Amongst the following compounds, the one that will not respond to Cannizzaro reaction upon treatment with alkali is

Which of the following compounds would not react with Lucas reagent at room temperature.

Amongst the following compounds, the one which would not respond to iodoform test is :

Which of the following will be dehydrated most readily in alkaline medium?

The correct order of basicity of the following compounds is

Which of the following reactions will not result in the formation of carbon-carbon bonds?

Point out the false statement.

The correct structure of the drug paracetamol is

Which of the following statements regarding Lanthanides is false?

Nitrogen dioxide is not produced on heating

The boiling points of HF, HCl, HBr and HI follow the order

In the solid state, PCl₅ exists as

Which statement is not correct for ortho and para hydrogen?

The acid in which O$$-$$O bonding is present is

The metal which can be used to obtain metallic Cu from aqueous CuSO₄ solution is

If radium and chlorine combine to form radium chloride, the compound would be

Which of the following arrangements is correct in respect of solubility in water?

The energy required to break one mole of hydrogen-hydrogen bonds in H₂ is 436 kJ. What is the longest wavelength of light required to break a single hydrogen-hydrogen bond?

The correct order of O$$-$$O bond length in O₂, H₂O₂ and O₃ is

The number of $$\sigma$$ and $$\pi$$ bonds between two carbon atoms in calcium carbide are

An element E loses one $$\alpha$$ and two $$\beta$$-particles in three successive stages. The resulting element will be

An element X belongs to fourth period and fifteenth group of the periodic table. Which of the following statements is true?

Which of the following plots represent an exothermic reaction?

If p$$^\circ$$ and p are the vapour pressure of the pure solvent and solution and n₁ and n₂ are the moles of solute and solvent respectively in the solution then the correct relation between p and p$$^\circ$$ is

Ionic solids with Schottky defect may contain in their structure

The condition for a reaction to occur spontaneously is

The order of equivalent conductance at infinite dilution for LiCl, NaCl and KCl is

The molar solubility (in mol L^$$-$$1) of a sparingly soluble salt MX₄ is 'S'. The corresponding solubility product is K_sp. S in terms of 'K_sp' is given by the relation

Ozonolysis of an alkene produces only one dicarbonyl compound. The structure of the alkene is

From the following compounds, choose the one which is not aromatic.

Identify X in the following sequence of reactions.

Compound X is tested and the results are shown in the table.

Test	Result
Aqueous sodium hydroxide is added, then heated gently. Dilute hydrochloric acid is added.	Gas given off which turns damp red litmus paper blue. Effervescence, gas given off which turns lime water milky and acidified $${K_2}C{r_2}{O_7}$$ paper green.

Which ions are present in compound 'X'?

The time taken for an electron to complete one revolution in Bohr orbit of hydrogen atom is

Amongst the following, which should have the highest rms speed at the same temperature?

The major products obtained during ozonolysis of 2, 3-dimethyl-1-butene and subsequent reductions with Zn and H₂O are

Choose the correct statement(s) among the following.

Which of the following statement(s) is (are) correct when a mixture of NaCl and K₂Cr₂O₇ is gently warmed with conc. H₂SO₄?

Of the following molecules, which have shape similar to CO₂ ?

In which of the following mixed aqueous solutions, pH = pK_a at equilibrium?

1. 100 mL of 0.1 M CH₃COOH + 100 mL of 0.1 MCH₃COONa

(2) 100 mL of 0.1 MCH₃COOH + 50 mL of 0.1 M NaOH

(3) 100 mL of 0.1 M CH₃COOH + 100 mL of 0.1 M NaOH

(4) 100 mL of 0.1 MCH₃COOH + 100 mL of 0.1 MNH₃

Amongst the following compounds, the one(s) which readily react with ethanolic KCN.

If the solution of the differential equation $$x{{dy} \over {dx}} + y = x{e^x}\,be\,xy = {e^x}\phi (x) + C$$, then $$\phi$$(x) is equal to

The order of the differential equation of all parabolas whose axis of symmetry along X-axis is

The line y = x + $$\lambda$$ is tangent to the ellipse 2x² + 3y² = 1. Then, $$\lambda$$ is

The area enclosed by $$y = \sqrt {5 - {x^2}} $$ and $$y = |x - 1|$$ is

Let S be the set of points, whose abscissae and ordinates are natural numbers. Let P $$ \in $$ S, such that the sum of the distance of P from (8, 0) and (0, 12) is minimum among all elements in S. Then, the number of such points P and S is

