Among the following metal carbonyl, the C-O bond order is lowest in

A solution of a metal ion when treated with KI gives a red precipitate which dissolves in excess KI to give a colourless solution. Moreover, the solution of metal ion treatment with a solution of cobalt (II) thiocyanate gives rise to a deep blue crystalline precipitate. The metal ion is:

Cyclohexene on ozonolysis followed by reaction with zinc dust and water gives compound E. Compound E on further treatment with aqueous KOH yields compound F. Compound F is :

The number of stereoisomers obtained by bromination of $$trans$$-2-butene is :

Among the following the least stable resonance structure is :

A positron is emitted from $$_{11}^{23}$$Na The ratio of the atomic mass and atomic number of the resulting nuclide is :

For the process $$\mathrm{H_2O}(l)$$ (1 bar, 373 K) $$\to$$ $$\mathrm{H_2O}(g)$$ (1 bar, 373 K), the correct set of thermodynamic parameters is:

Statement-1 : Alkali metals dissolves in liquid ammonia to give blue solutions

Statement-2 : Alkali metals in liquid ammonia give solvated species of the type $$\left[\mathrm{M}\left(\mathrm{NH}_{3}\right)_{n}\right]^{+} (\mathrm{M}=$$ alkali metals).

Statement-1 : Glucose gives a reddish-brown precipitate with Fehling's solution.

Statement-2 : Reaction of glucose with Fehling's solution gives $$\mathrm{CuO}$$ and gluconic acid.

Statement-1 : Molecules that are not superimposable on their mirror images are chiral.

Statement-2 : All chiral molecules have chiral centres.

Among the following, identify the correct statement.

While $$\mathrm{Fe}^{3+}$$ is stable, $$\mathrm{Mn}^{3+}$$ is not stable in acid solution because

Sodium fusion extract, obtained from aniline, on treatment with iron (II) sulphate and $$\mathrm{H}_{2} \mathrm{SO}_{4}$$ in presence of air gives a Prussian blue precipitate. The blue colour is due to the formation of

Which one of the following reagents is used in the above reaction?

The electrophile in this reaction is :

The structure of the intermediate I is

Match the reactions in Column I with nature of the reactions/type of the products in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 $$\times$$ 4 matrix given in the ORS.

Match the compounds/ions in Column I with their properties/reactions in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 $$\times$$ 4 matrix given in the ORS.

Match the crystal system/unit cells mentioned in Column I with their characteristic features mentioned in Column II. Indicate your answer by darkening the appropriate bubbles of the 4 $$\times$$ 4 matrix given in the ORS.

Let $$\mathrm{O(0,0), P(3,4), Q(6,0)}$$ be the vertices of the triangle OPQ. The point R inside the triangle OPQ is such that the triangles OPR, PQR, OQR are of equal area. The coordinates of R are

If $$|z|=1$$ and $$z \neq \pm 1$$, then all the values of $$\frac{z}{1-z^{2}}$$ lie on

$$\frac{d^{2} x}{d y^{2}}$$ equals :

The differential equation $$\frac{d y}{d x}=\frac{\sqrt{1-y^{2}}}{y}$$ determines a family of circles with :

Let $$\vec{a}, \vec{b}, \vec{c}$$ be unit vectors such that $$\vec{a}+\vec{b}+\vec{c}=\overrightarrow{0}$$. Which one of the following is correct?

Let $$\mathrm{ABCD}$$ be a quadrilateral with area 18 , with side $$\mathrm{A B}$$ parallel to the side $$\mathrm{C D}$$ and $$\mathrm{A B}=2 \mathrm{CD}$$. Let $$\mathrm{AD}$$ be perpendicular to $$\mathrm{AB}$$ and $$\mathrm{CD}$$. If a circle is drawn inside the quadrilateral ABCD touching all the sides, then its radius is :

Let $$f(x)=\frac{x}{\left(1+x^{n}\right)^{1 / n}}$$ for $$n \geq 2$$ and $$g(x)=\underbrace{(f o f o \ldots . o f)}_{f \text { occurs } n \text { times }}(x)$$. Then $$\int x^{n-2} g(x) d x$$ equals :

The letters of the word COCHIN are permuted and all the permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is :

Consider the planes $$3 x-6 y-2 z=15$$ and $$2 x+y-2 z=5$$.

STATEMENT - 1 : The parametric equations of the line of intersection of the given planes are $$x=3+14 t, y=1+2 t, z=15 t$$

STATEMENT - 2 : The vectors $$14 \hat{i}+2 \hat{j}+15 \hat{k}$$ is parallel to the line of intersection of the given planes.

STATEMENT - 1 : The curve $$y=\frac{-x^{2}}{2}+x+1$$ is symmetric with respect to the line $$x=1$$.

STATEMENT - 2 : A parabola is symmetric about its axis.

Let $$f(x)=2+\cos x$$ for all real $$x$$.

STATEMENT - 1 : For each real $$t$$, there exists a point $$c$$ in $$[t, t+\pi]$$ such that $$f^{\prime}(C)=0$$.

STATEMENT - 2 : $$f(t)=f(t+2 \pi)$$ for each real $$t$$.

Lines $$\mathrm{L}_{1}: y-x=0$$ and $$\mathrm{L}_{2}: 2 x+y=0$$ intersect the line $$\mathrm{L}_{3}: y+2=0$$ at $$\mathrm{P}$$ and $$\mathrm{Q}$$, respectively. The bisector of the acute angle between $$L_{1}$$ and $$L_{2}$$ intersects $$L_{3}$$ at $$R$$.

STATEMENT - 1 : The ratio PR : RQ equals $$2 \sqrt{2}: \sqrt{5}$$.

STATEMENT - 2 : In any triangle, bisector of an angle divides the triangle into two similar triangles.

