Exam Details
WB JEE 2017
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Questions
155
Duration
180 mins
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WB JEE- Previous Year Papers
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155questions
MCQ
142
91.6%
MSQ
13
8.4%
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PYP
WB JEE 2017
If $$\chi $$ stands for the magnetic susceptibility of a substance, $$\mu$$ for its magnetic permeability and $$\mu$$0 for the permeability of free space, then
PYP
WB JEE 2017
In the given circuit, the binary inputs at A and B are both 1 in one case and both 0 in the next case. The respective outputs at Y in these two cases will be
PYP
WB JEE 2017
If $$({\log _5}x)({\log _x}3x)({\log _{3x}}y) = {\log _x}{x^3}$$, then y equals
PYP
WB JEE 2017
Equilibrium constants for the following reactions at 1200 K are given
2H2O(g) $$\rightleftharpoons$$ 2H2(g) + O2(g), K1 = 6.4 $$\times$$ 10$$-$$8
2CO2(g) $$\rightleftharpoons$$ 2CO(g) + O2(g), K2 = 1.6 $$\times$$ 10$$-$$6
The equilibrium constant for the reaction?
H2(g) + CO2(g) $$\rightleftharpoons$$ CO(g) + H2O(g) at 1200 K will be
2H2O(g) $$\rightleftharpoons$$ 2H2(g) + O2(g), K1 = 6.4 $$\times$$ 10$$-$$8
2CO2(g) $$\rightleftharpoons$$ 2CO(g) + O2(g), K2 = 1.6 $$\times$$ 10$$-$$6
The equilibrium constant for the reaction?
H2(g) + CO2(g) $$\rightleftharpoons$$ CO(g) + H2O(g) at 1200 K will be
PYP
WB JEE 2017
Dissolving NaCN in de-ionised water will result in a solution having
PYP
WB JEE 2017
If a, b$$ \in $$ {1, 2, 3} and the equation ax2 + bx + 1 = 0 has real roots, then
PYP
WB JEE 2017
The probability that a non-leap year selected at random will have 53 Sunday is
PYP
WB JEE 2017
The number of unpaired electrons in $${[NiC{l_4}]^{2 - }}$$, $$Ni{(CO)_4}$$ and $${[Cu{(N{H_3})_4}]^{2 + }}$$ respectively are
PYP
WB JEE 2017
Let $$f(x) = \left\{ {\matrix{
{{{{x^p}} \over {{{(\sin x)}^q}}},} & {if\,0 < x \le {\pi \over 2}} \cr
{0,} & {if\,x = 0} \cr
} } \right.$$, $$(p,q \in R)$$. Then, Lagrange's mean value theorem is applicable to f(x) in closed interval [0, x]
PYP
WB JEE 2017
If the line ax + by + c = 0, ab $$ \ne $$ 0, is a tangent to the curve xy = 1 $$-$$ 2x, then
PYP
WB JEE 2017
The dimension of the universal constant of gravitation, G is
PYP
WB JEE 2017
If the given four electronic configurations.
