The number of element from the following that do not belong to lanthanoids is $$\mathrm{Eu}, \mathrm{Cm}, \mathrm{Er}, \

A conductivity cell with two electrodes (dark side) are half filled with infinitely dilute aqueous solution of a weak el

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At $$-20^{\circ} \mathrm{C}$$ and $$1 \mathrm{~atm}$$ pressure, a cylinder is filled with equal number of $$\mathrm{H}_2

The electron affinity value are negative for A. $$\mathrm{Be} \rightarrow \mathrm{Be}^{-}$$ B. $$\mathrm{N} \rightarrow

Consider the following complexes (A) $$\left[\mathrm{CoCl}\left(\mathrm{NH}_3\right)_5\right]^{2+}$$, (B) $$\left[\mathr

Functional group present in sulphonic acids is :

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Given below are two statements : Statement I : Gallium is used in the manufacturing of thermometers. Statement II : A th

The density of '$$x$$' $$\mathrm{M}$$ solution ('$$x$$' molar) of $$\mathrm{NaOH}$$ is $$1.12 \mathrm{~g} \mathrm{~mL}^{

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Which of the following statements are correct? A. Glycerol is purified by vacuum distillation because it decomposes at i

Which of the following material is not a semiconductor.

Which of the following is metamer of the given compound (X) ?

In Reimer - Tiemann reaction, phenol is converted into salicylaldehyde through an intermediate. The structure of interme

Which among the following aldehydes is most reactive towards nucleophilic addition reactions?

DNA molecule contains 4 bases whose structure are shown below. One of the structures is not correct, identify the incorr

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Given below are two statements : Statement I : Piciric acid is 2,4,6 - trinitrotoluene. Statement II : Phenol - 2,4 - di

The major product of the following reaction is P. $$\mathrm{CH}_3 \mathrm{C}\equiv\mathrm{C}-\mathrm{CH}_3$$ $$\xrightar

Time required for $$99.9 \%$$ completion of a first order reaction is _________ times the time required for completion o

Consider the dissociation of the weak acid HX as given below $$\mathrm{HX}(\mathrm{aq}) \rightleftharpoons \mathrm{H}^{+

An ideal gas, $$\overline{\mathrm{C}}_{\mathrm{v}}=\frac{5}{2} \mathrm{R}$$, is expanded adiabatically against a constan

The major products from the following reaction sequence are product A and product B. The total sum of $$\pi$$ electrons

The difference in the 'spin-only' magnetic moment values of $$\mathrm{KMnO}_4$$ and the manganese product formed during

$$9.3 \mathrm{~g}$$ of pure aniline upon diazotisation followed by coupling with phenol gives an orange dye. The mass of

Number of molecules from the following which can exhibit hydrogen bonding is _________. (nearest integer)

Among $$\mathrm{CrO}, \mathrm{Cr}_2 \mathrm{O}_3$$ and $$\mathrm{CrO}_3$$, the sum of spin-only magnetic moment values o

Frequency of the de-Broglie wave of electron in Bohr's first orbit of hydrogen atom is _________ $$\times 10^{13} \mathr

A circle is inscribed in an equilateral triangle of side of length 12. If the area and perimeter of any square inscribed

Let a variable line of slope $$m>0$$ passing through the point $$(4,-9)$$ intersect the coordinate axes at the points $$

Let $$A=\{n \in[100,700] \cap \mathrm{N}: n$$ is neither a multiple of 3 nor a multiple of 4$$\}$$. Then the number of e

Let $$C$$ be the circle of minimum area touching the parabola $$y=6-x^2$$ and the lines $$y=\sqrt{3}|x|$$. Then, which o

If $$A(3,1,-1), B\left(\frac{5}{3}, \frac{7}{3}, \frac{1}{3}\right), C(2,2,1)$$ and $$D\left(\frac{10}{3}, \frac{2}{3},