Time period T of a simple pendulum of length l is given by $$T = 2\pi \sqrt {{l \over g}} $$. If the length is increased by 2%, then an approximate change in the time period is

The cosine of the angle between any two diagonals of a cube is

If x is a positive real number different from 1 such that log_ax, log_bx, log_cx are in AP, then

If a, x are real numbers and | a | < 1, | x | < 1, then 1 + (1 + a) x + (1 + a + a²) x² + ..... $$\infty $$ is equal to

If $${\log _{0.3}}(x - 1) < {\log _{0.09}}(x - 1)$$, then x lies in the interval

The value of $$\sum\limits_{n = 1}^{13} {({i^n} + {i^{n + 1}})} $$, $$i = \sqrt { - 1} $$ is

If z₁, z₂, z₃ are imaginary numbers such that $$|{z_1}|\, = \,|{z_2}|\, = \,|{z_3}|\, = \,\left| {{1 \over {{z_1}}} + {1 \over {{z_2}}} + {1 \over {{z_3}}}} \right|\, = \,1$$, then $$|{z_1} + {z_2} + {z_3}|$$ is

If p, q are the roots of the equation x² + px + q = 0, then

The number of values of k, for which the equation x² $$-$$ 3x + k = 0 has two distinct roots lying in the interval (0, 1), are

The number of ways in which the letters of the word ARRANGE can be permuted such that the R's occur together, is

If $${1 \over {{}^5{C_r}}} + {1 \over {{}^6{C_r}}} = {1 \over {{}^4{C_r}}}$$, then the value of r is

For positive integer n, n³ + 2n is always divisible by

In the expansion of (x $$-$$ 1) (x $$-$$ 2) .... (x $$-$$ 18), the coefficient of x¹⁷ is

$$1 + {}^n{C_1}\cos \theta + {}^n{C_2}\cos 2\theta + ... + {}^n{C_n}\cos n\theta $$ equals

If x, y and z are greater than 1, then the value of $$\left| {\matrix{ 1 & {{{\log }_x}y} & {{{\log }_x}z} \cr {{{\log }_y}x} & 1 & {{{\log }_y}z} \cr {{{\log }_z}x} & {{{\log }_z}y} & 1 \cr } } \right|$$ is

Let A be a 3 $$ \times $$ 3 matrix and B be its adjoint matrix. If | B | = 64, then | A | is equal to

Let $$Q = \left[ {\matrix{ {\cos {\pi \over 4}} & { - \sin {\pi \over 4}} \cr {\sin {\pi \over 4}} & {\cos {\pi \over 4}} \cr } } \right]$$ and $$x = \left[ {\matrix{ {{1 \over {\sqrt 2 }}} \cr {{1 \over {\sqrt 2 }}} \cr } } \right]$$, then Q³x is equal to

Let R be a relation defined on the set Z of all integers and xRy, when x + 2y is divisible by 3, then

If A = {5ⁿ $$-$$ 4n $$-$$ 1 : n$$ \in $$N} and B = {16(n $$-$$ 1) : n$$ \in $$N}, then

If the function f : R $$ \to $$ R is defined by f(x) = (x² + 1)³⁵, $$\forall $$ x$$ \in $$R, then f is

Standard deviation of n observations a₁, a₂, a₃, ....., a_n is $$\sigma$$. Then, the standard deviation of the observations $$\lambda$$a₁, $$\lambda$$a₂, ....., $$\lambda$$a_n is

Let A and B be two events such that P(A $$ \cap $$ B) = $${1 \over 6}$$, P(A $$\cup$$ B) = $${31 \over 45}$$ and P($$\overline B $$) = $${7 \over 10}$$, then

The value of $$\cos 15^\circ \cos 7{{1^\circ } \over 2}\sin 7{{1^\circ } \over 2}$$ is

The smallest positive root of the equation tan x $$-$$ x = 0 lies in

If in a $$\Delta$$ABC, AD, BE and CF are the altitudes and R is the circumradius, then the radius of the circumcircle of $$\Delta$$DEF is

The points ($$-$$a, $$-$$b), (a, b), (0, 0) and (a², ab), a $$ \ne $$ 0, b $$ \ne $$ 0 are always

The line AB cuts off equal intercepts 2a from the axes. From any point P on the line AB perpendiculars PR and PS are drawn on the axes. Locus of mid-point of RS is

x + 8y $$-$$ 22 = 0, 5x + 2y $$-$$ 34 = 0, 2x $$-$$ 3y + 13 = 0 are the three sides of a triangle. The area of the triangle is