(i) n = 4, l = 1
(ii) n = 4, l = 0
(iii) n = 3, l = 2
(iv) n = 3, l = 1
are arranged in order of increasing energy, then the order will be
(i) n = 4, l = 1
(ii) n = 4, l = 0
(iii) n = 3, l = 2
(iv) n = 3, l = 1
are arranged in order of increasing energy, then the order will be
PYP
WB JEE 2017
The value of K in order that f(x) = sin x $$-$$ cos x $$-$$ kx + 5 decreases for all positive real values of x is given by
PYP
WB JEE 2017
Three vectors $$\overrightarrow A $$ = a$$\widehat i$$ + $$\widehat j$$ + $$\widehat k$$; $$\overrightarrow B $$ = $$\widehat i$$ + b$$\widehat j$$ + $$\widehat k$$ and $$\overrightarrow C $$ = $$\widehat i$$ + $$\widehat j$$ + c$$\widehat k$$ are mutually perpendicular ($$\widehat i$$, $$\widehat j$$ and k are unit vectors along X, Y and Z-axes respectively). The respective values of a, b and c are
PYP
WB JEE 2017
A solid rectangular sheet has two different coefficients of linear expansion $$\alpha$$1 and $$\alpha$$2 along its length and breadth respectively. The coefficient of surface expansion is (for $$\alpha$$1 t << 1, $$\alpha$$2t < <1)
PYP
WB JEE 2017
A small steel ball bounces on a steel plate held horizontally. On each bounce the speed of the ball arriving at the plate is reduced by a factor e (coefficient of restitution) in the rebound, so that Vupward = eVdownward. If the ball is initially dropped from a height of 0.4 m above the plate and if 10 seconds later the bouncing ceases, the value of e is
PYP
WB JEE 2017
Two particles A and B (both initially at rest) start moving towards each other under a mutual force of attraction. At the instant, when the speed of A is v and the speed of B is 2v, the speed of the centre of mass is
PYP
WB JEE 2017
A bullet of mass 4.2 $$ \times $$ 10$$-$$2 kg, moving at a speed of 300 ms$$-$$1, gets stuck into a block with a mass 9 times that of the bullet. If the block is free to move without any kind of friction, the heat generated in the process will be
PYP
WB JEE 2017
A block of mass 1 kg starts from rest at x = 0 and moves along the X-axis under the action of a force F = kt, where t is time and k = 1 Ns$$-$$1. The distance the block will travel in 6 seconds is
PYP
WB JEE 2017
A uniform capillary tube of length l and inner radius r with its upper end sealed is submerged vertically into water. The outside pressure is p0 and surface tension of water is $$\gamma$$. When a length x of the capillary is submerged into water, it is found that water levels inside and outside the capillary coincide. The value of x is
PYP
WB JEE 2017
2 moles of an ideal monoatomic gas is carried from a state (p0, V0) to state (2p0, 2V0) along a straight line path in a p-V diagram. The amount of heat absorbed by the gas in the process is given by
PYP
WB JEE 2017
A liquid of bulk modulus k is compressed by applying an external pressure such that its density increases by 0.01%. The pressure applied on the liquid is
PYP
WB JEE 2017
Temperature of an ideal gas, initially at 27$$^\circ$$C, is raised by 6$$^\circ$$C. The rms velocity of the gas molecules will
PYP
WB JEE 2017
If the pressure, temperature and density of an ideal gas are denoted by p, T and $$\rho $$, respectively, the velocity of sound in the gas is
PYP
WB JEE 2017
A uniform string of length L and mass M is fixed at both ends while it is subject to a tension T. It can vibrate at frequencies (v) given by the formula (where n = 1, 2, 3, ....)
PYP
WB JEE 2017
The velocity of a particle executing a simple harmonic motion is 13 ms$$-$$1, when its distance from the equilibrium position (Q) is 3 m and its velocity is 12 ms$$-$$1, when it is 5 m away from Q. The frequency of the simple harmonic motion is
PYP
WB JEE 2017
A particle with charge Q coulomb, tied at the end of an inextensible string of length R metre, revolves in a vertical plane. At the centre of the circular trajectory, there is a fixed charge of magnitude Q coulomb. The mass of the moving charge M is such that $$Mg = {{{Q^2}} \over {4\pi {\varepsilon _0}{R^2}}}$$. If at the highest position of the particle, the tension of the string just vanishes, the horizontal velocity at the lowest point has to be
PYP
WB JEE 2017
Consider the circuit shown in the figure where all the resistances are of magnitude 1 k$$\Omega$$. If the current in the extreme right resistance X is 1 mA, the potential difference between A and B is
PYP
WB JEE 2017
A charge of 0.8 coulomb is divided into two charges Q1 and Q2. These are kept at a separation of 30 cm. The force on Q1 is maximum when
PYP
WB JEE 2017
A unit negative charge with mass M resides at the mid-point of the straight line of length 2a adjoining two fixed charges of magnitude +Q each. If it is given a very small displacement x(x << a) in a direction perpendicular to the straight line, it will
PYP
WB JEE 2017
A positive charge Q is situated at the centre of a cube. The electric flux through any face of the cube is (in SI units)
PYP
WB JEE 2017
Consider the circuit given here. The potential difference VBC between the points B and C is
PYP
WB JEE 2017
The magnets of two suspended coil galvanometers are of the same strength so that they produce identical uniform magnetic fields in the region of the coils. The coil of the first one is in the shape of a square of side a and that of the second one is circular of radius $${a \over {\sqrt \pi }}$$. When the same current is passed through the coils, the ratio of the torque experienced by the first coil to that experienced by the second one is
PYP
WB JEE 2017
Three capacitors of capacitance 1.0, 2.0 and 5.0 $$\mu$$F are connected in series to a 10 V source. The potential difference across the 2.0$$\mu$$F capacitor is
PYP
WB JEE 2017
Consider the circuit shown in the figure.
