Identify the pair of species having same energy from the following. (The number given in the bracket corresponds to prin

Which one of the following corresponds to the wavelength of line spectrum of H atom in its Balmer series ? ( $R=$ Rydber

Identify the pair of element in which the number of $s$-electrons to $p$-electrons ratio is $2: 3$

Which of the following has the least electron gain enthalpy?

According to Fajan's rules, which of the following is not correct about covalent character?

Consider the following pairs. $$ \begin{array}{l|l|l} \hline & \text { Order } & \text { Property } \\ \hline \text { (A

An open vessel containing air was heated from $27^{\circ} \mathrm{C}$ to $727^{\circ} \mathrm{C}$. Some air was expelled

12 g of an element reacts with 32 g of oxygen. What is the equivalent weight of the element ?

The standard enthalpy of formation $\left(\Delta_f H^{\varphi}\right)$ of ammonia is $-46.2 \mathrm{~kJ} \mathrm{~mol}^{

At $T(\mathrm{~K}), K_c$ for the reaction, $A O_2(g)+B \mathrm{O}_2(g) \rightleftharpoons A \mathrm{O}_3(g)+B \mathrm{O}

Observe the following reactions. $$ \begin{aligned} & \text { I. } \mathrm{H}_2 \mathrm{O}(l)+2 \mathrm{Na}(s) \longrigh

What is the correct stability order of $\mathrm{KO}_2, \mathrm{RbO}_2, \mathrm{CsO}_2$ ?

Assertion (A) $\mathrm{MgO}, \mathrm{CaO}, \mathrm{SrO}$ and BaO are insoluble in water. Reason ( R ) In aqueous medium

Identify the element for which +1 oxidation state is more stable than +3 oxidation state.

Observe the oxides $\mathrm{CO}, \mathrm{B}_2 \mathrm{O}_3, \mathrm{SiO}_2, \mathrm{CO}_2, \mathrm{Al}_2 \mathrm{O}_3$.

The common components of photochemical smog are

The electron displacement effect observed in the given structures is known as

An alkene $X\left(\mathrm{C}_4 \mathrm{H}_8\right)$ exhibits geometrical isomerism. Oxidation of $A$ with $\mathrm{KMnO}

The number of activating and deactivating groups of the following are respectively $$ \begin{aligned} & -\mathrm{OCH}_2

$X$ and $Z$ respectively in the following reaction sequence are $\mathrm{C}_3 \mathrm{H}_6 \xrightarrow{X} Y \xrightarro

The molecular formula of a compound is $A B_2 \mathrm{O}_4$. Atoms of $O$ form ccp lattice. Atoms of $A$ (cation) occupy

Distilled water boils at 373.15 K and freezes at 273.15 K . A solution of glucose in distilled water boils at 373.202 K

Identify the correct statements from the following (A) At 298 K , the potential of hydrogen electrotle placed in a solu

For a first order reaction, a plot of $\ln k\left(Y\right.$-axis) and $\frac{1}{T}$ $(X$-axis) gave the straight line wi

Adsorption of a gas ( $A$ ) on an adsorbent follows Freundlich adsorption isotherm. The slope and intercept (on $Y$-axis

A low boiling point metal contains high boiling point metal as impurity. The correct refining method is

Which of the following when subjected to thermal decomposition will liberate dinitrogen ? (i) Sodium nitrate (ii) Ammoni

"Observe the following reaction. This reaction represents $$ 4 \mathrm{HCl}+\mathrm{O}_2 \xrightarrow[723 \mathrm{~K}]

Identify the set which is not correctly matched in the following.

Identify the correct statements from the following. (i) Ti (IV) is more stable than Ti (III) and Ti (II). (ii) Among $

The molecular formula of a coordinate complex is $\mathrm{CoH}_{12} \mathrm{O}_6 \mathrm{Cl}_3$. When one mole of this a

Match the following. List-I (Monomer/s) List-II (Name of polymer) A. C

The functional groups involved in the conversion of glucose to gluconic acid and gluconic acid to saccharic acid respect

Among the following the incorrect statement about chloramphenicol is

A halogen compound $X\left(\mathrm{C}_4 \mathrm{H}_9 \mathrm{Br}\right)$ on hydrolysis gave alcohol $Y$. The alcohol $Y$

An alcohol $X\left(\mathrm{C}_3 \mathrm{H}_{12} \mathrm{O}\right)$ when reacted with conc. HCl and anhydrous $\mathrm{Zn

Assertion (A) : Chlorobenzene is not formed in the reaction of phenol with thionyl chloride. Reason (R) : In phenol, ca

The $\mathrm{p} K_{\mathrm{a}}$ values of $X, Y, Z$ respectively are $8.3,7.1,10.2$. What are $X, Y, Z$ ?

