Which of the following statements is incorrect?

The calculated spin-only magnetic moment values in BM for $$\mathrm{[FeCl_4]^-}$$ and $$\mathrm{[Fe(CN)_6]^{3-}}$$ are

$$\mathrm{BrF_3}$$ self ionises as following

4f$$^2$$ electronic configuration is found in

The correct order of C = O bond length in ethyl propanoate (I), ethyl propenoate (II) and ethenyl propanoate (III) is

Select the molecule in which all the atoms may lie on a single plane is

The IUPAC name of

The relationship between the pair of compounds shown above are respectively,

The correct stability order of the following carbocations is (I) $$\mathrm{{H_2}\mathop C\limits^ \oplus - CH = CH - C

The correct order of boiling points of N-ethylethanamine (I), ethoxyethane (II) and butan-2-ol (III) is

Structure of M is,

The correct order of acidity of above compounds is

If all the nucleophilic substitution reactions at saturated carbon atoms in the above sequence of reactions follow SN2

The correct option for the above reaction is

Arrange the following in order of increasing mass I. 1 mole of N$$_2$$ II. 0.5 mole of O$$_3$$ III. $$3.011\times10^{23}

Two base balls (masses : m$$_1$$ = 100 g, and m$$_2$$ = 50 g) are thrown. Both of them move with uniform velocity, but t

What is the edge length of the unit cell of a body centred cubic crystal of an element whose atomic radius is 75 pm?

The root mean square (rms) speed of X$$_2$$ gas is x m/s at a given temperature. When the temperature is doubled, the X$

Which of the following would give a linear plot? (k is the rate constant of an elementary reaction and T is temp. in abs

The equivalent conductance of NaCl, HCl and CH$$_3$$COONa at infinite dilution are 126.45, 426.16 and 91 ohm$$^{-1}$$cm$

For the reaction A + B $$\to$$ C, we have the following data: .tg {border-collapse:collapse;border-spacing:0;} .tg td{

If in case of a radio isotope the value of half-life (T$$_{1/2}$$) and decay constant ($$\lambda$$) are identical in mag

Suppose a gaseous mixture of He, Ne, Ar and Kr is treated with photons of the frequency appropriate to ionize Ar. What i

A solution containing 4g of polymer in 4.0 litre solution at 27$$^\circ$$C shows an osmotic pressure of 3.0 $$\times$$ 1

The equivalent weight of KIO$$_3$$ in the given reaction is (M = molecular mass): $$\mathrm{2Cr{(OH)_3} + 4O{H^ - } + KI

At STP, the dissociation reaction of water is $$\mathrm{H_2O\rightleftharpoons H^+~(aq.)+OH^-~(aq.)}$$, and the pH of wa

Na$$_2$$CO$$_3$$ is prepared by Solvay process but K$$_2$$CO$$_3$$ cannot be prepared by the same because

The molecular shapes of SF$$_4$$, CF$$_4$$ and XeF$$_4$$ are

The species in which nitrogen atom is in a state of sp hybridisation is

The correct statement about the magnetic properties of $${\left[ {Fe{{(CN)}_6}} \right]^{3 - }}$$ and $${\left[ {Fe{F_6}

Nickel combines with a uninegative monodentate ligand (X$$^-$$) to form a paramagnetic complex [NiX$$_4$$]$$^{2-}$$. The

'$$\underline{\underline L} $$' in the above sequence of reaction is/are (where L $$\ne$$ M $$\ne$$ N)

'$$\underline G $$' in the above sequence of reactions is

Case - 1 : An ideal gas of molecular weight M at temperature T. Case - 2 : Another ideal gas of molecular weight 2M at t

63 g of a compound (Mol. Wt. = 126) was dissolved in 500 g distilled water. The density of the resultant solution as 1.1

An electron in the 5d orbital can be represented by the following (n, l, m) values

The conversion(s) that can be carried out by bromine in carbon tetrachloride solvent is/are

The correct set(s) of reactions to synthesize benzoic acid starting from benzene is/are

Which statement(s) is/are applicable above critical temperature?