The value of the resistance X for which the thermal power generated in it is practically independent of small variation of its resistance is
The value of the resistance X for which the thermal power generated in it is practically independent of small variation of its resistance is
PYP
WB JEE 2017
A particle with charge e and mass m, moving along the X-axis with a uniform speed u, enters a region where a uniform electric field E is acting along the Y-axis. The particle starts to move in a parabola. Its focal length (neglecting any effect of gravity) is
PYP
WB JEE 2017
A proton is moving with a uniform velocity of $${{{10}^6}}$$ ms$$-$$1 along the Y-axis, under the joint action of a magnetic field along Z-axis and an electric field of magnitude 2 $$ \times $$ 104 Vm$$-$$1 along the negative X-axis. If the electric field is switched off, the proton starts moving in a circle. The radius of the circle is nearly (given : $${e \over m}$$ ratio for proton $$ \approx $$ 108 Ckg$$-$$1)
PYP
WB JEE 2017
The magnetic field due to a current in a straight wire segment of length L at a point on its perpendicular bisector at a distance r(r >> L)
PYP
WB JEE 2017
Two monochromatic coherent light beams A and B have intensities L and $${{L \over 4}}$$, respectively. If these beams are superposed, the maximum and minimum intensities will be
PYP
WB JEE 2017
When the frequency of the AC voltage applied to a series LCR circuit is gradually increased from a low value, the impedance of the circuit
PYP
WB JEE 2017
The ratio of the diameter of the sun to the distance between the earth and the sun is approximately 0.009. The approximate diameter of the image of the sun formed by concave spherical mirror of radius of curvature 0.4 m is
PYP
WB JEE 2017
A point object is held above a thin equiconvex lens at its focus. The focal length is 0.1 m and the lens rests on a horizontal thin plane mirror. The final image will be formed at
PYP
WB JEE 2017
Two long parallel wires separated by 0.1 m carry currents of 1A and 2A, respectively in opposite directions. A third current-carrying wire parallel to both of them is placed in the same plane such that it feels no net magnetic force. It is placed at a distance of
PYP
WB JEE 2017
A parallel beam of light is incident on a glass prism in the shape of a quarter cylinder of radius R = 0.05 m and refractive index n = 1.5, placed on a horizontal table as shown in the figure. Beyond the cylinder, a patch of light is found whose the nearest distance x from the cylinder is
PYP
WB JEE 2017
The de-Broglie wavelength of an electron is $$0.4 \times {10^{ - 10}}$$ m when its kinetic energy is 1.0 keV. Its wavelength will be $$1.0 \times {10^{ - 10}}$$ m, when its kinetic energy is
PYP
WB JEE 2017
Which of the following has the dimension if [$$M{L^0}{T^{ - 2}}$$] ?
