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WB JEE 2016
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Questions
155
Duration
180 mins
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WB JEE- Previous Year Papers
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155questions
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137
88.4%
MSQ
18
11.6%
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PYP
WB JEE 2016
The correct order of basicity of the following compounds is
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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,
PYP
WB JEE 2016
If x = at + bt2, where x is in metre (m) and t is in hour (h), then unit of b will be
PYP
WB JEE 2016
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
PYP
WB JEE 2016
At a particular height, the velocity of an ascending body is u. The velocity at the same height while the body falls freely is
PYP
WB JEE 2016
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
PYP
WB JEE 2016
The perfect gas equation for 4g of hydrogen gas is
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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)
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
If the temperature of the Sun gets doubled, the rate of energy received on the Earth will increase by a factor of
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
A hollow metal sphere of radius R is charged with a charge Q. The electric potential and intensity inside the sphere are respectively
PYP
WB JEE 2016
Angle between an equipotential surface and electric lines of force is
PYP
WB JEE 2016
Equivalent capacitance between A and B in the figure is
PYP
WB JEE 2016
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)
PYP
WB JEE 2016
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
PYP
WB JEE 2016
A rectangular coil carrying-current is placed in a non-uniform magnetic field. On that coil, the total
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
The number of de-Broglie wavelengths contained in the second Bohr orbit of hydrogen atom is
PYP
WB JEE 2016
The potential difference V required for accelerating an electron to have the de-Broglie wavelength of 1 $$\mathop A\limits^o $$ is
PYP
WB JEE 2016
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
PYP
WB JEE 2016
For Fraunhoffer diffraction to occur
PYP
WB JEE 2016
The wavelength of second Balmer line in hydrogen spectrum is 600 nm. The wavelength for its third line in Lyman series is
PYP
WB JEE 2016
The distance between a light source and photoelectric cell is d. If the distance is decreased to $${d \over 2}$$, then
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
The time taken for an electron to complete one revolution in Bohr orbit of hydrogen atom is
PYP
WB JEE 2016
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?
PYP
WB JEE 2016
Amongst the following, which should have the highest rms speed at the same temperature?
PYP
WB JEE 2016
The molar solubility (in mol L$$-$$1) of a sparingly soluble salt MX4 is 'S'. The corresponding solubility product is Ksp. S in terms of 'Ksp' is given by the relation
PYP
WB JEE 2016
Which of the following plots represent an exothermic reaction?
PYP
WB JEE 2016
If radium and chlorine combine to form radium chloride, the compound would be
PYP
WB JEE 2016
In which of the following mixed aqueous solutions, pH = pKa 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
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
The condition for a reaction to occur spontaneously is
PYP
WB JEE 2016
The order of equivalent conductance at infinite dilution for LiCl, NaCl and KCl is
PYP
WB JEE 2016
An element X belongs to fourth period and fifteenth group of the periodic table. Which of the following statements is true?
PYP
WB JEE 2016
An element E loses one $$\alpha$$ and two $$\beta$$-particles in three successive stages. The resulting element will be
PYP
WB JEE 2016
Which of the following arrangements is correct in respect of solubility in water?
PYP
WB JEE 2016
Ionic solids with Schottky defect may contain in their structure
PYP
WB JEE 2016
Point out the false statement.
PYP
WB JEE 2016
Of the following molecules, which have shape similar to CO2 ?
PYP
WB JEE 2016
The metal which can be used to obtain metallic Cu from aqueous CuSO4 solution is
PYP
WB JEE 2016
The boiling points of HF, HCl, HBr and HI follow the order
PYP
WB JEE 2016
The number of $$\sigma$$ and $$\pi$$ bonds between two carbon atoms in calcium carbide are
PYP
WB JEE 2016
The correct order of O$$-$$O bond length in O2, H2O2 and O3 is
PYP
WB JEE 2016
Which statement is not correct for ortho and para hydrogen?
PYP
WB JEE 2016
In the solid state, PCl5 exists as
PYP
WB JEE 2016
Nitrogen dioxide is not produced on heating
PYP
WB JEE 2016
The acid in which O$$-$$O bonding is present is
PYP
WB JEE 2016
From the following compounds, choose the one which is not aromatic.
PYP
WB JEE 2016
Which of the following statements regarding Lanthanides is false?
PYP
WB JEE 2016
Which of the following statement(s) is (are) correct when a mixture of NaCl and K2Cr2O7 is gently warmed with conc. H2SO4?
