In the above reaction product 'P' is

The correct stability order of the following resonance structures of $$\mathrm{CH}_3-\mathrm{CH}=\mathrm{CH}-\mathrm{CHO

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The electronic configuration of Einsteinium is : (Given atomic number of Einsteinium $$=99$$)

Which of the following compound can give positive iodoform test when treated with aqueous $$\mathrm{KOH}$$ solution foll

Give below are two statements : Statement I : The higher oxidation states are more stable down the group among transitio

Which of the following compounds will give silver mirror with ammoniacal silver nitrate? A. Formic acid B. Formaldehyde

Total number of stereo isomers possible for the given structure :

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The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency

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Which out of the following is a correct equation to show change in molar conductivity with respect to concentration for

The correct increasing order for bond angles among $$\mathrm{BF}_3, \mathrm{PF}_3$$ and $$\mathrm{ClF}_3$$ is :

For a sparingly soluble salt $$\mathrm{AB}_2$$, the equilibrium concentrations of $$\mathrm{A}^{2+}$$ ions and $$B^{-}$$

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The incorrect statement about Glucose is :

Major product of the following reaction is

The coordination environment of $$\mathrm{Ca}^{2+}$$ ion in its complex with $$\mathrm{EDTA}^{4-}$$ is :

The incorrect statement regarding ethyne is

Based on Heisenberg's uncertainty principle, the uncertainty in the velocity of the electron to be found within an atomi

In the given TLC, the distance of spot A & B are 5 cm & 7 cm, from the bottom of TLC plate, respectively. $$\ma

Number of compounds from the following which cannot undergo Friedel-Crafts reactions is: _________ toluene, nitrobenzene

Total number of electrons present in $$\left(\pi^*\right)$$ molecular orbitals of $$\mathrm{O}_2, \mathrm{O}_2^{+}$$ and

A transition metal '$$\mathrm{M}$$' among $$\mathrm{Sc}, \mathrm{Ti}, \mathrm{V}, \mathrm{Cr}, \mathrm{Mn}$$ and $$\math

Consider the following first order gas phase reaction at constant temperature $$ \mathrm{A}(\mathrm{g}) \rightarrow 2 \m

When $$\Delta \mathrm{H}_{\mathrm{vap}}=30 \mathrm{~kJ} / \mathrm{mol}$$ and $$\Delta \mathrm{S}_{\mathrm{vap}}=75 \math

Consider the following test for a group-IV cation. $$\mathrm{M}^{2+}+\mathrm{H}_2 \mathrm{S} \rightarrow \mathrm{A} \tex

Number of oxygen atoms present in chemical formula of fuming sulphuric acid is ___________.

The vapor pressure of pure benzene and methyl benzene at $$27^{\circ} \mathrm{C}$$ is given as 80 Torr and 24 Torr, resp

Let the foci of a hyperbola $$H$$ coincide with the foci of the ellipse $$E: \frac{(x-1)^2}{100}+\frac{(y-1)^2}{75}=1$$

Let $$z$$ be a complex number such that the real part of $$\frac{z-2 i}{z+2 i}$$ is zero. Then, the maximum value of $$|

Let the range of the function $$f(x)=\frac{1}{2+\sin 3 x+\cos 3 x}, x \in \mathbb{R}$$ be $$[a, b]$$. If $$\alpha$$ and

Let $$\int_\limits0^x \sqrt{1-\left(y^{\prime}(t)\right)^2} d t=\int_0^x y(t) d t, 0 \leq x \leq 3, y \geq 0, y(0)=0$$.

