Exam Details
WB JEE 2019
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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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155questions
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142
91.6%
MSQ
13
8.4%
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PYP
WB JEE 2019
The half-life period of $${}_{53}{I^{125}}$$ is 60 days. The radioactivity after 180 days will be
PYP
WB JEE 2019
The second ionization energy of the following elements follows the order
PYP
WB JEE 2019
For the equilibrium, H2O(l) $$\rightleftharpoons$$ H2O(v), which of the following is correct?
PYP
WB JEE 2019
The density of the material of a cube can be estimated by measuring its mass and the length of one of its sides. If the maximum error in the measurement of mass and length are 0.3% and 0.2% respectively, the maximum error in the estimation of the density of the cube is approximately
PYP
WB JEE 2019
At constant pressure, the heat of formation of a compound is not dependent on temperature, when
PYP
WB JEE 2019
The melting points of (i) BeCl2 (ii) CaCl2 and (iii) HgCl2 follows the order
PYP
WB JEE 2019
Let a > b > 0 and I(n) = a1/n $$-$$ b1/n, J(n) = (a $$-$$ b)1/n for all n $$ \ge $$ 2, then
PYP
WB JEE 2019
Let $$f(x) = {x^4} - 4{x^3} + 4{x^2} + c,\,c \in R$$. Then
PYP
WB JEE 2019
Let $$A = \left[ {\matrix{
3 & 0 & 3 \cr
0 & 3 & 0 \cr
3 & 0 & 3 \cr
} } \right]$$. Then, the roots of the equation det $$(A - \lambda {I_3})$$ = 0 (where I3 is the identity matrix of order 3) are
PYP
WB JEE 2019
Let a, b, c be real numbers such that a + b + c < 0 and the quadratic equation ax2 + bx + c = 0 has imaginary roots. Then,
PYP
WB JEE 2019
The first electron affinity of C, N and O will be of the order
PYP
WB JEE 2019
If the radius of a spherical balloon increases by 0.1%, then its volume increases approximately by
PYP
WB JEE 2019
Two weights of the mass m1 and m2 (> m1) are joined by an inextensible string of negligible mass passing over a fixed frictionless pulley. The magnitude of the acceleration of the loads is
PYP
WB JEE 2019
A projectile thrown with an initial velocity of 10 ms$$-$$1 at an angle $$\alpha$$ with the horizontal, has a range of 5 m. Taking g = 10 ms$$-$$2 and neglecting air resistance, what will be the estimated value of $$\alpha$$?
PYP
WB JEE 2019
A body starts from rest, under the action of an engine working at a constant power and moves along a straight line. The displacement s is given as a function of time (t) as
PYP
WB JEE 2019
Two particles are simultaneously projected in the horizontal direction from a point P at a certain height. The initial velocities of the particles are oppositely directed to each other and have magnitude v each. The separation between the particles at a time when their position vectors (drawn from the point P) are mutually perpendicular, is
PYP
WB JEE 2019
A compressive force is applied to a uniform rod of rectangular cross-section so that its length decreases by 1%. If the Poisson's ratio for the material of the rod be 0.2, which of the following statements is correct?
"The volume approximately ................."
"The volume approximately ................."
PYP
WB JEE 2019
The correct dimensional formula for impulse is given by
PYP
WB JEE 2019
Two black bodies A and B have equal surface areas are maintained at temperatures 27$$^\circ$$C and 177$$^\circ$$C respectively. What will be the ratio of the thermal energy radiated per second by A to that by B?
PYP
WB JEE 2019
Two identical blocks of ice move in opposite directions with equal speed and collide with each other. What will be the minimum speed required to make both the blocks melt completely, if the initial temperatures of the blocks were $$-$$8$$^\circ$$C each? (Specific heat of ice is 2100 Jkg$$-$$1K$$-$$1 and latent heat of fusion of ice is 3.36 $$ \times $$ 105 Jkg$$-$$1)
PYP
WB JEE 2019
Consider the given diagram. An ideal gas is contained in a chamber (left) of volume V and is at an absolute temperature T. It is allowed to rush freely into the right chamber of volume V which is initially vacuum. The whole system is thermally isolated. What will be the final temperature of the equilibrium has been attained?
