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. Which of the following statement is correct?

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 electronegativity of chlorine on Mulliken scale, approximately equals to

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

1. Nitrogen (N) 2. Phosphorus (P) 3. Chlorine (Cl) 4. Fluorine (F)

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 H$$_2$$O

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-mass, temperature and universal gas constant.

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 conditions is true for the reaction?

Standard entropies of $$X_2, Y_2$$ and $$X Y_3$$ are 60, 40 and $$50 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}$$ respectively. At what temperature, the following reaction will be at equilibrium? [given: $$\Delta H \Upsilon=-30 \mathrm{~kJ}$$]

$$\frac{1}{2} X_2+\frac{3}{2} Y_2 \rightleftharpoons X Y_3$$

For the reaction $$\mathrm{SO}_2(g)+\frac{1}{2} \mathrm{O}_2(g) \rightleftharpoons \mathrm{SO}_3(g)$$, the percentage yield of product at different pressure is shown in the figure. Then, which among the following is true?

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

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 decrease in lattice energy.

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 sulphur are present. This is done by boiling the extract with Z. Identify X, Y and Z.

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 mass of Al = 27 g]

The molar conductivities $$\left(\lambda_{\mathrm{m}}^{\Upsilon}\right)$$ at infinite dilution of $$\mathrm{KBr}, \mathrm{HBr}$$ and $$\mathrm{KNH}_2$$ are 120.5, 420.6 and $$90.48 \mathrm{~S} \mathrm{~cm}^2 \mathrm{~mol}^{-1}$$ respectively. Find the value of $$\lambda_{\mathrm{m}}^\Upsilon$$ for $$\mathrm{NH}_3$$.

If the rate constant for a first order reaction is $$2.303 \times 10^{-3} \mathrm{~s}^{-1}$$. Find the time required to reduce $$4 \mathrm{~g}$$ of the reactant to $$0.2 \mathrm{~g}$$.

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.

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 heated. Compound B is insoluble in water but dissolves in NaOH solution forming a solution of compound C. The compound A on heating with coke gives a volatile metal D and a gas E which burns with a blue flame. Identify the possible species D and C can be respectively?

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

$$\begin{gathered}\mathrm{CH}_3 \mathrm{COCl} \stackrel{\text { (i) }\left(\mathrm{CH}_3\right)_3 \mathrm{Cd}}{\longrightarrow}(P) \\ (P)+\mathrm{CH}_3 \mathrm{CHO} \stackrel{\text { (ii) } \mathrm{NaOH}(a q), \Delta}{\longrightarrow} \text { ? }\end{gathered}$$

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 $$(g \circ f)(x)$$ is equal to

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 to $$\rightarrow([\cdot]$$ greatest integer function)

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

The equation whose roots are the values of the equation $$\left| {\matrix{ 1 & { - 3} & 1 \cr 1 & 6 & 4 \cr 1 & {3x} & {{x^2}} \cr } } \right| = 0$$ is

Let a and b be non-zero real numbers such that $$ab=5/2$$ and given $$A = \left[ {\matrix{ a & { - b} \cr b & a \cr } } \right]$$ and $$A{A^T} = 20I$$ ($$l$$ is unit matrix), then the equation whose roots are a and b is

If $$A=\left[\begin{array}{ccc}1 & -1 & 1 \\ 2 & 1 & -3 \\ 1 & 1 & 1\end{array}\right], 10 B=\left[\begin{array}{ccc}4 & 2 & 2 \\ -5 & 0 & \alpha \\ 1 & -2 & 3\end{array}\right]$$ and $$B=A^{-1}$$, then the value of $$\alpha$$ is

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 , then,

If $$a_1, a_2, \ldots . a_9$$ are in GP, then $$\left|\begin{array}{lll}\log a_1 & \log a_2 & \log a_3 \\ \log a_4 & \log a_5 & \log a_6 \\ \log a_7 & \log a_8 & \log a_9\end{array}\right|$$ is equal to

$$(\sin \theta-i \cos \theta)^3$$ 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 Arithmetic Progression, then $$a$$ cannot take the value

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 all the balls, so that no two black balls are adjacent is

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

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

$$\tan 2 \alpha \cdot \tan (30 Y-\alpha)+\tan 2 \alpha \cdot \tan (60 Y-\alpha)+\tan (60 \Upsilon-\alpha) \cdot \tan (30 \gamma-\alpha)$$ is equal to

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

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

If $$\tan ^{-1}\left[\frac{1}{1+1 \cdot 2}\right]+\tan ^{-1}\left[\frac{1}{1+2 \cdot 3}\right]+\ldots+\tan ^{-1} \left[\frac{1}{1+n(1+1)}\right]=\tan ^{-1}[x]$$, then $$x$$ is equal to

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 $$r_2 \leftrightarrow \angle B$$ and $$r_3 \leftrightarrow \angle C$$. If $$r$$ is the radius of inscribed circle, then, what is the value of $$\frac{a b-r_1 r_2}{r_3}$$ is equal to

