Find the mass of sodium carbonate in grams to form 100 ml 0.1 M solution in water?
( Molar mass of $\text{Na}_2\text{CO}_3$ = 106 g/mol)

What is number of hydrogen molecules needed to synthesize 3.4 g of ammonia by reaction with nitrogen?

If the velocity of the electron in Bohr's first orbit is $2.19 \times 10^6\ \text{Ms}^{-1}$, Calculate the de Broglie wavelength associated with it.
$[h = 6.626 \times 10^{-34}\ \text{J s}$ & Mass of electrons $= 9.10938 \times 10^{-31}$ kg $]$

Identify the group of periodic table that contains element Astatine.

What type of bond and type of overlapping present in $\text{N}_2$ molecule ?

Calculate the new pressure of the gas enclosed in a cylinder when it compressed from 5 L to 2 L at 1 atm and 300 K. The final temperature in this process is 500 K.

For a certain reaction, $\Delta H^0$ is $-345$ kJ and $\Delta S^0$ is $-123\ \text{JK}^{-1}$. At what temperature the change over from spontaneous to nonspontaneous will occur?

For a reaction to be spontaneous at all temperatures, the values of enthalpy change and entropy change should be

Find $\Delta n$ when 1 mol of each $\text{NH}_{3(g)}$ and $\text{HCl}_{(g)}$, reacts to form solid $\text{NH}_4\text{Cl}$.

What is the solubility product of binary sparingly soluble salt BA if 100 mL saturated solution of salt consist $10^{-4}$ moles at room temperature?

Calculate pOH of 0.001M HCl solution.

Identify from following the conjugate base of $[\text{Zn}(\text{H}_2\text{O})_4]^{2+}$

For the following redox reaction, find the correct statement.
$\text{Sn}^{2+} + 2\text{Fe}^{3+} \rightarrow \text{Sn}^{4+} + 2\text{Fe}^{2+}$

Which of the following is the most abundant element in universe?

What is the correct IUPAC name for a molecule that has two amino groups in opposing (para) locations around a benzene ring?

What is IUPAC name of the compound $\text{CH}_3\text{CH=CHCH=CHCOOH}$ ?

Match List I with List II

List I	List II
(A). Inductive effect	(I). Delocalization of $\pi$ electrons
(B). Hyper-conjugation	(II). Displacement of $\pi$ electrons
(C). Resonance effect	(III). Delocalization of $\sigma$ electrons
	(IV). Displacement of $\sigma$ electrons

Choose the correct answer from the options given below:

What are the reactants involved in Friedal Crafts alkylation?

Identify the false statement regarding magnetic properties of substance.
(A) Paramagnetic substances are weakly attracted.
(B) Diamagnetic substances are weakly attracted.
(C) Ferromagnetic substances strongly attracted.
(D) Diamagnetic substance strongly attracted

Calculate the number of atoms present in 1.625 g metal if it forms bcc unit cell structure.
$[ \rho \times a^3 = 3.25 \times 10^{-22}\ \text{g}]$

Identify the covalent crystal from the following.

If a 0.4 molal solution of a nonvolatile solute in organic solvent decreases its freezing point by 2.4 K., then the molal depression constant of solvent will be

Which of the following colligative properties is useful to determine the molar masses of proteins, polymers or colloids, with the greatest precision?

Calculate the concentration of silver nitrate solution if molar conductivity and conductivity of silver nitrate at $25^\circ$C are respectively 120 ohm$^{-1}$ cm$^2$ mol$^{-1}$ and 0.0024 ohm$^{-1}$ cm$^{-1}$.

The $E^0_{\text{cell}}$ of $\text{Al}_{(s)} | \text{Al}^{3+}(1\text{M}) || \text{Pb}^{2+}(1\text{M}) | \text{Pb}_{(s)}$ cell is 1.5 V if $E^0_{\text{Pb}}$ is $-0.14$ V then $E^0_{\text{Al}}$ will be

Which of the following is an electrolyte in dry cell ?

