If two particles A and B are moving with the same velocity, but wavelength of A is found to be double than that of B. Wh

The spectrum of helium is expected to be similar to that of

On the basis of Bohr’s model, the radius of the 3rd orbit is

To which group of the periodic table does an element having electronic configuration [Ar] 3d$$^5$$ 4s$$^2$$ belong?

Given that ionisation potential and electron gain enthalpy of chlorine are 13eV and 4 eV respectively. The electronegati

Which of the following represents the correct order of increasing electron gain enthalpy with negative sign for the elem

Which of the following will have maximum dipole moment?

In which of the following molecules/ions, the central atom is sp$$^2$$ hybridised? BF$$_3$$, NO$$_2^-$$, NH$$_2^-$$ and

For which molecules among the following, the resultant dipole moment ($$\propto$$) $$\ne$$ 0 ?

Which of the following graphs correctly represents Boyle’s Law?

The density of an ideal gas can be given by ........, where p, V, M, T and R respectively denote pressure, volume, molar

When 20 g of CaCO$$_3$$ is treated with 20 g of HCl, the mass of CO$$_2$$ formed would be

Which among the following species acts as a self-indicator?

If a chemical reaction is known to be non-spontaneous at 298 K but spontaneous at 350 K, then which among the following

Standard entropies of $$X_2, Y_2$$ and $$X Y_3$$ are 60, 40 and $$50 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$$ respectively.

For the reaction $$\mathrm{SO}_2(g)+\frac{1}{2} \mathrm{O}_2(g) \rightleftharpoons \mathrm{SO}_3(g)$$, the percentage yi

Which among the following denotes the correct relationship between $$K_p$$ and $$K_c$$ for the reaction, $$2 A(g) \right

Which metal oxide among the following gives H$$_2$$O$$_2$$ on treatment with dilute acid?

Assertion (A) K, Rb and Cs form superoxides. Reason (R) The stability of superoxides increases from K to Cs due to decre

When borax is dissolved in water, it gives an alkaline solution. The alkaline solution consists the following products

Identify (P) and (Q) in the following reaction.

Green chemistry refers to reactions which

Assertion (A) Sodium acetate on Kolbe’s electrolysis gives ethane. Reason (R) Methyl free radical is formed at cathode.

When difference in boiling points of two liquids is too small, then the separation is carried out by

In Lassaigne’s test for halogens, it is necessary to remove X and Y from the sodium fusion extract, if nitrogen and sulp

The following effect is known as

Which of the following will form an ideal solution?

The molal elevation constant is the ratio of elevation in boiling point to

When a current of 10 A is passes through molten AlCl$$_3$$ for 1.608 minutes. The mass of Al deposited will be [Atomic m

The molar conductivities $$\left(\lambda_{\mathrm{m}}^{\Upsilon}\right)$$ at infinite dilution of $$\mathrm{KBr}, \mathr

If the rate constant for a first order reaction is $$2.303 \times 10^{-3} \mathrm{~s}^{-1}$$. Find the time required to

A plot of $$\log (x / m)$$ versus $$\log (p)$$ for adsorption of a gas on a solid gives a straight line with a slope of

Match the following compounds with their corresponding physical properties. .tg {border-collapse:collapse;border-spaci

What is coordination number of the metal in $$\mathrm{{[Co{(en)_2}C{l_2}]^{2 + }}}$$ ?

A compound A is used in paints instead of salts of lead. Compound A is obtained when a white compound B is strongly heat

Identify the product of the following reaction.

The number of optical isomers possible for 2-bromo-3-chloro butane are

During the action of enzyme ‘zymase’ glucose is converted into .............., with the liberation of carbon dioxide gas

The total number of products formed in the following reaction sequence is $$\begin{gathered}\mathrm{CH}_3 \mathrm{COCl}

In the following reaction sequence, identify product ‘Q’ and reagent ‘R’.

Let $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ be defined by $$f(x)=2 x+1$$ and $$g(x)=x^2-2$$ determine $$(g \ci

Given, the function $$f(x)=\frac{a^x+a^{-x}}{2},(a>2)$$, then $$f(x+y)+f(x-y)$$ is equal to

If $$f$$ is a function defined on $$(0,1)$$ by $$f(x)=\min \{x-[x],-x-[x]\}$$, then $$(f \circ f o f o f)(x)$$ is equal

$$n \in N$$ then, the statement $$8 n+16 \leq 2^n$$ is true for

The equation whose roots are the values of the equation $$\left| {\matrix{ 1 & { - 3} & 1 \cr 1 & 6 & 4 \cr

Let a and b be non-zero real numbers such that $$ab=5/2$$ and given $$A = \left[ {\matrix{ a & { - b} \cr b & a