A vector makes equal angles $$\alpha$$ with $$X$$ and $$Y$$-axis, and $$90 \Upsilon$$ with $$Z$$-axis. Then, $$\alpha$$ is equal to (c) 45Yand 135Y (d) $90 \mathrm{Y}$

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 $$\hat{\mathbf{i}}+a \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{j}}+a \hat{\mathbf{k}}$$ and $$a \hat{\mathbf{i}}+\hat{\mathbf{k}}$$ becomes minimum, then $$a$$ is equal to

If $$\mathbf{a}=\frac{3}{2} \hat{\mathbf{k}}$$ and $$\mathbf{b}=\frac{2 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\mathbf{k}}}{2}$$, then angle between $$\mathbf{a}+\mathbf{b}$$ and $$\mathbf{a}-\mathbf{b}$$ is

Let $$\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}+5 \hat{\mathbf{k}}$$ and $$\mathbf{c}=7 \hat{\mathbf{i}}+9 \hat{\mathbf{j}}+11 \hat{\mathbf{k}}$$, then the area of parallelogram having diagonals $$\mathbf{a}+\mathbf{b}$$ and $$\mathbf{b}+\mathbf{c}$$ is

If $$\mathbf{a}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+3 \hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}+3 \hat{\mathbf{j}}-\hat{\mathbf{k}}$$ and $$\mathbf{c}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}-2 \hat{\mathbf{k}}$$, then the value of $$\left|\begin{array}{ccc}\mathbf{a} \cdot \mathbf{a} & \mathbf{a} \cdot \mathbf{b} & \mathbf{a} \cdot \mathbf{c} \\ \mathbf{b} \cdot \mathbf{a} & \mathbf{b} \cdot \mathbf{b} & \mathbf{b} \cdot \mathbf{c} \\ \mathbf{c} \cdot \mathbf{a} & \mathbf{c} \cdot \mathbf{b} & \mathbf{c} \cdot \mathbf{c}\end{array}\right|$$ is equal to

If $$\mathbf{a}$$ and $$\mathbf{b}$$ are two vectors such that $$|\mathbf{a}|=2, |\mathbf{b}|=3$$ and $$\mathbf{a}+t \mathbf{b}$$ and $$\mathbf{a}-t \mathbf{b}$$ are perpendicular, where $$t$$ is a positive scalar, then

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 GULATIONS remain the same, then the probability that there are exactly 4 letters between R and E is

A random variable X has the probability distribution

For the events E = {X is a prime number} and F = {X < 4}, then P(E $$\cup$$ F) is

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

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

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 the point $$(\alpha, \beta)$$, the value of $$\alpha^2+\beta^2$$ equals

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($$\alpha,\beta$$), then the value of $$13\alpha+13\beta$$ equals

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 the origin is

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 $$\left(\frac{1}{18}, \frac{11}{18}\right)$$, then the value of $$k$$ equals

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 $$m_1: m_2$$ equals

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, $$\left|\frac{a+b}{h}+\frac{8 h^2}{a b}\right|$$ is equal to

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 the circle $$x^2+y^2=r_3^2$$, then $$r_1, r_2$$ and $$r_3$$ are in

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 made by the circle $$x^2+y^2-x+3 y=0$$ on $$L_1$$ and $$L_2$$ are equal, then which of the following equations represent $$L_1$$

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, is units.

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 $$x^2+y^2-8 x+16 y+160=0$$ is

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 chord is ................ units.

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 ellipse, then the sum of maximum and minimum values of $$C P$$ is

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 whose area is $$a^2 \tan (\alpha)$$. Then, its eccentricity equals

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 of $$\overline{O P}$$ are $$(1,-2,-2)$$, then the coordinates of $$P$$ are

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

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

Find the value of $$k$$ for which the function $$f$$ is continuous.

If the function $$f(x)$$, defined below is continuous in the interval $$[0, \pi]$$, then $$f(x)=\left\{\begin{array}{cc}x+a \sqrt{2}(\sin x) & , \quad 0 \leq x < \frac{\pi}{4} \\ 2 x(\cot x)+b, & \frac{\pi}{4} \leq x \leq \frac{\pi}{2} \\ a(\cos 2 x)-b(\sin x), & \frac{\pi}{2} < x \leq \pi\end{array}\right.$$

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, find $$\frac{d y}{d x}$$ is equal to

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 $$f^{\prime}\left[h^{\prime}\left(g^{\prime}(x)\right)\right]$$ is equal to

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

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) the function $$f(x)=\log _{(1 / 4)} x$$ is strictly increasing on $$(0, \infty)$$.

(iii) a one-one function is always an increasing function.

(iv) $$f(x)=x^{1 / 3}$$ is strictly decreasing on $$R$$

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 of $$k$$ is equal to

$$\int \frac{e^x(x+3)}{(x+5)^3} d x$$ 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 $$\int \frac{1-(\cot x)^{2021}}{\tan x+(\cot x)^{2022}} d x=\frac{1}{A} \log\left|(\sin x)^{2023}+(\cos x)^{2023}\right|+c$$, then $$A$$ is equal to

$$\int_2^4\{|x-2|+|x-3|\} d x$$ 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 the air for ......... s.