The rate of reaction $\text{A} + \text{B} \rightarrow \text{P}$ is $4 \times 10^{-2}\ \text{mol dm}^{-3}\ \text{s}^{-1}$
When $[A] = 0.2\ \text{mole dm}^{-3}$ and $[B] = 0.1\ \text{mole dm}^{-3}$, What is the rate constant of reaction, if it is first order with respect to A and second order with respect to B ?

For the reaction $2\text{A} \longrightarrow 3\text{C} + \text{D}$, the rate of reaction is represented by

Which of the following is applicable to thin film?

What is the role of catalyst in catalytic reaction ?

Which of the following exhibits the minimum coagulating power for precipitating of positively charged ferric oxide sol ?

Identify weakest acid from following.

Which of the following elements has completely filled 4 f orbital at the expected ground state configuration?

Which of the following elements in +3 oxidation state forms colourless compounds?

Identify the complex having the highest number of unpaired electrons from following.

Which of the following ligands splits d orbitals to maximum level?

Which of the following is used as solvent for Grignard reagent?

Which of the following is a correct feature of the $\text{SN}^2$ mechanism?

In benzylic halides, the halogen atom is bonded to

Method of preparation of alkyl halide
$2\text{R-Br} + \text{Hg}_2\text{F}_2 \rightarrow 2\text{R-F} + \text{Hg}_2\text{Br}_2$
This reaction is known as

Which of following on oxidation forms propanone?

Identify the name of reaction when phenol reacts with chloroform in aqueous NaOH.

Which of the following compounds is obtained by Williamson synthesis ?

Which of the following is the strongest carboxylic acid?

Which of the following amines is not represented by formula $\text{C}_3\text{H}_9\text{N}$ ?

Which of the following statements are correct?
A) $\alpha$ - amino acids present in protein is L- amino acid.
B) Amino acids contain $\text{NH}_2$ as well as COOH group.
C) Number of amino group and carboxylic group are same in amino acids always.
D) Tryosine was firstly obtained from cheese.
Choose the correct alternatives from below:

During denaturation, which level of protein structure remains unchanged?

Identify the natural source of ascorbic acid from following.

Identify the monomers used to prepare bakelite from the following.

Which among the following is NOT a polyester polymer ?

If $x$, y, z are the sides of a right angled triangle, where z is the largest side, then $\dfrac{1}{\log_{x+z} y} + \dfrac{1}{\log_{z-x} y} =$

If $\omega$ is a complex cube root of unity, then the value of $\sin\left[\pi(\omega^{10} + \omega^{23}) - \dfrac{\pi}{4}\right] =$

If 6 boys and 3 girls are to be seated in a row for a photograph, then the probability that the end seats are occupied by the girls and no two girls are side by side is

A bag contains 23 balls, of which 7 are identical. The number of ways of selecting 12 balls from the bag is....

The approximate value of $(0.007)^{\frac{1}{3}}$ is

If $33\theta = \pi$, then the value of $\cos\theta \cos2\theta \cos4\theta \cos8\theta \cos16\theta$ is

If $\sec 4\theta - \sec 2\theta = 2$, then $\theta =$

The equation of the line passing through the point of intersection of the lines $x + 2y + 6 = 0$ and $2x - y = 2$ and making an intercept 5 on the y-axis is

The line $x + y = 3$ intersects the pair of straight lines $x^2 - 3xy + y^2 = 0$ at points A and B. Then the co-ordinates of the mid-point of AB are

The angle between the tangents drawn from the origin to the circle $(x-7)^2 + (y+1)^2 = 25$ is

The equation of the common tangent touching the circle $(x-3)^2 + y^2 = 9$ and the parabola $y^2 = 4x$ above the X-axis is

If $\lim\limits_{x \to \infty} \dfrac{(2x-1)^{19} \cdot (3x+2)^{11}}{(6x-5)^{30}} = 2^a \cdot 3^b$, then $a + b =$

The dual of the statement pattern $(p \wedge \sim q) \longrightarrow (q \wedge \sim p)$ is equivalent to

Negation of the statement "If an integer is greater than 4 and less than 5, then it is a multiple of 3", is

