Which of the following possess net dipole moment?

The number of $$\pi$$-bonds and $$\sigma$$-bonds present in naphthalene are respectively

The reaction in which $$\Delta H=\Delta U$$ is

The number of moles of electron required to reduce 0.2 mole of $$\mathrm{Cr}_2 \mathrm{O}_7^{-2}$$ to $$\mathrm{Cr}^{+3}

In the reaction $$\mathrm{B}(\mathrm{OH})_3+2 \mathrm{H}_2 \mathrm{O} \rightarrow\left[B(\mathrm{OH})_4\right]^{-}+\math

Match the following acids with their $$pKa$$ values : .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-c

Which of the following can be used to test the acidic nature of ethanol?

The reagents $$A, B$$ and $$C$$ respectively are

Propanoic acid undergoes HVZ reaction to give chloropropanoic acid. The product obtained is

$$P \xrightarrow{\mathrm{H}_2 / \text { Pd- } \mathrm{BaSO}_4} Q \xrightarrow[\text { (ii)Dil. } \mathrm{HCl}]{\text { (

Among the following, the main reactions occurring in blast furnace during extraction of iron from haematite are (i) $$\m

Which of the following pair contains 2 lone pair of electrons on the central atom?

Which of the following statement is correct?

0.1 mole of $$\mathrm{XeF}_6$$ is treated with $$1.8 \mathrm{~g}$$ of water. The product obtained is

In the reaction of gold with aquaregia, oxidation state of nitrogen changes from

The vitamin that helps in clotting of blood is

The polymer containing five methylene groups in it s repeating unit is

Cis-1, 4-polyisoprene is called

Which cleansing agent gets precipitated in hard water?

Anti-histamine among the following is

The elements in which electrons are progressively filled in $$4 f$$-orbital are called

Incorrect statement with reference to $$\mathrm{Ce}(Z=58)$$ is

A mixture of $$\mathrm{NaCl}$$ and $$\mathrm{K}_2 \mathrm{Cr}_2 \mathrm{O}_7$$ is heated with conc. $$\mathrm{H}_2 \math

Which of the following statements is wrong?

Which among the following is the strongest ligand?

Which of the following is a network crystalline solid?

The number of atoms in $$2.4 \mathrm{~g}$$ of body centred cubic crystal with edge length $$200 \mathrm{pm}$$ is (densit

1 mole of $$\mathrm{NaCl}$$ is doped with $$10^{-5}$$ mole of $$\mathrm{SrCl}_2$$. The number of cationic vacancies in t

A non-volatile solute, '$$A$$' tetramerises in water to the extent of $$80 \%.$$ $$2 .5 \mathrm{~g}$$ of '$$A$$' in $$10

Solution '$$A$$' contains acetone dissolved in chloroform and solution '$$B$$' contains acetone dissolved in carbon disu

The mass of $$\mathrm{AgCl}$$ precipitated when a solution containing $$11.70 \mathrm{~g}$$ of $$\mathrm{NaCl}$$ is adde

Two particle $$A$$ and $$B$$ are in motion. If the wavelength associated with '$$A$$' is $$33.33 \mathrm{~nm}$$, the wav

The first ionisation enthalpy of the following elements are in the order :

Solubility of AgCl is least in

Which of the following equations does not represent Charles's law for a given mass of gas at constant pressure?

Which is the most suitable reagent for the following conversion?

Which of the following is least soluble in water at $$298 \mathrm{~K}$$ ?

If aniline is treated with $$1: 1$$ mixture of conc. $$\mathrm{HNO}_3$$ and conc. $$\mathrm{H}_2 \mathrm{SO}_4$$, p-nitr

In nucleic acids, the nucleotides are joined together by

Which of the following is generally water insoluble?

Relative lowering of vapour pressure of a dilute solution of glucose dissolved in $$1 \mathrm{~kg}$$ of water is 0.002 .

