A subshell $$n=3, l=2$$ can accommodate maximum of

If the work function for the photoelectron emission of a metal is 3.75 eV, then the threshold wavelength of the radiation needed for the ejection of the electron is approximately

With increasing principal quantum number, the energy difference between adjacent energy levels in $$\mathrm{H}$$-atom ............ .

The electronegativity of the given elements increases in the order.

The first ionisation enthalpies of $$\mathrm{Mg}$$ and $$\mathrm{Al}$$ can be expected to be ............ .

Which of the following statements is/are correct?

1. Mercury is the only metal that exists as liquid at room temperature.

2. Among non-metals, carbon has the highest melting point.

3. Hydrogen is the most abundant element in the universe.

4. Oxygen is the most abundant element in the Earth's crust.

A covalent molecule '$$X Y^{\prime}$$' is found to have a dipole moment of $$1.5 \times 10^{-29} \mathrm{C} \cdot \mathrm{m}$$ and $$a$$ bond length of $$150 ~\mathrm{pm}$$. The percent ionic character of the bond will be

The hybridisation of $$\mathrm{Se}$$ in $$\mathrm{SeF}_4$$ and its geometry respectively are :

Incorrect matching amongst the following is (according to geometry of molecules)

When the temperature of a gas is increased from $$30^{\circ} \mathrm{C}$$ to $$930^{\circ} \mathrm{C}$$, the root mean square speed of the gas would

Three flasks of equal volume contain $$\mathrm{CH}_4, \mathrm{CO}_2$$ and $$\mathrm{Cl}_2$$ gases respectively. They will contain equal number of molecules, if

If the volume of $$15.9 \mathrm{~g}$$ of carbon tetrachloride is $$10 \mathrm{~mL}$$, calculate its density.

$$0.63 \mathrm{~g}$$ of oxalic acid is dissolved in order to obtain $$250 \mathrm{~cm}^3$$ of its solution. Find the normality of this solution. [oxalic acid $$\left.(\mathrm{COOH})_2 \cdot 2 \mathrm{H}_2 \mathrm{O}\right]$$

When an ideal gas expands isothermally from $$5 \mathrm{~m}^3$$ to $$10 \mathrm{~m}^3$$ at $$25^{\circ} \mathrm{C}$$ against a constant pressure of $$10^7 \mathrm{~Nm}^{-2}$$, then the work done on the gas is

Find the approximate value of $$(\Delta H-\Delta U)$$ in $$\mathrm{Jmol}^{-1}$$, for the formation of CO from its elements at $$298 \mathrm{~K} .\left(R=8.314 \mathrm{JK}^{-1} \mathrm{~mol}^{-1}\right)$$

Match the following columns.

The pH of 0.1 M solution of acetic acid will be [degree of dissociation of acetic acid is 0.0132]

The main constituent of enamel on the surface of teeth is

$$\mathrm{H}_3 \mathrm{BO}_3$$ or $$\mathrm{B}(\mathrm{OH})_3$$ is considered as an acid because its molecule

The element with maximum bond energy is

Identify the coldest region among the following layers of atmosphere.

Alcohols with molecular formula $$\mathrm{C}_n \mathrm{H}_{2 n+2} \mathrm{O}$$ are isomeric with

$$7.8 \mathrm{~g}$$ of a compound having molecular formula $$\mathrm{C}_6 \mathrm{H}_6$$, on reacting with $$\mathrm{CH}_3 \mathrm{COCl} / \mathrm{AlCl}_3$$ gives $$8.4 \mathrm{~g}$$ of a product which has molecular formula $$\mathrm{C}_8 \mathrm{H}_8 \mathrm{O}$$. Calculate the percentage yield of the product $$\mathrm{C}_8 \mathrm{H}_8 \mathrm{O}$$. (Given, atomic weights of $$\mathrm{H}, \mathrm{C}$$ and $$\mathrm{O}$$ respectively are 1, 12 and 16)

Arrange the following bases in decreasing order of basicity.

1. Aniline

2. o-nitroaniline

3. m-nitroaniline

4. p-nitroaniline

The complete combustion of one mole of benzene produces .......... grams of carbon dioxide.

A metal crystallises with a fcc lattice, the edge of whose unit cell is $$x \mathrm{~pm}$$. The diameter of this metal atom would be .............. pm.

