Which from following is semisynthetic polymer?

Identify reactant 'A' in following reaction.

An aqueous solution of strong monoacidic base is of $1 \times 10^{-4} \mathrm{M}$. What is the value of pH at $25^{\circ} \mathrm{C}$ ?

The correct stability order of alkyl substituted alkenes is

What is the volume occupied by 2.5 mol of ammonia gas at STP?

Which group element from following achieves noble gas configuration after gaining two electrons?

The reaction given below $2 \mathrm{NH}_{3(\mathrm{g})} \xrightarrow{\mathrm{Pt}} \mathrm{N}_{2(\mathrm{g})}+3 \mathrm{H}_{2(\mathrm{g})}$ has rate of reaction $2.5 \times 10^{-6} \mathrm{~mol} \mathrm{dm}^{-3} \mathrm{sec}^{-1}$ formation of $\mathrm{H}_{2(\mathrm{~g})}$ ?

Identify the correct statement about glucose from following.

In a solid, $\mathrm{B}^{-}$ions occupy corners of a cube forming ccp structure. If $\mathrm{A}^{+}$ion occupy half the tetrahedral voids, formula of the solid is

Calculate the radius of first orbit of He$^+$.

Identify reagent 'A' used in the following reaction?

Acidic buffer solution is prepared by mixing proportionate quantity of

Which among the following is NOT a feature of $\mathrm{S}_{\mathrm{N}} 2$ mechanism?

3.4 moles of an ideal gas occupies volume of 68 mL at 300 K . What would be the pressure of gas? $\left(\mathrm{R}=8.314 \mathrm{~J} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$

Which of the following alloys is used in construction of outer fuselage of ultra-high speed air craft?

Calculate the percentage dissociation of 0.05 M solution of weak electrolyte if its molar conductivity and molar conductivity at infinite dilution are respectively. $3.3 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$ and $132 \Omega^{-1} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$.

Identify the polymer used to obtain disposable cups and plates.

Beryllium shows diagonal relationship with

Which of the following is a simple ketone?

Calculate molar mass of a solute at 300 K if 400 mg of it is dissolved in 300 mL of water exerts osmotic pressure of 0.2 atm .

$$\left(\mathrm{R}=0.0821 \mathrm{~L} \mathrm{~atm} \mathrm{~K}^{-1} \mathrm{~mol}^{-1}\right)$$

According to carbinol system tert-butyl alcohol is named as

A system performs mechanical work equal to 15 kJ and looses 2 kJ of heat to surrounding. What is the change in internal energy of a system?

What is the designation of an orbital with quantum numbers $\mathrm{n}=4$ and $l=3$?

Which among the following properties is NOT exhibited by transition elements?

For reaction $\mathrm{A}+\mathrm{B} \rightarrow$ product, rate of reaction is $3.6 \times 10^{-2} \mathrm{sec}^{-1}$. When $[\mathrm{A}]=0.2 \mathrm{moldm}^{-3}$ and $[B]=0.1 \mathrm{moldm}^{-3}$, calculate rate constant of reaction if reaction is first order in A and second order is B ?

Which of following polymer does not contain

Unit cell of an element has edge length of 5$$\mathop A\limits^o $$ with density $4 \mathrm{~g} \mathrm{~cm}^{-3}$, if its atomic mass is 149, identify the crystal structure.

Which among the following gases is difficult to liquify?

Phenol on heating with zinc dust forms

The degree of dissociation of 0.01 M solution of $\mathrm{NH}_4 \mathrm{OH}$ is $4.2 \times 10^{-2}$. What is the percent dissociation of $\mathrm{NH}_4 \mathrm{OH}$ ?

Which among the following is an example of odd electron molecule?

Which among the following is a cationic complex?

The conductivity of 0.02 M solution of $\mathrm{AgNO}_3$ is $0.00216 \Omega^{-1} \mathrm{~cm}^{-1}$ at 298 K . What is its molar conductivity?

Which among following is a strongest base?