PYP
WB JEE 2019
A small spherical body of radius r and density $$\rho $$ moves with the terminal velocity v in a fluid of coefficient of viscosity $$\eta $$ and density $$\sigma$$. What will be the net force on the body?
PYP
WB JEE 2019
A horizontal fire hose with a nozzle of cross-sectional area $${5 \over {\sqrt {21} }} \times {10^{ - 3}}{m^2}$$ delivers a cubic metre of water in 10s. What will be the maximum possible increase in the temperature of water while it hits a rigid wall (neglecting the effect of gravity)?
PYP
WB JEE 2019
What will be the molar specific heat at constant volume of an ideal gas consisting of rigid diatomic molecules?
PYP
WB JEE 2019
The initial pressure and volume of a given mass of an ideal gas with $$\left( {{{{C_p}} \over {{C_V}}} = \gamma } \right)$$, taken in a cylinder fitted with a piston, are p0 and V0 respectively. At this stage the gas has the same temperature as that of the surrounding medium which is T0. It is adiabatically compressed to a volume equal to $${{{V_0}} \over 2}$$. Subsequently the gas is allowed to come to thermal equilibrium with the surroundings. What is the heat released to the surrounding?
PYP
WB JEE 2019
In the circuit shown in the figure all the resistance are identical and each has the value r$$\Omega $$. The equivalent resistance of the combination between the points A and B will remain unchanged even when the following pairs of points marked in the figure are connected through a resistance R.
PYP
WB JEE 2019
Assume that the earth moves around the sun in a circular orbit of radius R and there exists a planet which also move around the sun in a circular orbit with an angular speed twice as large as that of the earth. The earth of the orbit of the planet is
PYP
WB JEE 2019
A negative charge is placed at the midpoint between two fixed equal positive charges, separated by a distance 2d. If the negative charge is given a small displacement x(x < < d) perpendicular to the line joining the positive charges, how the force (F) developed on it will approximately depend on x?
PYP
WB JEE 2019
Eleven equal point charges, all of them having a charge +Q, are placed at all the hour positions of a circular clock of radius r, except at the 10 h position. What is the electric field strength at the centre of the clock?
PYP
WB JEE 2019
What is the current I shown in the given circuit?
PYP
WB JEE 2019
To which of the following quantities, the radius of the circular path of a charged particle moving at right angles to a uniform magnetic field is directly proportional?
PYP
WB JEE 2019
A particle with charge q moves with a velocity v in a direction perpendicular to the directions of uniform electric and magnetic fields, E and B respectively, which are mutually perpendicular to each other. Which one of the following gives the condition for which the particle moves undeflected in its original trajectory?
PYP
WB JEE 2019
A capacitor of capacitance C is connected in series with a resistance R and DC source of emf E through a key. The capacitor starts charging when the key is closed. By the time the capacitor has been fully charged, what amount of energy is dissipated in the resistance R?
PYP
WB JEE 2019
Five identical capacitors, of capacitance 20$$\mu$$F each, are connected to a battery of 150V, in a combination as shown in the diagram. What is the total amount of charge stored?
PYP
WB JEE 2019
A square conducting loop is placed near an infinitely long current carrying wire with one edge parallel to the wire as shown in the figure. If the current in the straight wire is suddenly halved, which of the following statements will be true?
"The loop will .........".
"The loop will .........".
PYP
WB JEE 2019
When the value of R in the balanced Wheatstone bridge, shown in the figure, is increased from 5$$\Omega $$ to 7$$\Omega $$, the value of S has to be increased by 3$$\Omega $$ in order to maintain the balance. What is the initial values of S?
PYP
WB JEE 2019
When a 60 mH inductor and a resistor are connected in series with an AC voltage source, the voltage leads the current by 60$$^\circ$$. If the inductor is replaced by a 0.5 $$\mu$$F capacitor, the voltage lags behind the current by 30$$^\circ$$. What is the frequency of the AC supply?
PYP
WB JEE 2019
An electric current 'I' enters and leaves a uniform circular wire of radius r through diametrically opposite points. A particle carrying a charge q moves along the axis of the circular wire with speed v. What is the magnetic force experienced by the particle when it passes through the centre of the circle?