PYP
WB JEE 2017
When a semiconducting device is connected in series with a battery and a resistance, a current is found to flow in the circuit. If however, the polarity of the battery is reversed, practically no current flows in the circuit. The device may be
PYP
WB JEE 2017
When light of frequency v1 is incident on a metal with work function W (where hv1 > W), then photocurrent falls to zero at a stopping potential of V1. If the frequency of light is increased to v2, the stopping potential changes to V2. Therefore, the charge of an electron is given by
PYP
WB JEE 2017
Let vn and En be the respective speed and energy of an electron in the nth orbit of radius rn, in a hydrogen atom, as predicted by Bohr's model. Then
PYP
WB JEE 2017
Radon-222 has a half-life of 3.8 days. If one starts with 0.064 kg of radon-222 left after 19 days will be
PYP
WB JEE 2017
You are supplied with 500 mL each of 2N HCl and 5N HCl. What is the maximum volume of 3M HCl that you can prepare using only these two solutions?
PYP
WB JEE 2017
Which of the following sets of quantum numbers represents the 19th electron of Cr(Z = 24) ?
PYP
WB JEE 2017
0.126 g of an acid is needed to completely neutralise 20 mL 0.1 (N) NaOH solution. The equivalent weight of the acid is
PYP
WB JEE 2017
In a flask, the weight ratio of CH4(g) and SO2(g) at 298 K and 1 bar is 1 : 2. The ratio of the number of molecules of SO2(g) and CH4(g) is
PYP
WB JEE 2017
What will be the normality of the salt solution obtained by neutralising x mL y (N) HCl with y mL x(N) NaOH, and finally adding (x + y) mL distilled water
PYP
WB JEE 2017
For same mass of two different ideal gases of molecular weights M1 and M2, Plots of log V vs log p at a given constant temperature are shown. Identify the correct option.
PYP
WB JEE 2017
PbCl2 is insoluble in cold water. Addition of HCl increases its solubility due to
PYP
WB JEE 2017
Of the following compounds, which one of the strongest Bronsted acid in a aqueous solution?
PYP
WB JEE 2017
C6H5F18 is a F18 radio-isotope labelled organic compound. F18 decays by positron emission. The product resulting on decay is
PYP
WB JEE 2017
Assuming the compounds to be completely dissociated in aqueous solution, identify the pair of the solutions that can be expected to be isotonic at the same temperature.
PYP
WB JEE 2017
How many faradays are required to reduce 1 mol of $$C{r_2}O_7^{2 - }$$ to Cr3+ in acid medium?
PYP
WB JEE 2017
The role of fluorspar, which is added in small quantities in the electrolytic reduction of alumina dissolved in fused cryolite is
PYP
WB JEE 2017
Which of the following solutions will turn violet when a drop of lime juice is added to it?
PYP
WB JEE 2017
During electrolysis of molten NaCl, some water was added. What will happen?
PYP
WB JEE 2017
The shape of $$XeF_5^ - $$ will be
PYP
WB JEE 2017
The ground state magnetic property of B2 and C2 molecules will be
PYP
WB JEE 2017
In a close-packed body-centred cubic lattice of potassium, the correct relation between the atomic radius (r) of potassium and the edge-length (a) of the cube is
PYP
WB JEE 2017
Which of the following atoms should have the highest 1st electron affinity?