The reagents/ chemicals $X$ and $Y$ that convert cyanobenzene to Schiff's base are

The correct statement(s) of the following is/are (A) Aniline forms a stable benzene diazonium chloride at 285 K . (B) N

If $f(x)=\frac{2 x-3}{3 x-2}$ and $f_n(x)=($ fofofo .......n times) $(x)$, then $f_{32}(x)=$

The domain of the real valued function $f(x)=\sqrt{\cos (\sin x)}+\cos ^{-1}\left(\frac{1+x^2}{2 x}\right)$ is

For $n \in N$ the largest positive integer that divides $81^n+20 n-1$ is $k$. If $S$ is the sum of all positive divisors

$A, B, C$ and $D$ are square matrices such that $A+B$ is symmetric, $A-B$ is skew-symmetric and $D$ is the transpose of

If $A$ is square matrix and $A^2+I=2 A$, then $A^9=$

$\operatorname{det}\left[\begin{array}{ccc}\frac{a^2+b^2}{c} & c & c \\\\ a & \frac{b^2+c^2}{a} & a \\\ b & b & \frac{c^

The system of simultaneous linear equations $$ \begin{aligned} & x-2 y+3 z=4,3 x+y-2 z=7 \\ & 2 x+3 y+z=6 \text { has }

If $\sqrt{5}-i \sqrt{15} \doteqdot r(\cos \theta+i \sin \theta),-\pi

The point $P$ denotes the complex number $z=x+i y$ in the argand plane. If $\frac{2 z-i}{z-2}$ is a purely real number,

$x$ and $y$ are two complex numbers such that $|x|=|y|=1$. If $\arg (x)=2 \alpha, \arg (y)=3 \beta$ and $\alpha+\beta=\f

One of the roots of the equation $x^{14}+x^9-x^5-1=0$ is

If the quadratic equation $3 x^2+(2 k+1) x-5 k=0$ has real and equal roots, then the value of $k$ such that $\frac{1}{2}

The equations $2 x^2+a x-2=0$ and $x^2+x+2 a=0$ have exactly one common root. If $a \neq 0$, then one of the roots of th

If $\alpha, \beta$ and $\gamma$ are the roots of the equation $2 x^3-3 x^2+5 x-7=0$, then $\sum \alpha^2 \beta^2=$

The sum of two roots of the equation $x^4-x^3-16 x^2+4 x+48=0$ is zero. If $\alpha, \beta, \gamma$ and $\delta$ are the

The sum of all the 4 -digit numbers formed by taking all the digits from $2,3,5,7$ without repetition, is

The number of ways in which 15 identical gold coins can be distributed among 3 persons such that each one gets atleast 3

The number of all possible combinations of 4 letters which are taken from the letters of the word 'ACCOMMODATION', is

If ${ }^n c_r=c_r$ and $2 \frac{c_1}{c_0}+4 \frac{c_2}{c_1}+6 \frac{c_3}{c_2}+\ldots .+2 n \frac{c_n}{c_{n-1}}=650$, the

When $|x|

If $\frac{x^4}{\left(x^2+1\right)(x-2)}=f(x)+\frac{A x+B}{x^2+1}+\frac{C}{x-2}$, then $f(14)+2 A-B=$

If the period of the function $f(x)=2 \cos (3 x+4)-3 \tan (2 x-3)+5 \sin (5 x)-7$ is $k$, then

If $\tan A

If $m \cos (\alpha+\beta)-n \cos (\alpha-\beta)$ $=m \cos (\alpha-\beta)+n \cos (\alpha+\beta)$, then $\tan \alpha \tan

