The wavelength associated with the electron moving in the first orbit of hydrogen atom with velocity $$2.2 \times 10^6 \

The energy required (in eV) to excite an electron of H -atom from the ground state to the third state is

An element '$$X$$' with the atomic number 13 forms a complex of the type $$[\mathrm{XCl}(\mathrm{H}_2 \mathrm{O})_5]^{2+

In which of the following oxides of three elements $$X, Y$$ and $$Z$$ are correctly arranged in the increasing order of

In the Lewis dot structure of carbonate ion shown under the formal charges on the oxygen atoms 1, 2 and 3 are respective

The set of species having only fractional bond order values is

Identify the correct variation of pressure and volume of a real gas $$(A)$$ and an ideal gas ($$B$$) at constant tempera

What are the oxidation numbers of S atoms in $$\mathrm{S}_4 \mathrm{O}_6^{2-}$$ ?

50 g of a substance is dissolved in 1 kg of water at $$+90^{\circ} \mathrm{C}$$. The temperature is reduced to $$+10^{\c

Identify the correct statements from the following. I. At 0 K , the entropy of pure crystalline materials approach zero.

Use the data from table to estimate the enthalpy of formation of $$\mathrm{CH}_3 \mathrm{CHO}$$. .tg {border-collapse:

At 500 K , for the reaction $$\mathrm{N}_2(\mathrm{~g})+3 \mathrm{H}_2(\mathrm{~g}) \rightleftharpoons 2 \mathrm{NH}_3(\

The relative basic strength of the compounds is correctly shown in the option.

Calcium carbide $$+\mathrm{D}_2 \mathrm{O} \longrightarrow \underline{X}+\mathrm{Ca}(\mathrm{OD})_2$$. The hybridisation

Identify the correct statements from the following. (A) $$\mathrm{BeSO}_4$$ is soluble in water. (B) BeO is an amphoteri

The two major constituents of Portland cement are

Identify the $$P$$ and $$Q$$ of the following reaction $$P+Q \longrightarrow\left[B(O H)_4\right]^{-}+\mathrm{H}_3 \math

Identify the species, which does not exist?

The IUPAC name of the following compound is

The gaseous mixture used for welding of metals is

An element crystallising in fcc lattice has a density of $$8.92 \mathrm{~g} \mathrm{~cm}^{-3}$$ and edge length of $$3.6

Which of the following statement is correct for fcc lattice?

0.05 mole of a non-volatile solute is dissolved in 500 g of water. What is the depression in freezing point of resultant

Which of the following form an ideal solution? I. Chloroethane and bromoethane II. Benzene and toluene III. $$n$$-hexane

96.5 amperes current is passed through the molten $$\mathrm{AlCl}_3$$ for 100 seconds. The mass of aluminium deposited a

The rate constant of a reaction at 500 K and 700 K are $$0.02 \mathrm{~s}^{-1}$$ and $$0.2 \mathrm{~s}^{-1}$$ respective

Match the following .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-color:black;border-style:solid;bord

The correct order of coagulating power of the following ions to coagulate the positive sol is $$\mathrm{\mathop {{{[Fe{{

Assertion (A) 16 th group elements have higher ionisation enthalpy values than 15 th group elements in the corresponding

Assertion (A) Fluorine has smaller negative electron gain enthalpy than chlorine. Reason (R) The electron-electron repul

Identify the isoelectronic pair of ions from the following.

The homoleptic complex in the following is

Carbohydrates are stored in plants and animals in which of the following forms respectively?

Glycylalanine is a dipeptide of which amino acids?

Identify the major product formed from the following reaction.

Identify the major product of the following reaction.

Identify the product(s) formed in the following reaction.

Which compound is formed on catalytic hydrogenation of carbon monoxide at high $$p$$ and high $$T$$ in presence of $$\ma

Identify the major product from the following reaction sequence.

