The kinetic energy of electrons emitted, when radiation of frequency $1.0 \times 10^{15} \mathrm{~Hz}$ hits a metal, is

In which of the following species, the ratio of $s$-electrons to $p$-electrons is same?

Identify the pair of elements in which the difference in atomic radii is maximum

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

Identify the pair in which difference in bond order value is maximum.

The pair of molecules/ions with same geometry but central atoms in them are in different states of hybridisation is

If the density of a mixture of nitrogen and oxygen gases at 400 K and l atm pressure is $0.920 \mathrm{gL}^{-1}$, what i

The incorrect rule regarding the determination of significant figures is

At 61 K , one mole of an ideal gas of 1.0 L volume expands isothermally and reversibly to a final volume of 10.0 L . Wha

At $T(\mathrm{~K}), K_C$ for the dissociation of $\mathrm{PCl}_5$ is $2 \times 10^{-2} \mathrm{~mol} \mathrm{~L}^{-1}$.

The dihedral angles in gaseous and solid phases of $\mathrm{H}_2 \mathrm{O}_2$ molecule respectively are

Identify the compound which gives $\mathrm{CO}_2$ more readily on heating?

The major components of cement are

Consider the following reactions (not balanced). $$ \begin{array}{r} \mathrm{BF}_3+\mathrm{NaH} \xrightarrow{450 \mathrm

Which of the following does not exist?

Methemoglobinemia is due to

The IUPAC name of the following compound is

The functional groups present in the product ' $X$ ' of the reaction given below are

Identify the major product $(P)$ in the following reaction sequence. $$ \left(\mathrm{CH}_3\right)_3 \mathrm{CBr} \xrigh

What is the percentage of carbon in the product ' $X$ ' formed in the given reaction? $+\mathrm{C}_2 \mathrm{H}_5 \math

Identify the correct statement about the crystal defects in solids.

Dry air contains $79 \% \mathrm{~N}_2$ and $21 \% \mathrm{O}_2$. At $T(\mathrm{~K})$, if Henry's law constants for $\mat

If the degree of dissociation of formic acid is $11.0 \%$, the molar conductivity of 0.02 M solution of it is (Given, $\

Consider the gaseous reaction, $$ A_2+B_2 \longrightarrow 2 A B $$ The following data was obtained for the above reactio

Adsorption of a gas a solid adsorbent follows. Freundlich adsorption isotherm. If $x$ is the mass of the gas adsorbed on

Consider the following reactions. $$ X+\mathrm{O}_2 \rightarrow \mathrm{Cu}_2 \mathrm{O}+\mathrm{SO}_2, \mathrm{Cu}_2 \m

$Y$ in the given sequence of reactions is $$ \begin{gathered} \mathrm{P}_4+x \mathrm{NaOH}+y \mathrm{H}_2 \mathrm{O} \xr

In contact process of manufacture of $\mathrm{H}_2 \mathrm{SO}_4$, the arsenic purifier used in the industrial plant con

$\mathrm{Pt}+3: 1$ mixture of $\left(\right.$ Conc. $\mathrm{HCl}+$ conc. $\left.\mathrm{HNO}_3\right) \rightarrow[\math

In which of the following, ions are correctly arranged in the increasing order of oxidising power?

Which of the following will have a spin only magnetic moment of 2.86 BM ?

The monomer which is present in both bakelite and melamine polymers is

Cellulose is a polysaccharide and is made of

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

Which of the following is an example of allylic halide?

Identify the correct statements about $Z$. $$ \mathrm{C}_2 \mathrm{H}_5 \mathrm{NH}_2 \xrightarrow[0^{\circ} \mathrm{C}]

Assertion (A) : Aldehydes are more reactive than ketones towards nucleophilic addition reactions Reason (R) : In aldehyd

Arrange the following in the correct order of their boiling points.

