 3 & 2\end{array}\right]$ and A .adj $\mathrm{A}=\mathrm{AA}^{\mathrm{T}}$, then $5 \mathrm{a}+\mathrm{b}=$

The common principal solution of the equations $\sin \theta=-\frac{1}{2}$ and $\tan \theta=\frac{1}{\sqrt{3}}$ is

The slopes of the lines represented by $6 x^2+2 \mathrm{hxy}+y^2=0$ are in the ratio $2: 3$, then $\mathrm{h}=$

If $\theta$ is an obtuse angle between vectors $\bar{a}$ and $\overline{\mathrm{b}}$ such that $|\overline{\mathrm{a}}|=5,|\overline{\mathrm{~b}}|=3$ and $|\overline{\mathrm{a}} \times \overline{\mathrm{b}}|=5 \sqrt{5}$ then $\bar{a} \cdot \bar{b}=$

If the plane $\frac{x}{2}-\frac{y}{3}-\frac{\mathrm{z}}{5}=1$ cuts the co-ordinate axes in points $\mathrm{A}, \mathrm{B}, \mathrm{C}$ respectively, then the area of the triangle $A B C$ is

The rate of increase of the population of a city is proportional to the population present at that instant. In the period of 40 years the population increased from 30,000 to 40,000 . At any time t the population is $(a)(b)^{\frac{t}{40}}$. Then the values of $a$ and $b$ are respectively

The probability that a student is not a swimmer is $\frac{1}{5}$. The probability that out of 5 students selected at random 4 are swimmers is

A player tosses two coins. He wins ₹ 10 , if 2 heads appears, ₹ 5 , if one head appear and ₹ 2 if no head appears. Then variance of winning amount is

Consider the probability distribution

$$ \begin{array}{|l|l|l|l|l|l|} \hline \mathrm{X}=x & 1 & 2 & 3 & 4 & 5 \\ \hline \mathrm{P}(\mathrm{X}=x) & \mathrm{K} & 2 \mathrm{~K} & \mathrm{~K}^2 & 2 \mathrm{~K} & 5 \mathrm{~K}^2 \\ \hline \end{array} $$

Then the value of $\mathrm{P}(\mathrm{X}>2)$ is

The equation of the curve passing through origin and satisfying $\left(1+x^2\right) \frac{\mathrm{d} y}{\mathrm{~d} x}+2 x y=4 x^2$ is

If $y=\tan ^{-1}\left(\frac{12 x-64 x^3}{1-48 x^2}\right)$, then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$

The order of the differential equation whose general solution is given by $y=\left(\mathrm{C}_1+\mathrm{C}_2\right) \sin \left(x+\mathrm{C}_3\right)-\mathrm{C}_4 \mathrm{e}^{x+\mathrm{C}_5}$ is (where $\mathrm{C}_1, \mathrm{C}_2, \mathrm{C}_3, \mathrm{C}_4, \mathrm{C}_5$ are arbitrary constants)

In L.P.P., the maximum value of objective function $\mathrm{Z}=6 x+3 y$ subject to constraints $x+y \leq 5, x+2 y \geq 4,4 x+y \leq 12, x, y \geq 0$ is

If the lines $x=a y-1=z-2$ and $x=3 y-2=\mathrm{bz}-2(\mathrm{ab} \neq 0)$ are coplanar, then

If $\left(\tan ^{-1} x\right)^2+\left(\cot ^{-1} x\right)^2=\frac{5 \pi^2}{8}$, then $x^2+1=$

If $p \equiv$ The switch $S_1$ is closed, $q \equiv$ The switch $\mathrm{S}_2$ is closed, $\mathrm{r} \equiv$ switch $\mathrm{S}_3$ is closed, then symbolic form of following switching circuit is equivalent to

Let $\mathrm{f}: \mathbb{R} \rightarrow \mathbb{R}$ is differentiable function having $\mathrm{f}(3)=3, \mathrm{f}^{\prime}(3)=\frac{1}{27}$ and $\mathrm{g}(x)= \begin{cases}\int_3^{\mathrm{f}(x)} \frac{3 \mathrm{t}^2}{x-3} \mathrm{dt}, & \text { if } x \neq 3 \\ \mathrm{~K}, & \text { if } x=3\end{cases}$ is continuous at $x=3$, then $\mathrm{K}=$

