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Two solutions A and B are prepared by dissolving 1 g of non-volatile solutes X and Y, respectively in 1 kg of water. The

$${K_{{a_1}}}$$, $${K_{{a_2}}}$$ and $${K_{{a_3}}}$$ are the respective ionization constants for the following reactions

The molar conductivity of a conductivity cell filled with 10 moles of 20 mL NaCl solution is $${\Lambda _{m1}}$$ and tha

The first ionization enthalpies of Be, B, N and O follow the order

The correct order of energy of absorption for the following metal complexes is : A : [Ni(en)3]2+ , B : [Ni(NH3)6]2+ , C

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Major product of the following reaction is

What is the major product of the following reaction?

Arrange the following in decreasing acidic strength.

$$C{H_3} - C{H_2} - CN\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{Ether}^{C{H_3}MgBr}} A\buildrel {{H_3}{O^ + }}

Glycosidic linkage between C1 of $$\alpha$$-glucose and C2 of $$\beta$$-fructose is found in

In base vs. acid titration, at the end point methyl orange is present as

56.0 L of nitrogen gas is mixed with excess hydrogen gas and it is found that 20 L of ammonia gas is produced. The volum

When the excited electron of a H atom from n = 5 drops to the ground state, the maximum number of emission lines observe

While performing a thermodynamics experiment, a student made the following observations. HCl + NaOH $$\to$$ NaCl + H2O $

For the decomposition of azomethane. CH3N2CH3(g) $$\to$$ CH3CH3(g) + N2(g), a first order reaction, the variation in par

The sum of number of lone pairs of electrons present on the central atoms of XeO3, XeOF4 and XeF6, is ______________

The spin-only magnetic moment value of M3+ ion (in gaseous state) from the pairs Cr3+ / Cr2+, Mn3+ / Mn2+, Fe3+ / Fe2+ a

A sample of 4.5 mg of an unknown monohydric alcohol, R-OH was added to methylmagnesium iodide. A gas is evolved and is c

The separation of two coloured substances was done by paper chromatography. The distances travelled by solvent front, su

The total number of monobromo derivatives formed by the alkanes with molecular formula C5H12 is (excluding stereo isomer

For $$z \in \mathbb{C}$$ if the minimum value of $$(|z-3 \sqrt{2}|+|z-p \sqrt{2} i|)$$ is $$5 \sqrt{2}$$, then a value Q

The number of real values of $$\lambda$$, such that the system of linear equations 2x $$-$$ 3y + 5z = 9 x + 3y $$-$$ z =

The number of bijective functions $$f:\{1,3,5,7, \ldots, 99\} \rightarrow\{2,4,6,8, \ldots .100\}$$, such that $$f(3) \

The remainder when $$(11)^{1011}+(1011)^{11}$$ is divided by 9 is

$$\lim\limits_{x \rightarrow \frac{\pi}{4}} \frac{8 \sqrt{2}-(\cos x+\sin x)^{7}}{\sqrt{2}-\sqrt{2} \sin 2 x}$$ is equal

If $$A$$ and $$B$$ are two events such that $$P(A)=\frac{1}{3}, P(B)=\frac{1}{5}$$ and $$P(A \cup B)=\frac{1}{2}$$, then

Let $$[t]$$ denote the greatest integer less than or equal to $$t$$. Then the value of the integral $$\int_{-3}^{101}\le

Let the point $$P(\alpha, \beta)$$ be at a unit distance from each of the two lines $$L_{1}: 3 x-4 y+12=0$$, and $$L_{2}

If the ellipse $$\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1$$ meets the line $$\frac{x}{7}+\frac{y}{2 \sqrt{6}}=1$$ on th

Let the foci of the ellipse $$\frac{x^{2}}{16}+\frac{y^{2}}{7}=1$$ and the hyperbola $$\frac{x^{2}}{144}-\frac{y^{2}}{\a

The shortest distance between the lines $$\frac{x+7}{-6}=\frac{y-6}{7}=z$$ and $$\frac{7-x}{2}=y-2=z-6$$ is :

Let $$\vec{a}=\hat{i}-\hat{j}+2 \hat{k}$$ and let $$\vec{b}$$ be a vector such that $$\vec{a} \times \vec{b}=2 \hat{i}-\

If the mean deviation about median for the numbers 3, 5, 7, 2k, 12, 16, 21, 24, arranged in the ascending order, is 6 th

$$2 \sin \left(\frac{\pi}{22}\right) \sin \left(\frac{3 \pi}{22}\right) \sin \left(\frac{5 \pi}{22}\right) \sin \left(\f

