Given below are two statements : Statement I : The decrease in first ionization enthalpy from B to Al is much larger tha

Given below are two statements : Statement I : Nickel is being used as the catalyst for producing syn gas and edible fat

Which of the following relations are correct? (A) $$\mathrm{\Delta U=q+p\Delta V}$$ (B) $$\mathrm{\Delta G=\Delta H-T\De

A solution of $$\mathrm{Cr O_5}$$ in amyl alcohol has a __________ colour.

According to MO theory the bond orders for $$\mathrm{O}$$$$_2^{2 - }$$, $$\mathrm{CO}$$ and $$\mathrm{NO^+}$$ respective

When a hydrocarbon A undergoes combustion in the presence of air, it requires 9.5 equivalents of oxygen and produces 3 e

A doctor prescribed the drug Equanil to a patient. The patient was likely to have symptoms of which disease?

The set of correct statements is : (i) Manganese exhibits +7 oxidation state in its oxide. (ii) Ruthenium and Osmium exh

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Correct order of spin only magnetic moment of the following complex ions is : (Given At.no. Fe : 26, Co : 27)

The major component of which of the following ore is sulphide based mineral?

Reaction of propanamide with $$\mathrm{Br_2/KOH(aq)}$$ produces :

Following tetrapeptide can be represented as (F, L, D, Y, I, Q, P are one letter codes for amino acids)

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The one giving maximum number of isomeric alkenes on dehydrohalogenation reaction is (excluding rearrangement)

The concentration of dissolved Oxygen in water for growth of fish should be more than $$\mathrm{\underline X }$$ ppm and

An indicator 'X' is used for studying the effect of variation in concentration of iodide on the rate of reaction of iodi

Find out the major product for the following reaction.

Find out the major products from the following reaction sequence.

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The volume of HCl, containing 73 g L$$^{-1}$$, required to completely neutralise NaOH obtained by reacting 0.69 g of met

The equilibrium constant for the reaction $$\mathrm{Zn(s)+Sn^{2+}(aq)}$$ $$\rightleftharpoons$$ $$\mathrm{Zn^{2+}(aq)+Sn

At 298 K $$\mathrm{N_2~(g)+3H_2~(g)\rightleftharpoons~2NH_3~(g),~K_1=4\times10^5}$$ $$\mathrm{N_2~(g)+O_2~(g)\rightlefth

A metal M forms hexagonal close-packed structure. The total number of voids in 0.02 mol of it is _________ $$\times$$ $$

The denticity of the ligand present in the Fehling's reagent is ___________.

When 0.01 mol of an organic compound containing 60% carbon was burnt completely, 4.4 g of CO$$_2$$ was produced. The mol

On heating, $$\mathrm{LiNO_3}$$ gives how many compounds among the following __________ $$\mathrm{Li_2O,N_2,O_2,LiNO_2,N

Total number of acidic oxides among $$\mathrm{N_2O_3,NO_2,N_2O,Cl_2O_7,SO_2,CO,CaO,Na_2O}$$ and $$\mathrm{NO}$$ is _____

Assume that the radius of the first Bohr orbit of hydrogen atom is 0.6 $$\mathrm{\mathop A\limits^o }$$. The radius of t

For conversion of compound A $$\to$$ B, the rate constant of the reaction was found to be $$\mathrm{4.6\times10^{-5}~L~m

The statement $$B \Rightarrow \left( {\left( { \sim A} \right) \vee B} \right)$$ is equivalent to :

Let $$y=y(x)$$ be the solution of the differential equation $$x{\log _e}x{{dy} \over {dx}} + y = {x^2}{\log _e}x,(x > 1)

Let R be a relation defined on $$\mathbb{N}$$ as $$a\mathrm{R}b$$ if $$2a+3b$$ is a multiple of $$5,a,b\in \mathbb{N}$$.

The letters of the word OUGHT are written in all possible ways and these words are arranged as in a dictionary, in a ser

If $$\overrightarrow a = \widehat i + 2\widehat k,\overrightarrow b = \widehat i + \widehat j + \widehat k,\overrighta

The plane $$2x-y+z=4$$ intersects the line segment joining the points A ($$a,-2,4)$$ and B ($$2,b,-3)$$ at the point C i

The number of 3 digit numbers, that are divisible by either 3 or 4 but not divisible by 48, is :

Let $$\mathrm{S} = \{ {w_1},{w_2},......\} $$ be the sample space associated to a random experiment. Let $$P({w_n}) = {{

Consider a function $$f:\mathbb{N}\to\mathbb{R}$$, satisfying $$f(1)+2f(2)+3f(3)+....+xf(x)=x(x+1)f(x);x\ge2$$ with $$f(

The set of all values of $$\lambda$$ for which the equation $${\cos ^2}2x - 2{\sin ^4}x - 2{\cos ^2}x = \lambda $$ has a

If the tangent at a point P on the parabola $$y^2=3x$$ is parallel to the line $$x+2y=1$$ and the tangents at the points

The area of the region $$A = \left\{ {(x,y):\left| {\cos x - \sin x} \right| \le y \le \sin x,0 \le x \le {\pi \over 2}

Let $$\overrightarrow a = 4\widehat i + 3\widehat j$$ and $$\overrightarrow b = 3\widehat i - 4\widehat j + 5\widehat

The value of the integral $$\int_1^2 {\left( {{{{t^4} + 1} \over {{t^6} + 1}}} \right)dt} $$ is

If the lines $${{x - 1} \over 1} = {{y - 2} \over 2} = {{z + 3} \over 1}$$ and $${{x - a} \over 2} = {{y + 2} \over 3} =

Let K be the sum of the coefficients of the odd powers of $$x$$ in the expansion of $$(1+x)^{99}$$. Let $$a$$ be the mid