(Take, g = 10 ms$$^{-2}$$)

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 up with constant acceleration. Then,

When a body is placed on a rough plane (coefficient of friction $$=~\propto$$ ) inclined at an angle $$\theta$$ to the horizontal, its acceleration is (acceleration due to gragvity $$=g$$ )

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. After the collision, if both balls move together, then the loss in kinetic energy due to collision is

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 is the time. Find the work done by the force in the first 4 s.

A particle of mass m, moving with a velocity v makes an elastic collision in one dimension with a stationary particle of mass m. During the collision, they remain in contact with each other for an extremely small time T. Their force of contact, with time is shown in the figure. Then, F₀

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 surface. They have equal magnitude of normal reaction.

Reason (R) The trains have different centripetal accelerations due to different speeds.

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 loaded by 255 g and put to oscillations is close to (g = 10 ms$$^{-2}$$)

A heavy brass sphere is hung from a spring and it executes vertical vibrations with period T. The sphere is now immersed in a non-viscous liquid with a density (1/10 )th that of brass. When set into vertical vibrations with the sphere remaining inside liquid all the time, the time period will be

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 against the gravitational force between them is

[G = 6.67 $$\times$$ 10$$^{-11}$$ Nm$$^2$$ kg$$^{-2}$$]

The Young's modulus of a rubber string of length $$12 \mathrm{~cm}$$ and density $$1.5 ~\mathrm{kgm}^{-3}$$ is $$5 \times 10^8 ~\mathrm{Nm}^{-2}$$. When this string is suspended vertically, the increase in its length due to its own weight is (Take, $$g=10 \mathrm{~ms}^{-2}$$ )

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 cm. Find the radius of the capillary tube used, if surface tension of water is 7.5 $$\times$$ 10$$^{-2}$$ Nm$$^{-1}$$. Angle of contact between water and glass is 0$$\Upsilon$$ and acceleration due to gravity is 10 ms$$^{-2}$$.

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 $$100 \Upsilon$$ and $$0^{\circ} \mathrm{C}$$. The temperature of a point $$9 \mathrm{~cm}$$ from $$A$$ is

If two rods of length $$L$$ and $$2 L$$, having coefficients of linear expansion $$\alpha$$ and $$2 \alpha$$ respectively are connected end-to-end, then find the average coefficient of linear expansion of the composite rod.

A system is taken from state-A to state-B along two different paths. The heat absorbed and work done by the system along these two paths are Q$$_1$$, Q$$_2$$ and W$$_1$$, W$$_2$$ respectively, then

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

A cylinder has a piston at temperature of $$30 \Upsilon$$C. There is all round clearance of $$0.08 \mathrm{~mm}$$ between the piston and cylinder wall if internal diameter of the cylinder is $$15 \mathrm{~cm}$$. What is the temperature at which piston will fit into the cylinder exactly?

$$\left(\alpha_p=1.6 \times 10^{-5} / \Upsilon\mathrm{C} \text { and } \alpha_c=1.2 \times 10^{-5} / \Upsilon\mathrm{C}\right)$$

A balloon contains 1500 m$$^3$$ of He at 27$$\Upsilon$$C and 4 atmospheric pressure, the volume of He at $$-3\Upsilon$$C temperature and 2 atmospheric pressure will be

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 these two waves. If the amplitudes at P produced by the two waves is 0.3 mm and 0.4 mm, the resultant amplitude of the point P will be, when AP $$-$$ BP = 25 cm and the velocity of sound is 350 ms$$^{-1}$$

In a diffraction pattern due to a single slit of width $$a$$, the first minimum is observed at an angle $$30 \Upsilon$$ when light of wavelength $$500 \mathrm{~nm}$$ is incident on the slit. The first secondary maximum is observed at an angle of

Which statement(s) among the following are incorrect?

(i) A negative test charge experiences a force opposite to the direction of the field.

(ii) The tangent drawn to a line of force represents the direction of electric field.

(iii) The electric field lines never intersect.

(iv) The electric field lines form a closed loop.

In the given circuit, if the potential difference between A and B is 80 V, then the equivalent capacitance between A and B and the charge on 10 $$\propto$$ F capacitor respectively, are

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

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 a distance r from the axis varies as shown in

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 vertical plane perpendicular to the geographic meridian. The apparent dip angle is $$\delta_2$$. The declination $$\theta$$ at the place is

Assertion (A) It is more difficult to move a magnet into a coil with more loops.

Reason (R) This is because emf induced in each current loop resists the motion of the magnet.

Two inductors A and B when connected in parallel are equivalent to a single inductor of inductance 1.5 H and when connected in series are equivalent to a single inductor of inductance 8H. Find the difference in the inductances of A and B.

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

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 photosensitive material. If $$2 \%$$ of the incident photons produce photoelectron, the number of photoelectrons emitted from an area of $$2 \mathrm{~cm}^2$$ of the surface is nearly

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 be given by

A transistor is connected in common emitter configuration. The collector supply is $$8 \mathrm{~V}$$ and the voltage drop across a resistor of $$800 \Omega$$ in the collector circuit is $$0.5 \mathrm{~V}$$. If the current gain factor $$\alpha$$ is 0.96, then the base current is