Arrange the following in decreasing order of their boiling points.

$$f(x)=\log \left(\left(\frac{2 x^2-3}{x}\right)+\sqrt{\frac{4 x^4-11 x^2+9}{|x|}}\right) \text { is }$$

Let $$f: R-\left\{\frac{-1}{2}\right\} \rightarrow R$$ be defined by $$f(x)=\frac{x-2}{2 x+1}$$. If $$\alpha$$ and $$\be

If $$A=\left[\begin{array}{lll}3 & -3 & 4 \\ 2 & -3 & 4 \\ 0 & -1 & 1\end{array}\right]$$, then $$A A^T$$ is a

If $$A X=D$$ represents the system of simultaneous linear equations $$x+y+z=6, 5 x-y+2 z=3$$ and $$2 x+y-z=-5$$, then (A

If $$A=\left[\begin{array}{ll}1 & 0 \\ 2 & 1\end{array}\right], B=\left[\begin{array}{ll}1 & 3 \\ 0 & 1\end{array}\right

Let $$G(x)=\left[\begin{array}{ccc}\cos x & -\sin x & 0 \\ \sin x & \cos x & 0 \\ 0 & 0 & 1\end{array}\right]$$. If $$x+

By simplifying $$i^{18}-3 i^7+i^2\left(1+i^4\right)(i)^{22}$$, we get

The values of $$x$$ for which $$\sin x+i \cos 2 x$$ and $$\cos x-i \sin 2 x$$ are conjugate to each other are

The locus of a point $$z$$ satisfying $$|z|^2=\operatorname{Re}(z)$$ is a circle with centre

If $$\sin ^4 \theta \cos ^2 \theta=\sum_\limits{n=0}^{\infty} a_{2 n} \cos 2 n \theta$$, then the least $$n$$ for which

If $$S=\left\{m \in R: x^2-2(1+3 m) x+7(3+2 m)=0\right.$$ has distinct roots}, then the number of elements in $$S$$ is

$$4^x-3^{x-\frac{1}{2}}=3^{x+\frac{1}{2}}-2^{2 x-1} \Rightarrow x=$$

The sum of the real roots of the equation $$x^4-2 x^3+x-380=0$$ is

If one root of the cubic equation $$x^3+36=7 x^2$$ is double of another, then the number of negative roots are

$$\text { If } 10{ }^n C_2=3^{n+1} C_3 \text {, then the value of } n \text { is }$$

There are 10 points in a plane, out of these 6 are collinear. If $$N$$ is the total number of triangles formed by joinin

205 students take an examination of whom 105 pass in English, 70 students pass in Mathematics and 30 students pass in bo

In an examination, the maximum marks for each of three subjects is $$n$$ and that for the fourth subject is $$2 n$$. The

$$\frac{2 x^2+1}{x^3-1}=\frac{A}{x-1}+\frac{B x+C}{x^2+x+1} \Rightarrow 7 A+2 B+C=$$

If $$\sin \theta=-\frac{3}{4}$$, then $$\sin 2 \theta=$$

$$\begin{aligned} & \frac{1}{\sin 1^{\circ} \sin 2^{\circ}}+\frac{1}{\sin 2^{\circ} \sin 3^{\circ}}+\ldots +\frac{1}{\si

Which of the following trigonometric values are negative? I. $$\sin \left(-292^{\circ}\right)$$ II. $$\tan \left(-190^{\

$$\text { If } \sin \theta+\operatorname{cosec} \theta=4, \text { then } \sin ^2 \theta+\operatorname{cosec}^2 \theta=$$

$$\sin ^2 \frac{2 \pi}{3}+\cos ^2 \frac{5 \pi}{6}-\tan ^2 \frac{3 \pi}{4}=$$

If $$2 \cosh 2 x+10 \sinh 2 x=5$$, then $$x=$$

In any $$\triangle A B C, \frac{\cos A}{a}+\frac{\cos B}{b}+\frac{\cos C}{c}=$$

In a $$\triangle A B C$$, if $$r_1=36, r_2=18$$ and $$r_3=12$$, then $$s=$$

In a $$\triangle A B C, a=6, b=5$$ and $$c=4$$, then $$\cos 2 A=$$

a, b, c are non-coplanar vectors. If $$\mathbf{a}+3 \mathbf{b}+4 \mathbf{c}=x(\mathbf{a}-2 \mathbf{b}+3 \mathbf{c})+y(\m