PYP
WB JEE 2017
The correct order of acid strengths of benzoic acid (X), peroxybenzoic acid (Y) and p-nitrobenzoic acid (Z) is
PYP
WB JEE 2017
When BaCl2 is added to an aqueous salt solution, a white precipitate is obtained. The anion among CO$$_3^{2 - }$$, SO$$_3^{2 - }$$ and SO$$_4^{2 - }$$ that was present in the solution can be
PYP
WB JEE 2017
The isomerisation of 1-butyne to 2-butyne can be achieved by treatment with
PYP
WB JEE 2017
The correct basicity order of the following lanthanide ions is
PYP
WB JEE 2017
Among Me3N, C5H5N and MeCN (Me = methyl group) the electronegativity of N is in the order
PYP
WB JEE 2017
In the IUPAC system, PhCH2CH2CO2H is named as
PYP
WB JEE 2017
The structure of the product P of the following reaction is
PYP
WB JEE 2017
Reduction of the lactol S 
with sodium borohydride gives
with sodium borohydride givesPYP
WB JEE 2017
For the reaction below
the structure of the product Q is
the structure of the product Q is
PYP
WB JEE 2017
The major product(s) obtained form the following reaction of 1 mole of hexadeuteriobenzene is/are
PYP
WB JEE 2017
The yield of acetanilide in the reaction (100% conversion) of 2 moles of aniline with 1 mole of acetic anhydride is
PYP
WB JEE 2017
The reduction of benzene diazonium chloride to phenyl hydrazine can be accomplished by
PYP
WB JEE 2017
The conversion of CH3 $$-$$ CH2 $$-$$ COOH to
can be accomplished by
can be accomplished by
PYP
WB JEE 2017
The compound that would produce a nauseating smell/odour with a hot mixture of chloroform and ethanolic potassium hydroxide is
PYP
WB JEE 2017
ADP and ATP differ in the number of
PYP
WB JEE 2017
The reaction sequence given below given product R.
The structure of the product R is
The structure of the product R is
PYP
WB JEE 2017
On R, the relation $$\rho$$ be defined by 'x$$\rho$$y holds if and only if x $$-$$ y is zero or irrational'. Then,
PYP
WB JEE 2017
On set A = {1, 2, 3}, relations R and S are given by
R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)},
S = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}. Then,
R = {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)},
S = {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}. Then,
PYP
WB JEE 2017
On the set R of real numbers we define xPy if and only if xy $$ \ge $$ 0. Then, the relation P is
PYP
WB JEE 2017
Let $$\alpha$$ and $$\beta$$ be the roots of $${x^2} + x + 1 = 0$$. If n be a positive integer, then $$\alpha$$n + $$\beta$$n is
PYP
WB JEE 2017
The greatest integer which divides $$(p + 1)(p + 2)(p + 3)...(p + q)$$ for all $$p \in N$$ and fixed $$q \in N$$ is
PYP
WB JEE 2017
On R, the set of real numbers, a relation $$\rho $$ is defined as 'a$$\rho $$b if and only if 1 + ab > 0'. Then,
PYP
WB JEE 2017
In a GP series consisting of positive terms, each term is equal to the sum of next two terms. Then, the common ratio of this GP series is
PYP
WB JEE 2017
If p, q are odd integers, then the roots of the equation $$2p{x^2} + (2p + q)x + q = 0$$ are
PYP
WB JEE 2017
Let $${(1 + x + {x^2})^9} = {a_0} + {a_1}x + {a_2}{x^2} + ... + {a_{18}}{x^{18}}$$. Then,
PYP
WB JEE 2017
For real x, the greatest value of $${{{x^2} + 2x + 4} \over {2{x^2} + 4x + 9}}$$ is
PYP
WB JEE 2017
The value of det A, where $$A\, = \left( {\matrix{
1 & {\cos \theta } & 0 \cr
{ - \cos \theta } & 1 & {\cos \theta } \cr
{ - 1} & { - \cos \theta } & 1 \cr
} } \right)$$, lies
PYP
WB JEE 2017
The linear system of equations
$$\left. \matrix{ 8x - 3y - 5z = 0 \hfill \cr 5x - 8y + 3z = 0 \hfill \cr 3x + 5y - 8z = 0 \hfill \cr} \right\}$$ has
$$\left. \matrix{ 8x - 3y - 5z = 0 \hfill \cr 5x - 8y + 3z = 0 \hfill \cr 3x + 5y - 8z = 0 \hfill \cr} \right\}$$ has
PYP
WB JEE 2017
The number of all numbers having 5 digits, with distinct digits is
PYP
WB JEE 2017
Out of 7 consonants and 4 vowels, words are formed each having 3 consonants and 2 vowels. The number of such words that can be formed is
PYP
WB JEE 2017
Let a, b, c be such that b(a + c) $$ \ne $$ 0. If $$\left| {\matrix{
a & {a + 1} & {a - 1} \cr
{ - b} & {b + 1} & {b - 1} \cr
c & {c - 1} & {c + 1} \cr
} } \right| + \left| {\matrix{
{a + 1} & {b + 1} & {c - 1} \cr
{a - 1} & {b - 1} & {c + 1} \cr
{{{( - 1)}^{n + 2}}a} & {{{( - 1)}^{n + 1}}b} & {{{( - 1)}^n}c} \cr
} } \right| = 0$$, then the value of n is
PYP
WB JEE 2017
Let $$A = \left( {\matrix{
{x + 2} & {3x} \cr
3 & {x + 2} \cr
} } \right),\,B = \left( {\matrix{
x & 0 \cr
5 & {x + 2} \cr
} } \right)$$. Then all solutions of the equation det (AB) = 0 is
PYP
WB JEE 2017
Let P be the set of all non-singular matrices of order 3 over R and Q be the set of all orthogonal matrices of order 3 over R. Then,
PYP
WB JEE 2017
For any vector x, where $$\widehat i$$, $$\widehat j$$, $$\widehat k$$ have their usual meanings the value of $${(x \times \widehat i)^2} + {(x \times \widehat j)^2} + {(x \times \widehat k)^2}$$ where $$\widehat i$$, $$\widehat j$$, $$\widehat k$$ have their usual meanings, is equal to
PYP
WB JEE 2017
Let $$A = \left( {\matrix{
1 & 1 & 1 \cr
0 & 1 & 1 \cr
0 & 0 & 1 \cr
} } \right)$$. Then, for positive integer n, An is
PYP
WB JEE 2017
If the sum of two unit vectors is a unit vector, then the magnitude of their difference is
PYP
WB JEE 2017
The expression $${{{{(1 + i)}^n}} \over {{{(1 - i)}^{n - 2}}}}$$ equals
PYP
WB JEE 2017
The complex number z satisfying the equation | z $$-$$ 1 | = | z + 1 | = 1 is
PYP
WB JEE 2017
The equation of the plane through (1, 2, $$-$$3) and (2, $$-$$2, 1) and parallel to X-axis is
PYP
WB JEE 2017
Mean of n observations x1, x2, ...., xn is $$\overline x $$. If an observation xq is replaced by xq' then the new mean is
PYP
WB JEE 2017
Three lines are drawn from the origin O with direction cosines proportional to (1, $$-$$1, 1), (2, $$-$$3, 0) and (1, 0, 3). The three lines are
PYP
WB JEE 2017
Let z = x + iy, where x and y are real. The points (x, y) in the X-Y plane for which $${{{z + i} \over {z - i}}}$$ is purely imaginary, lie on
PYP
WB JEE 2017
The possible values of x, which satisfy the trigonometric equation
$${\tan ^{ - 1}}\left( {{{x - 1} \over {x - 2}}} \right) + {\tan ^{ - 1}}\left( {{{x + 1} \over {x + 2}}} \right) = {\pi \over 4}$$ are
$${\tan ^{ - 1}}\left( {{{x - 1} \over {x - 2}}} \right) + {\tan ^{ - 1}}\left( {{{x + 1} \over {x + 2}}} \right) = {\pi \over 4}$$ are
PYP
WB JEE 2017
The point P(3, 6) is first reflected on the line y = x and then the image point Q is again reflected on the line y = $$-$$ x to get the image point Q'. Then, the circumcentre of the $$\Delta$$PQQ' is
PYP
WB JEE 2017
Let d1 and d2 be the lengths of the perpendiculars drawn from any point of the line $$7x - 9y + 10 = 0$$ upon the lines 3x + 4y = 5 and 12x + 5y = 7, respectively. Then,
PYP
WB JEE 2017
Transforming to parallel axes through a point (p, q), the equation $$2{x^2} + 3xy + 4{y^2} + x + 18y + 25 = 0$$ becomes $$2{x^2} + 3xy + 4{y^2} = 1$$. Then,
PYP
WB JEE 2017
Let A(2, $$-$$3) and B($$-$$ 2, 1) be two angular points of $$\Delta$$ABC. If the centroid of the triangle moves on the line 2x + 3y = 1, then the locus of the angular point C is given by
PYP
WB JEE 2017
The equation $$\sin x(\sin x + \cos x) = k$$ has real solutions, where k is a real number. Then,
PYP
WB JEE 2017
The axis of the parabola $${x^2} + 2xy + {y^2} - 5x + 5y - 5 = 0$$ is
PYP
WB JEE 2017
If the tangent to $${y^2} = 4ax$$ at the point $$(a{t^2},2at)$$ where | t | > 1 is a normal to $${x^2} - {y^2} = {a^2}$$ at the point $$(a\sec \theta ,a\tan \theta )$$, then
PYP
WB JEE 2017
If one of the diameters of the curve x2 + y2 $$-$$ 4x $$-$$ 6y + 9 = 0 is a chord of a circle with centre (1, 1), the radius of this circle is
PYP
WB JEE 2017
The locus of the mid-points of the chords of the circle $${x^2} + {y^2} + 2x - 2y - 2 = 0$$, which make an angle of 90$$^\circ$$ at the centre is
PYP
WB JEE 2017
The common chord of the circles $${x^2} + {y^2} - 4x - 4y = 0$$ and $$2{x^2} + 2{y^2} = 32$$ subtends at the origin an angle equal to
PYP
WB JEE 2017
The focus of the conic x2 $$-$$ 6x + 4y + 1 = 0 is
PYP
WB JEE 2017
Tangents are drawn to the ellipse $${{{x^2}} \over 9} + {{{y^2}} \over 5} = 1$$ at the ends of both latusrectum. The area of the quadrilateral, so formed is
PYP
WB JEE 2017
Let A($$-$$ 1, 0) and B(2, 0) be two points. A point M moves in the plane in such a way that $$\angle MBA$$ = 2$$\angle MAB$$. Then, the point M moves along
PYP
WB JEE 2017
B is an extremity of the minor axis of an ellipse whose foci are S and S'. If $$\angle SBS'$$ is a right angle, then the eccentricity of the ellipse is
PYP
WB JEE 2017
Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 19$$. Then, f(x) = 0 has
PYP
WB JEE 2017
The line segment joining the foci of the hyperbola $${x^2} - {y^2} + 1 = 0$$ is one of the diameters of a circle. The equation of the circle is
PYP
WB JEE 2017
Let P be the foot of the perpendicular from focus S of hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$ on the line bx $$-$$ ay = 0 and let C be the centre of the hyperbola. Then, the area of the rectangle whose sides are equal to that of SP and CP is
PYP
WB JEE 2017
Let for all x > 0, $$f(x) = \mathop {\lim }\limits_{n \to \infty } n({x^{1/n}} - 1)$$, then
PYP
WB JEE 2017
Let $$f:R \to R$$ be such that f is injective and $$f(x)f(y) = f(x + y)$$ for $$\forall x,y \in R$$. If f(x), f(y), f(z) are in G.P., then x, y, z are in
PYP
WB JEE 2017
$$\mathop {\lim }\limits_{x \to 0} {(\sin x)^{2\tan x}}$$ is equal to
PYP
WB JEE 2017
Let f : R $$ \to $$ R be twice continuously differentiable. Let f(0) = f(1) = f'(0) = 0. Then,
PYP
WB JEE 2017
Consider the non-constant differentiable function f one one variable which obeys the relation $${{f(x)} \over {f(y)}} = f(x - y)$$. If f' (0) = p and f' (5) = q, then f' ($$-$$5) is