PYP
WB JEE 2019
A parallel plate capacitor in series with a resistance of 100$$\Omega $$, an inductor of 20 mH and an AC voltage source of variable frequency shows resonance at a frequency of $${{1250} \over \pi }$$ Hz. If this capacitor is charged by a DC voltage source to a voltage 25 V, what amount of charge will be stored in each plate of the capacitor?
PYP
WB JEE 2019
A metallic loop is placed in a uniform magnetic field B with the plane of the loop perpendicular to B. Under which condition(s) given an emf will be induced in the loop? "If the loop is ............"
PYP
WB JEE 2019
A ray of light is reflected by a plane mirror. $${\widehat e_0}$$, $$\widehat e$$ and $$\widehat n$$ be the unit vectors along the incident ray, reflected ray and the normal to the reflecting surface respectively.
Which of the following gives an expression for $$\widehat e$$?
Which of the following gives an expression for $$\widehat e$$?
PYP
WB JEE 2019
A current 'I' is flowing along an infinite, straight wire, in the positive Z-direction and the same current is flowing along a similar parallel wire 5 m apart, in the negative Z-direction. A point P is at a perpendicular distance 3m from the first wire and 4m from the second. What will be magnitude of the magnetic field B of P?
PYP
WB JEE 2019
When the frequency of the light used is changed from $$4 \times {10^{14}}{s^{ - 1}}$$ to $$5 \times {10^{14}}{s^{ - 1}}$$, the angular width of the principal (central) maximum in a single slit Fraunhoffer diffraction pattern changes by 0.6 radian. What is the width of the slit (assume that the experiment is performed in vacuum)?
PYP
WB JEE 2019
To which of the following the angular velocity of the electron in the n-th Bohr orbit is proportional?
PYP
WB JEE 2019
A point object is placed on the axis of a thin convex lens of focal length 0.05 m at a distance of 0.2 m from the lens and its image is formed on the axis. If the object is now made to oscillate along the axis with a small amplitude of A cm, then what is the amplitude of oscillation of the image?
[you may assume, $${1 \over {1 + x}} \approx 1 - x$$, where x < < 1]
[you may assume, $${1 \over {1 + x}} \approx 1 - x$$, where x < < 1]
PYP
WB JEE 2019
In Young's experiment for the interference of light, the separation between the slits is d and the distance of the screen from the slits is D. If D is increased by 0.5% and d is decreased by 0.3% then for the light of a given wavelength , which one of the following is true? "The fringe width ..............
PYP
WB JEE 2019
A proton and an electron initially at rest are accelerated by the same potential difference. Assuming that a proton is 2000 times heavier than an electron, what will be the relation between the de Broglie wavelength of the proton ($$\lambda$$p) and that of electron ($$\lambda$$e)?
PYP
WB JEE 2019
A parent nucleus X undergoes $$\alpha$$-decay with a half-life of 75000 yrs. The daughter nucleus Y undergoes $$\beta$$-decay with a half-life of 9 months. In a particular sample, it is found that the rate of emission of $$\beta$$-particles is nearly constant (over several months) at $${10^7}/h$$. What will be the number of $$\alpha$$-particles emitted in an hour?
PYP
WB JEE 2019
Electrons are emitted with kinetic energy T from a metal plate by an irradiation of light of intensity J and frequency v. Then, which of the following will be true?
PYP
WB JEE 2019
In the circuit shown, what will be the current through the 6V zener?
PYP
WB JEE 2019
For a van der Waals' gas, the term $$\left( {{{ab} \over {{V^2}}}} \right)$$ represents some
PYP
WB JEE 2019
In the crystalline solid MSO4 . nH2O of molar mass 250 g mol$$-$$1, the percentage of anhydrous salt is 64 by weight. The value of n is
PYP
WB JEE 2019
Each of the two inputs A and B can assume values either 0 or 1. Then which of the following will be equal to $$\overline {A\,} $$ . $$\overline {B\,} $$?