In a triangle ABC, with the usual notations, $\angle B = \dfrac{\pi}{3}$, $\angle C = \dfrac{\pi}{4}$. If D divides BC internally in the ratio 1:3, then $\dfrac{\sin \angle BAD}{\sin \angle CAD} =$

Let $P_1$, $P_2$, $P_3$ be the altitudes of a triangle ABC from the vertices A, B, C respectively. If $\triangle$ denotes the area of the triangle and s is the semi-perimeter of the triangle, then $\dfrac{\cos A}{P_1} + \dfrac{\cos B}{P_2} + \dfrac{\cos C}{P_3} =$

If $A = \begin{bmatrix} 3 & 1 \\ -1 & 2 \end{bmatrix}$, $C = \begin{bmatrix} 7 & 3 \\ 0 & 6 \end{bmatrix}$ and $AB = C$, then the inverse of matrix B is

The element in the third row and the second column in the inverse matrix of a matrix $\begin{bmatrix} 1 & 3 & 3 \\ 3 & 1 & 3 \\ 3 & 3 & 4 \end{bmatrix}$ is

If $y = \tan^{-1}\sqrt{\dfrac{1 + \sin 2x}{1 - \sin 2x}}$, then $\dfrac{\text{d}y}{\text{d}x}$ at $x = \dfrac{\pi}{6}$ is

The value of $\tan^{-1}\left(\dfrac{\cos\left(\frac{19\pi}{4}\right) - 1}{\sin\left(\frac{\pi}{4}\right)}\right)$ is equal to

The value of f(0) so that the function $f(x) = \dfrac{(256 - 8x)^{\frac{1}{4}} - 4}{16 - 4(64 + 3x)^{\frac{1}{3}}}$, $x \neq 0$ is continuous at $x = 0$, is

The derivative of $\sin\left(\log\left(\dfrac{x+3}{x}\right)\right)$ is

If $e^y + xy = e$, then the ordered pair $\left(\dfrac{\text{d}y}{\text{d}x}, \dfrac{\text{d}^2 y}{\text{d}x^2}\right)$ at $x = 0$ is equal to

The surface area of a spherical ball is increasing at the rate of $4\pi\ \text{cm}^2$/second. The rate at which the radius is increasing when the surface area is $16\pi\ \text{cm}^2$ is

The maximum value of $\left(\dfrac{1}{x}\right)^x$, $x > 0$ is

The point on the curve $9y^2 = x^3$ where the normal to the curve makes equal intercepts with the co-ordinate axes is

A spherical mothball has initial radius 3 cm. Due to evaporation, the radius of the ball reduces to 1 cm in 4 months. In how many months would the mothball evaporate completely if the volume is lost at a rate proportional to the surface area ?

$\int \dfrac{x^2\, \text{d}x}{(x^2 + 2)(x^2 + 5)} =$

The value of $\int \dfrac{\sin^6 x + \cos^6 x}{\sin^2 x \cdot \cos^2 x}\, \text{d}x$ is

$\int \text{cosec}^{-1}\left(\sqrt{\dfrac{a+x}{x}}\right)\, \text{d}x =$

$\int\limits_{0}^{\pi} |\sin 2x|\, \text{d}x =$

If $f(x)$ is an even function, then $\int\limits_{-2}^{2} (|x| + f(x)\sin x)\, \text{d}x$ is

The area of the region bounded by the curves $y = |x - 4|$, $x = 3$ and $x = 5$, and the X-axis is

The solution of $\dfrac{\text{d}y}{\text{d}x} = \sin(x + y) + \cos(x + y)$ is

The order and degree of the differential equation $3 - \left(\dfrac{\text{d}^3 y}{\text{d}x^3}\right)^{\frac{7}{3}} = \left(\dfrac{\text{d}y}{\text{d}x}\right)^5$ are respectively

The solution of the differential equation $e^{-x}(y+1)\text{d}y + (\cos^2 x - \sin 2x)y\, \text{d}x = 0$, given that $y = 1$ when $x = 0$ is

A unit vector coplanar with $\hat{i} + \hat{j} + 2\hat{k}$ and $\hat{i} + 2\hat{j} + \hat{k}$ and perpendicular to $\hat{i} + \hat{j} + \hat{k}$ is