One litre solution of $$\mathrm{MgCl}_2$$ is electrolysed completely by passing a current of $$1 \mathrm{~A}$$ for $$16

An aqueous solution of $$\mathrm{CuSO}_4$$ is subjected to electrolysis using inert electrodes. The $$\mathrm{pH}$$ of t

Give $$E_{\mathrm{Mn}^{+7} \mid \mathrm{Mn}^{+2}}^0=1.5 \mathrm{~V}$$ and $$E_{\mathrm{Mn}^{+4}\mid \mathrm{Mn}^{+2}}^0=

The plot of $$t_{1 / 2} \mathrm{~v} / \mathrm{s}~[R]_0$$ for a reaction is a straight-line parallel to $$X$$-axis. The u

The metal nitrate that liberates $$\mathrm{NO}_2$$ on heating

Which of the following is not true regarding the usage of hydrogen as a fuel?

Resonance effect is not observed in

2-butyne is reduced to trans-but-2-ene using

Eutrophication causes

Addition of excess of $$\mathrm{AgNO}_3$$ to an aqueous solution of 1 mole of $$\mathrm{PdCl}_2 \cdot 4 \mathrm{NH}_3$$

The formula of pentaaquanitratochromium (III) nitrate is,

Which of the following halide undergoes hydrolysis on warming with water/aqueous $$\mathrm{NaOH}$$ ?

The compound having longest C$$-$$Cl bond is

The alkyl halides required to prepare by Wurtz reaction are

Which is a wrong statement?

1L of $$2 \mathrm{M~CH}_3 \mathrm{COOH}$$ is mixed with 1L of $$3 \mathrm{M} \mathrm{~C}_2 \mathrm{H}_5 \mathrm{OH}$$ to

Which of the following is an example of homogeneous catalysis?

Critical Micelle concentration for a soap solution is $$1.5 \times 10^{-4} \mathrm{~mol} \mathrm{~L}^{-1}$$. Micelle for

Oxidation state of copper is +1 in

The inverse of the matrix $$\left[\begin{array}{ccc}2 & 5 & 0 \\ 0 & 1 & 1 \\ -1 & 0 & 3\end{array}\right]$$ is

If $$P$$ and $$Q$$ are symmetric matrices of the same order then $$P Q-Q P$$ is

If $$3 A+4 B^{\prime}=\left[\begin{array}{ccc}7 & -10 & 17 \\ 0 & 6 & 31\end{array}\right]$$ and $$2 B+3 A^{\prime}\left

If $$A=\left[\begin{array}{ll}1 & 3 \\ 4 & 2\end{array}\right], B=\left[\begin{array}{cc}2 & -1 \\ -1 & 2\end{array}\rig

If the value of a third order determinant is 16, then the value of the determinant formed by replacing each of its eleme

$$\int x^3 \sin 3 x d x=$$

The area of the region above $$X$$-axis included between the parabola $$y^2=x$$ and the circle $$x^2+y^2=2 x$$ in square

The area of the region bounded by $$Y$$-axis, $$y=\cos x$$ and $$y=\sin x, 0 \leq x \leq \frac{\pi}{2}$$ is

The integrating factor of the differential equation $$\left(2 x+3 y^2\right) d y=y d x(y>0)$$ is

The equation of the curve passing through the point $$(1,1)$$ such that the slope of the tangent at any point $$(x, y)$$

Foot of the perpendicular drawn from the point $$(1,3,4)$$ to the plane $$2 x-y+z+3=0$$ is

Acute angel between the line $$\frac{(x-5)}{2}=\frac{y+1}{-1}=\frac{z+4}{1}$$ and the plane $$3 x-4 y-z+5=0$$ is

The distance of the point $$(1,2,1)$$ from the line $$\frac{x-1}{2}=\frac{y-2}{1}=\frac{z-3}{2}$$ is.

$$X Y$$ plane divides the line joining the points $$A(2,3,-5)$$ and $$B(-1,-2,-3)$$ in the ratio

The shaded region in the figure is the solution set of the inequations.