PYP
WB JEE 2019
At S.T.P. the volume of 7.5 g of a gas is 5.6 L. The gas is
PYP
WB JEE 2019
Which of the following mixtures will have the lowest pH at 298 K?
PYP
WB JEE 2019
Consider the following two first order reactions occurring at 298 K with same initial concentration of A :
(1) A $$\to$$ B; rate constant, k = 0.693 min$$-$$1
(2) A $$\to$$ C; half-life, t1/2 = 0.693 min
Choose the correct option.
(1) A $$\to$$ B; rate constant, k = 0.693 min$$-$$1
(2) A $$\to$$ C; half-life, t1/2 = 0.693 min
Choose the correct option.
PYP
WB JEE 2019
The quantity hv/KB corresponds to
PYP
WB JEE 2019
Consider, the radioactive disintegration
$${}_{82}{A^{210}}\buildrel {} \over \longrightarrow B\buildrel {} \over \longrightarrow C\buildrel {} \over \longrightarrow {}_{82}{A^{206}}$$
The sequence of emission can be
$${}_{82}{A^{210}}\buildrel {} \over \longrightarrow B\buildrel {} \over \longrightarrow C\buildrel {} \over \longrightarrow {}_{82}{A^{206}}$$
The sequence of emission can be
PYP
WB JEE 2019
In the equilibrium, H2 + I2 $$\rightleftharpoons$$ 2HI, if at a given temperature the concentration of the reactants are increased, the value of the equilibrium constant, KC, will
PYP
WB JEE 2019
The kinetic study of a reaction like vA $$\to$$ P at 300 K provides the following curve, where concentration is taken in mol dm$$-$$3 and time in min.
Identify the correct order (n) and rate constant (k)
Identify the correct order (n) and rate constant (k)
PYP
WB JEE 2019
If electrolysis of aqueous CuSO4 solution is carried out using Cu-electrodes, the reaction taking place at the anode is
PYP
WB JEE 2019
Which of these species will have non-zero magnetic moment?
PYP
WB JEE 2019
Which atomic species cannot be used as a nuclear fuel?
PYP
WB JEE 2019
The indicated atom is not a nucleophilic site in
PYP
WB JEE 2019
The charge carried by 1 millimole of Mn+ ions is 193 coulombs. The value of n is
PYP
WB JEE 2019
Identify the correct statement(s) :
PYP
WB JEE 2019
Which of the following chemicals may be used to identify three unlabelled beakers containing conc. NaOH, conc. H2SO4 and water?
PYP
WB JEE 2019
The compound, which evolves carbon dioxide on treatment with aqueous solution of sodium bicarbonate at 25$$^\circ$$C, is
PYP
WB JEE 2019
A copper coin was electroplated with Zn and then heated at high temperature until there is a change in colour. What will be the resulting colour?
PYP
WB JEE 2019
The reactive species in chlorine bleach is
PYP
WB JEE 2019
The H - N - H angle in ammonia is 107.6$$^\circ$$ while the H - P - H angle in phosphine is 93.5$$^\circ$$. Relative to phosphine, the p-character of the lone-pair on ammonia is expected to be
PYP
WB JEE 2019
In the Bayer's process, the leaching of alumina is done by using
PYP
WB JEE 2019
The correct order of the addition reaction rates of halogen acids with ethylene is
PYP
WB JEE 2019
The molecule/molecules that has/have delocalised lone pair(s) of electrons is/are
PYP
WB JEE 2019
The total number of isomeric linear dipeptides which can be synthesised from racemic alanine is
PYP
WB JEE 2019
The conformations of n-butane, commonly known as eclipsed, gauche and anti-conformations can be interconverted by
PYP
WB JEE 2019
Compounds with spin only magnetic moment equivalent to five unpaired electrons are
PYP
WB JEE 2019
The conductivity measurement of a coordination compound of cobalt (III) shows that it dissociates into 3 ions in solution. The compound is
PYP
WB JEE 2019
Haloform reaction with I2 and KOH will be respond by
PYP
WB JEE 2019
The compound (s), capable of producing achiral compound on heating at 100$$^\circ$$ is/are
PYP
WB JEE 2019
Oxidation of allyl alcohol with a peracid gives a compound of molecular formula C3H6O2, which contains an asymmetric carbon atom. The structure of the compound is
PYP
WB JEE 2019
For the reaction below, the product is Q.