The area bounded by the curve $y=4 x-x^2$ and X - axis in square units, is $\qquad$

The Cartesian equation of the plane $\overline{\mathrm{r}}=(2 \hat{\mathrm{i}}-3 \hat{\mathrm{j}})+\lambda(\hat{\mathrm{i}}+2 \hat{\mathrm{j}}-\hat{\mathrm{k}})+\mu(2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+\hat{\mathrm{k}})$ is

If the line $\frac{x-3}{2}=\frac{y+5}{-1}=\frac{z+2}{2}$ lies in the plane $\alpha x+3 y-z+\beta=0$, then values of $\alpha$ and $\beta$ respectively are ….

$$ \int_{\log \frac{1}{2}}^{\log 2} \sin \left(\frac{\mathrm{e}^x-1}{\mathrm{e}^x+1}\right) \mathrm{d} x= $$

If the vectors $\overline{\mathrm{a}}=\mathrm{c}\left(\log _7 x\right) \hat{\mathrm{i}}+2 \hat{\mathrm{j}}+3 \hat{\mathrm{k}} \quad$ and $\overline{\mathrm{b}}=\left(\log _\gamma x\right) \hat{\mathrm{i}}+3 \mathrm{c}\left(\log _\gamma x\right) \hat{\mathrm{j}}-4 \hat{\mathrm{k}}$ make obtuse angle for any $x>0$, then c belongs to

$$ \int_{\frac{-\pi}{4}}^{\frac{\pi}{4}} \sin ^{-4} x d x= $$

The altitude through vertex $A$ of $\triangle A B C$ with position vectors of points $A, B, C$ as $\bar{a}, \bar{b}, \bar{c}$ respectively is

$$ \int \frac{\mathrm{d} x}{(x+\mathrm{a})^{\frac{9}{7}}(x-\mathrm{b})^{\frac{5}{7}}}= $$

The lines $\bar{r}=(\hat{i}+\hat{j}-\hat{k})+\lambda(3 \hat{i}-\hat{j})$ and $\overline{\mathrm{r}}=(4 \hat{\mathrm{i}}-\hat{\mathrm{k}})+\mu(2 \hat{\mathrm{i}}+3 \hat{\mathrm{k}})$ are

If $\overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ are unit vectors and $|\overline{\mathrm{a}}|=7$, $\overline{\mathrm{a}} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})+\overline{\mathrm{b}} \times(\overline{\mathrm{c}} \times \overline{\mathrm{a}})=\frac{1}{2} \overline{\mathrm{a}}$, then angle between the vectors $\bar{a}$ and $\bar{c}$ and angle between the vectors $\overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ are respectively

With usual notations in $\triangle \mathrm{ABC}$, if $\angle \mathrm{B}=\frac{\pi}{2}$, and $\tan \frac{\mathrm{A}}{2}, \tan \frac{\mathrm{C}}{2}$ are roots of equation $\mathrm{p} x^2+\mathrm{qx}+\mathrm{r}=0$, $\mathrm{p} \neq 0$, then

$\int \frac{\mathrm{d} x}{x\left(x^3+1\right)}=$

If $\tan ^{-1}(x+1)+\tan ^{-1} x+\tan ^{-1}(x-1)=\tan ^{-1} 3$, then for $x<0$ the value of $500 x^4+270 x^2+997=$

Let $\mathrm{f}: \mathbb{R}-\{2\} \rightarrow \mathbb{R}-\{1\}$ defined by $\mathrm{f}(x)=\frac{x-3}{x-2}$ and $\mathrm{g}: \mathbb{R} \rightarrow \mathbb{R}$ defined by $\mathrm{g}(x)=3 x-2$, then sum of all values of $x$ for which $\mathrm{f}^{-1}(x)+\mathrm{g}^{-1}(x)=\frac{19}{6}$ is

There are 11 points in a plane of which 5 points are collinear. Then the total number of distinct quadrilaterals with vertices at these points is

$\int \frac{x^4 \cos \left(\tan ^{-1} x^5\right)}{1+x^{10}} d x$ equals

The length of the perpendicular drawn from the origin on the normal to the curve $x^2+2 x y-3 y^2=0$ at the point $(2,2)$ is