The constant term in the expansion of $$\left|\begin{array}{ccc}3 x+1 & 2 x-1 & x+2 \\ 5 x-1 & 3 x+2 & x+1 \\ 7 x-2 & 3

If $$[x]$$ represents the greatest integer function and $$f(x)=x-[x]-\cos x$$, then $$f^{\prime}\left(\frac{\pi}{2}\righ

If $$f(x)=\left\{\begin{array}{cl}\frac{\sin 3 x}{e^{2 x}-1} ; & x \neq 0 \\ k-2 ; & x=0\end{array}\right.$$ is continuo

If $$f(x)=\sin ^{-1}\left(\frac{2^{x+1}}{1+4^x}\right)$$ then $$f^{\prime}(0)=$$

If $$x=a \sec ^2 \theta$$ & $$y=a \tan ^2 \theta$$, then $$\frac{d^2 y}{d x^2}=$$

If $$\alpha$$ and $$\beta$$ are roots of the equation $$x^2=x+1=0$$, then $$\alpha^2+\beta^2$$ is

The number of 4 digit numbers without repetition that can be formed using the digits $$1,2,3,4,5,6,7$$ in which each num

The number of terms in the expansion of $$\left(x^2+y^2\right)^{25}-\left(x^2-y^2\right)^{25}$$ after simplification is

The third term of a GP is 9. The product of its first five terms is

A line cuts off equal intercepts on the co-ordinate axes. The angle made by this line with the positive direction of $$X

The eccentricity of the ellipse $$9 x^2+25 y^2=225$$ is

$$\sum_\limits{r=1}^n(2 r-1)=x$$ then, $$ \lim _\limits{n \rightarrow \infty}\left[\frac{1^3}{x^2}+\frac{2^3}{x^2}+\frac

The negative of the statement "All continuous functions are differentiable."

Mean and standard deviation of 100 items are 50 and 4 , respectively. The sum of all squares of the items is

Two letters are chosen from the letters of the word 'EQUATIONS'. The probability that one is vowel and the other is cons

$$f: R \rightarrow R$$ and $$g:[0, \infty) \rightarrow R$$ is defined by $$f(x)=x^2$$ and $$g(x)=\sqrt{x}$$. Which one o

If $$A=\{x \mid x \in N, x \leq 5\},B=\left\{x \mid x \in Z, x^2-5 x+6=0\right\}$$, then the number of onto functions fr

On the set of positive rational, a binary operation * is defined by $$a * b=\frac{2 a b}{5}$$. If $$2 * x=3^{-1}$$, then

$$\cos \left[2 \sin ^{-1} \frac{3}{4}+\cos ^{-1} \frac{3}{4}\right]=$$

If $$a+\frac{\pi}{2}

If $$|3 x-5| \leq 2$$ then

A random variable '$$X$$' has the following probability distribution .tg {border-collapse:collapse;border-spacing:0;}

If $$A$$ and $$B$$ are two events of a sample space $$S$$ such that $$P(A)=0.2, P(B)=0.6$$ and $$P(A \mid B)=0.5$$ then

If '$$X$$' has a binomial distribution with parameters $$n=6, p$$ and $$P(X=2)=12$$, $$P(X=3)=5$$ then $$P=$$

A man speaks truth 2 out of 3 times. He picks one of the natural numbers in the set $$S=\{1,2,3,4,5,6,7\}$$ and reports

The order of the differential equation $$y=C_1 e^{C_2+x}+C_3 e^{C_4+x}$$ is

If $$|\mathbf{a}|=16,|\mathbf{b}|=4$$, then $$\sqrt{|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2}=$$

If the angle between $$\mathbf{a}$$ & $$\mathbf{b}$$ is $$\frac{2 \pi}{3}$$ and the projection of $$\mathbf{a}$$ in the

A unit vector perpendicular to the plane containing the vector $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}+\hat{\mathbf{k}}$$

$$[\mathbf{a}+2 \mathbf{b}-\mathbf{c}, \mathbf{a}-\mathbf{b}, \mathbf{a}-\mathbf{b}-\mathbf{c}]=$$

$$\sqrt[3]{y} \sqrt{x}=\sqrt[6]{(x+y)^5}$$, then $$\frac{d y}{d x}=$$

Rolle's theorem is not applicable in which one of the following cases?