If $\vec{a} + \vec{b} + \vec{c} = \vec{0}$, $|\vec{a}| = |\vec{b}| = |\vec{c}| = 3$ and $\theta$ is the angle between $\vec{b}$ and $\vec{c}$ then $\tan^2\theta + \cot^2\theta =$

The altitude of the parallelopiped, whose coterminous edges are the vectors $\vec{a} = \hat{i} + \hat{j} + \hat{k}$, $\vec{b} = 2\hat{i} + 4\hat{j} - \hat{k}$, $\vec{c} = \hat{i} + \hat{j} + 3\hat{k}$, where $\vec{a}$, $\vec{b}$ are the sides of the base of parallelopiped, is

Let ABCD be a quadrilateral with $\overline{AB} = \vec{a}$, $\overline{AD} = \vec{b}$ and $\overline{AC} = 3\vec{a} + 2\vec{b}$. If its area is $\alpha$ times the area of the parallelogram with AB, AD as adjacent sides, then the value of $\alpha$ is equal to

Let $\vec{a} = \hat{i} + 2\hat{j} - 2\hat{k}$ and $\vec{b} = \hat{i} - \hat{j} + \hat{k}$. If $\vec{c}$ is a vector such that $\vec{a} \cdot \vec{c} = |\vec{c}|$, $|\vec{c} - \vec{a}| = 2\sqrt{2}$ and the angle between $\vec{a} \times \vec{b}$ and $\vec{c}$ is $60^\circ$, then $|(\vec{a} \times \vec{b}) \times \vec{c}|$ is equal to

The co-ordinates of the point where the line joining the points $(3,5,-7)$ and $(-2, 1, 8)$ is intersected by the YOZ plane are

If the lines $\vec{r} = (\hat{i} + m\hat{j} + 3\hat{k}) + \lambda(2\hat{i} + 3\hat{j} + 4\hat{k})$ and $\vec{r} = (4\hat{i} + \hat{j}) + \mu(5\hat{i} + m\hat{j} + \hat{k})$ intersect each other, then m =

If the lines $x = -1 + s$, $y = 3 - \lambda s$, $z = 1 + \lambda s$ and $x = \dfrac{t}{2}$, $y = 1 + t$, $z = 2 - t$ with parameters s and t, are coplanar, then $\lambda =$

The equation of the plane passing through the point $(1,2,1)$ and perpendicular to the planes $x + 2y + 2z - 7 = 0$ and $3x + 3y + 2z - 5 = 0$ is

The distance of the point $(1,0,-3)$ from the plane $x-y-z=9$ measured parallel to the line $\dfrac{x-2}{2} = \dfrac{y+2}{3} = \dfrac{z-6}{-6}$ is

The difference between the maximum and minimum values of the objective function $Z = 3x + 5y$, subject to the constraints $x + 3y \leq 60$, $x + y \geq 10$, $x - y \leq 0$, $x, y \geq 0$ is

For the following probability distribution, the standard deviation of the random variable X is

X	2	3	4
p(X=$x$)	0.2	0.5	0.3

A random variable X has the following probability distribution

X	1	2	3	4	5	6	7	8
P(X=$x$)	0.15	0.23	0.12	0.10	0.20	0.08	0.07	0.05

For the event E = { X is a prime number } and F = { X < 4 }, P(E$\cup$F) =

The probability that event A happens in a trial is 0.4. If three independent trials are made, then the probability that A happens at least once is.......

Let $\vec{A}$ and $\vec{B}$ are two non-zero vectors of different magnitude. Which one of the following is the correct equation ?

