The major product obtained in the following reaction is :

Which of the following compounds will behave as a reducing sugar in an aqueous KOH solution?

The correct sequence of reagents for the following conversion will be :

Sodium salt of an organic acid ‘X’ produces effervescence with conc. H₂SO₄. ‘X’ reacts with the acidified aqueous CaCl₂ solution to give a white precipitate which decolourises acidic solution of KMnO₄. ‘X’ is :

The major product obtained in the following reaction is :

3-Methyl-pent-2-ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stereoisomers for the product is :

Which of the following, upon treatment with tert-BuONa followed by addition of bromine water, fails to decolorize the colour of bromine?

The increasing order of the reactivity of the following halides for the S_N1 reaction is :

Which of the following compounds will form significant amount of meta product during mono-nitration reaction?

Which of the following molecules is least resonance stabilized?

In the following reactions, ZnO is respectively acting as a/an :

(a) ZnO + Na₂O $$\to$$ Na₂ZnO₂

(b) ZnO + CO₂ $$\to$$ ZnCO₃

On treatment of 100 mL of 0.1 M solution of CoCl₃. 6H₂O with excess AgNO₃; 1.2 $$\times$$ 10²² ions are precipitated. The complex is :

The most abundant elements by mass in the body of a healthy human adult are: Oxygen (61.4%); Carbon (22.9%), Hydrogen (10.0%); and Nitrogen (2.6%). The weight which a 75 kg person would gain if all ¹H atoms are replaced by ²H atoms is:

pK_a of a weak acid (HA) and pK_b of a weak base (BOH) are 3.2 and 3.4, respectively. The pH of their salt (AB) solution is :

Which of the following reactions is an example of a redox reaction?

Given
$$E_{C{l_2}/C{l^ - }}^o$$ = 1.36 V, $$E_{C{r^{3 + }}/Cr}^o$$ = - 0.74 V
$$E_{C{r_2}{O_7}^{2 - }/C{r^{3 + }}}^o$$ = 1.33 V, $$E_{Mn{O_4}^ - /Mn ^{2+}}^o$$ = 1.51 V
Among the following, the strongest reducing agent is :

Two reactions R₁ and R₂ have identical pre-exponential factors. Activation energy of R₁ exceeds that of R₂ by 10 kJ mol^–1. If k₁ and k₂ are rate constants for reactions R₁ and R₂ respectively at 300 K, then ln(k₂/k₁) is equal to :
(R = 8.314 J mol^–1 K^–1)

The freezing point of benzene decreases by 0.45⁰C when 0.2 g of acetic acid is added to 20g of benzene. If acetic acid associates to form a dimer in benzene, percentage association of acetic acid in benzene will be: (K_f for benzene = 5.12 K kg mol^–1)

$$\Delta $$U is equal to :

The group having isoelectronic species is:

Given, $${C_{(graphite)}} + {O_2} \to C{O_2}(g)$$;

$${\Delta _r}{H^o}$$ = - 393.5 kJ mol^-1

$${{\rm H}_2}(g)$$ + $${1 \over 2}{O_2}(g)$$$$\to {{\rm H}_2}{\rm O}(l)$$

$${\Delta _r}{H^o}$$ = - 285.8 kJ mol^-1

$$C{O_2}(g)$$ + $$2{{\rm H}_2}{\rm O}(l) \to$$ $$C{H_4}(g)$$ + $$2{O_2}(g)$$

$${\Delta _r}{H^o}$$ = + 890.3 kJ mol^-1

Based on the above thermochemical equations, the value of $${\Delta _r}{H^o}$$ at 298 K for the reaction

$${C_{(graphite)}}$$ + $$2{{\rm H}_2}(g) \to$$ $$C{H_4}(g)$$ will be :

The radius of the second Bohr orbit for hydrogen atom is:
(Planck’s Const. h = 6.6262 × 10^-34 Js; mass of electron = 9.1091 × 10^-31 kg; charge of electron (e) = 1.60210 × 10^-19 C; permittivity of vacuum ($${\varepsilon _0}$$) = 8.854185 × 10^-12 kg^-1 m^-3 A²)

Which of the following species is not paramagnetic?