Three vectors of magnitudes $$a, 2 a, 3 a$$ are along the directions of the diagonals of 3 adjacent faces of a cube that

If $$\mathbf{a}$$ is collinear with $$\mathbf{b}=3 \hat{i}+6 \hat{j}+6 \hat{k}$$ and $$\mathbf{a} \cdot \mathbf{b}=27$$,

Let $$a, b$$ and $$c$$ be unit vectors such that $$a$$ is perpendicular to the plane containing $$\mathbf{b}$$ and $$\ma

Let $$\mathbf{F}=2 \hat{i}+2 \hat{j}+5 \hat{k}, A=(1,2,5), B=(-1,-2,-3)$$ and $$\mathbf{B A} \times \mathbf{F}=4 \hat{i}

If the mean deviation of the data $$1,1+d 1+2 d, \ldots, 1+100 d,(d>0)$$ from their mean is 255, then '$$d$$' is equal t

The probability of getting a sum 9 when two dice are thrown is

If $$A$$ and $$B$$ are two events such that $$P(B) \neq 0$$ and $$P(B) \neq 1$$, then $$P(\bar{A} \mid \bar{B})$$ is

Two brothers $$X$$ and $$Y$$ appeared for an exam. Let $$A$$ be the event that $$X$$ has passed the exam and $$B$$ is th

A bag contains 4 red and 3 black balls. A second bag contains 2 red and 3 black balls. One bag is selected at random. If

In a Binomial distribution, if '$$n$$' is the number of trials and the mean and variance are 4 and 3 respectively, then

For a Poisson distribution, if mean $$=l$$, variance $$=m$$ and $$l+m=8$$, then $$e^4[1-P(X>2)]=$$

The locus of mid-points of points of intersection of $$x \cos \theta+y \sin \theta=1$$ with the coordinate axes is

Suppose $$P$$ and $$Q$$ lie on $$3 x+4 y-4=0$$ and $$5 x-y-4=0$$ respectively. If the mid-point of $$P Q$$ is $$(1,5)$$,

The length of intercept of $$x+1=0$$ between the lines $$3 x+2 y=5$$ and $$3 x+2 y=3$$ is

Suppose that the three points $$A, B$$ and $$C$$ in the plane are such that their $$x$$-coordinates as well as $$y$$-coo

Suppose the slopes $$m_1$$ and $$m_2$$ of the lines represented by $$a x^2+2 h x y+b y^2=0$$ satisfy $$3\left(m_1-m_2\ri

Suppose that the sides passing through the vertex $$(\alpha, \beta)$$ of a triangle are bisected at right angles by the

The radius of the circle having. $$3 x-4 y+4=0$$ and $$6 x-8 y-7=0$$ as its tangents is

A circle is such that $$(x-2) \cos \theta+(y-2) \sin \theta=1$$ touches it for all values of $$\theta$$. Then, the circl

The least distance of the point $$(10,7)$$ from the circle $$x^2+y^2-4 x-2 y-20=0$$ is

Suppose that the $$x$$-coordinates of the points $$A$$ and $$B$$ satisfy $$x^2+2 x-a^2=0$$ and their $$y$$-coordinates s

The radical centre of the three circles $$x^2+y^2-1=0, x^2+y^2-8 x+15=0$$ and $$x^2+y^2+10 y+24=0$$ is

Which of the following represents a parabola?

If the angle between the straight lines joining the foci and the ends of the minor axis of the ellipse $$\frac{x^2}{a^2}

The locus of point of intersection of tangents at the ends of normal chord of the hyperbola $$x^2-y^2=a^2$$ is

If $$e_1$$ and $$e_2$$ are the eccentricities of the hyperbola $$16 x^2-9 y^2=1$$ and its conjugate respectively. Then,

If P divides the line segment joining the points $$A(1,2,-1)$$ and $$B(-1,0,1)$$ externally in the ratio 1 : 2 and $$Q=(

If the direction cosines of a line are $$\left(\frac{a}{\sqrt{83}}, \frac{5}{\sqrt{83}}, \frac{c}{\sqrt{83}}\right)$$ an

