The maximum number of electrons present in an orbital with $$n = 4, l = 3$$ is

Which quantum number provides information about the shape of an orbital?

In which of the following, elements are arranged in the correct order of their electron gain enthalpies?

In second period of the long form of the periodic table an element $$X$$ has second lowest first ionisation enthalpy and

The set of molecules in which the central atom is not obeying the octet rule is

The formal charges of atoms (1), (2) and (3) in the ion is

From the following plots, find the correct option.

How many grams of Mg is required to completely reduce $$100 \mathrm{~mL}, 0.1 \mathrm{~M} \mathrm{~NO}_3^{-}$$ solution

What is the oxidation state of S in the sulphur containing product of the following reaction? $$\mathrm{SO}_3^{2-}(a q)+

Observe the following properties : Volume, enthalpy, density, temperature, heat capacity, pressure and internal energy.

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

Which of the following expression is correct?

The pH of 0.01 N lime water is

The empirical formula of calgon is

The pair of elements that form both oxides and nitrides, when burnt in air are

Among $$\mathrm{P}_4, \mathrm{~S}_8$$ and $$\mathrm{N}_2$$ the elements which undergo disproportionation when heated wit

Identify the correct statements about the anomalous behaviour of boron. I. Boron trihalides can form dimeric structures.

The hybridisations of carbon in graphite, diamond and $$\mathrm{C}_{60}$$ are respectively

The major product of the following reaction is

Identify the ortho and para-directing groups towards aromatic electrophilic substitution reactions from the following li

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Which of the following solids is not a molecular solid?

A solution containing 6.0 g of urea is isotonic with a solution containing 10 g of a non-electrolytic solute $$X$$. The

$$x \%(w / V)$$ solution of urea is isotonic with $$4 \%$$ $$(w / V)$$ solution of a non-volatile solute of molar mass $

38.6 amperes of current is passed for 100 seconds through an aqueous $$\mathrm{CuSO}_4$$ solution using platinum electro

The time required for completion of $$93.75 \%$$ of a first order reaction is $$x$$ minutes. The half-life of it (in min

The macromolecular colloids of the following are I. Starch solution II. Sulphur sol III. Synthetic detergent IV. Synthet

Assertion (A) Animal skins are colloidal in nature. Reason (R) Animal skin has positively charged particles.

In the reaction of phosphorus with conc. $$\mathrm{HNO}_3$$, the oxidised and reduced products respectively are

Which of the following is formed when $$\mathrm{SO}_3$$ is absorbed by concentrated $$\mathrm{H}_2 \mathrm{SO}_4$$ ?

Assertion (A) Transition metals and their complexes show catalytic activity. Reason (R) The activation energy of a react

The crystal field theory is successful in explaining which of the following? I. Ligands as point charges. II. Formation

Pernicious anemia is caused due to deficiency of which vitamin ?

Which of the following vitamins cannot be stored in the body?

Finkelstein reaction is used for the synthesis of

Which among the following will have highest density?

Identify the major product (Y) from the following reaction,

An aryl carboxylic acid on treatment with sodium hydrogen carbonate liberates a gaseous molecule. Identify the gas molec

Identify the major product of the following reaction.

Identify the major product of the following reaction,

$$\left\{x \in R / \frac{\sqrt{|x|^2-2|x|-8}}{\log \left(2-x-x^2\right)}\right.$$ is a real number $$\}=$$

The domain of the real valued function $$f(x)=\sin \left(\log \left(\frac{\sqrt{4-x^2}}{1-x}\right)\right.$$ is

If $$A=\left[\begin{array}{cc}2 & -3 \\ -4 & 1\end{array}\right]$$, then $$\left(A^T\right)^2+(12 A)^T=$$

If $$a, b, c$$ are respectively the 5 th, 8 th, 13 th terms of an arithmetic progression, then $$\left|\begin{array}{ccc

If $$A=\left[\begin{array}{ccc}1 & 0 & 0 \\ a & -1 & 0 \\ b & c & 1\end{array}\right]$$ is such that $$A^2=I$$, then

Let $$A=\left[\begin{array}{ccc}-2 & x & 1 \\ x & 1 & 1 \\ 2 & 3 & -1\end{array}\right]$$. If the roots of the equation

Multiplicative inverse of the complex number $$(\sin \theta, \cos \theta)$$ is

$$\sum_\limits{k=0}^{440} i^k=x+i y \Rightarrow x^{100}+x^{99} y+x^{242} y^2+x^{97} y^3=$$

A true statement among the following identities is

If $$e^{i \theta}=\operatorname{cis} \theta$$, then $$\sum_\limits{n=0}^{\infty} \frac{\cos (n \theta)}{2^n}=$$

If $$f(f(0))=0$$, where $$f(x)=x^2+a x+b, b \neq 0$$, then $$a+b=$$

The sum of the real roots of the equation $$|x-2|^2+|x-2|-2=0$$ is

If the difference between the roots of $$x^2+a x+b=0$$ and that of the roots of $$x^2+b x+a=0$$ is same and $$a \neq b$$

For what values of $$a \in Z$$, the quadratic expression $$(x+a)(x+1991)+1$$ can be factorised as $$(x+b)(x+c)$$, where

If a set $$A$$ has $$m$$-elements and the set $$B$$ has $$n$$-elements, then the number of injections from $$A$$ to $$B$

In how many ways can the letters of the word "MULTIPLE" be arranged keeping the position of the vowels fixed?

The least value of $$n$$ so that $${ }^{(n-1)} C_3+{ }^{(n-1)} C_4>{ }^n C_3$$

A natural number $$n$$ such that $$n!$$ ends in exactly 1000 zeroes is

If $$\frac{13 x+43}{2 x^2+17 x+30}=\frac{A}{2 x+5}+\frac{B}{x+6}$$, then $$A^2+B^2=$$

If $$A+B+C=\pi, \cos B=\cos A \cos C$$, then $$\tan A \tan C=$$

In a $$\triangle A B C,\left(\tan \frac{A}{2} \tan \frac{B}{2} \tan \frac{C}{2}\right)^2 \leq$$

The value of $$\tan \left(\frac{7 \pi}{8}\right)$$ is

$$1+\sec ^2 x \sin ^2 x=$$

In a $$\triangle A B C, 2(b c \cos A+a c \cos B+a b \cos C)=$$

If $$4+6\left(e^{2 x}+1\right) \tanh x=11 \cosh x+11 \sinh x$$ then $$x=$$

In a $$\triangle A B C, \frac{a}{b}=2+\sqrt{3}$$ and $$\angle C=60^{\circ}$$. Then, the measure of $$\angle A$$ is

If $$a=2, b=3, c=4$$ in a $$\triangle A B C$$, then $$\cos C=$$

In a $$\triangle A B C$$ $$(b+c) \cos A+(c+a) \cos B+(a+b) \cos C=$$

$$D, E, F$$ are respectively the points on the sides $$B C, C A$$ and $$A B$$ of a $$\triangle A B C$$ dividing them in

$$O A B C$$ is a tetrahedron. If $$D, E$$ are the mid-points of $$O A$$ and $$B C$$ respectively, then $$\mathbf{D E}=$$

If $$\mathbf{a}+\mathbf{b}+\mathbf{c}=0$$ and $$|\mathbf{a}|=7,|\mathbf{b}|=5,|\mathbf{c}|=3$$ then the angle between $$

If $$P$$ and $$Q$$ are two points on the curve $$y=2^{x+2}$$ in the rectangular cartesian coordinate system such that $$

If the equation of the plane passing through the point $$A(-2,1,3)$$ and perpendicular to the vector $$3 \hat{i}+\hat{j}