1 gram of a carbonate (M₂CO₃) on treatment with excess HCl produces 0.01186 mole of CO₂. The molar mass of M₂CO₃ in g mol^–1 is:

Let $$a$$, b, c $$ \in R$$. If $$f$$(x) = ax² + bx + c is such that
$$a$$ + b + c = 3 and $$f$$(x + y) = $$f$$(x) + $$f$$(y) + xy, $$\forall x,y \in R,$$

then $$\sum\limits_{n = 1}^{10} {f(n)} $$ is equal to

A man X has 7 friends, 4 of them are ladies and 3 are men. His wife Y also has 7 friends, 3 of them are ladies and 4 are men. Assume X and Y have no common friends. Then the total number of ways in which X and Y together can throw a party inviting 3 ladies and 3 men, so that 3 friends of each of X and Y are in this party, is:

If for a positive integer n, the quadratic equation

$$x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \right)$$$$ + .... + \left( {x + \overline {n - 1} } \right)\left( {x + n} \right)$$$$ = 10n$$

has two consecutive integral solutions, then n is equal to :

If S is the set of distinct values of 'b' for which the following system of linear equations

x + y + z = 1
x + ay + z = 1
ax + by + z = 0

has no solution, then S is :

If $$A = \left[ {\matrix{ 2 & { - 3} \cr { - 4} & 1 \cr } } \right]$$,

then adj(3A² + 12A) is equal to

Let $$\omega $$ be a complex number such that 2$$\omega $$ + 1 = z where z = $$\sqrt {-3} $$. If

$$\left| {\matrix{ 1 & 1 & 1 \cr 1 & { - {\omega ^2} - 1} & {{\omega ^2}} \cr 1 & {{\omega ^2}} & {{\omega ^7}} \cr } } \right| = 3k$$,

then k is equal to :

The function $$f:R \to \left[ { - {1 \over 2},{1 \over 2}} \right]$$ defined as

$$f\left( x \right) = {x \over {1 + {x^2}}}$$, is

If $$5\left( {{{\tan }^2}x - {{\cos }^2}x} \right) = 2\cos 2x + 9$$,

then the value of $$\cos 4x$$ is :

For three events A, B and C,

P(Exactly one of A or B occurs)
= P(Exactly one of B or C occurs)
= P (Exactly one of C or A occurs) = $${1 \over 4}$$
and P(All the three events occur simultaneously) = $${1 \over {16}}$$.

Then the probability that at least one of the events occurs, is :

If two different numbers are taken from the set {0, 1, 2, 3, ........, 10}; then the probability that their sum as well as absolute difference are both multiple of 4, is :

Let $$\overrightarrow a = 2\widehat i + \widehat j -2 \widehat k$$ and $$\overrightarrow b = \widehat i + \widehat j$$.

Let $$\overrightarrow c $$ be a vector such that $$\left| {\overrightarrow c - \overrightarrow a } \right| = 3$$,

$$\left| {\left( {\overrightarrow a \times \overrightarrow b } \right) \times \overrightarrow c } \right| = 3$$ and the angle between $$\overrightarrow c $$ and $\overrightarrow a \times \overrightarrow b$ is $$30^\circ $$.

Then $$\overrightarrow a .\overrightarrow c $$ is equal to :

Let k be an integer such that the triangle with vertices (k, – 3k), (5, k) and (–k, 2) has area 28 sq. units. Then the orthocentre of this triangle is at the point :

If $$\left( {2 + \sin x} \right){{dy} \over {dx}} + \left( {y + 1} \right)\cos x = 0$$ and y(0) = 1,

then $$y\left( {{\pi \over 2}} \right)$$ is equal to :

The area (in sq. units) of the region

$$\left\{ {\left( {x,y} \right):x \ge 0,x + y \le 3,{x^2} \le 4y\,and\,y \le 1 + \sqrt x } \right\}$$ is

Let $${I_n} = \int {{{\tan }^n}x\,dx} ,\,\left( {n > 1} \right).$$

If $${I_4} + {I_6}$$ = $$a{\tan ^5}x + b{x^5} + C$$, where C is a constant of integration,

then the ordered pair $$\left( {a,b} \right)$$ is equal to

The integral $$\int\limits_{{\pi \over 4}}^{{{3\pi } \over 4}} {{{dx} \over {1 + \cos x}}} $$ is equal to

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area (in sq. m) of the flower-bed, is :

If for $$x \in \left( {0,{1 \over 4}} \right)$$, the derivatives of

$${\tan ^{ - 1}}\left( {{{6x\sqrt x } \over {1 - 9{x^3}}}} \right)$$ is $$\sqrt x .g\left( x \right)$$, then $$g\left( x \right)$$ equals

$$\mathop {\lim }\limits_{x \to {\pi \over 2}} {{\cot x - \cos x} \over {{{\left( {\pi - 2x} \right)}^3}}}$$ equals

A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium. The kinetic energy – time graph of the particle will look like:

A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15cm from a converging lens of magnitude of focal length 20cm. A beam of parallel light falls on the diverging lens. The final image formed is:

In a Young’s double slit experiment, slits are separated by 0.5 mm, and the screen is placed 150 cm away. A beam of light consisting of two wavelengths, 650 nm and 520 nm, is used to obtain interference fringes on the screen. The least distance from the common central maximum to the point where the bright fringes due to both the wavelengths coincide is