Let the relations $$R_1$$ and $$R_2$$ on the set $$X=\{1,2,3, \ldots, 20\}$$ be given by $$R_1=\{(x, y): 2 x-3 y=2\}$$ a

Let the area of the region enclosed by the curves $$y=3 x, 2 y=27-3 x$$ and $$y=3 x-x \sqrt{x}$$ be $$A$$. Then $$10 A$$

$$\text { If } f(x)=\left\{\begin{array}{ll} x^3 \sin \left(\frac{1}{x}\right), & x \neq 0 \\ 0 & , x=0 \end{array}\righ

The shortest distance between the lines $$\frac{x-3}{2}=\frac{y+15}{-7}=\frac{z-9}{5}$$ and $$\frac{x+1}{2}=\frac{y-1}{1

Let $$y=y(x)$$ be the solution of the differential equation $$\left(2 x \log _e x\right) \frac{d y}{d x}+2 y=\frac{3}{x}

Let $$\alpha, \beta$$ be the distinct roots of the equation $$x^2-\left(t^2-5 t+6\right) x+1=0, t \in \mathbb{R}$$ and $

For $$\alpha, \beta \in \mathbb{R}$$ and a natural number $$n$$, let $$A_r=\left|\begin{array}{ccc}r & 1 & \frac{n^2}{2}

Let $$f:(-\infty, \infty)-\{0\} \rightarrow \mathbb{R}$$ be a differentiable function such that $$f^{\prime}(1)=\lim _\l

$$\int_\limits0^{\pi / 4} \frac{\cos ^2 x \sin ^2 x}{\left(\cos ^3 x+\sin ^3 x\right)^2} d x \text { is equal to }$$

The mean and standard deviation of 20 observations are found to be 10 and 2 , respectively. On rechecking, it was found

Let $$y=y(x)$$ be the solution of the differential equation $$\left(1+x^2\right) \frac{d y}{d x}+y=e^{\tan ^{-1} x}$$, $

The number of triangles whose vertices are at the vertices of a regular octagon but none of whose sides is a side of the

The function $$f(x)=\frac{x^2+2 x-15}{x^2-4 x+9}, x \in \mathbb{R}$$ is

The interval in which the function $$f(x)=x^x, x>0$$, is strictly increasing is

A company has two plants $$A$$ and $$B$$ to manufacture motorcycles. $$60 \%$$ motorcycles are manufactured at plant $$A

Let $$x_1, x_2, x_3, x_4$$ be the solution of the equation $$4 x^4+8 x^3-17 x^2-12 x+9=0$$ and $$\left(4+x_1^2\right)\le

Let a conic $$C$$ pass through the point $$(4,-2)$$ and $$P(x, y), x \geq 3$$, be any point on $$C$$. Let the slope of t

If the second, third and fourth terms in the expansion of $$(x+y)^n$$ are 135, 30 and $$\frac{10}{3}$$, respectively, th

Let $$\alpha \beta \gamma=45 ; \alpha, \beta, \gamma \in \mathbb{R}$$. If $$x(\alpha, 1,2)+y(1, \beta, 2)+z(2,3, \gamma)

Let $$P$$ be the point $$(10,-2,-1)$$ and $$Q$$ be the foot of the perpendicular drawn from the point $$R(1,7,6)$$ on th

Let the first term of a series be $$T_1=6$$ and its $$r^{\text {th }}$$ term $$T_r=3 T_{r-1}+6^r, r=2,3$$, ............