Which of the following mixtures act(s) as buffer solution?

$$\mathop {\lim }\limits_{x \to \infty } \left\{ {x - \root n \of {(x - {a_1})(x - {a_2})\,...\,(x - {a_n})} } \right\}$

Suppose $$f:R \to R$$ be given by $$f(x) = \left\{ \matrix{ 1,\,\,\,\,\,\,\,\,\,\,\mathrm{if}\,x = 1 \hfill \cr {e^

Let $$f:[1,3] \to R$$ be continuous and be derivable in (1, 3) and $$f'(x) = {[f(x)]^2} + 4\forall x \in (1,3)$$. Then

f(x) is a differentiable function and given $$f'(2) = 6$$ and $$f'(1) = 4$$, then $$L = \mathop {\lim }\limits_{h \to 0}

Let $${\cos ^{ - 1}}\left( {{y \over b}} \right) = {\log _e}{\left( {{x \over n}} \right)^n}$$, then $$A{y_2} + B{y_1} +

If $$I = \int {{{{x^2}dx} \over {{{(x\sin x + \cos x)}^2}}} = f(x) + \tan x + c} $$, then $$f(x)$$ is

If $$\int {{{dx} \over {(x + 1)(x - 2)(x - 3)}} = {1 \over k}{{\log }_e}\left\{ {{{|x - 3{|^3}|x + 1|} \over {{{(x - 2)}

the expression $${{\int\limits_0^n {[x]dx} } \over {\int\limits_0^n {\{ x\} dx} }}$$, where $$[x]$$ and $$\{ x\} $$ are

The value $$\int\limits_0^{1/2} {{{dx} \over {\sqrt {1 - {x^{2n}}} }}} $$ is $$(n \in N)$$

If $${I_n} = \int\limits_0^{{\pi \over 2}} {{{\cos }^n}x\cos nxdx} $$, then I$$_1$$, I$$_2$$, I$$_3$$ ... are in

If $$y = {x \over {{{\log }_e}|cx|}}$$ is the solution of the differential equation $${{dy} \over {dx}} = {y \over x} +

The function $$y = {e^{kx}}$$ satisfies $$\left( {{{{d^2}y} \over {d{x^2}}} + {{dy} \over {dx}}} \right)\left( {{{dy} \o

Given $${{{d^2}y} \over {d{x^2}}} + \cot x{{dy} \over {dx}} + 4y\cos e{c^2}x = 0$$. Changing the independent variable x

Let $$f(x) = \left\{ {\matrix{ {x + 1,} & { - 1 \le x \le 0} \cr { - x,} & {0

A missile is fired from the ground level rises x meters vertically upwards in t sec, where $$x = 100t - {{25} \over 2}{t

If a hyperbola passes through the point P($$\sqrt2$$, $$\sqrt3$$) and has foci at ($$\pm$$ 2, 0), then the tangent to th

A, B are fixed points with coordinates (0, a) and (0, b) (a > 0, b > 0). P is variable point (x, 0) referred to rectangu

The average length of all vertical chords of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1,a \le

The value of 'a' for which the scalar triple product formed by the vectors $$\overrightarrow \alpha = \widehat i + a\w

If the vertices of a square are $${z_1},{z_2},{z_3}$$ and $${z_4}$$ taken in the anti-clockwise order, then $${z_3} = $$

If the n terms $${a_1},{a_2},\,......,\,{a_n}$$ are in A.P. with increment r, then the difference between the mean of th

If $$1,{\log _9}({3^{1 - x}} + 2),{\log _3}({4.3^x} - 1)$$ are in A.P., then x equals

Reflection of the line $$\overline a z + a\overline z = 0$$ in the real axis is given by :

If one root of $${x^2} + px - {q^2} = 0,p$$ and $$q$$ are real, be less than 2 and other be greater than 2, then

The number of ways in which the letters of the word 'VERTICAL' can be arranged without changing the order of the vowels

n objects are distributed at random among n persons. The number of ways in which this can be done so that at least one o

Let $$P(n) = {3^{2n + 1}} + {2^{n + 2}}$$ where $$n \in N$$. Then

Let A be a set containing n elements. A subset P of A is chosen, and the set A is reconstructed by replacing the element

Let A and B are orthogonal matrices and det A + det B = 0. Then

Let $$A = \left( {\matrix{ 2 & 0 & 3 \cr 4 & 7 & {11} \cr 5 & 4 & 8 \cr } } \right)$$. Then

If the matrix Mr is given by $${M_r} = \left( {\matrix{ r & {r - 1} \cr {r - 1} & r \cr } } \right)$$ for r

Let $$\alpha,\beta$$ be the roots of the equation $$a{x^2} + bx + c = 0,a,b,c$$ real and $${s_n} = {\alpha ^n} + {\beta

Let A, B, C are subsets of set X. Then consider the validity of the following set theoretic statement:

Let X be a nonvoid set. If $$\rho_1$$ and $$\rho_2$$ be the transitive relations on X, then ($$\circ$$ denotes the compo

Let A and B are two independent events. The probability that both A and B happen is $${1 \over {12}}$$ and probability t

Let S be the sample space of the random experiment of throwing simultaneously two unbiased dice and $$\mathrm{E_k=\{(a,b

If $${1 \over 6}\sin \theta ,\cos \theta ,\tan \theta $$ are in G.P, then the solution set of $$\theta$$ is (Here $$n \i