The compound Q is
The compound Q is
PYP
WB JEE 2019
Cyclopentanol on reaction with NaH followed by CS2 and CH3I produces a/an
PYP
WB JEE 2019
One of the products of the following reaction is P.
Structure of P is
Structure of P is
PYP
WB JEE 2019
Let x1, x2 be the roots of $${x^2} - 3x + a = 0$$ and x3, x4 be the roots of $${x^2} - 12x + b = 0$$. If $${x_1} < {x_2} < {x_3} < {x_4}$$ and $${x_1},{x_2},{x_3},{x_4}$$ are in GP, then ab equals
PYP
WB JEE 2019
If $$\log _2^6 + {1 \over {2x}} = {\log _2}\left( {{2^{{1 \over x}}} + 8} \right)$$, then the value of x are
PYP
WB JEE 2019
Let f : X $$ \to $$ Y and A, B are non-void subsets of Y, then (where the symbols have their usual interpretation)
PYP
WB JEE 2019
Let S, T, U be three non-void sets and f : S $$ \to $$ T, g : T $$ \to $$ U be so that gof : s $$ \to $$ U is surjective. Then,
PYP
WB JEE 2019
A candidate is required to answer 6 out of 12 questions which are divided into two parts A and B, each containing 6 questions and he/she is not permitted to attempt more than 4 questions from any part. In how many different ways can he/she make up his/her choice of 6 questions?
PYP
WB JEE 2019
Let the relation $$\rho $$ be defined on R as a$$\rho $$b if 1 + ab > 0. Then,
PYP
WB JEE 2019
72n + 16n $$-$$1 (n$$ \in $$ N) is divisible by
PYP
WB JEE 2019
There are 7 greeting cards, each of a different colour and 7 envelopes of same 7 colours as that of the cards. The number of ways in which the cards can be put in envelopes, so that exactly 4 of the cards go into envelopes of respective colour is,
PYP
WB JEE 2019
If M is any square matrix of order 3 over R and if M' be the transpose of M, then adj(M') $$-$$ (adj M)' is equal to
PYP
WB JEE 2019
The number of irrational terms in the expansion of $${\left( {{3^{{1 \over 8}}} + {5^{{1 \over 4}}}} \right)^{84}}$$ is
PYP
WB JEE 2019
Let A be a square matrix of order 3 whose all entries are 1 and let I3 be the identity matrix of order 3. Then, the matrix $$A - 3{I_3}$$ is
PYP
WB JEE 2019
If $$A = \left( {\matrix{
5 & {5x} & x \cr
0 & x & {5x} \cr
0 & 0 & 5 \cr
} } \right)$$ and $$|A{|^2} = 25$$, then | x | is equal to
PYP
WB JEE 2019
The direction ratios of the normal to the plane passing through the points (1, 2, $$-$$3), ($$-$$1, $$-$$2, 1) and parallel to $${{x - 2} \over 2} = {{y + 1} \over 3} = {z \over 4}$$ is
PYP
WB JEE 2019
The equation of the plane, which bisects the line joining the points (1, 2, 3) and (3, 4, 5) at right angles is
PYP
WB JEE 2019
The position vectors of the points A, B, C and D are $$3\widehat i - 2\widehat j - \widehat k$$, $$2\widehat i - 3\widehat j + 2\widehat k$$, $$5\widehat i - \widehat j + 2\widehat k$$ and $$4\widehat i - \widehat j - \lambda \widehat k$$, respectively. If the points A, B, C and D lie on a plane, the value of $$\lambda$$ is
PYP
WB JEE 2019
Let $$\widehat \alpha $$, $$\widehat \beta $$, $$\widehat \gamma $$ be three unit vectors such that $$\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) = {1 \over 2}(\widehat \beta + \widehat \gamma )$$ where $$\widehat \alpha \, \times \,(\widehat \beta \times \widehat \gamma ) = $$$$(\widehat \alpha \,.\,\widehat \gamma )\widehat \beta - (\widehat \alpha \,.\,\widehat \beta )\widehat \gamma $$. If $$\widehat \beta $$ is not parallel to $$\widehat \gamma $$, then the angle between $$\widehat \alpha $$ and $$\widehat \beta $$ is
PYP
WB JEE 2019
Let A and B be two square matrices of order 3 and AB = O3, where O3 denotes the null matrix of order 3. Then,
PYP
WB JEE 2019
The system of equations
$$\eqalign{ & \lambda x + y + 3z = 0 \cr & 2x + \mu y - z = 0 \cr & 5x + 7y + z = 0 \cr} $$
has infinitely many solutions in R. Then,