If two liquids $$A$$ and $$B$$ form a minimum boiling azeotrope at some specific composition, then which statement among the following is correct?

The vapour pressure of a solvent decreased by 20 mm of Hg when a non-volatile solute was added to the solvent. The mole fraction of the solute in the solution is 0.5. What should be the mole fraction of the solvent for the decrease in the vapour pressure needs to be 10 mm of Hg?

For a $$A+B \rightarrow$$ products, the rate of the reaction is given by rate $$=k[A][B]^2$$. The units of rate constant $$(k)$$ will be

In the electrolysis of a CuSO$$_4$$ solution, how many grames of Cu are plated out on the cathode, in the time that is required to liberate 5.6 L of O$$_2$$(g), measured at 1 atm and 273 K, at the anode?

For an elementary reaction, $$X(g) \longrightarrow Y(g)+Z(g)$$, the $$t_{1 / 2}$$ is $$10 \mathrm{~min}$$. In what period of time would the concentration of $$X$$ be reduced to $$10 \%$$ of its original concentration?

Which statements among the following are correct?

1. Freundlich isotherm fails at high pressure of the gas.

2. $$\Delta H < 0$$ for both physical and chemical adsorption.

3. Physical adsorption in non-selective.

4. Chemical adsorption is reversible, whereas physical adsorption is irreversible.

Xenon best reacts with

The correct order of acidic character of the following is

In the following reactions (i) and (ii), the number of moles of chlorine gas released respectively are

(i) $$\mathrm{MnO}_2+4 \mathrm{HCl} \longrightarrow$$

(ii) $$\mathrm{KMnO}_4+16 \mathrm{HCl} \longrightarrow$$

A purple coloured compound of manganese $$(X)$$ decomposes on heating to liberate oxygen and forms compounds of manganese $$Y$$ and $$Z$$. Compound $$Z$$ reacts with $$\mathrm{KOH}$$ in presence of potassium nitrate to give compound $$Y$$. Compounds $$X, Y$$ and $$Z$$ respectively are

Match the following columns and choose the correct code.

The human body does not produce

Identify the best suitable reagent for the following reaction.

The major product of the following reaction sequence is

Let $$f(x)=(x+2)^2-2, x \geq-2$$. Then, $$f^{-1}(x)$$ is equal to

If $$f$$ is the greatest integers function defined on $$R$$ as $$f(x)=[x]$$ and $$g$$ is the modulus function defined on $R$ as $$g(x)=|x|$$, then the value of $$(g \circ f)\left(\frac{-5}{3}\right)$$ is

If $$f: R \rightarrow R$$ and $$g: R \rightarrow R$$ are two functions defined by $$f(x)=a x+b(a \neq 0), \forall x \in R$$ and $$g(x)=c x^3+d(c \neq 0), \forall x \in R$$, then $$(f \circ g)^{-1}(x)$$ is equal to

Using mathematical induction, the numbers $$a_n^{\prime}$$ s are defined by $$a_0=1, a_{n+1}=3 n^2+n+a_n (n \geq 0)$$, then $$a_n$$ is equal to

If $$k \in R$$ and $$\operatorname{det} A=\left|\begin{array}{lll}a_1 & b_1 & c_1 \\ a_2 & b_2 & c_2 \\ a_3 & b_3 & c_3\end{array}\right|=k$$, then $$\operatorname{det} B=\left|\begin{array}{ccc}a_1 & b_1 & c_1 \\ a_2+2 a_1 & b_2+2 b_1 & c_2+2 c_1 \\ a_3 & b_3 & c_3\end{array}\right|$$ is equal to

If $$A=\left[\begin{array}{llll}\sqrt{2020} & \sqrt{2021} & \sqrt{2021} & \sqrt{2023} \\ \sqrt{4040} & \sqrt{4042} & \sqrt{4044} & \sqrt{4046} \\ \sqrt{6060} & \sqrt{6063} & \sqrt{6066} & \sqrt{6069} \\ \sqrt{8080} & \sqrt{8084} & \sqrt{8088} & \sqrt{8092}\end{array}\right]$$, then the rank of $$A$$ is

If $$\left|\begin{array}{lll}x & x^2 & 1+x^3 \\ y & y^2 & 1+y^3 \\ z & z^2 & 1+z^3\end{array}\right|=0$$ and $$x, y$$ and $$z$$ are all distinct, then $$x y z$$ is equal to