The number of solutions of the equation $\sin 7 \theta-\sin 3 \theta=\sin 4 \theta$ that lie in the interval $(0, \pi)$,

$\cos ^{-1} \frac{3}{5}+\sin ^{-1} \frac{5}{13}+\tan ^{-1} \frac{16}{63}=$

If $\cosh ^{-1}\left(\frac{5}{3}\right)+\sinh ^{-1}\left(\frac{3}{4}\right)=k$, then $e^k=$

In a $\triangle A B C$, if $(a-b)^2 \cos ^2 \frac{C}{2}+(a+b)^2 \sin ^2 \frac{C}{2}=a^2+b^2$, then $\cos A=$

In a $\triangle A B C$, if $r_1 r_2+r_3=35, r_2 r_3+r_1=63$ and $r_3 r_1+r_2=45$, then $2 s=$

$\hat{\mathbf{i}}-2 \hat{\mathbf{j}}+\hat{\mathbf{k}}, 2 \hat{\mathbf{i}}+\hat{\mathbf{j}}-\hat{\mathbf{k}}$ and $\hat{\

A vector of magnitude $\sqrt{2}$ units along the internal bisector of the angle between the vectors $2 \hat{\mathbf{i}}-

If $\theta$ is the angle between the vectors $4 \hat{\mathbf{i}}-\hat{\mathbf{j}}+2 \hat{\mathbf{k}}$ and $\hat{\mathbf{

$\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are three vectors such that $|a|=3,|b|=2 \sqrt{2},|c|=5$ and $\mathbf{c}$ is p

If $\mathbf{a}, \mathbf{b}$ and $\mathbf{c}$ are non-coplanar vectors and the points $\lambda \mathbf{a}+3 \mathbf{b}-\m

The mean deviation about the mean for the following data is \begin{array}{c|l|l|l|l|l} \hline \text { Class interval } &

When 2 dice are thrown, it is observed that the sum of the numbers appeared on the top faces of both the dice is a prime

If 2 cards are drawn at random from a well shuffled pack of 52 playing cards from the same suit, then the probability of

A dealer gets refrigerators from 3 different manufacturing companies $C_1, C_2$ and $C_3 .25 \%$ of his stock is from $C

If the probability that a student selected at random from a particular college is good at mathematics is 0.6 , then the

If on an average 4 customers visit a shop in an hour, then the probability that more than 2 customers visit the shop in

The centroid of a variable $\triangle A B C$ is at the distance of 5 units from the origin. If $A=(2,3)$ and $B=(3,2)$,

When the origin is shifted to the point $(2, b)$ by translation of axes, the coordinates of the point $(a, 4)$ have chan

The slope of a line $L$ passing through the point $(-2,-3)$ is not defined. If the angle between the lines $L$ and $a x-

$(a, b)$ is the point of concurrency of the lines $x-3 y+3=0, k x+y+k=0$ and $2 x+y-8=0$. If the perpendicular distance

If $(4,3)$ and $(1,-2)$ are the end points of a diagonal of a square, then the equation of one of its sides is

Area of the triangle bounded by the lines given by the equations $12 x^2-20 x y+7 y^2=0$ and $x+y-1=0$ is

If $(1,1),(-2,2)$ and $(2,-2)$ are 3 points on a circle $S$, then the perpendicular distance from the centre of the circ

If the line $4 x-3 y+p=0(p+3>0)$ touches the circle $x^2+y^2-4 x+6 y+4=0$ at the point $(h, k)$, then $h-2 k=$

If the inverse point of the point $P(3,3)$ with respect to the circle $x^2+y^2-4 x+4 y+4=0$ is $Q(a, b)$, then $a+5 b=$

If the equation of the transverse common tangent of the circles $x^2+y^2-4 x+6 y+4=0$ and $x^2+y^2+2 x-2 y-2=0$ is $a x+

A circle $S \equiv x^2+y^2+2 g x+2 f y+6=0$ cuts another circle $x^2+y^2-6 x-6 y-6=0$ orthogonally. If the angle between

If $m_1$ and $m_2$ are the slopes of the direct common tangents drawn to the circles $x^2+y^2-2 x-8 y+8=0$ and $x^2+y^2-

If $(2,3)$ is the focus and $x-y+3=0$ is the directrix of a parabola, then the equation of the tangent drawn at the vert