Let $$A=\{1,2,3,4,5,6,7\}$$. Define $$B=\{T \subseteq A$$ : either $$1 \notin T$$ or $$2 \in T\}$$ and $$C=\{T \subseteq

Let $$f(x)$$ be a quadratic polynomial with leading coefficient 1 such that $$f(0)=p, p \neq 0$$, and $$f(1)=\frac{1}{3}

Let $$A=\left[\begin{array}{lll} 1 & a & a \\ 0 & 1 & b \\ 0 & 0 & 1 \end{array}\right], a, b \in \mathbb{R}$$. If for s

The sum of the maximum and minimum values of the function $$f(x)=|5 x-7|+\left[x^{2}+2 x\right]$$ in the interval $$\lef

Let $$y=y(x)$$ be the solution of the differential equation $$\frac{d y}{d x}=\frac{4 y^{3}+2 y x^{2}}{3 x y^{2}+x^{3}},

Let $$f$$ be a twice differentiable function on $$\mathbb{R}$$. If $$f^{\prime}(0)=4$$ and $$f(x) + \int\limits_0^x {(x

Let $${a_n} = \int\limits_{ - 1}^n {\left( {1 + {x \over 2} + {{{x^2}} \over 3} + \,\,.....\,\, + \,\,{{{x^{n - 1}}} \ov

Let the area enclosed by the x-axis, and the tangent and normal drawn to the curve $$4{x^3} - 3x{y^2} + 6{x^2} - 5xy - 8

Let $$x = \sin (2{\tan ^{ - 1}}\alpha )$$ and $$y = \sin \left( {{1 \over 2}{{\tan }^{ - 1}}{4 \over 3}} \right)$$. If $

The electric current in a circular coil of 2 turns produces a magnetic induction B1 at its centre. The coil is unwound a

A drop of liquid of density $$\rho$$ is floating half immersed in a liquid of density $${\sigma}$$ and surface tension $

Two billiard balls of mass 0.05 kg each moving in opposite directions with 10 ms$$-$$1 collide and rebound with the same

For a free body diagram shown in the figure, the four forces are applied in the 'x' and 'y' directions. What additional

Capacitance of an isolated conducting sphere of radius R1 becomes n times when it is enclosed by a concentric conducting

The ratio of wavelengths of proton and deuteron accelerated by potential Vp and Vd is 1 : $$\sqrt2$$. Then the ratio of

For an object placed at a distance 2.4 m from a lens, a sharp focused image is observed on a screen placed at a distance

Light wave travelling in air along x-direction is given by $${E_y} = 540\sin \pi \times {10^4}(x - ct)\,V{m^{ - 1}}$$.

When you walk through a metal detector carrying a metal object in your pocket, it raises an alarm. This phenomenon works

A current of 15 mA flows in the circuit as shown in figure. The value of potential difference between the points A and B

The length of a seconds pendulum at a height h = 2R from earth surface will be: (Given R = Radius of earth and accelerat

Sound travels in a mixture of two moles of helium and n moles of hydrogen. If rms speed of gas molecules in the mixture

An object is taken to a height above the surface of earth at a distance $${5 \over 4}$$ R from the centre of the earth.

A bag of sand of mass 9.8 kg is suspended by a rope. A bullet of 200 g travelling with speed 10 ms$$-$$1 gets embedded i

A ball is projected from the ground with a speed 15 ms$$-$$1 at an angle $$\theta$$ with horizontal so that its range an

The maximum error in the measurement of resistance, current and time for which current flows in an electrical circuit ar

Hydrogen atom from excited state comes to the ground state by emitting a photon of wavelength $$\lambda$$. The value of

A particle is moving in a straight line such that its velocity is increasing at 5 ms$$-$$1 per meter. The acceleration o

Three identical spheres each of mass M are placed at the corners of a right angled triangle with mutually perpendicular

A block of ice of mass 120 g at temperature 0$$^\circ$$C is put in 300 g of water at 25$$^\circ$$C. The x g of ice melts

$${x \over {x + 4}}$$ is the ratio of energies of photons produced due to transition of an electron of hydrogen atom fro

Two ideal diodes are connected in the network as shown in figure. The equivalent resistance between A and B is _________

Two parallel plate capacitors of capacity C and 3C are connected in parallel combination and charged to a potential diff

A convex lens of focal length 20 cm is placed in front of a convex mirror with principal axis coinciding each other. The

Magnetic flux (in weber) in a closed circuit of resistance 20 $$\Omega$$ varies with time t(s) at $$\phi$$ = 8t2 $$-$$ 9