Oxidation states of the metal in the minerals haematite and magnetite, respectively, are
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Oxidation states of the metal in the minerals haematite and magnetite, respectively, are
Among the following complexes $$(K-P), K_3[Fe(CN)_6](K), [Co(NH_3)_6]Cl_3 (L), Na_3[Co(oxalate)_3] (M), [Ni(H_2O)_6]Cl_2 (N), K_2[Pt(CN)_4] (O)$$ and $$[Zn(H_2O)_6](NO_3)_2 (P)$$ the diamegnetic complexes are
Passing $$H_2S$$ gasinto a mixture of $$Mn^{2+}, Ni^{2+}, Cu^{2+}$$ and $$Hg^{2+}$$ ions in an acidified aqueous solution precipitates
Consider the following cell reaction:
$$2Fe_{(s)} + O_{2(g)} + 4H^+_{(aq)} \rightarrow 2Fe^{2+}_{(aq)} + 2H_2O(l) E^\circ = 1.67 V$$ At $$[Fe^{2+}] = 10^{-3} M, P(O_2) = 0.1$$ atm and pH = 3, the cell potential at $$25^\circ C$$ is
The freezing point (in $$^\circ C$$) of a solution containing 0.1 g of $$K_3[Fe(CN)_6](Mol. Wt. 329)$$ in 100 g of water $$(K_f = 1.86 K kg mol^{-1})$$ is
Amongst the compounds given, the one that would form a brilliant colored dye on treatment with $$NaNO_2$$ in dil. HCl followed by addition to an alkaline solution of $$\beta$$-naphthol is
The major product of the following reaction is
The following carbohydrate is
Reduction of the metal centre in aqueous permanganateion involves
The equilibrium
$$2Cu^\mid \rightleftharpoons Cu^O + Cu^\parallel$$
in aqueous medium at $$25 ^\circ C$$ shifts towards the left in the presence of
For the first order reaction
$$2N_2O_5(g) \rightarrow 4NO_2(g) + O_2(g)$$
The correct functional group X and the reagent/reaction conditions Y in the following scheme are
Among the following, the number of compoundsthan can react with $$PCl_5$$ to give $$POCl_3$$ is $$O_2, CO_2, SO_2, H_2O, H_2SO_4, P_4O_{10}$$
The volume (in mL) of 0.1 M $$AgNO_3$$ required for complete precipitation of chloride ions present in 30 mL of 0.01 M solution of $$[Cr(H_2O)_5Cl]Cl_2$$, as silver chloride is close to
In 1 L saturated solution of $$AgCl[K_{sp}(AgCl) = 1.6 \times 10^{-10}]$$, 0.1 mol of $$CuCl[K_{sp}(CuCl) = 1.0 \times 10^{-6}]$$ is added. The resultant concentration of $$Ag^+$$ in the solution is $$1.6 \times 10^{-x}$$. The value of "x" is
The number of hexagonal faces that are present in a truncated octahedron is
The maximum number of isomers (including stereoisomers) that are possible on monochlorination of the following compound, is
The total number of contributing structures showing hyperconjugation (involving C-H bonds)for the following carbocation is
This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, gq, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in q and r, then for the particular question, against statement B, darken the bubbles corresponding to q andr in the ORS.
Match the transformations in column I with appropriate options in column II
Match the reactions in column I with appropriate types of steps/reactive intermediate involved in these reactions as given in column II
A light ray traveling in glass medium is incident on glass-air interface at an angle of incidence $$\theta$$. The reflected ( R ) and transmitted ( T ) intensities, both as function of $$\theta$$, are plotted. The correct sketch is
A satellite is moving with a constant speed ‘V’ in a circular orbit about the earth. An object of mass ‘m’ is ejected from the satellite such that it just escapes from the gravitational pull
of the earth. At the time of its ejection, the kinetic energy of the object is
A long insulated copper wire is closely wound asa spiral of ‘N’ turns. The spiral has inner radius ‘a’ and outer radius ‘b’. The spiral lies in the X-Y plane and a steady current ‘I’ flows through the wire. The Z-component of the magnetic field at the center of the spiral is
A point mass is subjected to two simultaneous sinusoidal displacements in x-direction, $$x_1(t) = A \sin \omega t$$ and $$x_2(t) = A \sin\left(\omega t + \frac{2 \pi}{3}\right)$$. Adding a third sinusoidal displacement $$x_3(t) = B \sin(\omega t + \phi)$$ brings the mass to a complete rest. The value of B and $$\phi$$ are
Which of the field patterns given below is valid for electric field as well as for magnetic field?