The equation $${r^2}{\cos ^2}\left( {\theta - {\pi \over 3}} \right) = 2$$ represents

Let A be the point (0, 4) in the xy-plane and let B be the point (2t, 0). Let L be the midpoint of AB and let the perpen

If $$4{a^2} + 9{b^2} - {c^2} + 12ab = 0$$, then the family of straight lines $$ax + by + c = 0$$ is concurrent at

The straight lines $$x + 2y - 9 = 0,3x + 5y - 5 = 0$$ and $$ax + by - 1 = 0$$ are concurrent if the straight line $$35x

ABC is an isosceles triangle with an inscribed circle with centre O. Let P be the midpoint of BC. If AB = AC = 15 and BC

Let O be the vertex, Q be any point on the parabola x$$^2$$ = 8y. If the point P divides the line segment OQ internally

The tangent at point $$(a\cos \theta ,b\sin \theta ),0

Let $$A(2\sec \theta ,3\tan \theta )$$ and $$B(2\sec \phi ,3\tan \phi )$$ where $$\theta + \phi = {\pi \over 2}$$ be

If the lines joining the focii of the ellipse $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$ where $$a > b$$,

If the distance between the plane $$\alpha x - 2y + z = k$$ and the plane containing the lines $${{x - 1} \over 2} = {{y

The angle between a normal to the plane $$2x - y + 2z - 1 = 0$$ and the X-axis is

Let $$f(x) = [{x^2}]\sin \pi x,x > 0$$. Then

If $$y = {\log ^n}x$$, where $${\log ^n}$$ means $${\log _e}{\log _e}{\log _e}\,...$$ (repeated n times), then $$x\log x

$$\int\limits_0^{2\pi } {\theta {{\sin }^6}\theta \cos \theta d\theta } $$ is equal to

If $$x = \sin \theta $$ and $$y = \sin k\theta $$, then $$(1 - {x^2}){y_2} - x{y_1} - \alpha y = 0$$, for $$\alpha=$$

In the interval $$( - 2\pi ,0)$$, the function $$f(x) = \sin \left( {{1 \over {{x^3}}}} \right)$$.

The average ordinate of $$y = \sin x$$ over $$[0,\pi ]$$ is :

The portion of the tangent to the curve $${x^{{2 \over 3}}} + {y^{{2 \over 3}}} = {a^{{2 \over 3}}},a > 0$$ at any point

If the volume of the parallelopiped with $$\overrightarrow a \times \overrightarrow b ,\overrightarrow b \times \overr

Given $$f(x) = {e^{\sin x}} + {e^{\cos x}}$$. The global maximum value of $$f(x)$$

Consider a quadratic equation $$a{x^2} + 2bx + c = 0$$ where a, b, c are positive real numbers. If the equation has no r

Let $${a_1},{a_2},{a_3},\,...,\,{a_n}$$ be positive real numbers. Then the minimum value of $${{{a_1}} \over {{a_2}}} +

Let $$A = \left( {\matrix{ 0 & 0 & 1 \cr 1 & 0 & 0 \cr 0 & 0 & 0 \cr } } \right),B = \left( {\matrix{

Let $$\rho$$ be a relation defined on set of natural numbers N, as $$\rho = \{ (x,y) \in N \times N:2x + y = 4\} $$. Th

From the focus of the parabola $${y^2} = 12x$$, a ray of light is directed in a direction making an angle $${\tan ^{ - 1

The locus of points (x, y) in the plane satisfying $${\sin ^2}x + {\sin ^2}y = 1$$ consists of

The value of $$\mathop {\lim }\limits_{n \to \infty } \left[ {\left( {{1 \over {2\,.\,3}} + {1 \over {{2^2}\,.\,3}}} \ri

The family of curves $$y = {e^{a\sin x}}$$, where 'a' is arbitrary constant, is represented by the differential equation

Let f be a non-negative function defined on $$\left[ {0,{\pi \over 2}} \right]$$. If $$\int\limits_0^x {(f'(t) - \sin 2

A balloon starting from rest is ascending from ground with uniform acceleration of 4 ft/sec$$^2$$. At the end of 5 sec,

If $$f(x) = 3\root 3 \of {{x^2}} - {x^2}$$, then

If z$$_1$$ and z$$_2$$ are two complex numbers satisfying the equation $$\left| {{{{z_1} + {z_2}} \over {{z_1} - {z_2}}}

A letter lock consists of three rings with 15 different letters. If N denotes the number of ways in which it is possible

If R and R$$^1$$ are equivalence relations on a set A, then so are the relations

Let f be a strictly decreasing function defined on R such that $$f(x) > 0,\forall x \in R$$. Let $${{{x^2}} \over {f({a^

A rectangle ABCD has its side parallel to the line y = 2x and vertices A, B, D are on lines y = 1, x = 1 and x = $$-$$1

Let $$f(x) = {x^m}$$, m being a non-negative integer. The value of m so that the equality $$f'(a + b) = f'(a) + f'(b)$$

Which of the following statements are true?