If $\mathrm{f}(x)=\log (1+x)-\frac{2 x}{2+x}$ then $\mathrm{f}(x)$ is increasing in

The angle $\theta$, at which the curves $y=3^x$ and $y=7^x$ intersect, is given by

The function $\mathrm{f}(x)=x^3-6 x^2+\mathrm{ax}+\mathrm{b}$ satisfies the conditions of Rolle's theorem in $[1,3]$. Then the values of $a$ and $b$ are respectively

If

$$ \sqrt{y-\sqrt{y-\sqrt{y-\ldots \ldots \ldots \infty}}}=\sqrt{x+\sqrt{x+\sqrt{x+\ldots \ldots \ldots \infty}}} $$

then $\frac{\mathrm{d} y}{\mathrm{~d} x}=$

If $x=\operatorname{sint}$ and $y=\sin p t$, then the value of

$$ \left(1-x^2\right) \frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}-x \frac{\mathrm{~d} y}{\mathrm{~d} x}+\mathrm{p}^2 y= $$

Let $\bar{a}=\hat{i}+\hat{j}-\hat{k}$ and $\bar{c}=5 \hat{i}-3 \hat{j}+2 \hat{k}$ and if $\overline{\mathrm{b}} \times \overline{\mathrm{c}}=\overline{\mathrm{a}}$ then $|\overline{\mathrm{b}}|=$

The circumradius of a triangle whose sides are 10 units, 8 units and 6 units is

The eccentricity of the hyperbola which passes through the points $(3,0)$ and $(3 \sqrt{2}, 2)$ is

$$ \cos ^4 \frac{\pi}{8}+\cos ^4 \frac{3 \pi}{8}+\cos ^4 \frac{5 \pi}{8}+\cos ^4 \frac{7 \pi}{8}= $$

The straight line passing through $(-3,6)$ and midpoint of the line segment joining the points $(4,-5)$ and ( $-2,9$ ) have inclination

The general solution of differential equation $\left(y^2-x^2\right) \mathrm{d} x=x y \mathrm{~d} y(x \neq 0)$ is

A force F is applied on a square plate of side L . If the percentage error in determining F is $3 \%$ and that in L is $2 \%$, then the percentage error in determining the pressure is

A bob of mass ' $m$ ' is tied by a massless string whose other end is wound on a flywheel (disc) of radius ' $R$ ' and mass ' $m$ '. When released from the rest, the bob starts falling vertically downwards. If the bob has covered a vertical distance ' $h$ ', then angular speed of wheel will be (There is no slipping between string and wheel, g - acceleration due to gravity)

A copper ring having a cut such as not to form a complete loop is held horizontally and a bar magnet is dropped through the ring with its length along the axis of the ring as shown in figure. The acceleration of the falling magnet is ( $\mathrm{g}=$ acceleration due to gravity)

In Young's double slit experiment, at two points $P$ and $Q$ on screen, waves from slits $S_1$ and $S_2$ have a path difference of 0 and $\frac{\lambda}{4}$ respectively. The ratio of intensities at point $P$ to that at $Q$ will be $\left(\cos 0^{\circ}=1, \cos 45^{\circ}=\frac{1}{\sqrt{2}}\right)$

One of the following values of inputs $\mathrm{A}, \mathrm{B}$ and C respectively gives output $(\mathrm{Y})$ of the following combination of logic gates as ' 1 ' is

A piece of semiconductor is connected in series in an electric circuit. On increasing the temperature, the current in the circuit will

Seven capacitors each of capacitance $2 \mu \mathrm{~F}$ are to be connected in a configuration to obtain an effective capacitance $\left(\frac{10}{11}\right) \mu \mathrm{F}$. The combination is

In an $L R$ circuit, the value of $L$ is $\left(\frac{0.3}{\pi}\right)$ henry and the value of R is $40 \Omega$, If in the circuit, an alternating e.m.f of 230 V at 50 cycles per second is connected, the impedance of the circuit and current will be respectively

The depth at which the value of acceleration due to gravity becomes $\left(\frac{1}{n}\right)$ times the value at the surface of the earth is

( $\mathrm{R}=$ radius of the earth)