What is the vapour pressure of a solution containing 0.1 mol of non volatile solute dissolved in 16.2 g water? $\left(\mathrm{P}_1^0=24 \mathrm{mmHg}\right.$, molar mass of water $18 \mathrm{~g} \mathrm{~mol}^{-1}$ )

Which of the following compounds does not undergo Williamson's synthesis?

Find the constant external pressure required to expand a gas from 2.5 L to 4.5 L if amount of work done is 500 J at 298 K ?

What is change in oxidation number of nitrogen when $\mathrm{NO}_3^{-}$is converted to $\mathrm{NH}_4^{+}$ion?

What type of hybridization is present in $\left[\mathrm{Co}\left(\mathrm{NH}_3\right)_6\right]^{3+}$ complex?

For a reaction $\mathrm{r}=\mathrm{k}[\mathrm{A}][\mathrm{B}]^2$, if concentration of $A$ is doubled the rate of reaction

The correct zwitter ion structure of glycine is

What is the volume of one particle in BCC structure if ' $a$ ' is edge length?

Identify product ' B ' in following reaction.

$$\mathrm{CH}_3-\mathrm{I}+\mathrm{KCN} \longrightarrow \mathrm{~A} \xrightarrow[\substack{\mathrm{C}_2 \mathrm{H}_2 \mathrm{OH} \\}]{\mathrm{Na}} \mathrm{B} $$

Which of the following alkenes does NOT exhibit cis-trans isomerism?

Carbonated water is an example of a solution of

Which of the following is vinylic halide?

In a particular reaction ' x ' kJ of heat is released by the system and ' y ' kJ of work done is done on the system. What is internal energy change?

Which of the following compounds contains S atom in its ring?

Which element from following combines with hydrogen to form a compound with lowest thermal stability?

What is the decreasing order of deposition of metal on electrode if standard reduction potentials are given as -

$\mathrm{Ag}^{+}\left|\mathrm{Ag}=0.80 \mathrm{~V}, \mathrm{Cu}^{2+}\right| \mathrm{Cu}=0.337 \mathrm{~V}$

$\mathrm{Sn}^{2+}\left|\mathrm{Sn}=-0.136 \mathrm{~V}, \mathrm{Cd}^{2+}\right| \mathrm{Cd}=-0.403 \mathrm{~V}$

If $x=\sin \theta, y=\sin ^3 \theta$, then $\frac{\mathrm{d}^2 y}{\mathrm{~d} x^2}$ at $\theta=\frac{\pi}{2}$ is

Let $P, Q, R$ and $S$ be the points on the plane with position vectors $-2 \hat{i}-\hat{j}, 4 \hat{i}, 3 \hat{i}+3 \hat{j}$ and $-3 \hat{i}+2 \hat{j}$ respectively. Then the quadrilateral PQRS must be a

If $y=\frac{x^{\frac{2}{3}}-x^{\frac{-1}{3}}}{x^{\frac{2}{3}}+x^{\frac{-1}{3}}}, x \neq 0$, then $(x+1)^2 y_1=$

The Number of values of C that satisfy the conclusion of Rolle's theorem in case of following function $\mathrm{f}(x)=\sin 2 \pi x, x \in[-1,1]$ is

An open tank with a square bottom, to contain 4000 cubic cm . of liquid, is to be constructed. The dimensions of the tank, so that the surface area of the tank is minimum, are

$$\int \operatorname{cosec}(x-a) \cdot \operatorname{cosec} x d x=$$

The contrapositive of the inverse of $\mathrm{p} \rightarrow(\mathrm{p} \rightarrow \mathrm{q})$ is

The area enclosed between the parabola $y^2=4 x$ and the line $y=2 x-4$ is

There are 3 sections in a question paper and each section contains 5 questions. A candidate has to answer a total of 5 questions, choosing at least one question from each section. Then the number of ways, in which the candidate can choose the questions, is

The order of the differential equation, whose solution is $y=\left(C_1+C_2\right) \mathrm{e}^x+C_3 \mathrm{e}^{x+C_4}$, is

If the sides of a rectangle are given by the equations $x=-2, x=6, y=-2, y=5$, then the equation of the circle, drawn on the diagonal of this rectangle as its diameter, is

