For the above three esters, the order of rates of alkaline hydrolysis is

Ph$$ - $$ CDO$$\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{Warm}^{50\% aq.NaOH}} $$ Ph$$ - $$ COO$$\mathop H\limi

The correct order of acidity for the following compounds is :

The reduction product of ethyl 3-oxobutanoate by NaBH4 in methanol is

What is the major product of the following reaction?

The maximum number of electrons in an atom in which the last electron filled has the quantum numbers n = 3, l = 2 and m

In the face centered cubic lattice structure of gold the closest distance between gold atoms is ('a' being the edge leng

The equilibrium constant for the following reactions are given at 25$$^\circ $$C$$2A$$ $$\rightleftharpoons$$ B + C, K1

Among the following, the ion which will be more effective for flocculation of Fe(OH)3 solution is :

The mole fraction of ethanol in water is 0.08. Its molality is

5 mL of 0.1 M Pb(NO3)2 is mixed with 10 mL of 0.02 M KI. The amount of PbI2 precipitated will be about

At 273 K temperature and 76 cm Hg pressure the density of a gas is 1.964 g L-1. The gas is

Equal masses of ethane and hydrogen are mixed in an empty container at 298 K. The fraction of total pressure exerted by

An ideal gas expands adiabatically against vacuum. Which of the following is correct for the given process?

Kf (water) = 1.86 K kg mol-1. The temperature at which ice begins to separate from a mixture of 10 mass % ethylene glyco

The radius of the first Bohr orbit of a hydrogen atom is 0.53 $$\times {10^-8}$$ cm. The velocity of the electron in the

Which of the following statements is not true for the reaction, 2F2 + 2H2O $$ \to $$ 4HF + O2 ?

The number of unpaired electrons in the uranium (92U) atom is

How and why does the density of liquid water change on prolonged electrolysis?

The difference between orbital angular momentum of an electron in a 4f -orbital and another electron in a 4s-orbital is

Which of the following has the largest number of atoms?

Indicate the correct IUPAC name of the coordination compound shown in the figure.

What will be the mass of one atom of 12C?

Bond order of He2, $$He_2^ + $$ and $$He_2^{2 + }$$ are respectively

To a solution of a colourless efflorescent sodium salt, when dilute acid is added, a colourless gas is evolved along wit

The reaction for obtaining the metal (M) from its oxide (M2O3) ore is given by$${M_2}{O_3}(s) + 2Al(l)\buildrel {Heat} \

In the extraction of Ca by electro reduction of molten CaCl2 some CaF2 is added to the electrolyte for the following rea

The total number of alkyl bromides (including stereoisomers) formed in the reaction $$M{e_3}C - CH = C{H_2} + HBr \to $$

The product in the above reaction is

Which of the following compounds is asymmetric?

For a reaction 2A + B $$ \to $$ P, when concentration of B alone is doubled, t1/2 does not change and when concentration

A solution is saturated with SrCO3 and SrF2. The $$[CO_3^{2 - }]$$ is found to be 1.2 $$ \times $$ 10-3 M. The concentra

A homonuclear diatomic gas molecule shows 2-electron magnetic moment. The one-electron and two-electron reduced species

$$C{H_3} - O - C{H_2} - Cl\mathrel{\mathop{\kern0pt\longrightarrow} \limits_\Delta ^{aq{.^\Theta }OH}} C{H_3} - O - C{H_

Which of the following reactions give(s) a meso-compound as the main product?

For spontaneous polymerisation, which of the following is (are) correct?

Which of the following statement(s) is/are incorrect?

SiO2 is attacked by which one/ones of the following?

$$Me - C \equiv C - Me\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{EtOH, - 33^\circ C}^{Na/N{H_3}(liq.)}} \underli

For the following carbocations, the correct order of stability is I. $$^ \oplus C{H_2} - COC{H_3}$$II. $$^ \oplus C{H_2}

Let cos$$^{ - 1}\left( {{y \over b}} \right) = \log {\left( {{x \over n}} \right)^n}$$. Then

Let $$\phi (x) = f(x) + f(1 - x)$$ and $$f(x) < 0$$ in [0, 1], then

$$\int {{{f(x)\phi '(x) + \phi (x)f'(x)} \over {(f(x)\phi (x) + 1)\sqrt {f(x)\phi (x) - 1} }}dx = } $$