In a coil of resistance 100 $$\Omega $$, a current is induced by changing the magnetic flux through it as shown in the figure. The magnitude of change in flux through the coil is:

When a current of 5 mA is passed through a galvanometer having a coil of resistance 15$$\Omega $$, it shows full scale deflection. The value of the resistance to be put in series with the galvanometer to convert it into a voltmeter of range 0 – 10V is:

A magnetic needle of magnetic moment 6.7 $$\times$$ 10^-2 A m² and moment of inertia 7.5 $$\times$$ 10^-6 kg m² is performing simple harmonic oscillations in a magnetic field of 0.01 T. Time taken for 10 complete oscillations is:

In the given circuit, the current in each resistance is:

Which of the following statements is false?

In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capacitance C will be:

An electric dipole has a fixed dipole moment $$\overrightarrow p $$, which makes angle $$\theta$$ with respect to x-axis. When subjected to an electric field $$\mathop {{E_1}}\limits^ \to = E\widehat i$$ , it experiences a torque $$\overrightarrow {{T_1}} = \tau \widehat k$$ . When subjected to another electric field $$\mathop {{E_2}}\limits^ \to = \sqrt 3 {E_1}\widehat j$$ it experiences a torque $$\mathop {{T_2}}\limits^ \to = \mathop { - {T_1}}\limits^ \to $$ . The angle $$\theta$$ is:

A capacitance of 2 $$\mu $$F is required in an electrical circuit across a potential difference of 1.0 kV. A large number of 1 $$\mu $$F capacitors are available which can withstand a potential difference of not more than 300 V. The minimum number of capacitors required to achieve this is:

An electron beam is accelerated by a potential difference V to hit a metallic target to produce X–rays. It produces continuous as well as characteristic X-rays. If $$\lambda $$_min is the smallest possible wavelength of X-ray in the spectrum, the variation of log$$\lambda $$_min with log V is correctly represented in:

C_P and C_v are specific heats at constant pressure and constant volume respectively. It is observed that
C_P – C_v = a for hydrogen gas
C_P – C_v = b for nitrogen gas
The correct relation between a and b is

The temperature of an open room of volume 30 m³ increases from 17^oC to 27^oC due to the sunshine. The atmospheric pressure in the room remains 1 $$ \times $$ 10⁵ Pa. If N_i and N_f are the number of molecules in the room before and after heating, then N_f – N_i will be :

An external pressure P is applied on a cube at 0^oC so that it is equally compressed from all sides. K is the bulk modulus of the material of the cube and $$\alpha$$ is its coefficient of linear expansion. Suppose we want to bring the cube to its original size by heating. The temperature should be raised by:

The variation of acceleration due to gravity $$g$$ with distance d from centre of the earth is best represented by (R = Earth’s radius):

A copper ball of mass 100 gm is at a temperature T. It is dropped in a copper calorimeter of mass 100 gm, filled with 170 gm of water at room temperature. Subsequently, the temperature of the system is found to be 75^oC. T is given by: (Given : room temperature = 30^oC, specific heat of copper = 0.1 cal/gm^oC)

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains same, the stress in the leg will change by a factor of :

A slender uniform rod of mass M and length $$l$$ is pivoted at one end so that it can rotate in a vertical plane (see figure). There is negligible friction at the pivot. The free end is held vertically above the pivot and then released. The angular acceleration of the rod when it makes an angle $$\theta$$ with the vertical is

The moment of inertia of a uniform cylinder of length $$l$$ and radius R about its perpendicular bisector is $$I$$. What is the ratio $${l \over R}$$ such that the moment of inertia is minimum?

A body of mass m = 10^–2 kg is moving in a medium and experiences a frictional force F = –kv². Its initial speed is v₀ = 10 ms^–1. If, after 10 s, its energy is $${1 \over 8}mv_0^2$$, the value of k will be:

A time dependent force F = 6t acts on a particle of mass 1 kg. If the particle starts from rest, the work done by the force during the first 1 sec. will be:

A body is thrown vertically upwards. Which one of the following graphs correctly represent the velocity vs time?

The following observations were taken for determining surface tension T of water by capillary method:
diameter of capillary, D = 1.25 $$\times$$ 10^-2 m
rise of water, h = 1.45 $$\times$$ 10^-2m
Using g = 9.80 m/s² and the simplified relation T = $${{rhg} \over 2} \times {10^3}N/m$$, the possible error in surface tension is closest to :

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = $${{\lambda _1}}$$/$${{\lambda _2}}$$, is given by:

A particle A of mass m and initial velocity v collides with a particle B of mass m/2 which is at rest. The collision is head on, and elastic. The ratio of the de-Broglie wavelengths $${\lambda _A}$$ to $${\lambda _B}$$ after the collision is: