1 gram of a carbonate (M2CO3) on treatment with excess HCl produces 0.01186 mole of CO2. The molar mass of M2CO3 in g mo

The radius of the second Bohr orbit for hydrogen atom is: (Planck’s Const. h = 6.6262 × 10-34 Js; mass of electron = 9.1

Which of the following species is not paramagnetic?

A metal crystallises in a face centred cubic structure. If the edge length of its unit cell is ‘a’, the closest approach

The most abundant elements by mass in the body of a healthy human adult are: Oxygen (61.4%); Carbon (22.9%), Hydrogen (1

$$\Delta $$U is equal to :

The group having isoelectronic species is:

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 a

Given, $${C_{(graphite)}} + {O_2} \to C{O_2}(g)$$; $${\Delta _r}{H^o}$$ = - 393.5 kJ mol-1 $${{\rm H}_2}(g)$$ + $${1 \ov

Given $$E_{C{l_2}/C{l^ - }}^o$$ = 1.36 V, $$E_{C{r^{3 + }}/Cr}^o$$ = - 0.74 V $$E_{C{r_2}{O_7}^{2 - }/C{r^{3 + }}}^o$$ =

pKa of a weak acid (HA) and pKb of a weak base (BOH) are 3.2 and 3.4, respectively. The pH of their salt (AB) solution i

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

Two reactions R1 and R2 have identical pre-exponential factors. Activation energy of R1 exceeds that of R2 by 10 kJ mol–

The Tyndall effect is observed only when following conditions are satisfied: (a) The diameter of the dispersed particles

Both lithium and magnesium display several similar properties due to the diagonal relationship; however, the one which i

In the following reactions, ZnO is respectively acting as a/an : (a) ZnO + Na2O $$\to$$ Na2ZnO2 (b) ZnO + CO2 $$\to$$ Zn

The products obtained when chlorine gas reacts with cold and dilute aqueous NaOH are :

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

A water sample has ppm level concentration of following anions F- = 10; $$SO_4^{2-}$$ = 100; $$NO_3^-$$ = 50 The anion/a

Which of the following molecules is least resonance stabilized?

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

The increasing order of the reactivity of the following halides for the SN1 reaction is :

3-Methyl-pent-2-ene on reaction with HBr in presence of peroxide forms an addition product. The number of possible stere

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

The major product obtained in the following reaction is :

Sodium salt of an organic acid ‘X’ produces effervescence with conc. H2SO4. ‘X’ reacts with the acidified aqueous CaCl2

The major product obtained in the following reaction is :

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

The formation of which of the following polymers involves hydrolysis reaction?

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

The function $$f:R \to \left[ { - {1 \over 2},{1 \over 2}} \right]$$ defined as $$f\left( x \right) = {x \over {1 + {x^2

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

If $$A = \left[ {\matrix{ 2 & { - 3} \cr { - 4} & 1 \cr } } \right]$$, then adj(3A2 + 12A) is equal

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 =

If for a positive integer n, the quadratic equation $$x\left( {x + 1} \right) + \left( {x + 1} \right)\left( {x + 2} \ri

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

The value of $$\left( {{}^{21}{C_1} - {}^{10}{C_1}} \right) + \left( {{}^{21}{C_2} - {}^{10}{C_2}} \right) + \left( {{}^

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$

For any three positive real numbers a, b and c, 9(25$${a^2}$$ + b2) + 25(c2 - 3$$a$$c) = 15b(3$$a$$ + c). Then

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

If for $$x \in \left( {0,{1 \over 4}} \right)$$, the derivatives of $${\tan ^{ - 1}}\left( {{{6x\sqrt x } \over {1 - 9{x

Twenty meters of wire is available for fencing off a flower-bed in the form of a circular sector. Then the maximum area

The normal to the curve y(x – 2)(x – 3) = x + 6 at the point where the curve intersects the y-axis passes through the po

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

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$

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 + \

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

The radius of a circle, having minimum area, which touches the curve y = 4 – x2 and the lines, y = |x| is :

A hyperbola passes through the point P$$\left( {\sqrt 2 ,\sqrt 3 } \right)$$ and has foci at $$\left( { \pm 2,0} \right)

If the image of the point P(1, –2, 3) in the plane, 2x + 3y – 4z + 22 = 0 measured parallel to the line, $${x \over 1} =

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 o

The distance of the point (1, 3, – 7) from the plane passing through the point (1, –1, – 1), having normal perpendicular

The eccentricity of an ellipse whose centre is at the origin is $${1 \over 2}$$. If one of its directrices is x = – 4, t

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

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

If two different numbers are taken from the set {0, 1, 2, 3, ........, 10}; then the probability that their sum as well

A box contains 15 green and 10 yellow balls. If 10 balls are randomly drawn, one-by-one, with replacement, then the vari

Let a vertical tower AB have its end A on the level ground. Let C be the mid-point of AB and P be a point on the ground

If $$5\left( {{{\tan }^2}x - {{\cos }^2}x} \right) = 2\cos 2x + 9$$, then the value of $$\cos 4x$$ is :

The following statement $$\left( {p \to q} \right) \to \left[ {\left( { \sim p \to q} \right) \to q} \right]$$ is :

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

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 =

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 fo

The moment of inertia of a uniform cylinder of length $$l$$ and radius R about its perpendicular bisector is $$I$$. What

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 fi

A man grows into a giant such that his linear dimensions increase by a factor of 9. Assuming that his density remains sa

The variation of acceleration due to gravity $$g$$ with distance d from centre of the earth is best represented by (R =

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 17

An external pressure P is applied on a cube at 0oC so that it is equally compressed from all sides. K is the bulk modulu

The temperature of an open room of volume 30 m3 increases from 17oC to 27oC due to the sunshine. The atmospheric pressur

CP and Cv are specific heats at constant pressure and constant volume respectively. It is observed that CP – Cv = a for

A particle is executing simple harmonic motion with a time period T. At time t = 0, it is at its position of equilibrium

A capacitance of 2 $$\mu $$F is required in an electrical circuit across a potential difference of 1.0 kV. A large numbe

An electric dipole has a fixed dipole moment $$\overrightarrow p $$, which makes angle $$\theta$$ with respect to x-axis

In the given circuit diagram when the current reaches steady state in the circuit, the charge on the capacitor of capaci

Which of the following statements is false?

In the given circuit, the current in each resistance 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 perform

When a current of 5 mA is passed through a galvanometer having a coil of resistance 15$$\Omega $$, it shows full scale d

In a coil of resistance 100 $$\Omega $$, a current is induced by changing the magnetic flux through it as shown in the f

An observer is moving with half the speed of light towards a stationary microwave source emitting waves at frequency 10

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 ligh

A diverging lens with magnitude of focal length 25 cm is placed at a distance of 15cm from a converging lens of magnitud

An electron beam is accelerated by a potential difference V to hit a metallic target to produce X–rays. It produces cont

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

Some energy levels of a molecule are shown in the figure. The ratio of the wavelengths r = $${{\lambda _1}}$$/$${{\lambd

A radioactive nucleus A with a half life T, decays into a nucleus B. At t = 0, there is no nucleus B. At sometime t, the

In a common emitter amplifier circuit using an n-p-n transistor, the phase difference between the input and the output v

In amplitude modulation, sinusoidal carrier frequency used is denoted by $${\omega _c}$$ and the signal frequency is den

The following observations were taken for determining surface tension T of water by capillary method: diameter of capill