If $$A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right], 10 B=\left[\begin{array}{ccc}4 &

The rank of the matrix $$\left[\begin{array}{ccc}4 & 2 & (1-x) \\ 5 & k & 1 \\ 6 & 3 & (1+x)\end{array}\right]$$ is 1 ,

If $$a_1, a_2, \ldots . a_9$$ are in GP, then $$\left|\begin{array}{lll}\log a_1 & \log a_2 & \log a_3 \\ \log a_4 & \lo

$$(\sin \theta-i \cos \theta)^3$$ is equal to

Real part of $$(\cos 4+i \sin 4+1)^{2020}$$ is

If $${({x^2} + 5x + 5)^{x + 5}} = 1$$, then the number of integers satisfying this equation is

Let $$f(x)=x^3+a x^2+b x+c$$ be polynomial with integer coefficients. If the roots of $$f(x)$$ are integer and are in Ar

The sum of the roots of the equation $$e^{4 t}-10 e^{3 t}+29 e^{2 t}-22 e^t+4=0$$ is

If a person has 3 coins of different denominations, the number of different sums can be formed is

There are 7 identical white balls and 3 identical black balls. The number of distinguishable arrangements in a row of al

The number of ways of distributing eight identical rings to three different girls so that every girl gets at least one r

If $$\frac{x^4}{(x-1)(x-2)}=f(x)+\frac{A}{x-1}+\frac{B}{x-2}$$, then

$$\tan 2 \alpha \cdot \tan (30 Y-\alpha)+\tan 2 \alpha \cdot \tan (60 Y-\alpha)+\tan (60 \Upsilon-\alpha) \cdot \tan (30

If $$\sin \alpha - \cos \alpha = m$$ and $$\sin 2\alpha = n - {m^2}$$, where $$ - \sqrt 2 \le m \le \sqrt 2 $$, then

The value of $$x$$ satisfying the equation $$3 \operatorname{cosec} x=4 \sin x$$ are

If $$\tan ^{-1}\left[\frac{1}{1+1 \cdot 2}\right]+\tan ^{-1}\left[\frac{1}{1+2 \cdot 3}\right]+\ldots+\tan ^{-1} \left[\

If $$\sinh u=\tan \theta$$, then $$\cosh u$$ is equal to

In a $$\Delta ABC$$, if a = 3, b = 4 and $$\sin A=\frac{3}{4}$$, then $$\angle CBA$$ is equal to

In $$\Delta ABC,A=75\Upsilon$$ and $$B=45\Upsilon$$, then the value of $$b+c\sqrt2$$ is equal to

In $$\triangle A B C$$, suppose the radius of the circle opposite to an $$\angle A$$ is denoted by $$r_1$$, similarly $$

A vector makes equal angles $$\alpha$$ with $$X$$ and $$Y$$-axis, and $$90 \Upsilon$$ with $$Z$$-axis. Then, $$\alpha$$

Angle made by the position vector of the point (5, $$-$$4, $$-$$3) with the positive direction of X-axis is

If D, E and F are respectively mid-points of AB, AC and BC in $$\Delta ABC$$, then BE + AF is equal to

If the volume of the parallelopiped formed by the vectors $$\hat{\mathbf{i}}+a \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\

If $$\mathbf{a}=\frac{3}{2} \hat{\mathbf{k}}$$ and $$\mathbf{b}=\frac{2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf

Let $$\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \h

If $$\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\

If $$\mathbf{a}$$ and $$\mathbf{b}$$ are two vectors such that $$|\mathbf{a}|=2, |\mathbf{b}|=3$$ and $$\mathbf{a}+t \ma

The variance of the variates 112, 116, 120, 125 and 132 about their AM is

Which of the following set of data has least standard deviation?

12 balls are distributed among 3 boxes, then the probability that the first box will contain 3 balls is

If the letters of the word REGULATIONS be arranged in such a way that relative positions of the letters of the word GULA

A random variable X has the probability distribution .tg {border-collapse:collapse;border-spacing:0;} .tg td{border-c

A die is tossed thrice. If event of getting an even number is a success, then the probability of getting at least 2 succ

If the axes are rotated through an angle $$45 \Upsilon$$, the coordinates of the point $$(2 \sqrt{2},-3 \sqrt{2})$$ in t

the sum of the squares of the intercepts made the line $$5x-2y=10$$ on the coordinate axes equals

For three consecutive odd integers $$a \cdot b$$ and $$c$$, if the variable line $$a x+b y+c=0$$ always passes through t

The line which is parallel to X-axis and crosses the curve $$y=\sqrt x$$ at an angle of 45$$\Upsilon$$ is

If $$2x+3y+4=0$$ is the perpendicular bisector of the line segment joining the points A(1, 2) and B($$\alpha,\beta$$), t