The value of $$\sum\limits_{n = 1}^{10} {} \int\limits_{ - 2n - 1}^{ - 2n} {{{\sin }^{27}}} x\,dx + \sum\limits_{n = 1}^

$$\int\limits_0^2 {[{x^2}]} \,dx$$ is equal to

If the tangent to the curve y2 = x3 at (m2, m3) is also a normal to the curve at (m2, m3), then the value of mM is

If $${x^2} + {y^2} = {a^2}$$, then $$\int\limits_0^a {\sqrt {1 + {{\left( {{{dy} \over {dx}}} \right)}^2}} dx = } $$

Let f, be a continuous function in [0, 1], then $$\mathop {\lim }\limits_{n \to \infty } \sum\limits_{j = 0}^n {{1 \over

Let f be a differentiable function with $$\mathop {\lim }\limits_{x \to \infty } f(x) = 0.$$ If $$y' + yf'(x) - f(x)f'(x

If $$x\sin \left( {{y \over x}} \right)dy = \left[ {y\sin \left( {{y \over x}} \right) - x} \right]dx,\,x > 0$$ and $

Let $$f(x) = 1 - \sqrt {({x^2})} $$, where the square root is to be taken positive, then

If the function $$f(x) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1$$ [a > 0] attains its maximum and minimum at p and q respect

If a and b are arbitrary positive real numbers, then the least possible value of $${{6a} \over {5b}} + {{10b} \over {3a}

If 2 log(x + 1) $$ - $$ log(x2 $$ - $$ 1) = log 2, then x =

The number of complex numbers p such that $$\left| p \right| = 1$$ and imaginary part of p4 is 0, is

The equation $$z\bar z + (2 - 3i)z + (2 + 3i)\bar z + 4 = 0$$ represents a circle of radius

The expression ax2 + bx + c (a, b and c are real) has the same sign as that of a for all x if

In a 12 storied building, 3 persons enter a lift cabin. It is known that they will leave the lift at different floors. I

If the total number of m-element subsets of the set A = {a1, a2, ..., an} is k times the number of m element subsets con

Let I(n) = nn, J(n) = 13.5 ......... (2n $$ - $$ 1) for all (n > 1), n $$ \in $$ N, then

If c0, c1, c2, ......, c15 are the binomial coefficients in the expansion of (1 + x)15, then the value of $${{{c_1}} \ov

Let A = $$\left( {\matrix{ {3 - t} \cr { - 1} \cr 0 \cr } \matrix{ {} \cr {} \cr {} \cr

Let $$A = \left[ {\matrix{ {12} & {24} & 5 \cr x & 6 & 2 \cr { - 1} & { - 2} & 3 \

Let $$A = \left( {\matrix{ a & b \cr c & d \cr } } \right)$$ be a 2 $$ \times $$ 2 real matrix with

If $$\left| {\matrix{ {{a^2}} & {bc} & {{c^2} + ac} \cr {{a^2} + ab} & {{b^2}} & {ca} \cr {

If f : S $$ \to $$ R, where S is the set of all non-singular matrices of order 2 over R and $$f\left[ {\left( {\matrix{

Let the relation p be defined on R by a p b holds if and only if a $$ - $$ b is zero or irrational, then

The unit vector in ZOX plane, making angles $$45^\circ $$ and $$60^\circ $$ respectively with $$\alpha = 2\widehat i +

Four persons A, B, C and D throw an unbiased die, turn by turn, in succession till one gets an even number and win the g

A rifleman is firing at a distant target and has only 10% chance of hitting it. The least number of rounds he must fire

$$\cos (2x + 7) = a(2 - \sin x)$$ can have a real solution for

The differential equation of the family of curves y = ex (A cos x + B sin x) where, A, B are arbitrary constants is

The equation $$r\,\cos \left( {\theta - {\pi \over 3}} \right) = 2$$ represents

The locus of the centre of the circles which touch both the circles x2 + y2 = a2 and x2 + y2 = 4ax externally is

Let each of the equations x2 + 2xy + ay2 = 0 and ax2 + 2xy + y2 = 0 represent two straight lines passing through the ori

A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x + y + 6 = 0 at P and Q respectively. Th

Area in the first quadrant between the ellipses x2 + 2y2 = a2 and 2x2 + y2 = a2 is

The equation of circle of radius $$\sqrt {17} $$ unit, with centre on the positive side of X-axis and through the point

The length of the chord of the parabola y2 = 4ax(a > 0) which passes through the vertex and makes an acute angle $$\a

A double ordinate PQ of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ is such that $$\Delta OP

If B and B' are the ends of minor axis and S and S' are the foci of the ellipse $${{{x^2}} \over {25}} + {{{y^2}} \over

The equation of the latusrectum of a parabola is x + y = 8 and the equation of the tangent at the vertex is x + y = 12.