The equation of the common tangent to the parabola $y^2=8 x$ and the circle $x^2+y^2=2$ is $a x+b y+2=0$. If $-\frac{a}{

Consider the parabola $25\left[(x-2)^2+(y+5)^2\right]=(3 x+4 y-1)^2$, match the characteristic of this parabola given i

If $6 x-5 y-20=0$ is a normal to the ellipse $x^2+3 y^2=K$, then $K=$

The point of intersection of two tangents drawn to the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{4}=1$ lie on the circle $x^

If the ratio of the perpendicular distances of a variable point $P(x, y, z)$ from the $X$-axis and from the $Y Z$ - plan

The direction cosines of two lines are connected by the relations $l-m+n=0$ and $2 l m-3 m n+n l=0$. If $\theta$ is the

A plane $\pi$ passes through the points $(5,1,2),(3,-4,6)$ and $(7,0,-1)$. If $p$ is the perpendicular distance from the

$\lim _{x \rightarrow 0} \frac{3^{\sin x}-2^{\tan x}}{\sin x}=$

If the function $$ f(x)=\left\{\begin{array}{cc} \frac{\cos a x-\cos 9 x}{x^2} & \text {, if } x \neq 0 \\ 16 & \text {,

If $ f(x)=\left\{\begin{array}{ll}\frac{8}{x^{3}}-6 x & \text {, if } 0 1\end{array}\right. $ is a real valued function

If $2 x^2-3 x y+4 y^2+2 x-3 y+4=0$, then $\left(\frac{d y}{d x}\right)_{(3,2)}=$

If $x=\frac{9 t^2}{1+t^4}$ and $y=\frac{16 t^2}{1-t^4}$ then $\frac{d y}{d x}=$

If $y=\sin a x+\cos b x$, then $y^{\prime \prime}+b^2 y=$

The radius of a sphere is 7 cm . If an error of 0.08 sq cm is made in measuring it, then the approximate error (in cubic

The curve $y=x^3-2 x^2+3 x-4$ intersects the horizontal line $y=-2$ at the point $P(h, k)$. If the tangent drawn to this

A particle moving from a fixed point on a straight line travels a distance $S$ metres in $t \mathrm{sec}$. If $S=t^3-t^2

If $f(x)=(2 x-1)(3 x+2)(4 x-3)$ is a real valued function defined on $\left[\frac{1}{2}, \frac{3}{4}\right]$, then the v

If the interval in which the real valued function $f(x)=\log \left(\frac{1+x}{1-x}\right)-2 x-\frac{x^3}{1-x^2}$ is decr

$\int(\sqrt{1-\sin x}+\sqrt{1+\sin x}) d x=f(x)+c$, where $c$ is the constant of integration. If $\frac{5 \pi}{2}$<$x

If $f(x)=\int \frac{\sin 2 x+2 \cos x}{4 \sin ^2 x+5 \sin x+1} d x$ and $f(0)=0$, then $f(\pi / 6)=$

$\int \frac{\left(1-4 \sin ^2 x\right) \cos x}{\cos (3 x+2)} d x=$

$\int \frac{\left(1-4 \sin ^2 x\right) \cos x}{\cos (3 x+2)} d x=$

$\lim \limits_{n \rightarrow \infty}\left[\left(1+\frac{1}{n^2}\right)\left(1+\frac{4}{n^2}\right)\left(1+\frac{9}{n^2}\

$\int_{-2}^2 x^4\left(4-x^2\right)^{\frac{7}{2}} d x=$

Area of the region enclosed between the curves $y^2=4(x+7)$ and $y^2=5(2-x)$ is

If the slope of the tangent drawn at any point $(x, y)$ on the curve $y=f(x)$ is $\left(6 x^2+10 x-9\right)$ and $f(2)=0

The general solution of the differential equation $\left(3 x^2-2 x y\right) d y+\left(y^2-2 x y\right) d x=0$ is

Regarding fundamental forces in nature, the correct statement is

The equation of motion of a damped oscillator is given by $m \frac{d^2 x}{d t^2}+b \frac{d x}{d t}+k x=0$. The dimension

A body is falling freely from the top of a tower of height 125 m . The distance covered by the body during the last seco