The line through the points (a, b) and ($$-$$a, $$-$$b), passes through the point

The locus of the point of intersection of the straight lines $${x \over a} + {y \over b} = K$$ and $${x \over a} - {y \over b} = {1 \over K}$$, where K is a non-zero real variable, is given by

The equation of a line parallel to the line 3x + 4y = 0 and touching the circle x² + y² = 9 in the first quadrant, is

A line passing through the point of intersection of x + y = 4 and x $$-$$ y = 2 makes an angle $${\tan ^{ - 1}}\left( {{3 \over 4}} \right)$$ with the X-axis. It intersects the parabola $${y^2} = 4(x - 3)$$ at points $$({x_1},{y_1})$$ and $$({x_2},{y_2})$$, respectively. Then, $$|{x_1},{y_2}|$$ is equal to

The equation of auxiliary circle of the ellipse $$16{x^2} + 25{y^2} + 32x - 100y = 284$$ is

If PQ is a double ordinate of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ such that $$\Delta OPQ$$ is equilateral. O being the centre. Then, the eccentricity e satisfies

If the vertex of the conic $${y^2} - 4y = 4x - 4a$$ always lies between the straight lines $$x + y = 3$$ and $$2x + 2y - 1 = 0$$, then

A straight line joining the points (1, 1, 1) and (0, 0, 0) intersects the plane 2x + 2y + z = 10 at

Angle between the planes x + y + 2z = 6 and 2x $$-$$ y + z = 9 is

If $$y = (1 + x)(1 + {x^2})(1 + {x^4})...(1 + {x^{2n}})$$, then the value of $$\left( {{{dy} \over {dx}}} \right)$$ at x = 0 is

If f(x) is an odd differentiable function defined on ($$-$$$$\infty $$, $$\infty $$) such that f'(3) = 2, then f'($$-$$3) is equal to

$$\mathop {\lim }\limits_{x \to 1} {\left( {{{1 + x} \over {2 + x}}} \right)^{{{(1 - \sqrt x )} \over {(1 - x)}}}}$$ is equal to

If $$f(x) = {\tan ^{ - 1}}\left[ {{{\log \left( {{e \over {{x^2}}}} \right)} \over {\log (e{x^2})}}} \right] + {\tan ^{ - 1}}\left[ {{{3 + 2\log x} \over {1 - 6\log x}}} \right]$$, then the value of f''(x) is equal to

$$\int {{{\log \sqrt x } \over {3x}}} dx$$ is equal to

$$\int {{2^x}[f'(x) + f(x)\log 2]dx} $$ is equal to

$$\int\limits_0^1 {\log \left( {{1 \over x} - 1} \right)} dx$$ is equal to

The value of

$$\mathop {\lim }\limits_{n \to \infty } \left\{ {{{\sqrt {n + 1} + \sqrt {n + 2} + ... + \sqrt {2n - 1} } \over {{n^{3/2}}}}} \right\}$$ is

The sum of n terms of the following series $${1^3} + {3^3} + {5^3} + {7^3} + ...$$ is

If $$\alpha$$ and $$\beta$$ are roots of ax² + bx + c = 0, then the equation whose roots are $$\alpha$$² and $$\beta$$², is

If $$\omega$$ is an imaginary cube root of unity, then the value of (2 $$-$$ $$\omega$$) (2 $$-$$ $$\omega$$²) + 2(3 $$-$$ $$\omega$$)(3 $$-$$ $$\omega$$²) + ... + (n $$-$$ 1) (n $$-$$ $$\omega$$)(n $$-$$ $$\omega$$²) is

If $${}^n{C_{r - 1}} = 36,{}^n{C_r} = 84$$ and $${}^n{C_{r + 1}} = 126$$, then the value of $${}^n{C_8}$$ is

In a group of 14 males and 6 females. 8 and 3 of the males and females, respectively are aged above 40 yr. The probability that a person selected at random from the group is aged above 40 yr given that the selected person is a female, is

The equation x³ $$-$$ yx² + x $$-$$ y = 0 represents

The locus of the mid-points of chords of the circle x² + y² = 1, which subtends a right angle at the origin, is

The locus of the mid-points of all chords of the parabola y² = 4ax through its vertex is another parabola with directrix

If [x] denotes the greatest integer less than or equal to x, then the value of the integral $$\int\limits_0^2 {{x^2}[x]\,dx} $$ equals