The solution set of the equation $\tan x+\sec x=2 \cos x$, in the interval $[0,2 \pi]$ is

If one of the lines represented by $a x^2+2 h x y+b y^2=0$ is perpendicular to $\mathrm{m} x+\mathrm{n} y=18$, then

If $\sin ^{-1}\left(\frac{x}{13}\right)+\operatorname{cosec}^{-1}\left(\frac{13}{12}\right)=\frac{\pi}{2}$, then the value of

The graphical solution set of the system of inequations $2 x+3 y \leq 6, x+4 y \geq 4, x \geq 0, y \geq 0$ is given by

The derivative of $\sin ^{-1}\left(2 x \sqrt{1-x^2}\right)$ w.r.t. $\sin ^{-1}\left(3 x-4 x^3\right)$ is

If $A=\left[\begin{array}{cc}5 a & -b \\ 3 & 2\end{array}\right]$ and $A \cdot \operatorname{adj} A=A A^T$, then $5 a+b$ is equal to

The function $\mathrm{f}(x)=2 x^3-9 x^2+12 x+2$ is decreasing in

$\int\left(1+x-\frac{1}{x}\right) \mathrm{e}^{x+\frac{1}{x}} \mathrm{~d} x$ is equal to

If the function $f(x)= \begin{cases}-2 \sin x & \text {, if } x \leq \frac{-\pi}{2} \\ A \sin x+B & , \text { if } \frac{-\pi}{2}< x<\frac{\pi}{2} \\ \cos x & , \text { if } x \geq \frac{\pi}{2}\end{cases}$ is continuous everywhere, then the values of $A$ and B are respectively

$$\int\limits_{\frac{\pi}{3}}^{\frac{\pi}{2}} \frac{\sqrt{1+\cos x}}{(1-\cos x)^{\frac{5}{2}}} d x=$$

If the complex number $z=x+i y$, where $i=\sqrt{-1}$, satisfies the condition $|z+1|=1$, then $z$ lies on

The general solution of the differential equation $\frac{d y}{d x}=\frac{3 e^{2 x}+3 e^{4 x}}{e^x+e^{-x}}$ is

If $\cos ^{-1} x=\alpha(0

If the points $\mathrm{P}, \mathrm{Q}$ and R are with the position vectors $\hat{i}-2 \hat{j}+3 \hat{k},-2 \hat{i}+3 \hat{j}+2 \hat{k}$ and $-8 \hat{i}+13 \hat{j}$ respectively, then these points are

A line makes $45^{\circ}$ angle with positive X -axis and makes equal angles with positive Y -axis ad Z-axis respectively, then the sum of the three angles which the line makes with positive X -axis, Y -axis and Z -axis is

If the lines $\frac{x-1}{2}=\frac{y+2}{3}=\frac{z-1}{4}$ and $\frac{x-3}{1}=\frac{y-\mathrm{k}}{2}=\frac{\mathrm{z}}{1}$ intersect, then k has the value

The vector equation of the plane through the line of intersection of the planes $x+y+z=1$ and $2 x+3 y+4 z=5$, which is perpendicular to the plane $x-y+z=0$, is

The equation of motion of a particle is $s=a t^2+b t+c$. If the displacement after 1 second is 20 m , velocity after 2 seconds is $30 \mathrm{~m} / \mathrm{sec}$ and the acceleration is $10 \mathrm{~m} / \mathrm{sec}^2$, then

One side and one diagonal of a parallelogram are represented by $3 \hat{i}+\hat{j}-\hat{k}$ and $2 \hat{i}+\hat{j}-2 \hat{k}$ respectively, then the area of parallelogram in square units is

If $\int \mathrm{e}^{x^2} \cdot x^3 \mathrm{dx}=\mathrm{e}^{x^2} \mathrm{f}(x)+\mathrm{c}$ and $\mathrm{f}(1)=0$ (where c is a constant of integration), then the value of $f(x)$ is

If $\cot ^{-1}(\sqrt{\cos \alpha})-\tan ^{-1}(\sqrt{\cos \alpha})=x$, then the value of $\sin x$ is

If $[x]^2-5[x]+6=0$, where $[\cdot]$ denotes the greatest integer function, then

The value of the integral $\int_0^{\frac{\pi}{2}} \frac{\sqrt{\cot x}}{\sqrt{\cot x}+\sqrt{\tan x}} \mathrm{dx}$ is

Variance of first n natural numbers is ________.