A ray of monochromatic light is incident on the plane surface of separation between two media $$\mathrm{X}$$ and $$\math

Three identical convex lenses each of focal length $$\mathrm{f}$$ are placed in a straight line separated by a distance

X-rays of wavelength $$\lambda$$ gets reflected from parallel planes of atoms in a crystal with spacing d between two p

If the potential energy of a hydrogen atom in the first excited state is assumed to be zero, then the total energy of n

In the given circuit, find the voltage drop $$\mathrm{V_L}$$ in the load resistance $$\mathrm{R_L}$$.

Consider the logic circuit with inputs A, B, C and output Y. How many combinations of A, B and C gives the output Y = 0

A particle of mass m is projected at a velocity u, making an angle $$\theta$$ with the horizontal (x-axis). If the angle

A body of mass 2 kg moves in a horizontal circular path of radius 5 m. At an instant, its speed is 2$$\sqrt5$$ m/s and i

In an experiment, the length of an object is measured to be 6.50 cm. This measured value can be written as 0.0650 m. The

A mouse of mass m jumps on the outside edge of a rotating ceiling fan of moment of inertia I and radius R. The fractiona

Acceleration due to gravity at a height H from the surface of a planet is the same as that at a depth of H below the sur

A uniform rope of length 4 m and mass 0.4 kg is held on a frictionless table in such a way that 0.6 m of the rope is han

The displacement of a plane progressive wave in a medium, travelling towards positive x-axis with velocity 4 m/s at t =

In a simple harmonic motion, let f be the acceleration and t be the time period. If x denotes the displacement, then |fT

As shown in the figure, a liquid is at same levels in two arms of a U-tube of uniform cross-section when at rest. If th

Six molecules of an ideal gas have velocities 1, 3, 5, 5, 6 and 5 m/s respectively. At any given temperature, if $$\math

As shown in the figure, a pump is designed as horizontal cylinder with a piston having area A and an outlet orifice hav

A given quantity of gas is taken from A to C in two ways; a) directly from A $$\to$$ C along a straight line and b) in

Two substances A and B of same mass are heated at constant rate. The variation of temperature $$\theta$$ of the substan

Consider a positively charged infinite cylinder with uniform volume charge density $$\rho > 0$$. An electric dipole

A thin glass rod is bent in a semicircle of radius R. A charge is non-uniformly distributed along the rod with a linear

12 $$\mu$$C and 6 $$\mu$$C charges are given to the two conducting plates having same cross-sectional area and placed f

A wire carrying a steady current I is kept in the x-y plane along the curve $$y=A \sin \left(\frac{2 \pi}{\lambda} x\ri

The figure represents two equipotential lines in x-y plane for an electric field. The x-component E$$_x$$ of the electr

An electric dipole of dipole moment $$\vec{p}$$ is placed at the origin of the co-ordinate system along the $$\mathrm{z}

The electric field of a plane electromagnetic wave of wave number k and angular frequency $$\omega$$ is given $$\vec{E}=

A charged particle in a uniform magnetic field $$\vec{B}=B_{0} \hat{k}$$ starts moving from the origin with velocity $$v

In an experiment on a circuit as shown in the figure, the voltmeter shows 8 V reading. The resistance of the voltmeter

An interference pattern is obtained with two coherent sources of intensity ratio n : 1. The ratio $$\mathrm{{{{I_{\max }

A circular coil is placed near a current carrying conductor, both lying on the plane of the paper. The current is flowi

An amount of charge Q passes through a coil of resistance R. If the current in the coil decreases to zero at a uniform r

A modified gravitational potential is given by $$\mathrm{V}=-\frac{\mathrm{GM}}{\mathrm{r}}+\frac{\mathrm{A}}{\mathrm{r}

There are n elastic balls placed on a smooth horizontal plane. The masses of the balls are $$\mathrm{m}, \frac{\mathrm{m

An earth's satellite near the surface of the earth takes about 90 min per revolution. A satellite orbiting the moon also

A bar magnet falls from rest under gravity through the centre of a horizontal ring of conducting wire as shown in figur

A uniform magnetic field B exists in a region. An electron of charge q and mass m moving with velocity v enters the regi

A train is moving along the tracks at a constant speed u. A girl on the train throws a ball of mass m straight ahead alo

A cyclic process is shown in p-v diagram and T-S diagram. Which of the following statements is/are true?

The figure shows two identical parallel plate capacitors A and B of capacitances C connected to a battery. The key K is

A charged particle of charge q and mass m is placed at a distance 2R from the centre of a vertical cylindrical region of