PYP
WB JEE 2017
If f'' (0) = k, k $$ \ne $$ 0, then the value of
$$\mathop {\lim }\limits_{x \to 0} {{2f(x) - 3f(2x) + f(4x)} \over {{x^2}}}$$ is
$$\mathop {\lim }\limits_{x \to 0} {{2f(x) - 3f(2x) + f(4x)} \over {{x^2}}}$$ is
PYP
WB JEE 2017
Two particles move in the same straight line starting at the same moment from the same point in the same direction. The first moves with constant velocity u and the second starts from rest with constant acceleration f. Then,
PYP
WB JEE 2017
If $$f(x) = {\log _5}{\log _3}x$$, then f'(e) is equal to
PYP
WB JEE 2017
Let I = $$\left| {\int {_{10}^{19}{{\sin x} \over {1 + {x^8}}}dx} } \right|$$. Then,
PYP
WB JEE 2017
If f(x) = xn, being a non-negative integer, then the values of n for which f'($$\alpha$$ + $$\beta$$) = f'($$\alpha$$) + f'($$\beta$$) for all $$\alpha$$, $$\beta$$ > 0 is
PYP
WB JEE 2017
Let, $$F(x) = {e^x},G(x) = {e^{ - x}}$$ and $$H(x) = G(F(x))$$, where x is a real variable. Then, $${{dH} \over {dx}}$$ at x = 0 is
PYP
WB JEE 2017
The chord of the curve $$y = {x^2} + 2ax + b$$, joining the points where x = $$\alpha$$ and x = $$\beta$$, is parallel to the tangent to the curve at abscissa x is equal to
PYP
WB JEE 2017
The value of the integral $$\int_0^1 {{e^{{x^2}}}} dx$$
PYP
WB JEE 2017
The value of $$\mathop {\lim }\limits_{n \to \infty } \left[ {{n \over {{n^2} + {1^2}}} + {n \over {{n^2} + {2^2}}} + ... + {1 \over {2n}}} \right]$$ is
PYP
WB JEE 2017
$$\int {{{{x^2} - 1} \over {{x^4} + 3{x^2} + 1}}dx} $$ (x > 0) is
PYP
WB JEE 2017
Let $${I_1} = \int_0^n {[x]} \,dx$$ and $${I_2} = \int_0^n {\{ x\} } \,dx$$, where [x] and {x} are integral and fractional parts of x and n $$ \in $$ N $$-$$ {1}. Then I1 / I2 is equal to
PYP
WB JEE 2017
Let f be a non-constant continuous function for all x $$ \ge $$ 0. Let f satisfy the relation f(x) f(a $$-$$ x) = 1 for some a $$ \in $$ R+. Then, $$I = \int_0^a {{{dx} \over {1 + f(x)}}} $$ is equal to
PYP
WB JEE 2017
$$\int {\cos (\log x)dx} $$ = F(x) + C, where C is an arbitrary constant. Here, F(x) is equal to
PYP
WB JEE 2017
If $$f(x) = \int_{ - 1}^x {|t|} \,dt$$, then for any $$x \ge 0,\,f(x)$$ is equal to
PYP
WB JEE 2017
If $$y = {e^{m{{\sin }^{ - 1}}x}}$$ then $$(1 - {x^2}){{{d^2}y} \over {d{x^2}}} - x{{dy} \over {dx}} - $$ky = 0, where k is equal to
PYP
WB JEE 2017
Solution of $${(x + y)^2}{{dy} \over {dx}} = {a^2}$$ ('a' belong a constant) is
PYP
WB JEE 2017
The integrating factor of the first order differential equation $${x^2}({x^2} - 1){{dy} \over {dx}} + x({x^2} + 1)y = {x^2} - 1$$ is
PYP
WB JEE 2017
$$\int_0^{100} {{e^{x - [x]}}} dx$$ is equal to
PYP
WB JEE 2017
The area of the figure bounded by the parabolas x = $$-$$ 2y2 and x = 1 $$-$$ 3y2 is
PYP
WB JEE 2017
Six wires, each of resistance r, are connected so as to form a tetrahedron. The equivalent resistance of the combination when current enters through one corner and leaves through some other corner is
PYP
WB JEE 2017
Which one of the following corresponds to a photon of highest energy?
PYP
WB JEE 2017
Let $$I = \int_0^{100\pi } {\sqrt {(1 - \cos 2x)} } \,dx$$, then
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