Let A be a $$n\times n$$ matrix such that A is upper-triangular. Then, $$adj (A)$$ is equal to

Let $$Z_1, Z_2$$ and $$Z_3$$ be three non zero complex numbers such that $$a=\left|Z_1\right|, b=\left|Z_2\right|$$ and $$c=\left|Z_3\right|$$, if the determinant $$\left|\begin{array}{lll}a & b & c \\ b & c & a \\ c & a & b\end{array}\right|=0$$, then

If $$\left|z_1+z_2\right|^2=\left|z_1\right|^2+\left|z_2\right|^2$$, where $$z_1$$ and $$z_2$$ are two complex numbers, then

A real value of $$x$$ will satisfy the equation, $$\left(\frac{3-4 i x}{3+4 i x}\right)=\alpha-i \beta,(\alpha, \beta$$ are real $$)$$, if

What is the value of $$(1-i \sqrt{3})^9$$ is equal to

$$\left(\frac{\sqrt{6}-\sqrt{2}}{4}+\frac{\sqrt{6}+\sqrt{2}}{4} i\right)^{2020}$$ is equal to

If $$f(10-x)=3 x^2+4 x-5$$ and $$f(x)=p x^2+q x+r$$, then $$p+q+r$$ is equal to

For $$a\ne b$$, if the equation $$x^2+ax+b=0$$ and $$x^2+bx+a=0$$ have a common root, then the value of $$a+b$$ is equal to

If the product of the roots of $$9x^3+112x^2-120x+a=0$$ is 12, then the value of $$a$$ is

$$2+\sqrt{5}, 1$$ are roots of the cubic equation given by

A set contains 11 elements. The number of subsets of the set which contain at most 5 elements is

If

$$\begin{aligned} \frac{2 x^4-x^3+3 x^2-x+4}{x^2-3 x+2} =f(x)+\frac{A}{x-1}+\frac{B}{x-2}\end{aligned}$$, then

Let $$\theta$$ be an angle in the standard position such that the point $$(-5,12)$$ lies on its terminal side, then

If $$\cos \frac{\pi}{4} \cos \frac{\pi}{8} \cos \frac{\pi}{16} \cos \frac{\pi}{32}=2^m \operatorname{cosec} \frac{\pi}{n}$$, then $$m+n$$ is equal to

If $$A+B+C=\frac{3 \pi}{2}$$, then $$\cos 2 A+\cos 2 B+\cos 2 C$$ is equal to

$$\tan ^{-1}(-2)-\tan ^{-1}(3)$$ is equal to

$$\sinh (x+y) \cosh (x-y)$$ is equal to

What is the value of $$(a-b)^2 \cos ^2 \frac{c}{2}+(a+b)^2 \sin ^2 \frac{c}{2}$$ 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 $$B, r_3 \leftrightarrow$$ angle $$C$$. If $$r_1=2, r_2=3$$ and $$r_3=6$$, then what is $$(a, b, c)$$ is equal to

If in $$\triangle A B C, a \tan A+b \tan B=(a+b). \tan \left(\frac{A+B}{2}\right)$$, then which of the following holds?

If $$\mathbf{a}=\hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}, \mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$$ and $$\mathbf{c}=x \hat{\mathbf{i}}+(x-2) \hat{\mathbf{j}}-\hat{\mathbf{k}}$$ and if the vector $$\mathbf{c}$$ lies in the plane of vectors $$\mathbf{a}$$ and $$\mathbf{b}$$ and then $$x$$ equals

Let $$u=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}$$ and $$v=3 \hat{\mathbf{i}}-5 \hat{\mathbf{j}}$$. Consider three points $$P, Q$$ and $$R$$ having the position vectors $$\left(\frac{5}{2}\right) \hat{\mathbf{i}}-2 \hat{\mathbf{j}} ;\left(\frac{7}{3}\right) \hat{\mathbf{i}}-\hat{\mathbf{j}}$$ and $$\left(\frac{9}{4}\right) \hat{\mathbf{i}}$$ respectively. Among these, the points in the line passing through $$u$$ and $$v$$ are

The point of intersection of the lines joining points $$\hat{\mathbf{i}}+2 \hat{\mathbf{j}}, 2 \hat{\mathbf{i}}-\hat{\mathbf{j}}$$ and $$-\hat{\mathbf{i}}, 2 \hat{\mathbf{i}}$$ is

