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WB JEE 2020

Exam Held on Sun Feb 02 2020 04:30:00 GMT+0000 (Coordinated Universal Time)
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Chemistry

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Ph$$ - $$ CDO$$\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{Warm}^{50\% aq...
The correct order of acidity for the following compounds is :<br><br><img src="h...
The reduction product of ethyl 3-oxobutanoate by NaBH<sub>4</sub> in methanol is...
What is the major product of the following reaction?<br><br><img src="https://ap...
The maximum number of electrons in an atom in which the last electron filled has...
In the face centered cubic lattice structure of gold the closest distance betwee...
The equilibrium constant for the following reactions are given at 25$$^\circ $$C...
Among the following, the ion which will be more effective for flocculation of Fe...
The mole fraction of ethanol in water is 0.08. Its molality is
5 mL of 0.1 M Pb(NO<sub>3</sub>)<sub>2</sub> is mixed with 10 mL of 0.02 M KI. T...
At 273 K temperature and 76 cm Hg pressure the density of a gas is 1.964 g L<sup...
Equal masses of ethane and hydrogen are mixed in an empty container at 298 K. Th...
An ideal gas expands adiabatically against vacuum. Which of the following is cor...
K<sub>f</sub> (water) = 1.86 K kg mol<sup>-1</sup>. The temperature at which ice...
The radius of the first Bohr orbit of a hydrogen atom is 0.53 $$\times {10^-8}$$...
Which of the following statements is not true for the reaction, 2F<sub>2</sub> +...
The number of unpaired electrons in the uranium (<sub>92</sub>U) atom is
How and why does the density of liquid water change on prolonged electrolysis?
The difference between orbital angular momentum of an electron in a 4f -orbital ...
Which of the following has the largest number of atoms?
Indicate the correct IUPAC name of the coordination compound shown in the figure...
What will be the mass of one atom of <sup>12</sup>C?
Bond order of He<sub>2</sub>, $$He_2^ + $$ and $$He_2^{2 + }$$ are respectively
To a solution of a colourless efflorescent sodium salt, when dilute acid is adde...
The reaction for obtaining the metal (M) from its oxide (M<sub>2</sub>O<sub>3</s...
In the extraction of Ca by electro reduction of molten CaCl<sub>2</sub> some CaF...
The total number of alkyl bromides (including stereoisomers) formed in the react...
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Which of the following compounds is asymmetric?
For a reaction 2A + B $$ \to $$ P, when concentration of B alone is doubled, t<s...
A solution is saturated with SrCO<sub>3</sub> and SrF<sub>2</sub>. The $$[CO_3^{...
A homonuclear diatomic gas molecule shows 2-electron magnetic moment. The one-el...
$$C{H_3} - O - C{H_2} - Cl\mathrel{\mathop{\kern0pt\longrightarrow} \limits_\Del...
Which of the following reactions give(s) a meso-compound as the main product?
For spontaneous polymerisation, which of the following is (are) correct?
Which of the following statement(s) is/are incorrect?
SiO<sub>2</sub> is attacked by which one/ones of the following?
$$Me - C \equiv C - Me\mathrel{\mathop{\kern0pt\longrightarrow} \limits_{EtOH, -...
For the following carbocations, the correct order of stability is <br><br>I. $$^...