The number of points at which the function f(x) = max {a $$-$$ x, a + x, b}, $$-$$ $$\infty $$ < x < $$\infty $$, 0 < a < b cannot be differentiable, is

For non-zero vectors a and b, if | a + b | < | a $$-$$ b |, then a and b are

General solution of $$y{{dy} \over {dx}} + b{y^2} = a\cos x,0 < x < 1$$ is

The points of the ellipse 16x² + 9y² = 400 at which the ordinate decreases at the same rate at which the abscissa increases is/are given by

The letters of the word COCHIN are permuted and all permutations are arranged in an alphabetical order as in an English dictionary. The number of words that appear before the word COCHIN is

If the matrix $$A = \left[ {\matrix{ 2 & 0 & 0 \cr 0 & 2 & 0 \cr 2 & 0 & 2 \cr } } \right]$$, then $${A^n} = \left[ {\matrix{ a & 0 & 0 \cr 0 & a & 0 \cr b & 0 & a \cr } } \right],n \in N$$, where

On the ellipse 4x² + 9y² = 1, the points at which the tangents are parallel to the line 8x = 9y, are

If $$\phi (t) = \left\{ \matrix{ 1,\,for\,0 \le t < 1, \hfill \cr 0,\,otherwise \hfill \cr} \right.$$, then $$\int\limits_{ - 300}^{3000} {\left( {\sum\limits_{r' = 2014}^{2016} {\phi (t - r')\phi (t - 2016)} } \right)} \,dt$$ is

If the equation x² + y² $$-$$ 10x + 21 = 0 has real roots x = $$\alpha$$ and y = $$\beta$$, then

If z = sin$$\theta$$ $$-$$ icos$$\theta$$, then for any integer n,

Let f : X $$ \to $$ X be such that f [f(x)] = x, for all x$$\in$$X and X$$ \subseteq $$R, then

If A, B are two events such that P(A $$\cup$$ B) $$ \ge $$ $${3 \over 4}$$ and $${1 \over 8}$$ $$ \le $$ P (A $$\cap$$ B) $$ \le $$ $${3 \over 8}$$, then

If the first and (2n $$-$$ 1)th terms of an AP, GP and HP are equal and their nth terms are respectively a, b, c, then always

The coordinates of a point on the line x + y + 1 = 0, which is at a distance $${1 \over 5}$$ unit from the line 3x + 4y + 2 = 0, are

If the parabola x² = ay makes an intercept of length $$\sqrt {40} $$ units on the line y $$-$$ 2x = 1, then, a is equal to

If f(x) is a function such that f'(x) = (x $$-$$ 1)²(4 $$-$$ x), then

Equivalent capacitance between A and B in the figure is

Two wires of same radius having lengths l₁ and l₂ and resistivities $${{\rho _1}}$$ and $${{\rho _2}}$$ are connected in series. The equivalent resistivity will be

A hollow metal sphere of radius R is charged with a charge Q. The electric potential and intensity inside the sphere are respectively

The potential difference V required for accelerating an electron to have the de-Broglie wavelength of 1 $$\mathop A\limits^o $$ is

The work function of Cesium is 2.27 eV. The cut-off voltage which stops the emission of electrons from a cesium cathode irradiated with light of 600 nm wavelength is

The number of de-Broglie wavelengths contained in the second Bohr orbit of hydrogen atom is

The wavelength of second Balmer line in hydrogen spectrum is 600 nm. The wavelength for its third line in Lyman series is

A ray of light strikes a glass plate at an angle of 60$$^\circ$$. If the reflected and refracted rays are perpendicular to each other, the refractive index of glass is

Light travels through a glass plate of thickness t and having refractive index $$\mu$$. If c be the velocity of light in vacuum, time taken by the light to travel through this thickness of glass is

If x = at + bt², where x is in metre (m) and t is in hour (h), then unit of b will be

The vectors $$\overrightarrow A $$ and $$\overrightarrow B $$ are such that | $$\overrightarrow A $$ + $$\overrightarrow B $$ | = | $$\overrightarrow A $$ $$-$$ $$\overrightarrow B $$ |. The angle between the two vectors will be

At a particular height, the velocity of an ascending body is u. The velocity at the same height while the body falls freely is

Two bodies of masses m₁ and m₂ are separated by a distance R. The distance of the centre of mass of the bodies from the mass m₁ is

The velocity of sound in air at 20$$^\circ$$C and 1 atm pressure is 344.2 m/s. At 40$$^\circ$$C and 2 atm pressure, the velocity of sound in air is approximately