The value of $$\frac{(\mathbf{a} \times \mathbf{b})^2+(\mathbf{a} \cdot \mathbf{b})^2}{2(\mathbf{a})^2(\mathbf{b})^2}$$ is

Let $$\mathbf{a}=\hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=\hat{\mathbf{j}}-\hat{\mathbf{k}}$$ and $$\mathbf{c}=\hat{\mathbf{k}}-\hat{\mathbf{i}}$$ if $$\mathbf{d}$$ is a unit vector such $$\mathbf{a} \cdot \mathbf{b}=0=[\mathbf{b} \mathbf{c} \mathbf{d}]$$, then $$\mathbf{d}$$ is

Let $$u$$ and $$v$$ be two non-zero vectors in $$R^3$$ with the intermediate angle $$45^{\circ}$$. Then $$|\mathbf{u} \times \mathbf{v}|$$ is equal to

The equation of the plane passing through $$3 \hat{\mathbf{i}}+2 \hat{\mathbf{j}}+6 \hat{\mathbf{k}}$$ and parallel to the vectors $$2 \hat{\mathbf{i}}+\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ and $$\hat{\mathbf{i}}-\hat{\mathbf{j}}+\hat{\mathbf{k}}$$ is

Given, $$\mathbf{a}=3 \hat{\mathbf{i}}-\hat{\mathbf{j}}, \mathbf{b}=2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-3 \hat{\mathbf{k}}$$ and $$\mathbf{b}=\mathbf{b}_1+\mathbf{b}_2$$ where $$\mathbf{b}_1$$ is parallel to $$\mathbf{a}$$ and $$\mathbf{b}_2$$ is perpendicular to $$\mathbf{a}$$. Then, $$\mathbf{b}_2$$ is equal to

If the mean of a data x is 10 and if all the observations are multiplied by 2, then the mean of new data is

A coin is tossed until a head appears or it has been tossed thrice. Given that head doesn’t appear on the first toss, the probability that coin tossed thrice is

Box-I contains 3 cards bearing numbers 1, 2, 3 , Box II contains 5 cards bearing numbers 1 , 2, 3, 4, 5 and Box III contains 7 cards bearing numbers 1, 2, 3, 4, 5, 6, 7. One card is drawn at random from each of the boxes. If $$x_i$$ be the number on the card drawn from the $$i$$ th box, $$i=1,2,3$$, then the probability that $$x_1+x_2+x_3$$ is odd is equal to

The range of a random variable $$X$$ is $$\{1,2,3, \ldots\}$$ and $$P(X=x)=\frac{C^x}{x !}$$. for $$x=1,2,3$$, ... Then, the value of $$C$$ is

Tom and Jerry play a game of alternately throwing an unfair coin. First one to get head wins. If Tom starts the game, he has 62.5% chance of winning the game. Suppose this coin is tossed 5 times, then the probability of getting exactly 3 head is

A point moves so that the sum of its distances from $$(a e, 0)$$ and $$(-a e, 0)$$ is $$2 a$$, then the equation to its locus, where $$b^2=a^2\left(1-e^2\right)$$ is

The point to which the origin should be shifted in order to eliminate the $$x$$ and $$y$$ terms from the equation $$9 x^2+4 y^2+10 x+12 y+1=0$$ is

If $$A(1,3)$$ and $$C(7,5)$$ are two opposite vertices of a square, then find the equation of a side passing through $$A$$.

$$C$$ is the centroid of the triangle with vertices $$(3,-1),(1,3)$$ and $$(2,4)$$. Let $$P$$ be the point of intersection of the lines $$x+3 y-1=0$$ and $$3 x-y+1=0$$. Then a line which passes through both points $$C$$ and $$P$$ would also passes through the point .......

The distance of the point $$(1,2)$$ from the line $$x+y+5=0$$ measured along the line parallel to $$3 x-y=7$$ is equal to

Find the equation of a line which passes through $$\left(2 \cos ^3(\theta), 2 \sin ^3(\theta)\right)$$ and is perpendicular to the line $$x \cos (\theta)-y \sin (\theta)=2 \cos (2 \theta)$$.