A horizontal pipeline carries water in a streamline flow. At a point along the pipe, where the cross-sectional area is $10 \mathrm{~cm}^2$, the velocity of water is $1 \mathrm{~m} / \mathrm{s}$ and pressure is 2000 Pa . The pressure of water at another point where the cross-sectional area $5 \mathrm{~cm}^2$ is

[Given $\rightarrow$ density of water $=1000 \mathrm{~kg} / \mathrm{m}^3$ ]

Two simple pendulums have first (A) bob of mass ' $M_1$ ' and length ' $L_1$ ', second (B) of mass ' $\mathrm{M}_2$ ' and length ' $\mathrm{L}_2$ '. $\mathrm{M}_1=\mathrm{M}_2$ and $\mathrm{L}_1=2 \mathrm{~L}_2$. If their total energies are same then the correct statement is

If the frequency of incident light in a photoelectric experiment is doubled, then stopping potential will

A constant force $\vec{F}=3 \hat{i}-2 \hat{j}-\hat{k}$ newton has a displacement $\vec{r}=2 \hat{i}-3 \hat{j}-3 \hat{k}$ metre in 2 second. The work done and the power are respectively

In a common emitter amplifier configuration, the current gain is 62 . The collector resistance and input resistance are $5 \mathrm{k} \Omega$ and $500 \Omega$ respectively. If the input voltage is 0.01 V , the output voltage will be

A thin uniform rod of length ' $L$ ' and mass ' $M$ ' is swinging freely about a horizontal axis passing through its end. Its maximum angular speed is ' $\omega$ '. Its centre of mass rises to a maximum height of

( $\mathrm{g}=$ acceleration due gravity)

In a biprism experiment a steady interference pattern is observed on the screen using a light of wavelength $5000 \mathop {\rm{A}}\limits^{\rm{o}}$. Without disturbing the set up of the experiment, the source of light is replaced by a source of wavelength $6400 \mathop {\rm{A}}\limits^{\rm{o}}$.

The fringe width will

Two girls are standing at the ends ' $A$ ' and ' $B$ ' of a ground where $\mathrm{AB}=\mathrm{b}$. The girl at ' B ' starts running in a direction perpendicular to ' $A B$ ' with velocity ' $\mathrm{V}_1$ '. The girl at ' A ' starts running simultaneously with velocity ' $\mathrm{V}_2$ ' and in shortest distance meets the other girl in time ' $t$ '. The value of ' $t$ ' is

A coil of wire of radius ' $r$ ' has 600 turns and a self-inductance of 108 mH . The self-inductance of a coil with same radius and 500 turns is

A sample of an ideal gas $\left(\gamma=\frac{5}{3}\right)$ is heated at constant pressure. If 100 J of heat is supplied to the gas, the work done by the gas is

Using Bohr's quantisation condition, what is the rotational energy in the second orbit for a diatomic molecule?

( $I=$ moment of inertia of diatomic molecule and $\mathrm{h}=$ Planck's constant)

Assuming the drops to be spherical, 27 identical drops of mercury are charged simultaneously to the same potential of 20 volt. If all the charged drops are made to combine to form one big drop, then potential of big drop will be

An object of mass ' $m$ ' moving with velocity ' $u$ ' collides with another stationary object of mass ' $M$ ' and stops just after the collision. The coefficient of restitution is

In the following figure magnitude of the magnetic field at the point $p$ is

A balloon is filled at $27^{\circ} \mathrm{C}$ and 1 atmospheric pressure by volume $500 \mathrm{~m}^3$ helium gas. At $-3^{\circ} \mathrm{C}$ and 0.5 atmospheric pressure, the volume of helium gas will be

As shown in the figure, $S_1$ and $S_2$ are identical springs with spring constant K each. The oscillation frequency of the mass ' $m$ ' is ' $f$ '. If the spring $\mathrm{S}_2$ is removed, the oscillation frequency will become

The volume of a metal sphere increases by $0.33 \%$ when its temperature is raised by $50^{\circ} \mathrm{C}$. The coefficient of linear expansion of the metal is

The amount of work done in blowing a soap bubble such that its diameter increases from 'd' to ' $D$ ' is ( $T=$ surface tension of solution)