The equation of the plane through the point $$(2, - 1, - 3)$$ and parallel to the lines$${{x - 1} \over 2} = {{y + 2} \o

The sine of the angle between the straight line $${{x - 2} \over 3} = {{y - 3} \over 4} = {{z - 4} \over 5}$$ and the pl

Let f(x) = sin x + cos ax be periodic function. Then,

The domain of $$f(x) = \sqrt {\left( {{1 \over {\sqrt x }} - \sqrt {x + 1} } \right)} $$ is

Let $$y = f(x) = 2{x^2} - 3x + 2$$. The differential of y when x changes from 2 to 1.99 is

If $$\mathop {\lim }\limits_{x \to 0} {\left( {{{1 + cx} \over {1 - cx}}} \right)^{{1 \over x}}} = 4$$, then $$\mathop {

Let f : R $$ \to $$ R be twice continuously differentiable (or f" exists and is continuous) such that f(0) = f(1) = f'(0

Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12$$.Then

The area of the region$$\{ (x,y):{x^2} + {y^2} \le 1 \le x + y\} $$ is

In open interval $$\left( {0,\,{\pi \over 2}} \right)$$

If the line y = x is a tangent to the parabola y = ax2 + bx + c at the point (1, 1) and the curve passes through ($$ - $

If the vectors $$\alpha = \widehat i + a\widehat j + {a^2}\widehat k,\,\beta = \widehat i + b\widehat j + {b^2}\wideha

Let z1 and z2 be two imaginary roots of z2 + pz + q = 0, where p and q are real. The points z1, z2 and origin form an eq

If P(x) = ax2 + bx + c and Q(x) = $$ - $$ax2 + dx + c, where ac $$ \ne $$ 0 [a, b, c, d are all real], then P(x).Q(x) =

Let $$A = \{ x \in R: - 1 \le x \le 1\} $$ and $$f:A \to A$$ be a mapping defined by $$f(x) = x\left| x \right|$$. Then

Let $$f(x) = \sqrt {{x^2} - 3x + 2} $$ and $$g(x) = \sqrt x $$ be two given functions. If S be the domain of fog and T b

Let p1 and p2 be two equivalence relations defined on a non-void set S. Then

Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of

Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. The portion of the tangent at any point of

A line cuts the X-axis at A(7, 0) and the Y-axis at B(0, $$ - $$5). A variable line PQ is drawn perpendicular to AB cutt

Let $$0 < \alpha < \beta < 1$$. Then, $$\mathop {\lim }\limits_{n \to \infty } \int\limits_{1/(k + \beta )}^{

$$\mathop {\lim }\limits_{x \to 1} \left( {{1 \over {1nx}} - {1 \over {(x - 1)}}} \right)$$

Let $$y = {1 \over {1 + x + lnx}}$$, then

Consider the curve $$y = b{e^{ - x/a}}$$, where a and b are non-zero real numbers. Then

The area of the figure bounded by the parabola $$x = - 2{y^2},\,x = 1 - 3{y^2}$$ is

A particle is projected vertically upwards. If it has to stay above the ground for 12 sec, then

The equation $${x^{{{(\log 3x)}^2}}} - {9 \over 2}\log 3\,x + 5 = 3\sqrt 3 $$ has

In a certain test, there are n questions. In this test 2n-i students gave wrong answers to at least i questions, where i

A and B are independent events. The probability that both A and B occur is $${1 \over {20}}$$ and the probability that n

The equation of the straight line passing through the point (4, 3) and making intercepts on the coordinate axes whose su

Consider a tangent to the ellipse $${{{x^2}} \over 2} + {{{y^2}} \over 1} = 1$$ at any point. The locus of the mid-point

Let $$y = {{{x^2}} \over {{{(x + 1)}^2}(x + 2)}}$$. Then $${{{d^2}y} \over {d{x^2}}}$$ is

Let $$f(x) = {1 \over 3}x\sin x - (1 - \cos \,x)$$. The smallest positive integer k such that $$\mathop {\lim }\limits_{

Tangent is drawn at any point P(x, y) on a curve, which passes through (1, 1). The tangent cuts X-axis and Y-axis at A a