Let the plane $$\pi$$ pass through the point (1, 0, 1) and perpendicular to the planes $$2x + 3y - z = 2$$ and $$x - y +

$$\lim _\limits{x \rightarrow-\infty} \log _e(\cosh x)+x=$$

If $$a, b$$ and $$c$$ are three distinct real numbers and $$\lim _\limits{x \rightarrow \infty} \frac{(b-c) x^2+(c-a) x+

$$\lim _\limits{x \rightarrow-\infty} \frac{3|x|-x}{|x|-2 x}-\lim _\limits{x \rightarrow 0} \frac{\log \left(1+x^3\right

If $$3 f(\cos x)+2 f(\sin x)=5 x$$, then $$f^{\prime}(\cos x)+f^{\prime}(\sin x)=$$

Assertion (A) $$\frac{d}{d x}\left(\frac{x^2 \sin x}{\log x}\right)=\frac{x^2 \sin x}{\log x}\left(\cot x+\frac{2}{x}-\f

If $$x=f(\theta)$$ and $$y=g(\theta)$$, then $$\frac{d^2 y}{d x^2}=$$

If the normal drawn at a point $$P$$ on the curve $$3 y=6 x-5 x^3$$ passes through $$(0,0)$$, then the positive integral

The line joining the points $$(0,3)$$ and $$(5,-2)$$ is a tangent to the curve $$y=\frac{c}{x+1}$$, then $$c=$$

$$y=x^3-a x^2+48 x+7$$ is an increasing function for all real values of $$x$$, then $$a$$ lies in the interval

If $$a, b>0$$, then minimum value of $$y=\frac{b^2}{a-x}+\frac{a^2}{x}, 0

The point on the curve $$y=x^2+4 x+3$$ which is closest to the line $$y=3 x+2$$ is

$$\int \frac{3 x+4}{x^3-2 x+4} d x=\log f(x)+C \Rightarrow f(3)=$$

$$\int \frac{e^{\tan ^{-1} x}}{1+x^2}\left[\left(\sec ^{-1} \sqrt{1+x^2}\right)^2+\cos ^{-1}\left(\frac{1-x^2}{1+x^2}\ri

$$\int \frac{d x}{(x-3)^{\frac{4}{5}}(x+1)^{\frac{6}{5}}}=$$

If $$I_n=\int\left(\cos ^n x+\sin ^n x\right) d x$$ and $$I_n-\frac{n-1}{n} I_{n-2} =\frac{\sin x \cos x}{n} f(x)$$, the

Let $$T>0$$ be a fixed number. $$f: R \rightarrow R$$ is a continuous function such that $$f(x+T)=f(x), x \in R$$ If $$I

$$\int_\limits1^3 x^n \sqrt{x^2-1} d x=6 \text {, then } n=$$

[ . ] represents greatest integer function, then $$\int_{-1}^1(x[1+\sin \pi x]+1) d x=$$

$$\begin{aligned} & \lim _{n \rightarrow \infty}\left[\frac{n}{(n+1) \sqrt{2 n+1}}+\frac{n}{(n+2) \sqrt{2(2 n+2)}}\right

The general solution of the differential equation $$\frac{d y}{d x}=\cos ^2(3 x+y)$$ is $$\tan ^{-1}\left(\frac{\sqrt{3}

If the general solution of the differential equation $$\cos ^2 x \frac{d y}{d x}+y=\tan x$$ is $$y=\tan x-1+C e^{-\tan x

Assertion (A) Order of the differential equations of a family of circles with constant radius is two. Reason (R) An alge

The energy of $$E$$ of a system is function of time $$t$$ and is given by $$E(t)=\alpha t-\beta t^3$$, where $$\alpha$$

A student is at a distance 16 m from a bus when the bus begins to move with a constant acceleration of $$9 \mathrm{~m} \

The component of a vector $$\mathbf{P}=3 \hat{i}+4 \hat{j}$$ along the direction $$(\hat{i}+2 \hat{j})$$ is

A projectile is launched from the ground, such that it hits a target on the ground which is 90 m away. The minimum veloc

If two vectors $$\mathbf{A}$$ and $$\mathbf{B}$$ are mutually perpendicular, then the component of $$\mathbf{A}-\mathbf{