If the mean of the data $$p, 6,6,7,8,11,15,16$$, is 3 times $$p$$, then the mean deviation of the data from its mean is

In a box, there are 8 red, 7 blue and 6 green balls. One ball is picked randomly. The probability that it is neither red

For two events $$A$$ and $$B$$, a true statement among the following is

Five digit numbers are formed by using digits $$1,2,3,4$$ and 5 without repetition. Then, the probability that the rando

A manager decides to distribute ₹ 20000 between two employees $$X$$ and $$Y$$. He knows $$X$$ deserves more than $$Y$$,

Which of the following is not a property of a Binomial distribution?

In a Binomial distribution $$B(n, p)$$, if the mean and variance are 15 and 10 respectively, then the value of the param

Suppose $$P$$ and $$Q$$ are the mid-points of the sides $$A B$$ and $$B C$$ of a triangle where $$A(1,3), B(3,7)$$ and $

Suppose $$\triangle A B C$$ is an isosceles triangle with $$\angle C=90^{\circ}, A=(2,3)$$ and $$B=(4,5)$$. Then, the ce

If the points of intersection of the coordinate axes and $$|x+y|=2$$ form a rhombus, then its area is

Suppose, in $$\triangle A B C, x-y+5=0, x+2 y=0$$ are respectively the equations of the perpendicular bisectors of the s

If the pair of straight lines $$9 x^2+a x y+4 y^2+6 x+b y-3=0$$ represents two parallel lines, then

A line passing through $$P(2,3)$$ and making an angle of $$30^{\circ}$$ with the positive direction of $$X$$-axis meets

For any real number $$t$$, the point $$\left(\frac{8 t}{1+t^2}, \frac{4\left(1-t^2\right)}{1+t^2}\right)$$ lies on a / a

The area of the circle passing through the points $$(5, \pm 2),(1,2)$$ is

The ratio of the largest and shortest distances from the point $$(2,-7)$$ to the circle $$x^2+y^2-14 x-10 y-151=0$$ is

A circle has its centre in the first quadrant and passes through $$(2,3)$$. If this circle makes intercepts of length 3

The image of the point $$(3,4)$$ with respect to the radical axis of the circles $$x^2+y^2+8 x+2 y+10=0$$ and $$x^2+y^2+

Suppose a parabola passes through $$(0,4),(1,9)$$ and $$(4,5)$$ and has its axis parallel to the $$Y$$-axis. Then, the e

The focal distances of the point $$\left(\frac{4}{\sqrt{5}}, \frac{3}{\sqrt{5}}\right)$$ on the ellipse $$\frac{x^2}{4}+

If the normal to the rectangular hyperbola $$x^2-y^2=1$$ at the point $$P(\pi / 4)$$ meets the curve again at $$Q(\theta

If the vertices and foci of a hyperbola are respectively $$( \pm 3,0)$$ and $$( \pm 4,0)$$, then the parametric equation

If $$x$$-coordinate of a point $$P$$ on the line joining the points $$Q(2,2,1)$$ and $$R(5,2,-2)$$ is 4, then the $$y$$-

If $$(2,3, c)$$ are the direction ratios of a ray passing through the point $$C(5, q, 1)$$ and also the mid-point of the

If the equation of the plane which is at a distance of $$1 / 3$$ units from the origin and perpendicular to a line whose

If $$[\cdot]$$ denotes greatest integer function, then $$\lim _\limits{x \rightarrow \frac{-3}{5}} \frac{1}{\dot{x}}\lef

If $$l, m(l

Let $$f(x)=\left\{\begin{array}{cl}\frac{1}{|x|}, & \text { for }|x|>1 \\ a x^2+b, & \text { for }|x| \leq 1\end{array}\

If $$x \neq 0$$ and $$f(x)$$ satisfies $$8 f(x)+6 f(1 / x) =x+5$$, then $$\frac{d}{d x}\left(x^2 f(x)\right)$$ at $$x=1$

$$\frac{d}{d x}\left(\lim _{x \rightarrow 2} \frac{1}{y-2}\left(\frac{1}{x}-\frac{1}{x+y-2}\right)\right)=$$

If $$f(x)=\left\{\begin{array}{cc}\frac{x^2 \log (\cos x)}{\log (1+x)} & , \quad x \neq 0 \\ 0 & , x=0\end{array}\right.