In an a.c. circuit, a resistance ' $R$ ' is connected in series with an inductance ' $L$ '. If phase angle between voltage and current is $45^{\circ}$, the value of inductive reactance will be $\left(\tan 45^{\circ}=1\right)$

In an open end organ pipe of length ' $L$ ', if the velocity of sound is ' V ', then the fundamental frequency will be (Neglect end correction)

Two batteries of e.m.f 4 V and 8 V with internal resistance $1 \Omega$ and $2 \Omega$ respectively are connected in a circuit with a resistance of $9 \Omega$ as shown in the figure. The current and potential difference between the points ' P ' and ' Q ' is $\mathrm{R}=9 \Omega$

At what speed should a source of sound move so that the observer finds the apparent frequency equal to half the original frequency?

A particle starts oscillating simple harmonically from its mean position with time period ' $T$ '. At time $\mathrm{t}=\frac{\mathrm{T}}{6}$, the ratio of the potential energy to kinetic energy of the particle is

$$ \left[\sin 30^{\circ}=\cos 60^{\circ}=0 \cdot 5, \cos 30^{\circ}=\sin 60^{\circ}=\sqrt{3} / 2\right] $$

A coil of ' $n$ ' turns and resistance $R \Omega$ is connected in series with a resistance $\frac{R}{2}$. The combination is moved for time ' $t$ ' second through magnetic flux $\phi_1$ to $\phi_2$. The induced current in the circuit is

An electron of mass ' $m$ ' and charge ' $e$ ' initially at rest gets accelerated by a constant electric field ' E '. The rate of change of de-Broglie wavelength of the electron at time ' $t$ ' is

(Ignore relativistic effect)( $\mathrm{h}=$ Planck's constant)

The moment of inertia of a solid sphere of mass ' $m$ ' and radius ' $R$ ' about its diametric axis is ' $I$ '. Its moment of inertia about a tangent in the plane is

A glass cube of length 21 cm has a small air bubble trapped inside. When viewed normally from the opposite face, its apparent distance is 6 cm . The refractive index of glass and the actual distance of the air bubble from the first surface respectively are

Two identical metal plates are given charges $q_1$ and $q_2\left(q_2 < q_1\right)$ respectively. If they are now brought close together to form a parallel plate capacitor with capacitance ' C ', the potential difference ' $V$ ' between the plates is

In hydrogen atom in its ground state, the first Bohr orbit has radius ' $\mathrm{r}_1$ '. When the atom is raised to one of its excited states, the electrons orbital velocity becomes one-third. The radius of that orbit is

Heat supplied $d Q=$ increased in internal energy dU is true for

With a resistance ' X ' connected in series with a galvanometer of resistance $100 \Omega$, it acts as a voltmeter of range $0-15 \mathrm{~V}$. To double the range, a resistance of $1500 \Omega$ is to be connected in series with ' X '. The value of ' X ' in ohm is

When one end of a capillary tube is dipped in water, the height of water column is ' $h$ '. The upward force of 105 dyne due to surface tension is balanced by the force due to the weight of water column. The inner circumference of the capillary tube is

(Surface tension of water $=7 \times 10^{-2} \mathrm{~N} / \mathrm{m}$ )

A tuning fork gives 5 beats per second with 40 cm length of sonometer wire. If the length of the wire is shortened by 1 cm , the number of beats is still the same. The frequency of the fork is

A circular coil carrying current ' T ' has a radius ' $r$ ' and ' $n$ ' turns. The magnetic field along the axis of a coil at a distance ' $2 \sqrt{2} r$ ', from its centre is ( $\mu_0=$ permeability of free space, $n$ is very small)

Two equally charged small balls placed at a fixed distance experience a force ' $F$ '. A similar uncharged ball after touching one of them is placed at the middle point between the two balls. the force experienced by this ball is

An a.c. source of frequency ' f ' is connected to a circuit containing an inductance ' $L$ ' and resistance ' R ' in series. The impedance of this circuit is

In a single slit diffraction experiment, slit of width ' $a$ ' is illuminated by light of wavelength ' $\lambda$ ' and the width of the central maxima in diffraction pattern is measured as ' $y$ '. When half of the slit is covered and illuminated by light of wavelength (1.5) $\lambda$, the width of the central maximum in diffraction pattern becomes

To protect the instrument from magnetic field, it is completely surrounded by