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WBJEE
List of top Questions asked in WBJEE- 2023
A train is moving along the tracks at a constant speed u. A girl on the train throws a ball of mass m straight ahead along the direction of motion of the train with speed v with respect to herself. Then,
WBJEE - 2023
WBJEE
Physics
Motion in a plane
\(\lim_{x\rightarrow \infty}\)
{
\(x-\sqrt[n]{(x-a_1)(x-a_2)......(x-a_n)}\)
} where a
1
,a
2
,.....a
n
are positive rational numbers.The limit
WBJEE - 2023
WBJEE
Mathematics
Limits
A body of mass 2 kg moves in a horizontal circular path of radius 5m. In an instant its speed is
\(2\sqrt5\)
m/s and is increasing at the rate of 3 m/s
2
.The magnitude of the force acting on the body at the instant is,
WBJEE - 2023
WBJEE
Physics
Motion in a plane
A rectangle ABCD has its side parallel to the line y=2x and vertices A,B,D are on y=1,x=1 and x=-1 respectively. The coordinate of C can be
WBJEE - 2023
WBJEE
Mathematics
Straight lines
If z
1
and z
2
are two complex numbers satisfying the equation
\(|\frac{z_1+z_2}{z_1-z_2}|=1\)
, then
\(\frac{z_1}{z_2}\)
may be
WBJEE - 2023
WBJEE
Mathematics
complex numbers
A ray of monochromatic light is incident on the plane surface of separation between two media X and Y with the angle of incidence 'i' in medium X and angle of refraction 'r' in medium Y. The given graph shows the relation between sin i and sin r. If V
x
and V
y
are the velocities of the ray in media X and Y respectively, Then which of the following is true?
WBJEE - 2023
WBJEE
Physics
Ray optics and optical instruments
Let x be a nonvoid set.If ρ1 and ρ2 be the transitive relations of x, then-(° denotes the compositions of relations )
WBJEE - 2023
WBJEE
Mathematics
Relations
If 4a
2
+9b
2
-c
2
+12ab=0, then the family of straight lines ax+by+c=0 is concurrent at
WBJEE - 2023
WBJEE
Mathematics
Straight lines
(i)
(ii)
(iii)
The correct order of C = O bond length in ethyl propanoate(I), ethyl propenoate(II) and ethenyl propanoate(III) is
WBJEE - 2023
WBJEE
Chemistry
Chemical bonding and molecular structure
The function
\(y=e^{kr}\)
satisfies
\((\frac{d^2y}{dx^2}+\frac{dy}{dx})(\frac{dy}{dx}-y)=y\frac{dy}{dx}\)
. It is valid for
WBJEE - 2023
WBJEE
Mathematics
second order derivative
The value of 'a' for which the scaler triple product formed by the vectors
\(\vec\alpha=\hat{i}+a\hat{j}+\hat{k}\)
,
\(\vec{\beta}=\hat{j}+a\hat{k}\)
and
\(\vec{\gamma}=a\hat{i}+\hat{k}\)
is maximum, is
WBJEE - 2023
WBJEE
Mathematics
Vector Algebra
An electric dipole of dipole moment p is placed at the origin of the coordinate system along the z-axis. The amount of work required to move a charge 'q' from the point (a,0,0) to the point (0,0,a) is
WBJEE - 2023
WBJEE
Physics
Electric Dipole
If
\(\int \frac{dx}{(x+1)(x-2)(x-3)}=\frac{1}{k}log_e\left \{ \frac{|x-3|^3|x+1|}{(x-2)^4}\right \}+c\)
, then the value of k is
WBJEE - 2023
WBJEE
Mathematics
Integrals of Some Particular Functions
A cyclic process is shown in the p-v diagram and T-S diagram. Which of the following statement(s) is/are true?
WBJEE - 2023
WBJEE
Physics
First law of thermodynamics
A charged particle of charge q and mass m is placed at a distance 2R from the center of a vertical cylindrical region of radius R where the magnetic field varies as
\(\vec{B}=(4t^2-2t+6)k\)
, where t is time. Then which of the following statement(s) is/are true?
WBJEE - 2023
WBJEE
Physics
Moving charges and magnetism
A uniform magnetic field b exists in a region. An electron of charge q and mass m moving with velocity v enters the region in a direction perpendicular to the magnetic field. Considering Bohr angular momentum quantization, which of the following statement(s) is/are true?
WBJEE - 2023
WBJEE
Physics
Magnetic properties of materials
The figure shows two identical parallel plate capacitors A and B of capacitances C connected to a battery. The key K is initially closed. The switch is now opened and the free spaces between the plates of the capacitors are filled with a dielectric constant 3. Then which of the following statement(s) is/are true?
WBJEE - 2023
WBJEE
Physics
electrostatic potential and capacitance
Let
\(A=\begin{pmatrix}2&0&3\\4&7&11\\5&4&8\end{pmatrix}\)
. Then
WBJEE - 2023
WBJEE
Mathematics
Determinants
A charged particle in a uniform magnetic field
\(\vec{B}=B_0\hat{k}\)
starts moving from the origin with velocity
\(v=3\hat{i}+4\hat{k}\)
m/s.The trajectory of the particle and the time
\(t\)
at which it reaches 2m above the x-y plane are
WBJEE - 2023
WBJEE
Physics
Magnetic Field
A uniform rope of length 4 m and mass 0.4kg is held on a frictionless table in such a way that 0.6m of the rope is hanging over the edge. The work done to pull the hanging part of the rope onto the table is, (Assuming g=10m/s
2
)
WBJEE - 2023
WBJEE
Physics
laws of motion
If
\(I_n=\int_{0}^{\frac{\pi}{2}}cos^nxcos\,nxdx\)
, then
\(I_1,I_2,I_3\)
.....are in
WBJEE - 2023
WBJEE
Mathematics
Definite Integral
As shown in the figure, a liquid is at the same levels in two arms of a U-tube of uniform cross-section when at rest. If the U-tube moves with an acceleration 'f' towards the right,the difference in liquid heights between the two arms of the U-tube will be,(acceleration due to gravity=g)
WBJEE - 2023
WBJEE
Physics
mechanical properties of fluid
Let f be a strictly decreasing function defined on R such that f(x)>0,∀x∈R. Let
\(\frac{x^2}{f(a^2+5a+3)}+\frac{y^2}{f(a+15)}=1\)
be an ellipse with a major axis along the y-axis. The value of 'a' can lie in the interval(s)
WBJEE - 2023
WBJEE
Mathematics
Functions
If
\(\frac{1}{6}\)
sinθ.cosθ.tanθ are in G.P, then the solution set θ is
WBJEE - 2023
WBJEE
Mathematics
Trigonometric Functions
X-rays of wavelength λ get reflected from parallel planes of atoms in a crystal with spacing d between two planes as shown in the figure. If the two reflected beams interfare constructively,Then the condition for maxima will be(n is the order of interference fringe)
WBJEE - 2023
WBJEE
Physics
Wave optics
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