What is the major product $Z$ in the given reaction sequence? $$ \left(\mathrm{CH}_3\right)_2 \mathrm{C}=\mathrm{O} \xri

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

The domain of the real valued function $f(x)=\sqrt[3]{\frac{x-2}{2 x^2-7 x+5}}+\log \left(x^2-x-2\right)$ is

$f$ is a real valued function satisfying the relation $f\left(3 x+\frac{1}{2 x}\right)=9 x^2+\frac{1}{4 x^2}$. If $f\lef

$\frac{1}{3 \cdot 6}+\frac{1}{6 \cdot 9}+\frac{1}{9 \cdot 12}+\ldots \ldots .$. to 9 terms $=$

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $\left|\begin{array}{lll}x & 2 & 2 \\ 2 & x & 2 \\ 2 & 2 &

If $\mathrm{A}=\left[\begin{array}{lll}1 & 2 & 2 \\ 3 & 2 & 3 \\ 1 & 1 & 2\end{array}\right]$ and $\mathrm{A}^{-1}=\left

If $A X=D$ represents the system of linear equations $3 x-4 y+7 z+6=0,5 x+2 y-4 z+9=0$ and $8 x-6 y-z+5=0$, then

If $(x, y, z)=(\alpha, \beta, \gamma)$ is the unique solution of the system of simultaneous linear equations $3 x-4 y+z+

If $\frac{(2-i) x+(1+i)}{2+i}+\frac{(1-2 i) y+(1-i)}{1+2 i}=1-2 i$, then $2 x+4 y=$

If $z=1-\sqrt{3} i$, then $z^3-3 z^2+3 z=$

The product of all the values of $(\sqrt{3}-i)^{\frac{2}{5}}$ is

The number of common roots among the 12 th and 30th roots of unity is

$\alpha$ is a root of the equation $\frac{x-1}{\sqrt{2 x^2-5 x+2}}=\frac{41}{60}$. If $-\frac{1}{2}

If $4+3 x-7 x^2$ attains its maximum value $M$ at $x=\alpha$ and $5 x^2-2 x+1$ attains its minimum value $m$ at $x=\beta

If $\alpha, \beta, \gamma$ are the roots of the equation $2 x^3-5 x^2+4 x-3=0$, then $\Sigma \alpha \beta(\alpha+\beta)=

$\alpha, \beta, \gamma, 2$ and $\varepsilon$ are the roots of the equation $$ \begin{aligned} & \alpha, \beta, \gamma+4

Among the 4 -digit numbers that can be formed using the digits $1,2,3,4,5$ and 6 without repeating any digit, the number

If the number of circular permutations of 9 distinct things taken 5 at a time is $n_1$ and the number of linear permutat

The number of ways in which 4 different things can be distributed to 6 persons so that no person gets all the things is

If the coefficients of 3 consecutive terms in the expansion of $(1+x)^{23}$ are in arithmetic progression, then those te

The numerically greatest term in the expansion of $(3 x-16 y)^{15}$, when $x=\frac{2}{3}$ and $y=\frac{3}{2}$, is

If $\frac{3 x^4-2 x^2+1}{(x-2)^4}=A+\frac{B}{x-2}+\frac{C}{(x-2)^2}$ $+\frac{D}{(x-2)^3}+\frac{E}{(x-2)^4}$, then $2 A+3

The maximum value of the function $f(x)=3 \sin ^{12} x+4 \cos ^{16} x$ is

If $A+B+C=2 S$, then $\sin (S-A) \cos (S-B)-\sin (S-C) \cos S=$

If $\cos x+\cos y=\frac{2}{3}$ and $\sin x-\sin y=\frac{3}{4}$, then $\sin (x-y)+\cos (x-y)=$

The solution set of the equation $\cos ^2 2 x+\sin ^2 3 x=1$ i

If $2 \tan ^{-1} x=3 \sin ^{-1} x$ and $x \neq 0$, then $8 x^2+1=$

Match the functions given in List I with their relevant characteristics from List II. .tg {border-collapse:collapse;bo

In a $\triangle A B C$, if $\tan \frac{A}{2}: \tan \frac{B}{2}: \tan \frac{C}{2}=15: 10: 6$, then $\frac{a}{b-c}=$