$$\eqalign{ & \lambda x + y + 3z = 0 \cr & 2x + \mu y - z = 0 \cr & 5x + 7y + z = 0 \cr} $$
has infinitely many solutions in R. Then,
PYP
WB JEE 2019
Let z be a complex number such that the principal value of argument, arg z > 0. Then, arg z $$-$$ arg($$-$$ z) is
PYP
WB JEE 2019
The general value of the real angle $$\theta$$, which satisfies the equation, $$(\cos \theta + i\sin \theta )(\cos 2\theta + i\sin 2\theta )...(\cos n\theta + i\sin n\theta ) = 1$$ is given by, (assuming k is an integer)
PYP
WB JEE 2019
A problem in mathematics is given to 4 students whose chances of solving individually are $${{1 \over 2}}$$, $${{1 \over 3}}$$, $${{1 \over 4}}$$ and $${{1 \over 5}}$$. The probability that the problem will be solved at least by one student is
PYP
WB JEE 2019
For any non-zero complex number z, the minimum value of | z | + | z $$-$$ 1 | is
PYP
WB JEE 2019
The polar coordinate of a point P is $$\left( {2, - {\pi \over 4}} \right)$$. The polar coordinate of the point Q which is such that line joining PQ is bisected perpendicularly by the initial line, is
PYP
WB JEE 2019
If X is a random variable such that $$\sigma$$(X) = 2.6, then $$\sigma$$(1 $$-$$ 4X) is equal to
PYP
WB JEE 2019
If $${e^{\sin x}} - {e^{-\sin x}} - 4 = 0$$, then the number of real values of x is
PYP
WB JEE 2019
The three sides of a right angled triangle are in GP (geometric progression). If the two acute angles be $$\alpha$$ and $$\beta$$, then tan$$\alpha$$ and tan$$\beta$$ are
PYP
WB JEE 2019
A variable line passes through a fixed point $$({x_1},{y_1})$$ and meets the axes at A and B. If the rectangle OAPB be completed, the locus of P is, (O being the origin of the system of axes).
PYP
WB JEE 2019
The graphs of the polynomial x2 $$-$$ 1 and cos x intersect
PYP
WB JEE 2019
If $$\theta \in R$$ and $${{1 - i\cos \theta } \over {1 + 2i\cos \theta }}$$ is real number, then $$\theta $$ will be (when I : Set of integers)
PYP
WB JEE 2019
The angles of a triangle are in the ratio 2 : 3 : 7 and the radius of the circumscribed circle is 10 cm. The length of the smallest side is
PYP
WB JEE 2019
If P(0, 0), Q(1, 0) and R$$\left( {{1 \over 2},{{\sqrt 3 } \over 2}} \right)$$ are three given points, then the centre of the circle for which the lines PQ, QR and RP are the tangents is
PYP
WB JEE 2019
A variable line passes through the fixed point $$(\alpha ,\beta )$$. The locus of the foot of the perpendicular from the origin on the line is
PYP
WB JEE 2019
If the point of intersection of the lines 2ax + 4ay + c = 0 and 7bx + 3by $$-$$ d = 0 lies in the 4th quadrant and is equidistant from the two axes, where a, b, c and d are non-zero numbers, then ad : bc equals to
PYP
WB JEE 2019
A variable circle passes through the fixed point A(p, q) and touches X-axis. The locus of the other end of the diameter through A is
PYP
WB JEE 2019
A straight line through the point (3, $$-$$2) is inclined at an angle 60$$^\circ$$ to the line $$\sqrt 3 x + y = 1$$. If it intersects the X-axis, then its equation will be
PYP
WB JEE 2019
Straight lines x $$-$$ y = 7 and x + 4y = 2 intersect at B. Points A and C are so chosen on these two lines such that AB = AC. The equation of line AC passing through (2, $$-$$7) is
PYP
WB JEE 2019
Let P(4, 3) be a point on the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over {{b^2}}} = 1$$. If the normal at P intersects the X-axis at (16, 0), then the eccentricity of the hyperbola is
PYP
WB JEE 2019
The equation of the directrices of the hyperbola $$3{x^2} - 3{y^2} - 18x + 12y + 2 = 0$$ is
PYP
WB JEE 2019
For the hyperbola $${{{x^2}} \over {{{\cos }^2}\alpha }} - {{{y^2}} \over {{{\sin }^2}\alpha }} = 1$$, which of the following remains fixed when $$\alpha$$ varies?