The interval in which the function $$f(x)=x^3-6 x^2+9 x+10$$ is increasing in

The sides of an equilateral triangle are increasing at the rate of $$4 \mathrm{~cm} / \mathrm{sec}$$. The rate at which

The value of $$\sqrt{24.99}$$ is

$$\int_\limits{-3}^3 \cot ^{-1} x d x=$$

$$\int \frac{1}{\sqrt{x}+x \sqrt{x}} d x=$$

$$\begin{aligned} & \int \frac{2 x-1}{(x-1)(x+2)(x-3)} d x \\ & \quad=A \log |x-1|+B \log |x+2|+C \log |x-3|+K \end{alig

$$\int_\limits0^2\left[x^2\right] d x=$$

$$\int_\limits0^1 \sqrt{\frac{1+x}{1-x}} d x=$$

If $$U$$ is the universal set with 100 elements; $$A$$ and $$B$$ are two set such that $$n(A)=50, n(B)=60, n(A \cap B)=2

The domain of the function $$f: R \rightarrow R$$ defined by $$f(x)=\sqrt{x^2-7 x+12}$$ is

If $$\cos x=|\sin x|$$ then, the general solution is

$$\sqrt{3} \operatorname{cosec} 20^{\circ}-\sec 20^{\circ}=$$

If $$P(n): 2^n

Which one of the following nuclei has shorter mean life?

The conductivity of semiconductor increases with increase in temperature because

For a transistor amplifier, the voltage gain

In the following circuit, what are P and Q?

An antenna uses electromagnetic waves of frequency $$5 \mathrm{~MHz}$$. For proper working, the size of the antenna shou

A magnetic needle has a magnetic moment of $$5 \times 10^{-2} \mathrm{~Am}^2$$ and moment of inertia $$8 \times 10^{-6}

A toroid has 500 turns per meter length. If it carries a current of $$2 \mathrm{A}$$, the magnetic energy density inside

Consider the situation given in figure. The wire $$A B$$ is slid on the fixed rails with a constant velocity. If the wir

The frequency of an alternating current is $$50 \mathrm{~Hz}$$. What is the minimum time taken by current to reach its p

The readings of ammeter and voltmeter in the following circuit are respectively

Two metal plates are separated by $$2 \mathrm{~cm}$$. The potentials of the plates are $$-10 \mathrm{~V}$$ and $$+30 \ma

The equivalent capacitance between A and B is

A capacitor of capacitance $$C$$ charged by an amount $$Q$$ is connected in parallel with an uncharged capacitor of capa

Though the electron drift velocity is small and electron charge is very small, a conductor can carry an appreciably larg

Masses of three wires of copper are in the ratio $$1: 3: 5$$ and their lengths are in the ratio $$5: 3: 1$$. The ratio o

If $$P, Q$$ and $$R$$ are physical quantities having different dimensions, which of the following combinations can never

The given graph shows the variation of velocity $$v$$ with position $$x$$ for a particle moving along a straight line W

The trajectory of a projectile projected from origin is given by the equation $$y=x-\frac{2 x^2}{5}$$. The initial veloc

An object with mass $$5 \mathrm{~kg}$$ is acted upon by a force, $$\mathbf{F}=(-3 \hat{\mathbf{i}}-4 \hat{\mathbf{j}}) \

During inelastic collision between two objects, which of the following quantity always remains conserved?