The equation of the pair of straight lines perpendicular to the pair $$2 x^2+3 x y+2 y^2+10 x+5 y=0$$ and passing though

If the centroid of the triangle formed by the lines $$2 y^2+5 x y-3 x^2=0$$ and $$x+y=k$$ is $$\left(\frac{1}{18}, \frac

If $$m_1$$ and $$m_2,\left(m_1>m_2\right)$$ are the slopes of the lines represented by $$5 x^2-8 x y+3 y^2=0$$, then $$m

If the slope of one of the lines represented by $$a x^2+2 h x y+b y^2=0$$ is the square of the other then, $$\left|\frac

Find the equations of the tangents drawn to the circle $$x^2+y^2=50$$ at the points where the line $$x+7=0$$ meets it.

If the chord of contact of tangents from a point on the circle $$x^2+y^2=r_1^2$$ to the circle $$x^2+y^2=r_2^2$$ touches

Find the equation of the circle passing through $$(1,-2)$$ and touching the $$X$$-axis at $$(3,0)$$.

Let $$L_1$$ be a straight line passing through the origin and $$L_2$$ be the straight line $$x+y=1$$. If the intercepts

The radius of the circle whose center lies at $$(1,2)$$ while cutting the circle $$x^2+y^2+4 x+16 y-30=0$$ orthogonally,

The point which has the same power with respect to each of the circles $$x^2+y^2-8 x+40=0, x^2+y^2-5 x+16=0$$ and $$x^2+

If one end of focal chord of the parabola $$y^2=8x$$ is $$\left(\frac{1}{2},2\right)$$, then the length of the focal cho

If a point $$P(x, y)$$ moves along the ellipse $$\frac{x^2}{25}+\frac{y^2}{16}=1$$ and if $$C$$ is the center of the ell

The asymptotes of the hyperbola $$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$$, with any tangent to the hyperbola form a triangle

The ratio in which the YZ-plane divides the line joining (2, 4, 5) and (3, 5, $$-$$4) is

The direction cosines of a line which makes equal angles with the coordinate axes are

Let $$O$$ be the origin and $$P$$ be a point which is at a distance of 3 units from the origin. If the direction ratios

$$\lim _\limits{z \rightarrow 1} \frac{z^{(1 / 3)}-1}{z^{(1 / 6)}-1}$$ is equal to

$$f(x)=\left\{\begin{array}{cc} \frac{72^x-9^x-8^x+1}{\sqrt{2}-\sqrt{1+\cos x}}, & x \neq 0 \\ K \log 2 \log 3, & x=0 \e

If the function $$f(x)$$, defined below is continuous in the interval $$[0, \pi]$$, then $$f(x)=\left\{\begin{array}{cc}

If $$y=x+\frac{1}{x}$$, then which among the following holds?

If $$y=\tan ^{-1}\left(\frac{\sqrt{1+x^2}+\sqrt{1-x^2}}{\sqrt{1+x^2}-\sqrt{1-x^2}}\right)$$, where $$x^2 \leq 1$$. Then,

If $$3 \sin x y+4 \cos x y=5$$, then $$\frac{d y}{d x}$$ is equal to

$$f(x)=\sqrt{x^2+1}: g(x)=\frac{x+1}{x^2+1}: h(x)=2 x-3$$, then the value of $$f^{\prime}\left[h^{\prime}\left(g^{\prime

If the error committed in measuring the radius of a circle is 0.05%, then the corresponding error in calculating its are

The stationary points of the curve $$y=8 x^2-x^4-4$$ are

Which statement among the following is true? (i) the function $$f(x)=x|x|$$ is strictly increasing on $$R-\{0\}$$. (ii)

For which value(s) of $$a$$ $$f(x)=-x^3+4 a x^2+2 x-5$$ is decreasing for every $$x$$ ?

The distance between the origin and the normal to the curve $$y=e^{2 x}+x^2$$ drawn at $$x=0$$ is units

If $$\int \frac{d x}{x\left(\sqrt{\left.x^4-1\right)}\right.}=\frac{1}{k} \sec ^{-1}\left(x^k\right)$$, then the value o

$$\int \frac{e^x(x+3)}{(x+5)^3} d x$$ is equal to

If $$\int \frac{(x-1)^2}{\left(x^2+1\right)^2} d x=\tan ^{-1}(x)+g(x)+k$$, then $$g(x)$$ is equal to

If $$\int \frac{1-(\cot x)^{2021}}{\tan x+(\cot x)^{2022}} d x=\frac{1}{A} \log\left|(\sin x)^{2023}+(\cos x)^{2023}\rig

$$\int_2^4\{|x-2|+|x-3|\} d x$$ is equal to

$$\int\limits_{-1 / 2}^{1 / 2}\left\{[x]+\log \left(\frac{1+x}{1-x}\right)\right\} d x$$ is equal to

The solution of the differential equation $$\frac{d^2 y}{d x^2}+y=0$$ is

An electric generator is based on

Which of the following decreases, in motion on a straight line, with constant retardation?