A wire has mass $(0.3 \pm 0.003)$ gram, radius $(0.5 \pm 0.005)$ mm and length $(6 \pm 0.06)$ cm. The maximum error in the measurement of density is

A batsman hits a ball with a velocity 'v', making an angle of $60^\circ$ with the vertical. After some time direction of velocity is making an angle of $60^\circ$ with the horizontal. The speed of the ball at this instant is
$\left[\cos(60^\circ) = \dfrac{1}{2}, \cos(30^\circ) = \dfrac{\sqrt{3}}{2}\right]$

A particle at rest starts moving with constant angular acceleration '$\alpha$' in a circular path of radius 'r'. At certain instant, the magnitude of centripetal acceleration is $\left(\dfrac{1}{3}\right)^{rd}$ the tangential acceleration. The relation between linear speed (V) and angular acceleration ($\alpha$) is

A car of mass m is crossing the convex bridge of radius of curvature R with speed V. At the highest point the thrust is ($g$ = gravitational acceleration)

A bucket containing water is revolved in vertical circle of radius r. To prevent the water from falling down, the period of revolution required is ($g$ = gravitational acceleration)

In case of perfectly elastic collision,

The distance of the two planets A and B from the sun are '$r_A$' and '$r_B$' respectively such that $r_B = 100\, r_A$. The ratio of the speed of planet A to that of planet B is (both the planets are revolving around the sun)

A square frame of each side L is dipped in a soap solution and taken out, the force acting on the film formed is ( T = surface tension of soap solution)

Three liquids have same surface tension and densities $\rho_1$, $\rho_2$ and $\rho_3$ ($\rho_1 < \rho_2 < \rho_3$). In three identical capillaries rise of liquid is same. The corresponding angle of contact $\theta_1$, $\theta_2$ and $\theta_3$ are related as

The excess pressure inside the first soap bubble of radius $R_1$ is three times that inside the second soap bubble of radius $R_2$. The ratio of volumes of the first to second bubble is

The ratio of the thermal conductivity of two rods of different materials is 6:5. The two rods of same area of cross section and same thermal resistance will have the length in the ratio

A black rectangular surface of area A emits energy E per second at $127^\circ$C. If length and breadth is reduced to half of initial value and temperature is raised to $527^\circ$C then energy emitted becomes

The energy spectrum of a black body exhibits a maximum around a wavelength $\lambda$. The temperature of a black body is now changed such that the energy is maximum at wavelength $2\lambda/3$. The power radiated by the black body will now increase by a factor of

In a cyclic process, work done by the system is

The average translational kinetic energy of a molecule in a gas is $E_1$. The kinetic energy of the electron (e) accelerated from rest through potential difference 'V' volt is $E_2$. The temperature at which $E_1 = E_2$ possible is (N = number of molecules, R = gas constant)

An ideal gas is expanded adiabatically. How many times has the gas to be expanded to reduce the r.m.s. speed of molecules 3 times ? ($\gamma = 1.5$)

A body of mass $0.4$ kg performs simple harmonic motion. It experiences a restoring force of $0.4$ N when its displacement from the mean position is 4 cm. The force constant and magnitude of acceleration respectively are

The minimum phase difference between two simple harmonic motions is
$x_1 = \dfrac{1}{\sqrt{2}} \sin \omega t + \dfrac{1}{\sqrt{2}} \cos \omega t$
$x_2 = \sin \omega t + \cos \omega t$     $\left[ \sin \dfrac{\pi}{4} = \cos \dfrac{\pi}{4} = \dfrac{1}{\sqrt{2}} \right]$

A pendulum clock is running slow, In order to correct it, we should

A simple harmonic progressive wave is represented by $y = A \sin(120\pi t + 3x)$. The distance between two points on the wave at a phase difference of $\dfrac{\pi}{3}$ radian is

A pipe open at both ends has a fundamental frequency 'f' in air. The pipe is dipped in water, so that $\dfrac{2}{3}^{rd}$ length of pipe is in water, Now the fundamental frequency of the air column is

To increase the frequency of transverse oscillations of a stretched string by 40%, the tension must be increased by

When open pipe is closed from one end then second overtone of closed pipe is higher in frequency by 100 Hz than first overtone of open pipe. The fundamental frequency of open end pipe will be (Neglect end correction)

For a uniformly charged plane sheet, the variation of electric field (E) with distance (d) is correctly shown graphically in graph

A point charge 'Q' is placed at the centre of the line joining two equal charges '+q' and '+q'. The value of 'Q' when the system is in equilibrium is

Capacitors of capacities $C_1$ and $C_2$ are connected in series. If the combination is connected to a supply of V volt then the potential difference across capacitor $C_2$ is