The perfect gas equation for 4g of hydrogen gas is

If the temperature of the Sun gets doubled, the rate of energy received on the Earth will increase by a factor of

A particle vibrating simple harmonically has an acceleration of 16 cms^$$-$$2 when it is at a distance of 4 cm from the mean position. Its time period is

Work done for a certain spring when stretched through 1 mm is 10 joule. The amount of work that must be done on the spring to stretch it further by 1 mm is

If the rms velocity of hydrogen gas at a certain temperature is c, then the rms velocity of oxygen gas at the same temperature is

For air at room temperature, the atmospheric pressure is 1.0 $$ \times $$ 10⁵ Nm^$$-$$2 and density of air is 1.2 kgm^$$-$$3. For a tube of length 1.0 m, closed at one end, the lowest frequency generated is 84 Hz. The value of $$\gamma$$ (ratio of two specific heats) for air is

A gas bubble of 2 cm diameter rises through a liquid of density 1.75 g cm^$$-$$3 with a fixed speed of 0.35 cms^$$-$$1. Neglect the density of the gas. The coefficient of viscosity of the liquid is

The temperature of the water of a pond is 0$$^\circ$$C while that of the surrounding atmosphere is $$-$$20$$^\circ$$C. If the density of ice is $$\rho$$, coefficient of thermal conductivity is k and latent heat of melting is L, then the thickness Z of ice layer formed increases as a function of time t is

1000 droplets of water having 2 mm diameter each coalesce to form a single drop. Given the surface tension of water is 0.072 Nm^$$-$$1. The energy loss in the process is

A Zener diode having break-down voltage 5.6 V is connected in reverse bias with a battery of emf 10 V and a resistance of 100 $$\Omega$$ in series. The current flowing through the Zener diode is

In case of a bipolar transistor $$\beta$$ = 45. The potential drop across the collector resistance of 1 k$$\Omega$$ is 5V. The base current is approximately

An electron enters an electric field having intensity $$E = 3\widehat i + 6\widehat j + 2\widehat k$$ Vm^$$-$$1 and magnetic field having induction $$B = 2\widehat i + 3\widehat j$$ T with a velocity $$v = 2\widehat i + 3\widehat j$$ ms^$$-$$1. The magnitude of the force acting on the electron is (Given, $$e = - 1.6 \times {10^{ - 19}}$$ C)

Two coils of self-inductances 6 mH and 8 mH are connected in series and are adjusted for highest coefficient of coupling. Equivalent self-inductance L for the assembly is approximately

A 1 $$\mu$$F capacitor C is connected to a battery of 10 V through a resistance 1 M$$\Omega$$. The voltage across C after 1 s is approximately

Two equal resistances, 400 $$\Omega$$ each, are connected in series with a 8 V battery. If the resistance of first one increases by 0.5%, the change required in the resistance of the second one in order to keep the potential difference across it unaltered is to

Angle between an equipotential surface and electric lines of force is

A current I = I₀e^{$$-$$$$\lambda$$t} is flowing in a circuit consisting of a parallel combination of resistance R and capacitance C. The total charge over the entire pulse period is

For Fraunhoffer diffraction to occur

The temperature of a blackbody radiation enclosed in a container of volume V is increased from 100$$^\circ$$C to 1000$$^\circ$$C. The heat required in the process is

A mass of 1 kg is suspended by means of a thread. The system is (i) lifted up with an acceleration of 4.9 ms^$$-$$2. (ii) lowered with an acceleration of 4.9 ms^$$-$$2. The ratio of tension in the first and second case is

The effective resistance between A and B in the figure is $${7 \over {12}}\Omega $$ if each side of the cube has 1$$\Omega$$ resistance. The effective resistance between the same two points, when the link AB is removed, is

A charged particle of mass m₁ and charge q₁ is revolving in a circle of radius r. Another charged particle of charge q₂ and mass m₂ is situated at the centre of the circle. If the velocity and time period of the revolving particle be v and T respectively, then

The distance between a light source and photoelectric cell is d. If the distance is decreased to $${d \over 2}$$, then

A train moves from rest with acceleration $$\alpha$$ and in time t₁ covers a distance x. It then decelerates to rest at constant retardation $$\beta$$ for distance y in time t₂. Then,

A drop of water detaches itself from the exit of a tap when ($$\sigma$$ = surface tension of water, $$\rho$$ = density of water, R = radius of the tap exit, r = radius of the drop)

A rectangular coil carrying-current is placed in a non-uniform magnetic field. On that coil, the total