Suppose three coins are tossed simultaneously. If $X$ denotes the number of heads, then probability distribution of x is

Four fair dice are thrown independently 27 times. Then the expected number of times, at least two dice show up a three or a five is

If $0< x<1$, then $\sqrt{1+x^2}\left[\left\{x \cos \left(\cot ^{-1} x\right)+\sin \left(\cot ^{-1} x\right)\right\}^2-1\right]^{\frac{1}{2}}$ is equal to

If the vector $\overline{\mathrm{c}}$ lies in the plane of $\overline{\mathrm{a}}$ and $\overline{\mathrm{b}}$, where $\overline{\mathrm{a}}=\hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}, \overline{\mathrm{b}}=\hat{\mathrm{i}}+\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and $\overline{\mathrm{c}}=x \hat{\mathrm{i}}-(2-x) \hat{\mathrm{j}}-\hat{\mathrm{k}}$, then the value of $x$ is

The equation of a line passing through the point $(2,-1,1)$ and parallel to the line joining the points $\hat{i}+2 \hat{j}+2 \hat{k}$ and $-\hat{i}+4 \hat{j}+\hat{k}$ is

The foot of the perpendicular drawn from origin to a plane is $\mathrm{M}(2,1,-2)$, then vector equation of the plane is

If $f(1)=1, f^{\prime}(1)=3$, then the derivative of $\mathrm{f}(\mathrm{f}(\mathrm{f}(x)))+(\mathrm{f}(x))^2$ at $x=1$ is

In a triangle ABC , with usual notations, $\frac{\cos \mathrm{B}+\cos \mathrm{C}}{\mathrm{b}+\mathrm{c}}+\frac{\cos \mathrm{A}}{\mathrm{a}}$ has the value

If $\mathrm{f}(x)=\frac{x}{x+1}, x \neq-1$ and (fof) $(x)=\mathrm{F}(x)$, then $\int \mathrm{F}(x) \mathrm{d} x$ is

If p : The total prime numbers between 2 to 100 are 26.

q : Zero is a complex number.

$r$ : Least common multiple (L.C.M.) of 6 and 7 is 6 .

Then which of the following is correct?

$$\lim _\limits{x \rightarrow 2} \frac{3^x+3^{3-x}-12}{3^{3-x}-3^{\frac{x}{2}}}=$$

$$\int_0^{\frac{\pi}{4}} \frac{\sec ^2 x}{(1+\tan x)(2+\tan x)} d x=$$

If two fair dice are rolled, then the probability that the sum of the numbers on the upper faces is at least 9, is

After $t$ seconds, the acceleration of a particle, which starts from rest and moves in a straight line is $\left(8-\frac{\mathrm{t}}{5}\right) \mathrm{cm} / \mathrm{s}^2$, then velocity of the particle at the instant, when the acceleration is zero, is

If $\mathrm{A}+\mathrm{B}=225^{\circ}$, then $\frac{\cot \mathrm{A}}{1+\cot \mathrm{A}} \cdot \frac{\cot \mathrm{B}}{1+\cot \mathrm{B}}$, if it exists, is equal to

The figure shows currents in a part of electric circuit. Then current I is

A metal disc of radius R rotates with an angular velocity $\omega$ about an axis perpendicular to its plane passing through its centre in a magnetic field of induction B acting perpendicular to the plane of the disc. The induced e.m.f. between the rim and axis of the disc is

A body of mass $m$ slides down an incline and reaches the bottom with a velocity V . If the same mass were in the form of a disc which rolls down this incline, the velocity of the disc at bottom would have been

For a particle executing S.H.M. having amplitude A, the speed of the article is $\left(\frac{1}{3}\right)^{\text {rd }}$ of its maximum speed when the displacement from the mean position is