When a ball is thrown with a velocity of 50 ms$$^{-1}$$ at an angle 30$$\Upsilon$$ with the horizontal, it remains in th

One of the rectangular components of a force of 40 N is 20$$\sqrt3$$ N. What is the other rectangular component?

An object dropped in a stationary lift takes time $$t_1$$ to reach the floor. It takes time $$t_2$$ when lift is moving

When a body is placed on a rough plane (coefficient of friction $$=~\propto$$ ) inclined at an angle $$\theta$$ to the h

A metal ball of mass 2 kg moving with a velocity of 36 km/h has a head on collision with a stationary ball of mass 3 kg.

A body of mass 8 kg, under the action of a force, is displaced according to the equation, $$s=\frac{t^2}{4}$$ m, where t

A particle of mass m, moving with a velocity v makes an elastic collision in one dimension with a stationary particle of

Which of the following type of wheels of same mass and radius will have largest moment of inertia?

The sum of moments of all the particles in a system about its centre of mass is always

Assertion (A) Two identical trains move in opposite senses in equatorial plane with same speeds relative to the Earth’s

A spring is stretched by 0.40 m when a mass of 0.6 kg is suspended from it. The period of oscillations of the spring loa

A heavy brass sphere is hung from a spring and it executes vertical vibrations with period T. The sphere is now immersed

A particle is kept on the surface of a uniform sphere of mass 1000 kg and radius 1 m. The work done per unit mass agains

The acceleration due to gravity at a height (1/20)th of the radius of Earth above the Earth's surface is 9 ms$$^{-2}$$.

The Young's modulus of a rubber string of length $$12 \mathrm{~cm}$$ and density $$1.5 ~\mathrm{kgm}^{-3}$$ is $$5 \time

The lower end of a capillary tube is dipped into water and it is observed that the water in capillary tube rises by 7.5

An ideal liquid flows through a horizontal tube of variable diameter. The pressure is lowest where the

In a steady state, the temperature at the end $$A$$ and end $$B$$ of a $$20 \mathrm{~cm}$$ long rod $$A B$$ are $$100 \U

If two rods of length $$L$$ and $$2 L$$, having coefficients of linear expansion $$\alpha$$ and $$2 \alpha$$ respectivel

A system is taken from state-A to state-B along two different paths. The heat absorbed and work done by the system along

A gas ($$\gamma$$ = 1.5 ) is suddenly compressed to (1/4 )th its initial volume. Then, find the ratio of its final to in

A cylinder has a piston at temperature of $$30 \Upsilon$$C. There is all round clearance of $$0.08 \mathrm{~mm}$$ betwee

A balloon contains 1500 m$$^3$$ of He at 27$$\Upsilon$$C and 4 atmospheric pressure, the volume of He at $$-3\Upsilon$$C

The sources of sound A and B produce a wave of 350 Hz in same phase. A particle P is vibrating under an influence of the

In a diffraction pattern due to a single slit of width $$a$$, the first minimum is observed at an angle $$30 \Upsilon$$

Which statement(s) among the following are incorrect? (i) A negative test charge experiences a force opposite to the dir

In the given circuit, if the potential difference between A and B is 80 V, then the equivalent capacitance between A and

A cell of emf 1.8 V gives a current of 17 A when directly connected to an ammeter of resistance 0.06 $$\Omega$$. Interna

In which of the following case no force exerted by a magnetic field on a charge?

A long thin hollow metallic cylinder of radius R has a current i ampere. The magnetic induction B away from the axis at

The plane of a dip circle is set in the geographic meridian and the apparent dip is $$\delta_1$$. It is then set in a ve

Assertion (A) It is more difficult to move a magnet into a coil with more loops. Reason (R) This is because emf induced

Two inductors A and B when connected in parallel are equivalent to a single inductor of inductance 1.5 H and when connec

A resonant frequency of a current is $$f$$. If the capacitance is made four times the initial value, then the resonant f

The law which states that a variation in an electric field causes magnetic field, is

Radiation of wavelength $$300 \mathrm{~nm}$$ and intensity $$100 \mathrm{~W}-\mathrm{m}^{-2}$$ falls on the surface of a

Potential energy between a proton and an electron is given by $$U=\frac{K e^2}{3 R^3}$$, then radius of Bohr's orbit can

A transistor is connected in common emitter configuration. The collector supply is $$8 \mathrm{~V}$$ and the voltage dro