A ball of mass 0.2 kg rests on a vertical post of height 5 m. A bullet of mass 0.01 kg, traveling with a velocity V m/s in a horizontal direction, hits the centre of the ball. After the collision, the ball and bullet travel independently. The ball hits the ground at a distance of 20 m and the bullet at a distance of 100 m from the foot of the post. The initial velocity V of the bullet is
The density of a solid ball is to be determined in an experiment. The diameter of the ball is measured with a screw gauge, whose pitch is 0.5 mm and there are 50 divisions on the circular scale. The reading on the main scale is 2.5 mm and that on the circular scale is 20 divisions. If the measured mass of the ball has a relative error of 2%, the relative percentage error in the density is
A wooden block performs SHM on a frictionless surface with frequency, $$v_0$$. The block carries a charge +Q on its surface. If now a uniform electric field $$\overrightarrow{E}$$ is switched-on as shown, then the SHM of the block will be
Two solid spheres A and B of equal volumes but of different densities $$d_A$$ and $$d_B$$ are connected by a string. They are fully immersed in a fluid of density $$d_F$$. They get arranged into an equilibrium state as shown in the figure with a tension in the string. The arrangement is possible only if
A series R-C circuit is connected to AC voltage source. Consider two cases; (A) when C is without a dielectric medium and (B) when C is filled with dielectric of constant 4. The
current $$I_R$$ through the resistor and voltage $$V_C$$ across the capacitor are comparedin the two cases. Whichof the following is/are true?
Which of the following statement(s) is/are correct?
A thin ring of mass 2 kg and radius 0.5 m is rolling without slipping on a horizontal plane with velocity 1 m/s. A small ball of mass 0.1 kg, moving with velocity 20 m/s in the opposite direction, hits the ring at a height of 0.75 m and goes vertically up with velocity 10 m/s. Immediately after the collision
A train is moving along a straight line with a constant acceleration ‘a’. A boy standing in the train throwsa ball forward with a speed of 10 m/s, at an angle of $$60^\circ$$ to the horizontal. The boy has to move forward by 1.15 m inside the train to catch the ball backat the initial height. The acceleration of the train, in $$m/s^2$$, is
A block of mass 0.18 kg is attached to a spring of force-constant 2 N/m. The coefficient of friction between the block and the floor is 0.1. Initially the block is at rest and the spring is un-stretched. An impulse is given to the block as shown in the figure. The block slides a distance of 0.06 m and comes to rest for the first time. The initial velocity of the block in m/s is V = N/10. Then N is
Two batteries of different emfs and different internal resistances are connected as shown. The voltage across AB in volts is
Water (with refractive index = $$\frac{4}{3}$$) in a tank is 18 cm deep. Oil of refractive index $$\frac{7}{4}$$ lies on water making a convex surface of radius of curvature ‘R = 6 cm’ as shown. Consider oil to act as a thin lens. An object ‘S’ is placed 24 cm above water surface. The location of its image is at ‘x’ cm above the bottom of the tank. Then ‘x’ is
A series R-C combination is connected to an AC voltage of angular frequency $$\omega = 500$$ radian/s. If the impedance of the R-C circuit is $$R\sqrt{1.25}$$, the time constant
(in millisecond) of the circuit is
A silver sphere of radius 1 cm and work function 4.7 eV is suspended from an insulating thread in free-space. It is under continuous illumination of 200 nm wavelength light. As photoelectrons are emitted, the sphere gets charged and acquires a potential. The maximum number of photoelectrons emitted from the sphere is $$A \times 10^Z$$ (where 1 < A < 10). The value of ‘Z’ is
This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, g, r, s and t) in Column II. Any given statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in q and r, then for the particular question, against statement B, darken the bubbles corresponding to q and r in the ORS.
One mole of a monatomic ideal gas is taken through a cycle ABCDA as shown in the P-V diagram. Column II gives the characteristics involved in the cycle. Match them with each of the processes given in Column I.
Column I shows four systems, each of the same length L, for producing standing waves. The lowest possible natural frequency of a system is called its fundamental frequency, whose wavelength is denoted as $$\lambda_f$$. Match each system with statements given in Column II describing the nature and wavelength of the standing waves.