The minimum energy required to launch a satellite of mass $m$ from the surface of a planet of mass $M$ and radius $R$ in a circular orbit at an altitude of $2 R$ is

The core used in transformers are laminated to

The end correction for the vibrations of air column in a tube of circular cross-section will be more if the tube is

If the work done in blowing a soap bubble of volume ' V ' is ' W ', then the work done in blowing a soap bubble of volume ' 2 V ' will be

A coil has inductance H . The ratio of its reactance when it is connected first to an a.c. source and then to d.c. source is

A particle of mass m collides with another stationary particle of mass $M$. The particle $m$ stops just after collision. The coefficient of restitution is

In the circuit shown in the following figure, the potential difference cross $3 \mu \mathrm{~F}$ capacitor is

Sodium light $\left(\lambda=6 \times 10^{-7} \mathrm{~m}\right)$ is used to produce interference pattern. The observed fringe width is 0.12 mm . The angle between the two wave trains is

The motion of a particle is described by the equation $a=-b x$ where ' $a$ ' is the acceleration, x is the displacement from the equilibrium position and b is a constant. The periodic time will be

Acceleration of an electron in the first Bohr's orbit is proportional to $\mathrm{m}=$ mass of electron, $\mathrm{r}=$ radius of the orbit, $\mathrm{h}=$ Planck's constant)

A cylindrical rod is having temperatures $\theta_1$ and $\theta_2$ at its ends. The rate of heat flow is $\mathrm{Q} J / \mathrm{S}$. All the linear dimensions of the rod are doubled by keeping the temperature constant. The new rate of flow of heat is

A resistor of $50 \Omega$, inductor of self inductance $\left(\frac{3}{\pi^2}\right) \mathrm{H}$ and a capacitor of unknown capacity are connected in series to an a.c. source of 100 V and 50 Hz . When the voltage and current are in phase, the value of capacitance is (nearly)

A monoatomic ideal gas, initially at temperature $T_1$ is enclosed in a cylinder fitted with frictionless piston. The gas is allowed to expand adiabatically to a temperature $T_2$ by releasing the piston suddenly. $L_1$ and $L_2$ are the lengths of the gas columns before and after the expansion respectively. The ratio $T_2 / T_1$ is

Charges of $2 \mu \mathrm{C}$ and $-3 \mu \mathrm{C}$ are placed at two points A and B separated by 1 m . The distance of the point from A , where net potential is zero, is

For detecting light intensity we use

A ball is released from the top of a tower of height Hm . It takes T second to reach the ground. The height of the ball from the ground after $\frac{T}{4}$ second is

1000 small balls, each weighing 1 gram, strike one square cm of area per second with a velocity $50 \mathrm{~m} / \mathrm{s}$ in a normal direction and rebound with the same velocity. The value of pressure on the surface will be

A wave is given by $Y=3 \sin 2 \pi\left(\frac{t}{0.04}-\frac{x}{0.01}\right)$ where Y is in cm . Frequency of the wave and maximum acceleration will be $\left(\pi^2=10\right)$

Two concentric circular coils A and B having radii 20 cm and 10 cm respectively lie in the same plane. The current in coil A is 0.5 A in anticlockwise direction. The current in coil B , so that net magnetic field at the common centre is zero, is

The radius of gyration of a circular disc of radius R and mass m rotating about diameter as axis is

What is the current in the following junction diode circuit?

When a certain metallic surface is illuminated with monochromatic light wavelength $\lambda$, the stopping potential for photoelectric current is $4 \mathrm{~V}_0$. When the same surface is illuminated with light of wavelength $3 \lambda$, the stopping potential is $\mathrm{V}_0$. The threshold wavelength for this surface for photoelectric effect is

A plate of refractive index 1.6 is introduced in the path of light from one of the slits in Young's double slit experiment then