The value of $$p$$ for which the equation $$x^2+p x y+y^2-5 x-7 y+6=0$$ represents a pair of straight lines is

If one of the line represented by $$-a x^2+2 h x y+b y^2=0$$ passes through $$(2,3)$$ and the other passes through $$(4,5)$$, then $$a+2 h+b$$ equals

The equation of the pair of straight lines parallel to $$x$$-axis and touching the circle $$x^2+y^2-6 x-4 y-12=0$$ is

If the lines represented by the equation $$2 x^2-p x y+2 y^2=0$$ are real, then the value of $$p$$ lies in the interval

The points where the circle $$x^2+y^2-3 x -4 y+2=0$$ cuts the $$X$$-axis are

The center and radius of the circle $$x^2+y^2+8 x+10 y-8=0$$ respectively are and units

The poles of the tangents to the circle $$x^2+y^2=4$$ with respect to the circle $$(x+2)^2+y^2=8$$, lie on

If the power of the point $$(1,6)$$ with respect to the circle $$x^2+y^2+4 x-6 y-a=0$$ is $$-16$$ then $$a$$ equals

The equation of radical axis of the circles $$x^2+y^2+4 x+6 y+7=0$$ and $$4 x^2+4 y^2+8 x+12 y-9=0$$ is

The radical axis of the circles $$S_1: x^2+y^2-4 x+6 y-10=0$$ and $$S_2 : x^2+y^2+2 x-6 y+2=0$$, cut the circle $$S_1$$ in

The point of intersection of the latus rectum and axis of the parabola $$y^2+4 x+2 y-8=0$$ is

If the focal chord of the hyperbola subtends a right angle at the center, then its eccentricity is

The direction cosines of the line joining the points $$(-2,4,-5)$$ and $$(1,2,3)$$ are

The points (2, 3, 4), ($$-$$1, $$-$$2, 1) and (5, 8, 7) are

The sum of intercepts of the plane $$4 x+3 y+2 z=2$$ on the coordinate axes is

If $$\lim _\limits{x \rightarrow 0}\left(\frac{11 x^3-3 x+4}{13 x^3-5 x^2-7}\right)=\frac{a}{b}$$, then the value of $$a+b$$ equals

$$\lim _\limits{x \rightarrow 1} \frac{(1-x)\left(1-x^2\right) \ldots\left(1-x^{2 n}\right)}{\left\{(1-x)\left(1-x^2\right) \ldots \ldots\left(1-x^n\right)\right\}^2}= $$ _____________, $$\forall n \in N$$

If $$f(x)=\frac{\log _e\left(1+x^2(\tan x)\right)}{\sin x^3}, x \neq 0$$ is to be continuous at $$x=0$$, then $$f(0)$$ must be equal to

If $$x=\sec \theta-\cos \theta$$ and $$y=\sec ^n \theta-\cos ^n \theta$$, then $$\left(x^2+4\right)\left(\frac{d y}{d x}\right)^2$$ is equal to

If $$f(x)=\left|\begin{array}{ccc}x & x^2 & x^3 \\ 1 & 2 x & 3 x^2 \\ 0 & 2 & 6 x\end{array}\right|$$, then the ratio $$f^{\prime \prime}(x): f^{\prime}(x)$$ is equal to

If $$y=\log _{\cot x} \tan x-\log _{\tan x} \cot x +\tan ^{-1}\left(\frac{4 x}{4-x^2}\right)$$, then $$\frac{d y}{d x}$$ is equal to

If $$y=\sin (\sin x)$$ and $$y^{\prime \prime}+f(x) \cdot y^{\prime}+g(x) \cdot y=0$$, then $$f(x) \cdot g(x)$$ is equal to

A spherical iron ball 10 cm in radius is coated with a layer of ice of uniform thickness, which melts at a rate of 50 cm$$^3$$ /min. When the thickness of the ice is 15 cm, the rate at which the thickness of ice decreases is ........ cm/min.

Find the minimum value of $$2x+3y$$, when $$xy=6$$.

The volume of a spherical balloon is increasing at the rate of $$30 \mathrm{~cm}^3$$ per minute. Find the rate of change of surface area of the balloon, when its radius is $$6 \mathrm{~cm}$$.