Two parallel plate air capacitors are connected in parallel. Each capacitor has plate area $A/2$ and separation between the plates is $d$ and $2d$ respectively. The equivalent capacity of the combination is

( $\epsilon_0$ = absolute permittivity of free space)

In metre bridge experiment, the resistance in the left gap is 15 $\Omega$ and in the right gap is 45 $\Omega$. The bridge is balanced. The distance of the null point from the centre of the wire is

A potentiometer wire is 4m long and potential difference of 2V is maintained between the ends. The e.m.f. of the cell which balances against a length of 80 cm of the potentiometer wire is

An iron rod is placed parallel to magnetic field intensity 1000 A/m. The magnetic flux through the rod is $3 \times 10^{-4}$ Wb and its cross-sectional area is $1.5\ \text{cm}^2$. The magnetic permeability of rod in $\text{Wb/}_{\text{A-m}}$ is

A charge moves in a circular path perpendicular to a magnetic field. The time period of revolution is independent of

A long wire is bent into a circular coil of one turn and then into a circular coil of smaller radius having n turns. If the same current is passed in both the cases, the ratio of magnetic field produced at the centre for one turn to that of n turns is

A thin ring of radius 'R' metre has charge 'q' coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of 'f' revolution/s. The value of magnetic induction at the centre of the ring in $\text{Wb/m}^2$ is

( $\mu_0$ = permeability of free space )

Two concentric circular coils having radii $r_1$ and $r_2$ ($r_2 << r_1$) are placed co-axially with centres coinciding. The mutual inductance of the arrangement is (Both coils have single turn, $\mu_0$ = permeability of free space)

Two solenoids A and B of equal number of turns have their lengths and radii in the same ratio $1 : 3$. The ratio of the self-inductance of solenoid A to that of B will be

An electric lamp connected in series with a capacitor and an a.c source is glowing with certain brightness. On reducing the frequency of source the brightness of the lamp

A series resonant circuit consists of an inductor 'L' and capacitor 'C' which produces resonant frequency 'f'. If 'L' is increased by '2L' and 'C' is changed to '9C' the resonant frequency will be

In an LCR series circuit, at resonance,

The angle of minimum deviation produced by a thin prism in air is $\delta_1$. What will be the minimum deviation ($\delta_2$) if the prism is immersed in liquid ?
$\left[ {}^a n_g = \dfrac{3}{2}, \ {}^a n_\ell = \dfrac{1}{3} \right]$

In the phenomenon of refraction of light for the same angle of incidence

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

Light of wavelength $\lambda$ is incident on a single slit of width 'a' and the distance between slit and screen is 'D'. In diffraction pattern, if slit width is equal to the width of the central maximum then 'D' is equal to

When a metallic surface is illuminated with a radiation of wavelength '$\lambda$', the stopping potential is 'V'. If the same surface is illuminated with radiation of wavelength $6\lambda$, the stopping potential is $\left(\dfrac{V}{12}\right)$. The threshold wavelength for the surface is

In photoelectric effect experiment, if the frequency of incident radiation ($v$) is increased, keeping all other factors constant, the stopping potential, ( $v > v_0$) ($v_0$ = threshold frequency)

The electron in hydrogen atom is initially in the second excited state. When it finally moves to ground state, the maximum number of spectral lines emitted are

In the hydrogen atom, radii of the first four Bohr orbits are related as

In the logic circuit diagram, when all the four inputs, A, B, C, D are 'one' the outputs $Y_1$, $Y_2$, $Y_3$ are respectively (1, 1, 0). When the inputs A and C are changed to zero and B and D are still 'one', then the outputs $Y_1$, $Y_2$, $Y_3$ are respectively change to

In the diagram shown, the resistance between points A and B is '$R_1$' when an ideal diode D is forward biased and is '$R_2$' when ideal diode D is reverse biased. The ratio $R_1 / R_2$ is

In common emitter amplifier, a change of $0.2$ mA in the base current causes a change of $5$ mA in the collector current. If input resistance is $2$ k$\Omega$ and voltage gain is $75$, the load resistance used in the circuit is