A body is travelling with $$10 \mathrm{~ms}^{-1}$$ on a rough horizontal surface. It's velocity after 2 s is $$4 \mathrm

A small disc of mass $$m$$ slides down with initial velocity zero from the top $$(A)$$ of a smooth hill of height $$H$$

A block of mass 50 kg is pulled with a constant speed of $$4 \mathrm{~ms}^{-1}$$ across a horizontal floor by an applied

Ball $$A$$ of mass 1 kg moving along a straight line with a velocity of $$4 \mathrm{~ms}^{-1}$$ hits another ball $$B$$

A solid cylinder of radius $$R$$ is at rest at a height $$h$$ on an inclined plane. If it rolls down then its velocity o

A particle is executing simple harmonic motion with an instantaneous displacement $$x=A \sin ^2\left(\omega t-\frac{\pi}

If the amplitude of a lightly damped oscillator decreases by $$1.5 \%$$ then the mechanical energy of the oscillator los

Statement (A) Two artificial satellites revolving in the same circular orbit have same period of revolution. Statement (

Two wires $$A$$ and $$B$$ of same cross-section are connected end to end. When same tension is created in both wires, th

5 g of ice at $$-30^{\circ} \mathrm{C}$$ and 20 g of water at $$35^{\circ} \mathrm{C}$$ are mixed together in a calorime

A hydraulic lift is shown in the figure. The movable pistons $$A, B$$ and $$C$$ are of radius $$10 \mathrm{~cm}, 100 \ma

An iron sphere having diameter $$D$$ and mass $$M$$ is immersed in hot water so that the temperature of the sphere incre

The work done by a Carnot engine operating between 300 K and 400 K is 400 J. The energy exhausted by the engine is

The slopes of the isothermal and adiabatic $$p-V$$ graphs of a gas are by $$S_I$$ and $$S_A$$ respectively. If the heat

The number of rotational degrees of freedom of a diatomic molecule

Two cars are moving towards each other at the speed of $$50 \mathrm{~ms}^{-1}$$. If one of the cars blows a horn at a fr

A needle is lying at the bottom of a water tank of height 12 cm. The apparent depth of the needle measured by a microsco

Young's double slit experiment is conducted with monochromatic light of wavelength 5000$$\mathop A\limits^o $$, with sli

A large number of positive charges each of magnitude $$q$$ are placed along the $$X$$-axis at the origin and at every 1

The capacitance between the points A and B in the following figure.

The electric field in a region of space is given as $$\mathbf{E}=\left(5 \mathrm{NC}^{-1}\right) x \hat{i}$$. Consider p

In the given circuit values of $$I_1, I_2, I_3$$ are respectively

The resistance of wire at $$0^{\circ} \mathrm{C}$$ is $$20 \Omega$$. If the temperature coefficient of the resistance is

An electron having kinetic energy of 100 eV circulates in a path of radius 10 cm in a magnetic field. The magnitude of m

A particle of mass $$2.2 \times 10^{-30} \mathrm{~kg}$$ and charge $$1.6 \times 10^{-19} \mathrm{C}$$ is moving at a spe

Two short magnets of equal dipole moments $$M$$ are fastened perpendicularly at their centres. The magnitude of the magn

A circular loop of wire of radius 14 cm is placed in magnetic field directed perpendicular to the plane of the loop. If

An $$R-L-C$$ circuit consists of a $$150 \Omega$$ resistor, $$20 \mu \mathrm{F}$$ capacitor and a 500 mH inductor connec

The magnetic field in a plane electromagnetic wave is given as $$\mathbf{B}=\left(3 \times 10^{-7} \mathrm{~T}\right) \

In Young's double slit experiment the slits are 3 mm apart and are illuminated by light of two wavelengths $$3750 \matho

The following statement is correct in the case of photoelectric effect

An electron in the hydrogen atom excites from 2nd orbit to 4th orbit then the change in angular momentum of the electron

Choose the correct statement of the following

A ancient discovery found a sample, where $$75 \%$$ of the original carbon ($$\mathrm{C}^{14}$$) remains. Then the age o

Frequencies in the UHF range normally propagate by means of