Which one of the following statements is correct?

Which one of the following statements is correct?

Which one of the following statements is correct?

The line $$y=x$$ meets $$y=k e^{\mathrm{x}}$$ for $$k \leq 0$$ at

The positive value of $$k$$ for which $$k e^{x}-x=0$$ has only one root is

For $$k > 0$$, the set of all values of $$k$$ for which $$k e^{x}-x=0$$ has two distinct roots is

Let $$f(x) = {{{x^2} - 6x + 5} \over {{x^2} - 5x + 6}}$$.

Match the conditions/expressions in Column I with statements in Column II.

Let $$(x,y)$$ be such that $${\sin ^{ - 1}}(ax) + {\cos ^{ - 1}}(y) + {\cos ^{ - 1}}(bxy) = {\pi \over 2}$$.

Match the statements in Column I with the statements in Column II.

Match the statements in Column I with the properties Column II.

A student performs an experiment to determine the Young's modulus of a wire, exactly 2 m long, by Searle's method. In a particular reading, the student measures the extension in the length of the wire to be 0.8 mm with an uncertainty of $$\pm0.05\;\mathrm{mm}$$ at a load of exactly 1.0 kg. The student also measures the diameter of the wire to be 0.4 mm with an uncertainty of $$\pm0.01\;\mathrm{mm}$$. Take g = 9.8 m/s² (exact). The Young's modulus obtained from the reading is

In the experiment to determine the speed of sound using a resonance column,

A small object of uniform density rolls up a curved surface with an initial velocity $$v$$. It reaches up to a maximum height of $$\frac{3 v^{2}}{4 g}$$ with respect to the initial position. The object is

Water is filled up to a height $$h$$ in a beaker of radius $$R$$ as shown in the figure. The density of water is $$\rho$$, the surface tension of water is $$T$$ and the atmospheric pressure is P. Consider a vertical section $$A B C D$$ of the water column through a diameter of the beaker. The force on water on one side of this section by water on the other side of this section has magnitude

A spherical portion has been removed from a solid sphere having a charge distributed uniformly in its volume as shown in the figure. The electric field inside the emptied space is

Positive and negative point charges of equal magnitude are kept at $$\left(0,0, \frac{a}{2}\right)$$ and $$\left(0,0, \frac{-a}{2}\right)$$, respectively. The work done by the electric field when another positive point charge is moved from $$(-a, 0,0)$$ to $$(0, a, 0)$$ is

A magnetic field $$\overrightarrow{\mathrm{B}}=\mathrm{B}_{0} \hat{j}$$ exists in the region $$a < x < 2 a$$ and $$\overrightarrow{\mathrm{B}}=-\mathrm{B}_{0} \hat{j}$$, in the region $$2 a < x < 3 a$$, where $$\mathrm{B}_{0}$$ is a positive constant. A positive point charge moving with a velocity $$\vec{v}=v_{0} \hat{i}$$, where $$v_{0}$$ is a positive constant, enters the magnetic field at $$x=a$$. The trajectory of the charge in this region can be like,

Electrons with de-Broglie wavelength $$\lambda$$ fall on the target in an X-ray tube. The cut-off wavelength of the emitted X-rays is

STATEMENT 1

If there is no external torque on a body about its center of mass, then the velocity of the center of mass remains constant.

Because

STATEMENT 2

The linear momentum of an isolated system remains constant.

STATEMENT 1

A cloth covers a table. Some dishes are kept on it. The cloth can be pulled out without dislodging the dishes from the table.

STATEMENT 2

For every action there is an equal and opposite reaction.

STATEMENT 1

A vertical iron rod has a coil of wire wound over it at the bottom end. An alternating current flows in the coil. The rod goes through a conducting ring as shown in the figure. The ring can float at a certain height above the coil.

Because

STATEMENT 2

In the above situation, a current is induced in the ring which interacts with the horizontal component of the magnetic field to produce an average force in the upward direction.

STATEMENT 1

The total translational kinetic energy of all the molecules of a given mass of an ideal gas is 1.5 times the product of its pressure and its volume.

Because

STATEMENT 2

The molecules of a gas collide with each other and the velocities of the molecules change due to the collision.

The speed of sound of the whistle is

The distribution of the sound intensity of the whistle as observed by the passengers in train $$\mathrm{A}$$ is best represented by

The spread of frequency as observed by the passengers in train B is

Light travels as a

The phases of the light wave at $$c, d, e$$ and $$f$$ are $$\phi_c, \phi_d, \phi_{e}$$ and $$\phi_{f}$$ respectively.

It is given that $$\phi_{c} \neq \phi_{f}$$.

Speed of the light is

Column I describe some situations in which a small object moves. Column II describes some characteristics of these motions. Match the situation in Column I with the characteristics in Column II and indicate your answer by darkening appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

Two wires each carrying a steady current I are shown in four configurations in Column I. Some of the resulting effects are described in Column II. Match the statements in Column I with the statements in Column II and indicate your answer by darkening appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.

	Column I		Column II
(A)	Point P is situated midway between the wires.	(P)	The magnetic fields (B) at P due to the currents in the wire are in same direction.
(B)	Point P is situated at the mid-point of the line joining the centers of the circular wires, which have same radii.	(Q)	The magnetic fields (B) at P due to the currents in the wires are in opposite directions.
(C)	Point P is situated at the mid-point of the line joining the centers of the circular wires, which have same radii.	(R)	There is no magnetic field at P.
(D)	Point P is situated at the common center of the wires.	(S)	The wires repel each other.

Column I gives some devices and Column II gives some process on which the functioning of these devices depend. Match the devices in Column I with the processes in Column II and indicate your answer by darkening appropriate bubbles in the $$4 \times 4$$ matrix given in the ORS.