Two vertices of a triangle $$\mathrm{ABC}$$ are $$\mathrm{A}(3,-1)$$ and $$\mathrm{B}(-2,3)$$, and its orthocentre is $$

The integral $$\int_\limits{1 / 4}^{3 / 4} \cos \left(2 \cot ^{-1} \sqrt{\frac{1-x}{1+x}}\right) d x$$ is equal to

Let $$\alpha, \beta ; \alpha>\beta$$, be the roots of the equation $$x^2-\sqrt{2} x-\sqrt{3}=0$$. Let $$\mathrm{P}_n=\al

If $$\log _e y=3 \sin ^{-1} x$$, then $$(1-x^2) y^{\prime \prime}-x y^{\prime}$$ at $$x=\frac{1}{2}$$ is equal to

If an unbiased dice is rolled thrice, then the probability of getting a greater number in the $$i^{\text {th }}$$ roll t

$$\lim _\limits{x \rightarrow \frac{\pi}{2}}\left(\frac{\int_{x^3}^{(\pi / 2)^3}\left(\sin \left(2 t^{1 / 3}\right)+\cos

The value of the integral $$\int_\limits{-1}^2 \log _e\left(x+\sqrt{x^2+1}\right) d x$$ is

Between the following two statements: Statement I : Let $$\vec{a}=\hat{i}+2 \hat{j}-3 \hat{k}$$ and $$\vec{b}=2 \hat{i}+

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Let $$B=\left[\begin{array}{ll}1 & 3 \\ 1 & 5\end{array}\right]$$ and $$A$$ be a $$2 \times 2$$ matrix such that $$A B^{

$$\lim _\limits{x \rightarrow 0} \frac{e-(1+2 x)^{\frac{1}{2 x}}}{x}$$ is equal to

Consider the line $$\mathrm{L}$$ passing through the points $$(1,2,3)$$ and $$(2,3,5)$$. The distance of the point $$\le

The area (in square units) of the region enclosed by the ellipse $$x^2+3 y^2=18$$ in the first quadrant below the line $

Let $$a, a r, a r^2$$, ............ be an infinite G.P. If $$\sum_\limits{n=0}^{\infty} a r^n=57$$ and $$\sum_\limits{n=

The sum of the coefficient of $$x^{2 / 3}$$ and $$x^{-2 / 5}$$ in the binomial expansion of $$\left(x^{2 / 3}+\frac{1}{2

Let $$\vec{a}=2 \hat{i}+\alpha \hat{j}+\hat{k}, \vec{b}=-\hat{i}+\hat{k}, \vec{c}=\beta \hat{j}-\hat{k}$$, where $$\alph

Let $$A=\{(x, y): 2 x+3 y=23, x, y \in \mathbb{N}\}$$ and $$B=\{x:(x, y) \in A\}$$. Then the number of one-one functions

Let $$A, B$$ and $$C$$ be three points on the parabola $$y^2=6 x$$ and let the line segment $$A B$$ meet the line $$L$$

Consider the matrices : $$A=\left[\begin{array}{cc}2 & -5 \\ 3 & m\end{array}\right], B=\left[\begin{array}{l}20 \\ m\en

For a differentiable function $$f: \mathbb{R} \rightarrow \mathbb{R}$$, suppose $$f^{\prime}(x)=3 f(x)+\alpha$$, where $

Consider the circle $$C: x^2+y^2=4$$ and the parabola $$P: y^2=8 x$$. If the set of all values of $$\alpha$$, for which

The square of the distance of the image of the point $$(6,1,5)$$ in the line $$\frac{x-1}{3}=\frac{y}{2}=\frac{z-2}{4}$$

Let the set of all values of $$p$$, for which $$f(x)=\left(p^2-6 p+8\right)\left(\sin ^2 2 x-\cos ^2 2 x\right)+2(2-p) x

The number of integers, between 100 and 1000 having the sum of their digits equals to 14 , is __________.