The set of all values of $$\mathrm{t\in \mathbb{R}}$$, for which the matrix $$\left[ {\matrix{ {{e^t}} & {{e^{ - t}}(

The value of the integral $$\int\limits_{1/2}^2 {{{{{\tan }^{ - 1}}x} \over x}dx} $$ is equal to :

The shortest distance between the lines $${{x - 1} \over 2} = {{y + 8} \over -7} = {{z - 4} \over 5}$$ and $${{x - 1} \o

Let $$f$$ and $$g$$ be the twice differentiable functions on $$\mathbb{R}$$ such that $$f''(x)=g''(x)+6x$$ $$f'(1)=4g'(1

A circle with centre (2, 3) and radius 4 intersects the line $$x+y=3$$ at the points P and Q. If the tangents at P and Q

A triangle is formed by the tangents at the point (2, 2) on the curves $$y^2=2x$$ and $$x^2+y^2=4x$$, and the line $$x+y

Let $$a_1=b_1=1$$ and $${a_n} = {a_{n - 1}} + (n - 1),{b_n} = {b_{n - 1}} + {a_{n - 1}},\forall n \ge 2$$. If $$S = \sum

The total number of 4-digit numbers whose greatest common divisor with 54 is 2, is __________.

Let $$X=\{11,12,13,....,40,41\}$$ and $$Y=\{61,62,63,....,90,91\}$$ be the two sets of observations. If $$\overline x $$

If the equation of the normal to the curve $$y = {{x - a} \over {(x + b)(x - 2)}}$$ at the point (1, $$-$$3) is $$x - 4y

Let $$\alpha = 8 - 14i,A = \left\{ {z \in c:{{\alpha z - \overline \alpha \overline z } \over {{z^2} - {{\left( {\over

Let $$\alpha_1,\alpha_2,....,\alpha_7$$ be the roots of the equation $${x^7} + 3{x^5} - 13{x^3} - 15x = 0$$ and $$|{\alp

Let $$\{ {a_k}\} $$ and $$\{ {b_k}\} ,k \in N$$, be two G.P.s with common ratios $${r_1}$$ and $${r_2}$$ respectively su

Let A be a symmetric matrix such that $$\mathrm{|A|=2}$$ and $$\left[ {\matrix{ 2 & 1 \cr 3 & {{3 \over 2}} \cr

With the help of potentiometer, we can determine the value of emf of a given cell. The sensitivity of the potentiometer

The ratio of de-Broglie wavelength of an $$\alpha$$ particle and a proton accelerated from rest by the same potential is

A force acts for 20 s on a body of mass 20 kg, starting from rest, after which the force ceases and then body describes

The equation of a circle is given by $$x^2+y^2=a^2$$, where a is the radius. If the equation is modified to change the o

A square loop of area 25 cm$$^2$$ has a resistance of 10 $$\Omega$$. The loop is placed in uniform magnetic field of mag

Substance A has atomic mass number 16 and half life of 1 day. Another substance B has atomic mass number 32 and half lif

Heat energy of 184 kJ is given to ice of mass 600 g at $$-12^\circ \mathrm{C}$$. Specific heat of ice is $$\mathrm{2222.

The modulation index for an A.M. wave having maximum and minimum peak-to-peak voltages of 14 mV and 6 mV respectively is

Identify the correct statements from the following : A. Work done by a man in lifting a bucket out of a well by means of

A scientist is observing a bacteria through a compound microscope. For better analysis and to improve its resolving powe

Given below are two statements : Statement I : Electromagnetic waves are not deflected by electric and magnetic field. S

The time taken by an object to slide down 45$$^\circ$$ rough inclined plane is n times as it takes to slide down a perfe

For the given figures, choose the correct options :

An object moves at a constant speed along a circular path in a horizontal plane with center at the origin. When the obje

The time period of a satellite of earth is 24 hours. If the separation between the earth and the satellite is decreased

The electric current in a circular coil of four turns produces a magnetic induction 32 T at its centre. The coil is unwo

A fully loaded boeing aircraft has a mass of $$5.4\times10^5$$ kg. Its total wing area is 500 m$$^2$$. It is in level fl

For the given logic gates combination, the correct truth table will be

At 300 K, the rms speed of oxygen molecules is $$\sqrt {{{\alpha + 5} \over \alpha }} $$ times to that of its average s

A point charge $$2\times10^{-2}~\mathrm{C}$$ is moved from P to S in a uniform electric field of $$30~\mathrm{NC^{-1}}$$

A particle of mass 100 g is projected at time t = 0 with a speed 20 ms$$^{-1}$$ at an angle 45$$^\circ$$ to the horizont

In an experiment of measuring the refractive index of a glass slab using travelling microscope in physics lab, a student

A null point is found at 200 cm in potentiometer when cell in secondary circuit is shunted by 5$$\Omega$$. When a resist

An inductor of inductance 2 $$\mathrm{\mu H}$$ is connected in series with a resistance, a variable capacitor and an AC

A particle of mass 250 g executes a simple harmonic motion under a periodic force $$\mathrm{F}=(-25~x)\mathrm{N}$$. The

A metal block of base area 0.20 m$$^2$$ is placed on a table, as shown in figure. A liquid film of thickness 0.25 mm is

A car is moving on a circular path of radius 600 m such that the magnitudes of the tangential acceleration and centripet

Unpolarised light is incident on the boundary between two dielectric media, whose dielectric constants are 2.8 (medium $

For a charged spherical ball, electrostatic potential inside the ball varies with $$r$$ as $$\mathrm{V}=2ar^2+b$$. Here,

When two resistance $$\mathrm{R_1}$$ and $$\mathrm{R_2}$$ connected in series and introduced into the left gap of a mete