In a $\triangle A B C, \frac{a\left(r_1+r_2 r_3\right)}{r_1-r+r_2+r_3}=$

$\mathbf{a}, \mathbf{b}, \mathbf{c}$ are non-coplanar vectors. If the three points $\lambda a-2 b+c, 2 a+\lambda b-2 \ma

If $\hat{\mathbf{i}}+\hat{\mathbf{j}}, \hat{\mathbf{j}}+\hat{\mathbf{k}}, \hat{\mathbf{k}}+\hat{\mathbf{i}}, \hat{\mathb

If $\mathrm{a}, \mathrm{b}$ are two vectors such that $|\mathrm{a}|=3,|\mathrm{~b}|=4$, $|\mathbf{a}+\mathbf{b}|=\sqrt{3

$r$ is a vector perpendicular to the planet, determined by the vectors $2 \hat{\mathbf{i}}-\hat{\mathbf{j}}$ and $\hat{\

$\mathbf{b}=\hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \mathbf{k}, \quad \mathbf{c}=\hat{\mathbf{i}}+2 \hat{\mathbf{j}}-\hat{\m

The variance of the following continuous frequency distribution is .tg {border-collapse:collapse;border-spacing:0;}

Among the 5 married couples, if the names of 5 men are matched with the names of their wives randomly, then the probabil

If 3 dice are thrown, the probability of getting 10 as the sum of the three numbers that appeared on the top faces of th

Three similar urns $A, B, C$ contain 2 red and 3 white balls; 3 red and 2 white balls; 1 red and 4 white balls respectiv

If a random variable X has the following probability distribution, then the mean of $X$ is $$ \begin{array}{c|c|c|c|c}

A A fair coin is tossed a fixed number of times. If the probability of getting 5 heads is equal to the probability of ge

If the ratio of the distances of a variable point $P$ from the point $(1,1)$ and the line $x-y+2=0$ is $1: \sqrt{2}$, th

If the origin is shifted to the point $\left(\frac{3}{2},-2\right)$ by the translation of axes, then the transformed equ

$L \equiv x \cos \alpha+y \sin \alpha-p=0$ represents a line perpendicular to the line $x+y+1=0$. If $p$ is positive, $\

$(-2,-1),(2,5)$ are two vertices of a triangle and $\left(2, \frac{5}{3}\right)$ is its orthocenter. If $(m, n)$ is the

$L_1 \equiv 2 x+y-3=0$ and $L_2 \equiv a x+b y+c=0$ are two equal sides of an isosceles triangle. If $L_3 \equiv x+2 y+1

The slope of one of the pair of lines $2 x^2+h x y+6 y^2=0$ is thrice the slope of the other line, then $h=$

If $P\left(\frac{\pi}{4}\right), Q\left(\frac{\pi}{3}\right)$ are two points on the circle $x^2+y^2-2 x-2 y-1=0$, then t

The power of a point $(2,0)$ with respect to a circle $S$ is -4 and the length of the tangent drawn from the point $(1,1

The pole of the line $x-5 y-7=0$ with respect to the circle $S \equiv x^2+y^2-2 x+4 y+1=0$ is $P(a, b)$. If $C$ is the c

The equation of the pair of transverse common tangents drawn to the circles $x^2+y^2+2 x+2 y+1=0$ and $x^2+y^2-2 x-2 y+1

If a circle passing through the point $(1,1)$ cuts the circles $x^2+y^2+4 x-5=0$ and $x^2+y^2-4 y+3=0$ orthogonally, the

Length of the common chord of the circles $x^2+y^2-6 x+5=0$ and $x^2+y^2+4 y-5=0$ is

$P$ and $Q$ are the extremities of a focal chord of the parabola $y^2=4 a x$. If $P=(9,9)$ and $Q=(p, q)$, then $p-q=$

The number of normals that can be drawn through the point $(9,6)$ to the parabola $y^2=4 x$ is

The equations of the directrices of the elmpse $9 x^2+4 y^2-18 x-16 y-11=0$ are

$L_1^{\prime}$ is the end of a latus rectum of the ellipse $3x=2 \pm \frac{\sqrt{5}}{\sqrt{5}}$ $3 x^2+4 y^2=12$ which i

$(p, q)$ is the point of intersection of a latus rectum and an asymptote of the hyperbola $9 x^2-16 y^2=144$. If $p>0$ a

$A(3,2,-1), B(4,1,0), C(2,1,4)$ are the vertices of a $\triangle A B C$. If the bisector of $B A C$ ! intersects the sid

$(3,0,2)$ and $(0,2, k)$ are the direction ratios of two lines and $\theta$ is the angle between them. If $|\cos \theta|

A plane $(\pi)$ passing through the point $(1,2,-3)$ is perpendicular to the planes $x+y-z+4=0$ and $2 x-y+z+1=0$. If th

$\lim _{\theta \rightarrow \frac{\pi^{-}}{2}} \frac{8 \tan ^4 \theta+4 \tan ^2 \theta+5}{(3-2 \tan \theta)^4}=$

Define $ f: R \rightarrow R $ by $ f(x)=\left\{\begin{array}{cl}\frac{1-\cos 4 x}{x^{2}}, & x 0\end{array}\right. $ The

If $y=\frac{\tan x \cos ^{-1} x}{\sqrt{1-x^2}}$, then the value of $\frac{d y}{d x}$, when $x=0$ is

If $y(\cos x)^{\sin x}=(\sin x)^{\sin x}$, then the value of $\frac{d y}{d x}$ at $x=\frac{\pi}{4}$ is

If $x=\cos 2 t+\log (\tan t)$ and $y=2 t+\cot 2 t$, then $\frac{d y}{d x}=$

If $y=44 x^{45}+45 x^{-44}$, then $y^n=$

The approximate value of $\sqrt[3]{730}$ obtained by the application of derivatives is

If $\theta$ is the acute angle between the curves $y^2=x$ and $x^2+y^2=2$, then $\tan \theta=$

The vertical angle of a right circular cone is $60^{\circ}$. If water is being poured in to the cone at the rate of $\fr

A right circular cone is inscribed in a sphere of radius 3 units. If the volume of the cone is maximum, then semi-vertic

If $f(x)=k x^3-3 x^2-12 x+8$ is strictly decreasing for all $x \in R$, then

$\int e^{-2 x}\left(\tan 2 x-2 \sec ^2 2 x \tan 2 x\right) d x=$

If $\int x^3 \sin 3 x d x=f(x) \cos 3 x+g(x) \sin 3 x+C$, then 27 $(f(x)+x g(x))=$

$\int \frac{d x}{9 \cos ^2 2 x+16 \sin ^2 2 x}=$

$\int \frac{2 \cos 3 x-3 \sin 3 x}{\cos 3 x+2 \sin 3 x} d x=$

$ \int_{\frac{-3}{4}}^{\frac{\pi-6}{8}} \log (\sin (4 x+3)) d x= $

$\int_0^{16} \frac{\sqrt{x}}{1+\sqrt{x}} d x=$

$\int_0^{32 \pi} \sqrt{1-\cos 4 x} d x=$

The general solution of the differential equation $(9 x-3 y+5) d y=(3 x-y+1) d x$ is

The general solution of the differential equation $\frac{d y}{d x}=\frac{2 y^2+1}{2 y^3-4 x y+y}$ is

The related effort to derive the properties of a bigger, more complex system from the properties and interactions of its

The error in the measurement of resistance, when $(10 \pm 05)$ A current passing through it produces a potential differe

A stone is thrown vertically up from the top end of a window of height 1.8 m with a velocity of $8 \mathrm{~ms}^{-1}$. T

A cannon placed on a cliff at a height of 375 m fires a cannon ball with a velocity of $100 \mathrm{~ms}^{-1}$ at an ang

A 20 ton truck is travelling along a curved path of radius 240 m . If the centre of gravity of the truck above the groun

A block of mass $m$ with an initial kinetic energy $E$ moves up an inclined plane of inclination $\theta$. If $\mu$ is t