For $$n \in \mathrm{N}$$, if $$\cot ^{-1} 3+\cot ^{-1} 4+\cot ^{-1} 5+\cot ^{-1} n=\frac{\pi}{4}$$, then $$n$$ is equal

Let $$r_k=\frac{\int_0^1\left(1-x^7\right)^k d x}{\int_0^1\left(1-x^7\right)^{k+1} d x}, k \in \mathbb{N}$$. Then the va

Let $$\vec{a}=2 \hat{i}-3 \hat{j}+4 \hat{k}, \vec{b}=3 \hat{i}+4 \hat{j}-5 \hat{k}$$ and a vector $$\vec{c}$$ be such th

Let $$L_1, L_2$$ be the lines passing through the point $$P(0,1)$$ and touching the parabola $$9 x^2+12 x+18 y-14=0$$. L

A bullet of mass $$50 \mathrm{~g}$$ is fired with a speed $$100 \mathrm{~m} / \mathrm{s}$$ on a plywood and emerges with

The specific heat at constant pressure of a real gas obeying $$P V^2=R T$$ equation is:

The correct truth table for the following logic circuit is :

Electromagnetic waves travel in a medium with speed of $$1.5 \times 10^8 \mathrm{~m} \mathrm{~s}^{-1}$$. The relative pe

To find the spring constant $$(k)$$ of a spring experimentally, a student commits $$2 \%$$ positive error in the measure

The value of unknown resistance $$(x)$$ for which the potential difference between $$B$$ and $$D$$ will be zero in the a

A light string passing over a smooth light pulley connects two blocks of masses $$m_1$$ and $$m_2\left(\right.$$ where $

To project a body of mass $$m$$ from earth's surface to infinity, the required kinetic energy is (assume, the radius of

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Which of the following phenomena does not explain by wave nature of light. A. reflection B. diffraction C. photoelectric

Four particles $$A, B, C, D$$ of mass $$\frac{m}{2}, m, 2 m, 4 m$$, have same momentum, respectively. The particle with

In photoelectric experiment energy of $$2.48 \mathrm{~eV}$$ irradiates a photo sensitive material. The stopping potentia

While measuring diameter of wire using screw gauge the following readings were noted. Main scale reading is $$1 \mathrm{

Given below are two statements : Statement I : In an LCR series circuit, current is maximum at resonance. Statement II :

$$\sigma$$ is the uniform surface charge density of a thin spherical shell of radius R. The electric field at any point

An element $$\Delta l=\Delta x\hat{i}$$ is placed at the origin and carries a large current $$I=10 \mathrm{~A}$$. The ma

A small ball of mass $$m$$ and density $$\rho$$ is dropped in a viscous liquid of density $$\rho_0$$. After sometime, th

A train starting from rest first accelerates uniformly up to a speed of $$80 \mathrm{~km} / \mathrm{h}$$ for time $$t$$,

A sample contains mixture of helium and oxygen gas. The ratio of root mean square speed of helium and oxygen in the samp

The ratio of the shortest wavelength of Balmer series to the shortest wavelength of Lyman series for hydrogen atom is :

A big drop is formed by coalescing 1000 small droplets of water. The ratio of surface energy of 1000 droplets to that of

If the radius of earth is reduced to three-fourth of its present value without change in its mass then value of duration

A particle is doing simple harmonic motion of amplitude $$0.06 \mathrm{~m}$$ and time period $$3.14 \mathrm{~s}$$. The m

Three infinitely long charged thin sheets are placed as shown in figure. The magnitude of electric field at the point $$

Radius of a certain orbit of hydrogen atom is 8.48 $$\mathop A\limits^o$$. If energy of electron in this orbit is $$E /

For three vectors $$\vec{A}=(-x \hat{i}-6 \hat{j}-2 \hat{k}), \vec{B}=(-\hat{i}+4 \hat{j}+3 \hat{k})$$ and $$\vec{C}=(-8

The refractive index of prism is $$\mu=\sqrt{3}$$ and the ratio of the angle of minimum deviation to the angle of prism

A wire of resistance $$R$$ and radius $$r$$ is stretched till its radius became $$r / 2$$. If new resistance of the stre

When a $$d c$$ voltage of $$100 \mathrm{~V}$$ is applied to an inductor, a $$d c$$ current of $$5 \mathrm{~A}$$ flows th

A circular coil having 200 turns, $$2.5 \times 10^{-4} \mathrm{~m}^2$$ area and carrying $$100 \mu \mathrm{A}$$ current