Let P(6, 3) be a point on the hyperbola $$\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$$. If the normal at the point P intersects the x-axis at (9, 0), then the eccentricity of the hyperbola is
A value of b for which the equations
$$x^2 + bx - 1 = 0$$
$$x^2 + x + b = 0$$,
have one root in common is
Let $$\omega \neq 1$$ be a cube root of unity and S bethe set of all non-singular matrices of the form
$$\begin{bmatrix}1 & a & b\\\omega & 1 & c\\\omega^2 & \omega & 1\end{bmatrix}$$,
where each of a, b, and c is either $$\omega$$ or $$\omega^2$$. Then the number of distinct matrices in the set S is
The circle passing through the point (-1,0) and touching the y-axis at (0, 2) also passes through the point
If
$$\lim_{x \rightarrow 0} \left[1 + x \ln (1 + b^2)\right]^{\frac{1}{x}} = 2b \sin \theta, b > 0 $$ and $$\theta \in (-\pi, \pi]$$, then the value of $$\theta$$ is
Let $$f:[-1, 2] \rightarrow [0, \infty)$$ be a continuous function such that $$f(x) = f(1 - x)$$ for all $$x \in [-1, 2]$$. Let $$R_1 = \int_{-1}^{2} x f(x)dx$$ and $$R_2$$ be the area of the region bounded by y = f(x), x = -1, x = 2, and the x-axis. Then
Let $$f(x) = x^2$$ and $$g(x) = \sin x$$ for all $$x \in R$$. Then the set of all x satisfying $$(f\circ g \circ g \circ f)(x) = (g\circ g \circ f)(x)$$, where $$(f \circ g)(x) = f(g(x))$$, is
Let (x, y) be any point on the parabola $$y^2 = 4x$$. Let P be the point that divides the line segment from (0, 0) to (x, y) in the ratio 1:3. Then the locus of P is
If
$$f(x) = \begin{cases}-x-\frac{\pi}{2}, & x \leq -\frac{\pi}{2}\\-\cos x, & -\frac{\pi}{2}<x \leq 0\\x-1, & 0 < x \leq 1\\\ln x, & x > 1\end{cases}$$, then
Let E and F be two independent events. The probability that exactly one of them occurs is $$\frac{11}{25}$$ and the probability of none of them occurring is $$\frac{2}{25}$$. If P(T) denotes the probability of occurrence of the event T , then
Let L be anormal to the parabola $$y^2 = 4x$$. If L passes through the point (9, 6), then L is given by
Let $$f : (0, 1) \rightarrow R$$ be defined by
$$f(x) = \frac{b - x}{1 - bx}$$, where b is a constant such that 0 < b < 1. Then
Let $$\omega = e^{\frac{i \pi}{3}}$$ and a, b, c, x, y, z be non-zero complex numbers such that
$$a + b + c = x$$
$$a + b \omega + c \omega^2 = y$$
$$a + b \omega^2 + c \omega = z$$.
Ten the value of $$\frac{\mid x \mid^2 + \mid y \mid^2 + \mid z \mid^2}{\mid a \mid^2 + \mid b \mid^2 + \mid c \mid^2}$$ is
The number of distinct real roots of $$x^4 - 4x^3 + 12 x^2 + x - 1 = 0$$ is
Let $$y'(x) + y(x)g'(x) = g(x)g'(x), y(0) = 0, x \in R$$, where $$f'(x)$$ denotes $$\frac{d f(x)}{dx}$$ and $$g(x)$$ is a given non-constant differentiable function on R with g(0) = g(2) = 0. Then the value of y(2) is
Let M be a $$3 \times 3$$ matrix satisfying
$$M\begin{bmatrix}0\\1\\0 \end{bmatrix} = \begin{bmatrix}-1\\2\\3 \end{bmatrix}, M\begin{bmatrix}1\\-1\\0 \end{bmatrix} = \begin{bmatrix}1\\1\\-1 \end{bmatrix}$$, and $$M\begin{bmatrix}1\\1\\1 \end{bmatrix} = \begin{bmatrix}0\\0\\12 \end{bmatrix}$$. Then the sum of the diagonal entries of M is
Let $$\overrightarrow{a} = -\hat{i} - \hat{k}, \overrightarrow{b} = -\hat{i} + \hat{k}$$ and $$\overrightarrow{c} = \hat{i} + 2\hat{j} + 3\hat{k}$$ be three given vectors. If $$\overrightarrow{r}$$ is a vector such that $$\overrightarrow{r} \times \overrightarrow{b} = \overrightarrow{c} \times \overrightarrow{b}$$ and $$\overrightarrow{r} . \overrightarrow{a} = 0$$, then the value of $$\overrightarrow{r} . \overrightarrow{b}$$ is
The straight line 2x - 3y = 1 divides the circular region $$x^2 + y^2 \leq 6$$ into two parts. If
$$S = \left\{\left(2, \frac{3}{4}\right), \left(\frac{5}{2}, \frac{3}{4}\right), \left(\frac{1}{4}, -\frac{1}{4}\right), \left(\frac{1}{8}, \frac{1}{4}\right)\right\}$$,
then the number of point(s) in S lying inside the smaller part is
This section contains 2 questions. Each question has four statements (A, B, C and D) given in Column I and five statements (p, q, r, s and t) in Column II. Any given
statement in Column I can have correct matching with ONE or MORE statement(s) given in Column II. For example, if for a given question, statement B matches with the statements given in q and r, then for the particular question, against statement B, darken the bubbles corresponding to q and r in the ORS.
Match the statements given in Column I with the values given in Column II
Match the statements given in Column I with the intervals/union of intervals given in Column II
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