PYP
WB JEE 2016
Amongst the following compounds, the one(s) which readily react with ethanolic KCN.
PYP
WB JEE 2016
Which of the following reactions will not result in the formation of carbon-carbon bonds?
PYP
WB JEE 2016
Choose the correct statement(s) among the following.
PYP
WB JEE 2016
The major products obtained during ozonolysis of 2, 3-dimethyl-1-butene and subsequent reductions with Zn and H2O are
PYP
WB JEE 2016
Identify X in the following sequence of reactions.
PYP
WB JEE 2016
Ozonolysis of an alkene produces only one dicarbonyl compound. The structure of the alkene is
PYP
WB JEE 2016
Compound X is tested and the results are shown in the table.
Which ions are present in compound 'X'?
| 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'?
PYP
WB JEE 2016
Which of the following will be dehydrated most readily in alkaline medium?
PYP
WB JEE 2016
Amongst the following compounds, the one that will not respond to Cannizzaro reaction upon treatment with alkali is
PYP
WB JEE 2016
Which of the following compounds would not react with Lucas reagent at room temperature.
PYP
WB JEE 2016
The correct structure of the drug paracetamol is
PYP
WB JEE 2016
Amongst the following compounds, the one which would not respond to iodoform test is :
PYP
WB JEE 2016
Let R be a relation defined on the set Z of all integers and xRy, when x + 2y is divisible by 3, then
PYP
WB JEE 2016
If A = {5n $$-$$ 4n $$-$$ 1 : n$$ \in $$N} and B = {16(n $$-$$ 1) : n$$ \in $$N}, then
PYP
WB JEE 2016
If p, q are the roots of the equation x2 + px + q = 0, then
PYP
WB JEE 2016
If a, x are real numbers and | a | < 1, | x | < 1, then 1 + (1 + a) x + (1 + a + a2) x2 + ..... $$\infty $$ is equal to
PYP
WB JEE 2016
The sum of n terms of the following series $${1^3} + {3^3} + {5^3} + {7^3} + ...$$ is
PYP
WB JEE 2016
If $${\log _{0.3}}(x - 1) < {\log _{0.09}}(x - 1)$$, then x lies in the interval
PYP
WB JEE 2016
If the equation x2 + y2 $$-$$ 10x + 21 = 0 has real roots x = $$\alpha$$ and y = $$\beta$$, then
PYP
WB JEE 2016
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
PYP
WB JEE 2016
If $${}^n{C_{r - 1}} = 36,{}^n{C_r} = 84$$ and $${}^n{C_{r + 1}} = 126$$, then the value of $${}^n{C_8}$$ is
PYP
WB JEE 2016
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
PYP
WB JEE 2016
If $${1 \over {{}^5{C_r}}} + {1 \over {{}^6{C_r}}} = {1 \over {{}^4{C_r}}}$$, then the value of r is
PYP
WB JEE 2016
If $$\alpha$$ and $$\beta$$ are roots of ax2 + bx + c = 0, then the equation whose roots are $$\alpha$$2 and $$\beta$$2, is
PYP
WB JEE 2016
Let A be a 3 $$ \times $$ 3 matrix and B be its adjoint matrix. If | B | = 64, then | A | is equal to
PYP
WB JEE 2016
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
PYP
WB JEE 2016
The cosine of the angle between any two diagonals of a cube is
PYP
WB JEE 2016
For positive integer n, n3 + 2n is always divisible by
PYP
WB JEE 2016
In the expansion of (x $$-$$ 1) (x $$-$$ 2) .... (x $$-$$ 18), the coefficient of x17 is
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
If z = sin$$\theta$$ $$-$$ icos$$\theta$$, then for any integer n,
PYP
WB JEE 2016
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
PYP
WB JEE 2016
Standard deviation of n observations a1, a2, a3, ....., an is $$\sigma$$. Then, the standard deviation of the observations $$\lambda$$a1, $$\lambda$$a2, ....., $$\lambda$$an is
PYP
WB JEE 2016
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
PYP
WB JEE 2016
The value of $$\sum\limits_{n = 1}^{13} {({i^n} + {i^{n + 1}})} $$, $$i = \sqrt { - 1} $$ is
PYP
WB JEE 2016
The order of the differential equation of all parabolas whose axis of symmetry along X-axis is
PYP
WB JEE 2016
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
PYP
WB JEE 2016
The area enclosed by $$y = \sqrt {5 - {x^2}} $$ and $$y = |x - 1|$$ is
PYP
WB JEE 2016
If x is a positive real number different from 1 such that logax, logbx, logcx are in AP, then
PYP
WB JEE 2016
The number of ways in which the letters of the word ARRANGE can be permuted such that the R's occur together, is
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
If the function f : R $$ \to $$ R is defined by f(x) = (x2 + 1)35, $$\forall $$ x$$ \in $$R, then f is
PYP
WB JEE 2016
The smallest positive root of the equation tan x $$-$$ x = 0 lies in
PYP
WB JEE 2016
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
PYP
WB JEE 2016
The value of $$\cos 15^\circ \cos 7{{1^\circ } \over 2}\sin 7{{1^\circ } \over 2}$$ is
PYP
WB JEE 2016
$$1 + {}^n{C_1}\cos \theta + {}^n{C_2}\cos 2\theta + ... + {}^n{C_n}\cos n\theta $$ equals
PYP
WB JEE 2016
The points ($$-$$a, $$-$$b), (a, b), (0, 0) and (a2, ab), a $$ \ne $$ 0, b $$ \ne $$ 0 are always
PYP
WB JEE 2016
A straight line joining the points (1, 1, 1) and (0, 0, 0) intersects the plane 2x + 2y + z = 10 at
PYP
WB JEE 2016
$$\int {{{\log \sqrt x } \over {3x}}} dx$$ is equal to
PYP
WB JEE 2016
Angle between the planes x + y + 2z = 6 and 2x $$-$$ y + z = 9 is
PYP
WB JEE 2016
If f(x) is an odd differentiable function defined on ($$-$$$$\infty $$, $$\infty $$) such that f'(3) = 2, then f'($$-$$3) is equal to
PYP
WB JEE 2016
The equation x3 $$-$$ yx2 + x $$-$$ y = 0 represents
PYP
WB JEE 2016
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
PYP
WB JEE 2016
For non-zero vectors a and b, if | a + b | < | a $$-$$ b |, then a and b are
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
If the parabola x2 = ay makes an intercept of length $$\sqrt {40} $$ units on the line y $$-$$ 2x = 1, then, a is equal to
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
The locus of the mid-points of chords of the circle x2 + y2 = 1, which subtends a right angle at the origin, is
PYP
WB JEE 2016
The line through the points (a, b) and ($$-$$a, $$-$$b), passes through the point
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
The locus of the mid-points of all chords of the parabola y2 = 4ax through its vertex is another parabola with directrix
PYP
WB JEE 2016
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
PYP
WB JEE 2016
The equation of auxiliary circle of the ellipse $$16{x^2} + 25{y^2} + 32x - 100y = 284$$ is
PYP
WB JEE 2016
The line y = x + $$\lambda$$ is tangent to the ellipse 2x2 + 3y2 = 1. Then, $$\lambda$$ is
PYP
WB JEE 2016
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
PYP
WB JEE 2016
The equation of a line parallel to the line 3x + 4y = 0 and touching the circle x2 + y2 = 9 in the first quadrant, is
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
On the ellipse 4x2 + 9y2 = 1, the points at which the tangents are parallel to the line 8x = 9y, are
PYP
WB JEE 2016
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
PYP
WB JEE 2016
Let f : X $$ \to $$ X be such that f [f(x)] = x, for all x$$\in$$X and X$$ \subseteq $$R, then
PYP
WB JEE 2016
$$\mathop {\lim }\limits_{x \to 1} {\left( {{{1 + x} \over {2 + x}}} \right)^{{{(1 - \sqrt x )} \over {(1 - x)}}}}$$ is equal to
PYP
WB JEE 2016
$$\int {{2^x}[f'(x) + f(x)\log 2]dx} $$ is equal to
PYP
WB JEE 2016
$$\int\limits_0^1 {\log \left( {{1 \over x} - 1} \right)} dx$$ is equal to
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
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
$$\mathop {\lim }\limits_{n \to \infty } \left\{ {{{\sqrt {n + 1} + \sqrt {n + 2} + ... + \sqrt {2n - 1} } \over {{n^{3/2}}}}} \right\}$$ is
PYP
WB JEE 2016
If f(x) is a function such that f'(x) = (x $$-$$ 1)2(4 $$-$$ x), then
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WB JEE 2016
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
PYP
WB JEE 2016
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
PYP
WB JEE 2016
General solution of $$y{{dy} \over {dx}} + b{y^2} = a\cos x,0 < x < 1$$ is
PYP
WB JEE 2016
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
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