The number of those tangents to the curve $$y^2-2 x^3-4 y+8=0$$ which pass through the point $$(1,2)$$ is

If the straight line $$x \cos \alpha+y \sin \alpha=p$$ touches the curve $$\left(\frac{x}{a}\right)^n+\left(\frac{y}{b}\

Condition that 2 curves $$y^2=4 a x, x y=c^2$$ cut orthogonally is

A closed cylinder of given volume will have least surface area when the ratio of its height and base radius is

Two particles $$P$$ and $$Q$$ located at the points $$P\left(t, t^3-16 t-3\right), Q\left(t+1, t^3-6 t-6\right)$$ are mo

If $$f(x)=\int x^2 \cos ^2 x\left(2 x \tan ^2 x-2 x-6 \tan x\right) d x$$ and $$f(0)=\pi$$, then $$f(x)=$$

If $$\int \frac{e^{\sqrt{x}}}{\sqrt{x}}(x+\sqrt{x}) d x=e^{\sqrt{x}}[A x+B \sqrt{x}+C]+K$$ then $$A+B+C=$$

If $$\int \frac{1+\sqrt{\tan x}}{\sin 2 x} d x=A \log \tan x+B \tan x+C$$, then $$4 A-2 B=$$

$$\int \frac{1+\tan x \tan (x+a)}{\tan x \tan (x+a)} d x=$$

If $$I_n=\int_0^{\pi / 4} \tan ^n x d x$$, then $$\frac{1}{I_2+I_4}+\frac{1}{I_3+I_5}+\frac{1}{I_4+I_6}=$$

$$\int_0^{\pi / 4} e^{\tan ^2 \theta} \sin ^2 \theta \tan \theta d \theta=$$

$$\int_{\pi / 4}^{5 \pi / 4}(|\cos t| \sin t+|\sin t| \cos t) d t=$$

If $$f(x)=\max \{\sin x, \cos x\}$$ and $$g(x)=\min \{\sin x, \cos x\}$$, then $$\int_0^\pi f(x) d x+\int_0^\pi g(x) d x

If $$l$$ and $$m$$ are order and degree of a differential equation of all the straight lines at constant distance of $$P

If $$2 x-y+C \log (|x-2 y-4|)=k$$ is the general solution of $$\frac{d y}{d x}=\frac{2 x-4 y-5}{x-2 y+2}$$, then $$C=$$

By eliminating the arbitrary constants from $$y=(a+b) \sin (x+c)-d e^{x+e+f}$$, then differential equation has order of

In SI units, $$\mathrm{kg}-\mathrm{m}^2 \mathrm{~s}^{-2}$$ is equivalent to which of the following?

An object moving along $$X$$-axis with a uniform acceleration has velocity $$\mathbf{v}=\left(12 \mathrm{cms}^{-1}\right

A force $$\mathbf{F}_1$$ of magnitude 4 N acts on an object of mass 1 kg , at origin in a direction $$30^{\circ}$$ above

$$y=\left(P t^2-Q t^3\right) \mathrm{~m}$$ is the vertical displacement of a ball which is moving in vertical plane. The

A cricket ball of mass 50 g having velocity $$50 \mathrm{~cm} \mathrm{~s}^{-1}$$ to stopped in 0.5 s. The force applied

Two masses $$M_1$$ and $$M_2$$ are arranged as shown in the figure. Let $$a$$ be the magnitude of the acceleration of th

A ball of mass 300 g is dropped from a height 10 m above a sandy ground. On reaching the ground, it penetrates through a

Two balls $$A$$ and $$B$$, of masses $$M$$ and $$2 M$$ respectively collide each other. If the ball $$A$$ moves with a s

A solid sphere of radius $$R$$ has its outer half removed, so that its radius becomes $$(R / 2)$$. Then its moment of in

Which of the following is not true about vectors $$\mathbf{A}, \mathbf{B}$$ and $$\mathbf{C}$$ ?