A body $P$ is projected at an angle of $30^{\circ}$ with the horizontal and another body $Q$ is projected at an angle of

A car is moving on circular track banked at an angle of $45^{\circ}$. If the maximum permissible speed of the car to avo

A block of mass 0.5 kg is at rest on a horizontal table. The coefficient of kinetic friction between the table and the b

The sphere $A$ of mass $m$ moving with a constant velocity hits another sphere $B$ of mass $2 m$ at rest. If the coeffic

A solid sphere rolls down without slipping from the top of an inclined plane of height 28 m and angle of inclination $30

Four identical particles each of mass $m$ are kept at the four corners of a square of side $a$. If one of the particles

In a time $t$ amplitude of vibrations of a damped oscillator becomes half of its initial value, then the mechanical ener

The energy required to take a body from the surface of the earth to a height equal to the radius of the earth is $W$. Th

A steel wire of length 3 m and a copper wire of length 2.2 m are connected end to end. When the combination is stretched

The height of water level in a tank of uniform cross-section is 5 m . The volume of the water leaked in 5 s through a ho

The work done in increasing the diameter of a soap bubble from 2 cm to 4 cm is (Surface tension of soap solution $=3.5 \

The temperature on a fahrenheit temperature scale that is twice the temperature on a celsius temperature scale is

The temperatures of equal masses of three different liquids $A, B$ and $C$ are $15^{\circ} \mathrm{C}, 24^{\circ} \mathr

The efficiency of a reversible heat engine working between two temperatures is $50 \%$. The coefficient of performance o

The total internal energy of 4 moles of a diatomic gas at a temperature of $27^{\circ} \mathrm{C}$ is (gas constant $=83

A car travelling at a speed of 54 kmph towards a wall sounds horn of frequency 400 Hz . The difference in the frequencie

The speed of a transverse wave in a stretched string $A$ is $v$. Another string $B$ of same length and same radius is su

For a combination of two convex lenses of focal lengths $f_1$ and $f_2$ to act as a glass slab, the distance of separati

If a ray of light passes through an equilateral prism such that the angle of incidence and the angle of emergence are bo

Young's double slit experiment is performed with monochromatic light of wavelength $6000 \mathring{A}$. If the intensity

Two positive point charges are separated by a distance of 4 m in air. If the sum of the two charges is $36 \mu \mathrm{C

Three capacitors of capacitances $10 \mu \mathrm{~F}, 5 \mu \mathrm{~F}$ and $20 \mu \mathrm{~F}$ are connected in serie

When the temperature of a wire is increased from 303 K to 356 K , the resistance of the wire increases by $10 \%$. The t

Three resistors of resistances $10 \Omega, 20 \Omega$ and $30 \Omega$ are connected as shown in the figure. If the point

A particle of charge 2 C is moving with a velocity of $(3 \hat{\mathbf{i}}+4 \hat{\mathrm{j}}) \mathrm{ms}^{-1}$ in the

A rectangular coil of 400 turns and $10^{-2} \mathrm{~m}^2$ area, carrying a current of 0.5 A is placed in a uniform mag

The most exotic diamagnetic materials are

Two circular coils of radii $r_1$ and $r_2\left(r_1 \ll r_2\right)$ are placed coaxially with their centres coinciding.

In a series $L-C-R$ circuit, if the current leads the source voltage, then

If the amplitude of the magnetic field part of a harmonic electromagnetic wave in vacuum is 270 nT , the amplitude of th

If Planck's constant is $6.63 \times 10^{-34} \mathrm{Js}$, then the slope of a graph drawn between cut-off voltage and

At room temperature, gaseous hydrogen is bombarded with a beam of electrons of 13.6 eV energy. The series to which the e

The half-life of a radioactive substance is 12 min . The time gap between $28 \%$ decay and $82 \%$ decay of the radioac

An element consists of a mixture of three isotopes $A, B$ and $C$ of masses $m_1, m_2$ and $m_3$, respectively. If the r

The concentration of electrons in an intrinsic semiconductor is $6 \times 10^{15} \mathrm{~m}^{-3}$. On doping with an i

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

The heights of the transmitting and receiving antennas are 33.8 m and 64.8 m respectively. The maximum distance between