If $$g(x)=\frac{1}{6} f\left(3 x^2-1\right)+\frac{1}{2} f\left(1-x^2\right), \forall x \in R$$, where $$f^{\prime \prime}(x) > 0, \forall x \in R$$. Then, $$g(x)$$ is increasing in the interval

If the function $$f(x)=2 x^3-9 a x^2+12 a^2 x+1$$ attains its maximum and minimum at $$p$$ and $$q$$ respectively, such that $$p^2=q$$, then $$a$$ equals

If $$f^{\prime}(x)=x+\frac{1}{x}$$, then $$f(x)$$ is equal to

If $$f(x)=\frac{1}{\left(\cos ^2 x\right) \sqrt{1+\tan x}}$$, then its antiderivative $$F(x)=$$ ........, given, $$F(0)=4$$

If the primitive of $$\cos (\log x)$$ is $$f(x)\{\cos (g(x))+\sin (h(x))\}$$, then which among the following is true?

$$\int \frac{\sec x}{\sqrt{\sin (2 x+\theta)+\sin \theta}} d x$$ is equal to

If $$\int_\limits0^\pi \log (\sin x) d x=8 k$$, then $$\int_\limits0^{\frac{\pi}{4}} \log (1+\tan x) d x$$ is equal to

If $$\int_\limits0^1 x^m(1-x)^n d x=k \int_\limits0^1 x^n(1-x)^m d x$$, then the value of $k$ equals

The equation of the curve passing through the point $$\left(0, \frac{\pi}{4}\right)$$ and satisfying the differential equation $$\left(e^x \tan y\right) d x\left.+\left(1+e^x\right) \sec ^2 y\right) d y=0$$ is given by

Which year was declared as the International year of Physics?

One angstrom $$(\mathop A\limits^o )$$ is equal to

An object is moving with a uniform acceleration which is parallel to its instantaneous direction of motion. The displacement-velocity graph of this object is

A hiker stands on the edge of a cliff $$490 \mathrm{~m}$$ above the ground and throws a stone horizontally with an initial speed of $$15 \mathrm{~ms}^{-1}$$. The speed with which it hits the ground is

Two paper screens $$A$$ and $$B$$ are separated by $$150 \mathrm{~m}$$. A bullet pierces $$A$$ and than $$B$$. The hole in $$B$$ is $$15 \mathrm{~cm}$$ below the hole in $$A$$. If the bullet is travelling horizontally at the time of hitting $$A$$, then the velocity of the bullet at $$A$$ is $$\left(\mathrm{g}=10 \mathrm{~ms}^{-2}\right)$$

A 30 kg slab B rests on a frictionless floor as shown in the figure. A 10 kg block A rests on top of the slab B. The coefficients of static and kinetic friction between the block A and the slab B are 0.60 and 0.40, respectively. When block A is acted upon by a horizontal force of 100 N, as shown, find the resulting acceleration of the slab B. (g = 9.8 ms$$^2$$ )

Image

A ball of mass 3 kg, moving with a speed of 100 ms$$^{-1}$$, strikes a wall at an angle 60$$^\circ$$ (as shown in figure). The ball rebounds at the same speed and remains in contact with the wall for 0.2 s, the force exerted by the ball on the wall is

An engine develops 20 kW of power. How much time will it take to lift a mass of 200 kg to a height of 40 m? (g = 10 ms$$^{-2}$$ )

Two bodies having kinetic energy in the ratio 4 : 1, are moving with same linear velocity. The ratio of their masses is

Water is falling on the blades of a turbine from a height of $$25 \mathrm{~m}$$ and $$3 \times 10^3 \mathrm{~kg}$$ of water pours on the blade per minute. If the whole of energy is transferred to the turbine, then power delivered is

As solid sphere of mass $$M$$ and radius $$R$$ spins about an axis passing through its centre making $$600 \mathrm{~rpm}$$. Its kinetic energy of rotation is

Two fly wheels $$A$$ and $$B$$ are mounted side by side with frictionless bearings on a common shaft. Their moments of inertia about the shaft are $$5.0 \mathrm{~kg}-\mathrm{m}^2$$ and $$20.0 \mathrm{~kg}-\mathrm{m}^2$$, respectively. Wheel $$A$$ is made to rotate at $$10 \mathrm{~rev}$$ per second. Wheel $$B$$, initially stationary, is now coupled to $$A$$ with the help of a clutch. The rotation speed of the wheels will become

In case of a forced vibration, the resonance wave becomes very sharp when the

If the Earth stops rotating in its orbit about the sun, there will be variation in the weight of our bodies at

At what depth below surface of the Earth, the acceleration due to gravity will be half of its value that at $$1600 \mathrm{~km}$$ above the surface of the Earth?