PYP
WB JEE 2019
S and T are the foci of an ellipse and B is the end point of the minor axis. If STB is equilateral triangle, the eccentricity of the ellipse is
PYP
WB JEE 2019
The length of conjugate axis of a hyperbola is greater than the length of transverse axis. Then, the eccentricity e is
PYP
WB JEE 2019
P is the extremity of the latusrectum of ellipse $$3{x^2} + 4{y^2} = 48$$ in the first quadrant. The eccentric angle of P is
PYP
WB JEE 2019
Let $$f:R \to R$$ be defined by $$f(x) = {x^2} - {{{x^2}} \over {1 + {x^2}}}$$ for all $$x \in R$$. Then,
PYP
WB JEE 2019
A point is in motion along a hyperbola $$y = {{10} \over x}$$ so that its abscissa x increases uniformly at a rate of 1 unit per second. Then, the rate of change of its ordinate when the point passes through (5, 2)
PYP
WB JEE 2019
Equation of a tangent to the hyperbola 5x2 $$-$$ y2 = 5 and which passes through an external point (2, 8) is
PYP
WB JEE 2019
The limit of the interior angle of a regular polygon of n sides as n $$ \to $$ $$\infty $$ is
PYP
WB JEE 2019
$$\mathop {\lim }\limits_{x \to {0^ + }} ({x^n}\ln x),\,n > 0$$
PYP
WB JEE 2019
Consider the function f(x) = cos x2. Then,
PYP
WB JEE 2019
Let $$a = \min \{ {x^2} + 2x + 3:x \in R\} $$ and $$b = \mathop {\lim }\limits_{\theta \to 0} {{1 - \cos \theta } \over {{\theta ^2}}}$$. Then $$\sum\limits_{r = 0}^n {{a^r}{b^{n - r}}} $$ is
PYP
WB JEE 2019
The value of $$\mathop {\lim }\limits_{x \to {0^ + }} {x \over p}\left[ {{q \over x}} \right]$$ is
PYP
WB JEE 2019
Let $$f:[1,3] \to R$$ be a continuous function that is differentiable in (1, 3) an
f'(x) = | f(x) |2 + 4 for all x$$ \in $$ (1, 3). Then,
f'(x) = | f(x) |2 + 4 for all x$$ \in $$ (1, 3). Then,
PYP
WB JEE 2019
Consider the function $$f(x) = {{{x^3}} \over 4} - \sin \pi x + 3$$
PYP
WB JEE 2019
$$\mathop {\lim }\limits_{x \to {0^ + }} {({e^x} + x)^{1/x}}$$
PYP
WB JEE 2019
A particle starts at the origin and moves 1 unit horizontally to the right and reaches P1, then it moves $${1 \over 2}$$ unit vertically up and reaches P2, then it moves $${1 \over 4}$$ unit horizontally to right and reaches P3, then it moves $${1 \over 8}$$ unit vertically down and reaches P4, then it moves $${1 \over 16}$$ unit horizontally to right and reaches P5 and so on. Let Pn = (xn, yn) and $$\mathop {\lim }\limits_{n \to \infty } {x_n} = \alpha $$ and $$\mathop {\lim }\limits_{n \to \infty } {y_n} = \beta $$. Then, ($$\alpha$$, $$\beta$$) is
PYP
WB JEE 2019
If $$\int {{2^{{2^x}}}.\,{2^x}dx} = A\,.\,{2^{{2^x}}} + C$$, then A is equal to
PYP
WB JEE 2019