Mathematics

Let cos$$^{ - 1}\left( {{y \over b}} \right) = \log {\left( {{x \over n}} \right...
Let $$\phi (x) = f(x) + f(1 - x)$$ and $$f(x) &lt; 0$$ in [0, 1], then
$$\int {{{f(x)\phi '(x) + \phi (x)f'(x)} \over {(f(x)\phi (x) + 1)\sqrt {f(x)\ph...
The value of <br><br>$$\sum\limits_{n = 1}^{10} {} \int\limits_{ - 2n - 1}^{ - 2...
$$\int\limits_0^2 {[{x^2}]} \,dx$$ is equal to
If the tangent to the curve y<sup>2</sup> = x<sup>3</sup> at (m<sup>2</sup>, m<s...
If $${x^2} + {y^2} = {a^2}$$, then $$\int\limits_0^a {\sqrt {1 + {{\left( {{{dy}...
Let f, be a continuous function in [0, 1], then $$\mathop {\lim }\limits_{n \to ...
Let f be a differentiable function with $$\mathop {\lim }\limits_{x \to \infty }...
If $$x\sin \left( {{y \over x}} \right)dy = \left[ {y\sin \left( {{y \over x}} \...
Let $$f(x) = 1 - \sqrt {({x^2})} $$, where the square root is to be taken positi...
If the function $$f(x) = 2{x^3} - 9a{x^2} + 12{a^2}x + 1$$ [a &gt; 0] attains it...
If a and b are arbitrary positive real numbers, then the least possible value of...
If 2 log(x + 1) $$ - $$ log(x<sup>2</sup> $$ - $$ 1) = log 2, then x =
The number of complex numbers p such that $$\left| p \right| = 1$$ and imaginary...
The equation $$z\bar z + (2 - 3i)z + (2 + 3i)\bar z + 4 = 0$$ represents a circl...
The expression ax<sup>2</sup> + bx + c (a, b and c are real) has the same sign a...
In a 12 storied building, 3 persons enter a lift cabin. It is known that they wi...
If the total number of m-element subsets of the set A = {a<sub>1</sub>, a<sub>2<...
Let I(n) = n<sup>n</sup>, J(n) = 13.5 ......... (2n $$ - $$ 1) for all (n &gt; 1...
If c<sub>0</sub>, c<sub>1</sub>, c<sub>2</sub>, ......, c<sub>15</sub> are the b...
Let A = $$\left( {\matrix{ {3 - t} \cr { - 1} \cr 0 \cr } \matr...
Let $$A = \left[ {\matrix{ {12} &amp; {24} &amp; 5 \cr x &amp; 6 &amp; 2...
Let $$A = \left( {\matrix{ a &amp; b \cr c &amp; d \cr } } \right)$$...
If $$\left| {\matrix{ {{a^2}} &amp; {bc} &amp; {{c^2} + ac} \cr {{a^2} +...
If f : S $$ \to $$ R, where S is the set of all non-singular matrices of order 2...
Let the relation p be defined on R by a p b holds if and only if a $$ - $$ b is ...
The unit vector in ZOX plane, making angles $$45^\circ $$ and $$60^\circ $$ resp...
Four persons A, B, C and D throw an unbiased die, turn by turn, in succession ti...
A rifleman is firing at a distant target and has only 10% chance of hitting it. ...
$$\cos (2x + 7) = a(2 - \sin x)$$ can have a real solution for
The differential equation of the family of curves y = e<sup>x</sup> (A cos x + B...
The equation $$r\,\cos \left( {\theta - {\pi \over 3}} \right) = 2$$ represent...
The locus of the centre of the circles which touch both the circles x<sup>2</sup...
Let each of the equations x<sup>2</sup> + 2xy + ay<sup>2</sup> = 0 and ax<sup>2<...
A straight line through the origin O meets the parallel lines 4x + 2y = 9 and 2x...
Area in the first quadrant between the ellipses x<sup>2</sup> + 2y<sup>2</sup> =...
The equation of circle of radius $$\sqrt {17} $$ unit, with centre on the positi...
The length of the chord of the parabola y<sup>2</sup> = 4ax(a &gt; 0) which pass...
A double ordinate PQ of the hyperbola $${{{x^2}} \over {{a^2}}} - {{{y^2}} \over...
If B and B' are the ends of minor axis and S and S' are the foci of the ellipse ...
The equation of the latusrectum of a parabola is x + y = 8 and the equation of t...
The equation of the plane through the point $$(2, - 1, - 3)$$ and parallel to th...
The sine of the angle between the straight line $${{x - 2} \over 3} = {{y - 3} \...
Let f(x) = sin x + cos ax be periodic function. Then,
The domain of $$f(x) = \sqrt {\left( {{1 \over {\sqrt x }} - \sqrt {x + 1} } \ri...
Let $$y = f(x) = 2{x^2} - 3x + 2$$. The differential of y when x changes from 2 ...
If $$\mathop {\lim }\limits_{x \to 0} {\left( {{{1 + cx} \over {1 - cx}}} \right...
Let f : R $$ \to $$ R be twice continuously differentiable (or f" exists and is ...
Let $$f(x) = {x^{13}} + {x^{11}} + {x^9} + {x^7} + {x^5} + {x^3} + x + 12$$.<br>...
The area of the region<br><br>$$\{ (x,y):{x^2} + {y^2} \le 1 \le x + y\} $$ is
In open interval $$\left( {0,\,{\pi \over 2}} \right)$$
If the line y = x is a tangent to the parabola y = ax<sup>2</sup> + bx + c at th...
If the vectors $$\alpha = \widehat i + a\widehat j + {a^2}\widehat k,\,\beta =...
Let z<sub>1</sub> and z<sub>2</sub> be two imaginary roots of z<sup>2</sup> + pz...
If P(x) = ax<sup>2</sup> + bx + c and Q(x) = $$ - $$ax<sup>2</sup> + dx + c, whe...
Let $$A = \{ x \in R: - 1 \le x \le 1\} $$ and $$f:A \to A$$ be a mapping define...
Let $$f(x) = \sqrt {{x^2} - 3x + 2} $$ and $$g(x) = \sqrt x $$ be two given func...
Let p<sub>1</sub> and p<sub>2</sub> be two equivalence relations defined on a no...
Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. Th...
Consider the curve $${{{x^2}} \over {{a^2}}} + {{{y^2}} \over {{b^2}}} = 1$$. Th...
A line cuts the X-axis at A(7, 0) and the Y-axis at B(0, $$ - $$5). A variable l...
Let $$0 &lt; \alpha &lt; \beta &lt; 1$$. Then, $$\mathop {\lim }\limits_{n \to...
$$\mathop {\lim }\limits_{x \to 1} \left( {{1 \over {1nx}} - {1 \over {(x - 1)}}...
Let $$y = {1 \over {1 + x + lnx}}$$, then
Consider the curve $$y = b{e^{ - x/a}}$$, where a and b are non-zero real number...
The area of the figure bounded by the parabola $$x = - 2{y^2},\,x = 1 - 3{y^2}$...
A particle is projected vertically upwards. If it has to stay above the ground f...
The equation $${x^{{{(\log 3x)}^2}}} - {9 \over 2}\log 3\,x + 5 = 3\sqrt 3 $$ ha...
In a certain test, there are n questions. In this test 2<sup>n-i</sup> students ...
A and B are independent events. The probability that both A and B occur is $${1 ...
The equation of the straight line passing through the point (4, 3) and making in...
Consider a tangent to the ellipse $${{{x^2}} \over 2} + {{{y^2}} \over 1} = 1$$ ...
Let $$y = {{{x^2}} \over {{{(x + 1)}^2}(x + 2)}}$$. Then $${{{d^2}y} \over {d{x^...
Let $$f(x) = {1 \over 3}x\sin x - (1 - \cos \,x)$$. The smallest positive intege...
Tangent is drawn at any point P(x, y) on a curve, which passes through (1, 1). T...