The intensity of light emerging from one of the slits in a Young's double slit experiment is found to be 1.5 times the i

In a Fraunhofer diffraction experiment, a single slit of width 0.5 mm is illuminated by a monochromatic light of wavelen

If R is the Rydberg constant in cm-1, then hydrogen atom does not emit any radiation of wavelength in the range of

A nucleus X emits a $$\beta $$-particle to produce a nucleus Y. If their atomic masses are Mx and My respectively, then

For nuclei with mass number close to 119 and 238, the binding energies per nucleon are approximately 7.6 MeV and 8.6 MeV

A common emitter transistor amplifier is connected with a load resistance of 6 k$$\Omega $$ . When a small AC signal of

In the circuit shown, the value of $$\beta $$ of the transistor is 48. If the supplied base current is 200 $$\mu $$A, wh

The frequency v of the radiation emitted by an atom when an electron jumps from one orbit to another is given by v = k$$

Consider the vectors $$A = \hat i + \hat j - \hat k$$ ,$$B = 2\hat i - \hat j + \hat k$$ and $$C = {1 \over {\sqrt 5 }}\

A fighter plane, flying horizontally with a speed 360 km/h at an altitude of 500 m drops a bomb for a target straight ah

A block of mass m rests on a horizontal table with a coefficient of static friction $$\mu $$. What minimum force must be

A tennis ball hits the floor with a speed v at an angle $$\theta $$ with the normal to the floor. If the collision is in

The bob of a swinging second pendulum (one whose time period is 2 s) has a small speed v0 at its lowest point. It height

A steel and a brass wire, each of length 50 cm and cross-sectional area 0.005 cm2 hang from a ceiling and are 15 cm apar

Which of the following diagrams correctly shows the relation between the terminal velocity vT of a spherical body fallin

An ideal gas undergoes the cyclic process abca as shown in the given p - V diagramIt rejects 50J of heat during ab and a

A container AB in the shape of a rectangular parallelopiped of length 5 m is divided internally by a movable partition P

When 100 g of boiling water at 100$$^\circ $$ C is added into a calorimeter containing 300 g of cold water at 10$$^\circ

As shown in the figure, a point charge q1 = + 1 $$ \times $$ 10-6 C is placed at the origin in xy-plane and another poin

Four identical point masses, each of mass m and carrying charge + q are placed at the corners of a square of sides a on

A very long charged solid cylinder of radius a contains a uniform charge density p. Dielectric constant of the material

A galvanometer can be converted to a voltmeter of full scale deflection V0 by connecting a series resistance R1 and can

As shown in the figure, a single conducting wire is bent to form a loop in the form of a circle of radius r concentrical

As shown in the figure, a wire is bent to form a D-shaped closed loop, carrying current I, where the curved part is a se

What will be the equivalent resistance between the terminals A and B of the infinite resistive network shown in the figu

When a DC voltage is applied at the two ends of a circuit kept in a closed box, it is observed that the current graduall

Consider the circuit shown.If all the cells have negligible internal resistance, what will be the current through the 2$

Consider a conducting wire of length L bent in the form of a circle of radius R and another conductor of length a (a &lt

An object, is placed 60 cm in front of a convex mirror of focal length 30 cm. A plane mirror is now placed facing the ob

A thin convex lens is placed just above an empty vessel of depth 80 cm. The image of a coin kept at the bottom of the ve

A conducting circular loop of resistance 20$$\Omega $$ and cross-sectional area 20 $$ \times $$ 10-2 m2 is placed perpe

A pair of parallel metal plates are kept with a separation d. One plate is at a potential + V and the other is at ground

A metallic block of mass 20 kg is dragged with a uniform velocity of 0.5 ms-1 on a horizontal table for 2.1 s. The coeff

Consider an engine that absorbs 130 cal of heat from a hot reservoir and delivers 30 cal heat to a cold reservoir in eac

Two pith balls, each carrying charge + q are hung from a hook by two springs. It is found that when each charge is tripl

A point source of light is used in an experiment of photoelectric effects. If the distance between the source and the ph

Two metallic spheres of equal outer radii are found to have same moment of inertia about their respective diameters. The

A simple pendulum of length l is displaced, so that its taught string is horizontal and then released. A uniform bar piv

A 400$$\Omega $$ resistor, a 250 mH inductor and a 2.5 $$\mu $$F capacitor are connected in series with an AC source of

A charged particle moves with constant velocity in a region, where no effect of gravity is felt but an electrostatic fie