A body is executing S.H.M. At a displacement $$x$$ its potential energy is 9 J and at a displacement $$y$$ its potential

As shown in the figure, an iron block $$A$$ of volume $$0.25 \mathrm{~m}^3$$ is attached to a spring $$S$$ of unstretche

A uniform solid sphere of radius $$R$$ produces a gravitational acceleration of $$a_0$$ on its surface. The distance of

In a hydraulic lift, compressed air exerts a force $$F$$ on a small piston of radius 3 cm . Due to this pressure the sec

In a $$U$$-shaped tube the radius of one limb is 2 mm and that of other limb is 4 mm . A liquid of surface tension $$0.0

A steady flow of a liquid of density $$\rho$$ is shown in figure. At point 1, the area of cross-section is $$2 A$$ and t

A metal tape is calibrated at $$25^{\circ} \mathrm{C}$$. On a cold day when the temperature is $$-15^{\circ} \mathrm{C}$

A gas is expanded from an initial state to a final state along a path on a $$p$$-$$V$$ diagram. The path consists of (i)

The temperature of the sink of a Carnot engine is 250 K . In order to increase the efficiency of the Carnot engine from

In non-rigid diatomic molecule with an additional vibrational mode

Speed of sound in air near room temperature is approximately

The radii of curvature of a double convex lens are 4 cm and 8 cm . If the refractive index of the material of the lens i

When monochromatic light of wavelength 600 nm is used in Young's double slit experiment, the fifth order bright fringe i

A solid sphere of radius $$R$$ carries a positive charge $$Q$$ distributed uniformly throughout its volume. A very thin

Assertion (A) In a region of constant potential, the electric field is zero and there can be no charge inside the region

Statement (A) Inside a charged hollow metal sphere, $$E=0, V \neq 0$$, (where, $$E=$$ electric field, $$V=$$ electric po

The electrons take $$40 \times 10^3$$ s to dirift from one end of a metal wire of length 2 m to its other end. The area

The current 'I' in the circuit shown in the figure is

A toroid has a non ferromagnetic core of inner radius 24 cm and outer radius 25 cm , around which 4900 turns of a wire a

A steel wire of length $$l$$ and magnetic moment $$M$$ is bent into a semicircular arc of radius $$R$$. The new magnetic

A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down a

A circular coil has 100 turns, radius 3 cm and resistance $$4 \Omega$$. This coil is co-axial with a solenoid of 200 tur

Capacitive reactance of a capacitor in an AC circuit is $$3 \mathrm{k} \Omega$$. If this capacitor is connected to a new

A light of intensity $$12 \mathrm{Wm}^{-2}$$ incidents on a black surface of area $$4 \mathrm{~cm}^2$$. The radiation pr

The electric field $$(E)$$ and magnetic field $$(B)$$ of an electromagnetic wave passing through vacuum are given by $$\

In a photoelectric experiment light of wavelength 800 nm produces photoelectrons with the smallest de-Broglie wavelength

A hydrogen atom at the ground level absorbs a photon and is excited n = 4 level. The potential energy of the electron in

The radius of an atomic nucleus of mass number 64 is 4.8 fermi. Then the mass number of another atomic nucleus of radius

Consider the statements In a semiconductor (A) There are no free electrons at 0 K. (B) There are no free electrons at an

A carrier wave is used to transmit a message signal. If the peak voltage of modulating signal and carrier signal are inc