A man of mass 80 kg goes to the market on a scooter of mass 100 kg with certain speed. On application of brakes, the sto

A thin uniform wire of mass $m$ and linear mass density $\rho$ is bent in the form of a circular loop. The moment of ine

Three particles $A, B$ and $C$ of masses $m, 2 m$ and $3 m$ are moving towards north, south and east respectively. If th

A particle of mass 4 mg is executing simple harmonic motion along $X$-axis with an angular frequency of $40 \mathrm{rad}

The ratio of the accelerations due to gravity at heights 1280 km and 3200 km above the surface of the earth is (Radius o

If the length of a string is $P$ when the tension in it is 6 N and its length is $Q$ when the original length of the str

The excess pressure inside a soap bubble of radius 0.5 cm is balanced by the pressure due to an oil column of height 4 m

Water flows through a horizontal pipe of variable cross-section at the rate of $12 \pi$ litre per minute. The velocity o

When 54 g of ice at $-20^{\circ} \mathrm{C}$ is mixed with 25 g of steam at $100^{\circ} \mathrm{C}$, then the final mix

A solid sphere at a temperature $T \mathrm{~K}$ is cut in to two hemisphere. The ratio of energies radiated by one hemis

If $d Q, d U$ and $d W$ are heat energy absorbed, change in internal energy and external work done respectively by a dia

If the temperature of a gas increased from $27^{\circ} \mathrm{C}$ to $159^{\circ} \mathrm{C}$, the increase in the rms

A boy standing on a platform observes the frequency of a train horn as it passes by. The change in the frequency noticed

If three sources of sound of frequencies $(n-1), n$ and $(n+1)$ are vibrated together, the number of beats produced and

A small angled prism is made of a material of refractive index $\frac{3}{2}$. The ratio of the angles of minimum deviati

If you are using eye glasses of power 2 D, your near point is

The diameter of the objective of a telescope is 3.6 m . The limit of resolution of the telescope for a light of waveleng

Two point charges of magnitudes $-8 \mu \mathrm{C}$ and $+32 \mu \mathrm{C}$ are separated by a distance of 15 cm in air

If half of the space between the plates of a parallel plate capacitor is filled with a medium of dielectric constant 4 ,

The potential difference between the ends of a straight conductor of length 20 cm is 16 V . If the drift speed of the el

The potential difference $V$ across the filament of the bulb shown in the given Wheatstone bridge varies as $V=i(2 i+1)$

Two points $A$ and $B$ on the axis of a circular current loop are at distances of 4 cm and $3 \sqrt{3} \mathrm{~cm}$ fro

Two charged particles $A$ and $B$ of masses $m$ and $2 m$, charges $2 q$ and $3 q$ respectively moving with same velocit

If a bar magnet of moment $10^{-4} \mathrm{Am}^2$ is kept in a uniform magnetic field of $12 \times 10^{-3} \mathrm{~T}$

A train with an axle of length 1.66 m is moving towards north with a speed of $90 \mathrm{kmh}^{-1}$. If the vertical co

The natural frequency of an $L-C$ circuit is 120 kHz . When the capacitor in the circuit is totally filled dielectric ma

A plane electromagnetic wave of electric and magnetic fields $E_0$ and $B_0$ respectively incidents on a surface. If the

If the de-Broglie wavelength of a neutron at a temperature of $77^{\circ} \mathrm{C}$ is $\lambda$, then the de-Broglie

The ratio of the wavelengths of radiation emitted when an electron in the hydrogen atom jumps from 4th orbit to 2 nd orb

The half lives of two radioactive material $A$ and $B$ are respectively $T$ and $2 T$. If the ratio of the initial masse

The energy released by the fission of one uranium nucleus is 200 MeV . The number of fissions per second required to pro

A zener diode of zener voltage 30 V is connected in circuit as shown in the figure. The maximum current through the zene

Two logic gates are connected as shown in the figure. If the inputs are $A=1$ and $B=0$, then the values of $Y_1$ and $Y

A message signal of peak voltage 12 V is used to amplitude modulate a carrier signal of frequency 1.2 MHz . The amplitud