Physics

The intensity of light emerging from one of the slits in a Young's double slit e...
In a Fraunhofer diffraction experiment, a single slit of width 0.5 mm is illumin...
If R is the Rydberg constant in cm<sup>-1</sup>, then hydrogen atom does not emi...
A nucleus X emits a $$\beta $$-particle to produce a nucleus Y. If their atomic ...
For nuclei with mass number close to 119 and 238, the binding energies per nucle...
A common emitter transistor amplifier is connected with a load resistance of 6 k...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l1cgxlrq/8ed992...
The frequency v of the radiation emitted by an atom when an electron jumps from ...
Consider the vectors $$A = \hat i + \hat j - \hat k$$ ,$$B = 2\hat i - \hat j + ...
A fighter plane, flying horizontally with a speed 360 km/h at an altitude of 500...
A block of mass m rests on a horizontal table with a coefficient of static frict...
A tennis ball hits the floor with a speed v at an angle $$\theta $$ with the nor...
The bob of a swinging second pendulum (one whose time period is 2 s) has a small...
A steel and a brass wire, each of length 50 cm and cross-sectional area 0.005 cm...
Which of the following diagrams correctly shows the relation between the termina...
An ideal gas undergoes the cyclic process abca as shown in the given p - V diagr...
A container AB in the shape of a rectangular parallelopiped of length 5 m is div...
When 100 g of boiling water at 100$$^\circ $$ C is added into a calorimeter cont...
As shown in the figure, a point charge q<sub>1</sub> = + 1 $$ \times $$ 10<sup>-...
Four identical point masses, each of mass m and carrying charge + q are placed a...
A very long charged solid cylinder of radius a contains a uniform charge density...
A galvanometer can be converted to a voltmeter of full scale deflection V<sub>0<...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l1ci8nbb/fe4af1...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l1cmq1r2/ff0089...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l1d7wao9/2c5bb2...
<img src="https://app-content.cdn.examgoal.net/fly/@width/image/1l1cmuk5g/ac8cff...
Consider the circuit shown.<br><br><img src="https://app-content.cdn.examgoal.ne...
Consider a conducting wire of length L bent in the form of a circle of radius R ...
An object, is placed 60 cm in front of a convex mirror of focal length 30 cm. A ...
A thin convex lens is placed just above an empty vessel of depth 80 cm. The imag...
A conducting circular loop of resistance 20$$\Omega $$ and cross-sectional area...
A pair of parallel metal plates are kept with a separation d. One plate is at a ...
A metallic block of mass 20 kg is dragged with a uniform velocity of 0.5 ms<sup>...
Consider an engine that absorbs 130 cal of heat from a hot reservoir and deliver...
Two pith balls, each carrying charge + q are hung from a hook by two springs. It...
A point source of light is used in an experiment of photoelectric effects. If th...
Two metallic spheres of equal outer radii are found to have same moment of inert...
A simple pendulum of length l is displaced, so that its taught string is horizon...
A 400$$\Omega $$ resistor, a 250 mH inductor and a 2.5 $$\mu $$F capacitor are c...
A charged particle moves with constant velocity in a region, where no effect of ...

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