In Rutherford experiment, for head-on collision of $$\alpha$$-particles with a gold nucleus, the impact parameter is

Frequency of revolution of an electron revolving in $$n$$th orbit of $$\mathrm{H}$$-atom is proportional to

A hydrogen atom is ground state absorbs $$10.2 \mathrm{~eV}$$ of energy. The orbital angular momentum of the electron is

The end product of decay of $${ }_{90} \mathrm{Th}^{232}$$ is $${ }_{82} \mathrm{~Pb}^{208}$$. The number of $$\alpha$$

Two protons are kept at a separation of $$10 \mathrm{~nm}$$. Let $$F_n$$ and $$F_e$$ be the nuclear force and the electr

Two particles which are initially at rest move towards each other under the action of their mutual attraction. If their

A particle is moving uniformly along a straight line as shown in the figure. During the motion of the particle from $$A$

A satellite is orbiting close to the earth and has a kinetic energy $$K$$. The minimum extra kinetic energy required by

A wire is stretched such that its volume remains constant. The poission's ratio of the material of the wire is

A cylindrical container containing water has a small hole at height of $$H=8 \mathrm{~cm}$$ from the bottom and at a dep

A transparent medium shows relation between $$i$$ and $$r$$ as shown. If the speed of light in vacuum is $$c$$, the Brew

If Young's double slit experiment, using monochromatic light of wavelength $$\lambda$$, the intensity of light at a poin

Due to Doppler's effect the shift in wavelength observed is $$0.1 \mathop A\limits^o$$ for a star producing wavelength $

An electron is moving with an initial velocity $$\mathbf{v}=v_0 \hat{\mathbf{i}}$$ and is in a uniform magnetic field $$

Light of certain frequency and intensity incident on a photosensitive material causes photoelectric effect. If both the

A certain charge $$2 Q$$ is divided at first into two parts $$q_1$$ and $$q_2$$. Later the charges are placed at a certa

A particle of mass $$m$$ and charge $$q$$ is placed at rest in uniform electric field $$E$$ and then released. The kinet

An electric dipole is kept in non-uniform electric field. It generally experiences

The figure gives the electric potential $$V$$ as a function of distance through four regions on $$x$$-axis. Which of the

A system of two charges separated by a certain distance apart stores electrical potential energy. If the distance betwee

In a cyclotron a charged particle

The number of turns in a coil of galvanometer is tripled, then

A circular current loop of magnetic moment $$M$$ is in a arbitrary orientation in an external uniform magnetic field $$\

In a permanent magnet at room temperature

Coersivity of a magnet where the ferromagnet gets completely demagnetized is $$3 \times 10^3 \mathrm{~Am}^{-1}$$. The mi

An inductor of inductance $$L$$ and resistor $$R$$ are joined together in series and connected by a source of frequency

An electromagnetic wave is travelling in $$x$$-direction with electric field vector given by, $$\mathbf{E}_y=E_0 \sin (k

The phenomenon involved in the reflection of radio-waves by ionosphere is similar to

A point object is moving uniformly towards the pole of a concave mirror of focal length $$25 \mathrm{~cm}$$ along its ax

A certain prism is found to produce a minimum deviation of $$38^{\circ}$$. It produce a deviation of $$44^{\circ}$$ when

In the given circuit, the current through 2$$\Omega$$ resistor is

Kirchhoff 's junction rule is a reflection of

The variation of terminal potential difference $$V$$ with current flowing through a cell is as shown. The emf and intern

In a potentiometer experiment, the balancing point with a cell is at a length $$240 \mathrm{~cm}$$. On shunting the cell

The magnetic fields at the centre O in the given figure is

An aluminium sphere is dipped into water. Which of the following is true?

A thermodynamic system undergoes a cyclic process $$A B C$$ as shown in the diagram. The work done by the system per cyc

One mole of $$\mathrm{O}_2$$ gas is heated at constant pressure starting at $$27^{\circ} \mathrm{C}$$. How much energy m

A piston is performing S.H.M. in the vertical direction with a frequency of $$0.5 \mathrm{~Hz}$$. A block of $$10 \mathr

The equation of a stationary wave is $$y=2 \sin \left(\frac{\pi x}{15}\right) \cos (48 \pi t)$$. The distance between a