Two particles A and B move from rest along a straight line with constant accelerations f and h, respectively. If A takes m seconds more than B and describes n units more than that of B acquiring the same speed, then
PYP
WB JEE 2019
Let f(x) be a derivable function, f'(x) > f(x) and f(0) = 0. Then,
PYP
WB JEE 2019
Let f(x) > 0 for all x and f'(x) exists for all x. If f is the inverse function of h and $${h'(x) = {1 \over {1 + \log x}}}$$. Then, f'(x) will be
PYP
WB JEE 2019
Let f and g be differentiable on the interval I and let a, b $$ \in $$ I, a < b. Then,
PYP
WB JEE 2019
y = $$\int {\cos \left\{ {2{{\tan }^{ - 1}}\sqrt {{{1 - x} \over {1 + x}}} } \right\}} dx$$ is an equation of a family of
PYP
WB JEE 2019
If $$\int {\cos x\log \left( {\tan {x \over 2}} \right)} dx$$ = $$\sin x\log \left( {\tan {x \over 2}} \right)$$ + f(x), then f(x) is equal to (assuming c is a arbitrary real constant).
PYP
WB JEE 2019
The value of the integral $$\int\limits_{ - 1}^1 {\left\{ {{{{x^{2015}}} \over {{e^{|x|}}({x^2} + \cos x)}} + {1 \over {{e^{|x|}}}}} \right\}} dx$$ is equal to
PYP
WB JEE 2019
The value of the integration
$$\int\limits_{ - {\pi \over 4}}^{\pi /4} {\left( {\lambda |\sin x| + {{\mu \sin x} \over {1 + \cos x}} + \gamma } \right)} dx$$
$$\int\limits_{ - {\pi \over 4}}^{\pi /4} {\left( {\lambda |\sin x| + {{\mu \sin x} \over {1 + \cos x}} + \gamma } \right)} dx$$
PYP
WB JEE 2019
The value of $$\mathop {\lim }\limits_{x \to 0} {1 \over x}\left[ {\int\limits_y^a {{e^{{{\sin }^2}t}}dt - } \int\limits_{x + y}^a {{e^{{{\sin }^2}t}}dt} } \right]$$ is equal to
PYP
WB JEE 2019
$$\mathop {\lim }\limits_{n \to \infty } {3 \over n}\left[ {1 + \sqrt {{n \over {n + 3}}} + \sqrt {{n \over {n + 6}}} + \sqrt {{n \over {n + 9}}} + ... + \sqrt {{n \over {n + 3(n - 1)}}} } \right]$$
PYP
WB JEE 2019
Let $${I_n} = \int\limits_0^1 {{x^n}} {\tan ^{ - 1}}xdx$$. If $${a_n}{I_{n + 2}} + {b_n}{I_n} = {c_n}$$ for all n $$ \ge $$ 1, then
PYP
WB JEE 2019
Which one of the following electronic arrangements is absurd?
PYP
WB JEE 2019
General solution of $${(x + y)^2}{{dy} \over {dx}} = {a^2},a \ne 0$$ is (C is an arbitrary constant)
PYP
WB JEE 2019
The general solution of the differential equation $$\left( {1 + {e^{{x \over y}}}} \right)dx + \left( {1 - {x \over y}} \right){e^{x/y}}dy = 0$$ is (C is an arbitrary constant)
PYP
WB JEE 2019
Let P and T be the subsets of k, y-plane defined by
P = {(x, y) : x > 0, y > 0 and x2 + y2 = 1}
T = {(x, y) : x > 0, y > 0 and x8 + y8 < 1}
Then, P $$ \cap $$ T is
P = {(x, y) : x > 0, y > 0 and x2 + y2 = 1}
T = {(x, y) : x > 0, y > 0 and x8 + y8 < 1}
Then, P $$ \cap $$ T is
PYP
WB JEE 2019
The area bounded by y = x + 1 and y = cos x and the X-axis, is
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