The viscous force between two liquid layers is

In the given reaction

$${ }_z \mathrm{X}^A \rightarrow{ }_{z+1} \mathrm{Y}^A \rightarrow{ }_{z-1} \mathrm{~K}^{A-4} \rightarrow{ }_{z-1} \mathrm{~K}^{\mathrm{A}-4}$$

radioactive radiations are emitted in the sequence

Two point charges $+q_1$ and $q_2$ repel each other with a force of $100 \mathrm{~N} . q_1$ is increased by $10 \%$ and $q_2$ is decreased by $10 \%$. If they are kept at their original positions the change in the force of repulsion between them is

In an ideal gas at temperature $T$, the average force that a molecule applies on the walls of a closed container depends on $T$ as $\mathrm{T}^{\mathrm{x}}$. The value of $x$ is

Which one of the following graph represent correctly the variation of impedance $(\mathrm{Z})$ of a series LCR circuit with the frequency $(v)$ of applied a.c.?

A galvanometer may be converted into ammeter or a voltmeter. In which of the following cases the resistance of the device so obtained will be the largest?

A glass prism ' A ' deviates the red and blue rays through $10^{\circ}$ and $12^{\circ}$ respectively. A second prism ' B ' deviates them through $8^{\circ}$ and $10^{\circ}$ respectively. The ratio of their dispersive powers is (A to B)

In an electric field due to charge $Q$, a charge $q$ moves from point A to B as shown in the figure. The work done is ( $\varepsilon_0=$ permittivity of free space)

An air cored coil has a self inductance 0.1 H . A soft iron core of relative permeability 1000 is introduced and the number of turns is reduced $\left(\frac{1}{10}\right)^{\text {th }}$. The value of self inductance is

Heat engine operating between temperature $T_1$ and $T_2$ has efficiency $\frac{1}{6}$. When $T_2$ is lowered by 62 K , its efficiency increases to $\frac{1}{3}$. Then $T_1$ and $T_2$ respectively are

The angle of minimum deviation produced by a thin prism in air is $\delta_1$. If it is immersed in water the angle of minimum deviation is

$$\left[\mathrm{a}_{\mathrm{g}}=\frac{3}{2}, \mathrm{a}_{\mathrm{w}}=\frac{4}{3}\right]$$

An electron is revolving in a circular orbit of radius $r$ in a hydrogen atom. The angular momentum of the electron is L . The relation between dipole moment (m) associated with it, gyromagnetic ratio ( R ) and L is

A p-n junction diode as a rectifier converts

A ball rises to surface at a constant velocity in liquid whose density is 3 times greater than that of the material of the ball. The ratio of force of friction acting on the rising ball to its weight is

Three infinite straight wires $\mathrm{A}, \mathrm{B}$ and C carry currents as shown in figure. The resultant force on wire $B$ is directed

Velocity of sound waves in air is $330 \mathrm{~m} / \mathrm{s}$. For a particular sound wave in air, path difference of 40 cm is equivalent to phase difference of $1.6 \pi$. frequency of this wave is

In Young's double slit experiment, the intensity of light at a point on the screen where the path difference is $\lambda$ is x units, $\lambda$ being the wavelength of light used. The intensity at a point where the path difference is $\frac{\lambda}{4}$ will be $\left(\cos 2 \pi=1, \cos \frac{\pi}{2}=0\right)$

The stopping potential as a function of frequency of incident radiation is plotted for two different photoelectric surfaces A and B. The graph shows that the work function of A is

The absolute temperature of a gas is determined by

The density of a new planet is twice that of earth. The acceleration due to gravity at the surface of the planet is equal to that at the surface of earth. If $R$ is the radius of earth, then radius of the planet would be

A particle is moving in a circle with uniform speed. It has constant

A string has mass per unit length of $10^{-6} \mathrm{~kg} / \mathrm{cm}$ The equation of simple harmonic wave produced in it is $\mathrm{Y}=0.2 \sin (2 \mathrm{x}+80 \mathrm{t}) \mathrm{m}$. The tension in the string is

A spring has length L and force constant K . It is cut into two springs of length $L_1$ and $L_2$ such that $\mathrm{L}_1=\mathrm{NL}_2$ ( N is an integer). The force constant of spring of length $L_1$ is