The dimensions of stress is

What causes the free surface of a liquid to have minimum area?

Assertion (A) The upper surface of the wing of an aeroplane is made convex and the lower surface is made concave.

Reason (R) The air currents at the top have smaller velocity and thus less pressure at the bottom than at the top.

A glass vessel of volume $$V_o$$ is completely filled with a liquid and its temperature is raised by $$\Delta T$$. What volume of the liquid will flow over, if the coefficient of linear expansion of glass is $$\alpha_g$$ and coefficient of volume expansion of the liquid is $$\gamma_l$$ ?

A Carnot engine whose heat sink is at 27$$^\circ$$C has an efficiency of 40%. By how much should its source temperature be changed, so as to increase its efficiency to 60%?

A diatomic gas is heated at constant pressure, what fraction of the heat energy is used to increase the internal energy?

An ideal gas is taken from state-1 to state- 2 through optional path $$A, B, C$$ and $$D$$ as shown in the $$p$$ - $$V$$ diagram. Let $$Q, W$$ and $$U$$ represent the heat supplied, work done and change in internal energy respectively, then

When the temperature of an ideal gas is increased from 27$$^\circ$$C to 127$$^\circ$$C. Calculate the percentage increase in its $$v_{rms}$$.

Two waves are represented by $$x_1=A \sin \left(\omega t+\frac{\pi}{6}\right) \text { and } x_2=A \cos \omega t \text {. }$$ Then, the phase difference between them is

Assertion (A) The focal length of lens does not change when red light is replaced by blue light.

Reason (R) The focal length of lens does not depend on colour of light used.

The wavefront is a surface in which

Two charges $$10 ~\mu \mathrm{C}$$ and $$-10 ~\mu \mathrm{C}$$ are placed at points $$A$$ and $$B$$ separated by a distance of $$10 \mathrm{~cm}$$. Find the electric field at a point $$P$$ on the perpendicular bisector of $$A B$$, at a distance of $$12 \mathrm{~cm}$$ from its mid-point.

When a number of charged liquid drops coalesce, which of the following quantity does not change?

What is the angle between maximum value of potential gradient and equipotential surface?

The conductivity of a conductor decreases with temperature because, on heating

Torque required to hold a small circular coil of 10 turns, area of $$2 \times 10^{-4} \mathrm{~m}^2$$ area of carrying 0.5 A current in the middle of a long solenoid of $$10^3$$ turns per metre carrying $$3 \mathrm{~A}$$ current, with its axis perpendicular to the axis of the solenoid is

Two concentric coils each of radius equal to $$4 \pi ~\mathrm{cm}$$ are placed at right angles to each other. If $$10 \mathrm{~A}$$ and $$24 \mathrm{~A}$$ are the currents flowing through the coils respectively, then the magnetic induction at the centre of the coils will be

An AC generator consists of a coil of 100 turns and is of cross-sectional area $$3 \mathrm{~m}^2$$. It is rotating at a constant angular speed of $$60 \mathrm{~rads}^{-1}$$ in a uniform magnetic field of $$0.04 \mathrm{~T}$$. Resistance of the coil is $$360 \Omega$$. What is the maximum power dissipation in the coil?

Assertion (A) Magnetic flux is a vector quantity.

Reason (R) Value of magnetic flux can be positive negative or zero.

The output current versus time curve of a rectifier is shown in the figure. The average value of output current in this case is ........... .

The shortest wavelength of X-rays emitted from an X-ray tube depends upon ........... .

If a photocell is illuminated with a radiation of 1240 $$\mathop A\limits^o $$, the stopping potential is found to be 8V. Then, the work-function of the emitter and the threshold wavelength are

The wavelength of the first spectral line of the Lyman series of hydrogen spectrum is

Which of the following nuclear reactions is possible?

A change of $$0.04 \mathrm{~V}$$ takes place between the base and the emitter when an input signal is connected to the common emitter transistor amplifier. As a result, $$20 ~\mu \mathrm{A}$$ change takes place in the base current and a change of $$2 \mathrm{~mA}$$ takes place in the collector current. The input resistance and AC current gain are