Let the inverse trigonometric functions take principal values. The number of real solutions of the equation $$2 \sin ^{-

If $$\left(\frac{1}{\alpha+1}+\frac{1}{\alpha+2}+\ldots . .+\frac{1}{\alpha+1012}\right)-\left(\frac{1}{2 \cdot 1}+\frac

The effective resistance between $$A$$ and $$B$$, if resistance of each resistor is $$R$$, will be :

In the truth table of the above circuit the value of X and Y are :

Two cars are travelling towards each other at speed of $$20 \mathrm{~m} \mathrm{~s}^{-1}$$ each. When the cars are $$300

A nucleus at rest disintegrates into two smaller nuclei with their masses in the ratio of $$2: 1$$. After disintegration

A satellite of $$10^3 \mathrm{~kg}$$ mass is revolving in circular orbit of radius $$2 R$$. If $$\frac{10^4 R}{6} \mathr

The magnetic field in a plane electromagnetic wave is $$\mathrm{B}_{\mathrm{y}}=\left(3.5 \times 10^{-7}\right) \sin \le

A real gas within a closed chamber at $$27^{\circ} \mathrm{C}$$ undergoes the cyclic process as shown in figure. The gas

Five charges $$+q,+5 q,-2 q,+3 q$$ and $$-4 q$$ are situated as shown in the figure. The electric flux due to this confi

UV light of $$4.13 \mathrm{~eV}$$ is incident on a photosensitive metal surface having work function $$3.13 \mathrm{~eV}

The $$I$$-$$V$$ characteristics of an electronic device shown in the figure. The device is :

The energy released in the fusion of $$2 \mathrm{~kg}$$ of hydrogen deep in the sun is $$E_H$$ and the energy released i

A hydrogen atom in ground state is given an energy of $$10.2 \mathrm{~eV}$$. How many spectral lines will be emitted due

A proton and a deutron $$(q=+\mathrm{e}, m=2.0 \mathrm{u})$$ having same kinetic energies enter a region of uniform magn

The temperature of a gas is $$-78^{\circ} \mathrm{C}$$ and the average translational kinetic energy of its molecules is

The excess pressure inside a soap bubble is thrice the excess pressure inside a second soap bubble. The ratio between th

A spherical ball of radius $$1 \times 10^{-4} \mathrm{~m}$$ and density $$10^5 \mathrm{~kg} / \mathrm{m}^3$$ falls freel

The de-Broglie wavelength associated with a particle of mass $$m$$ and energy $$E$$ is $$h / \sqrt{2 m E}$$. The dimensi

A square loop of side $$15 \mathrm{~cm}$$ being moved towards right at a constant speed of $$2\mathrm{~cm} / \mathrm{s}$

A $$1 \mathrm{~kg}$$ mass is suspended from the ceiling by a rope of length $$4 \mathrm{~m}$$. A horizontal force '$$F$$

The following figure represents two biconvex lenses $$L_1$$ and $$L_2$$ having focal length $$10 \mathrm{~cm}$$ and $$15

The resultant of two vectors $$\vec{A}$$ and $$\vec{B}$$ is perpendicular to $$\vec{A}$$ and its magnitude is half that

An electric field $$\vec{E}=(2 x \hat{i}) N C^{-1}$$ exists in space. A cube of side $$2 \mathrm{~m}$$ is placed in the

To determine the resistance (R) of a wire, a circuit is designed below. The $$V$$-$$I$$ characteristic curve for this ci

A circular disc reaches from top to bottom of an inclined plane of length $$l$$. When it slips down the plane, if takes

A force $$(3 x^2+2 x-5) \mathrm{N}$$ displaces a body from $$x=2 \mathrm{~m}$$ to $$x=4 \mathrm{~m}$$. Work done by this

A particle of mass $$0.50 \mathrm{~kg}$$ executes simple harmonic motion under force $$F=-50(\mathrm{Nm}^{-1}) x$$. The

At room temperature $$(27^{\circ} \mathrm{C})$$, the resistance of a heating element is $$50 \Omega$$. The temperature c

A straight magnetic strip has a magnetic moment of $$44 \mathrm{~Am}^2$$. If the strip is bent in a semicircular shape,

Monochromatic light of wavelength $$500 \mathrm{~nm}$$ is used in Young's double slit experiment. An interference patter

A capacitor of reactance $$4 \sqrt{3} \Omega$$ and a resistor of resistance $$4 \Omega$$ are connected in series with an