>
WBJEE
>
Mathematics
List of top Mathematics Questions asked in WBJEE
Let $f(x) = x^2 + x \sin x - \cos x$. Then
WBJEE - 2022
WBJEE
Mathematics
Differentiation
From a balloon rising vertically with uniform velocity $v$ ft/sec, a piece of stone is let go. The height of the balloon above the ground when the stone reaches the ground after 4 sec is [g = 30 ft/sec²]
WBJEE - 2022
WBJEE
Mathematics
Kinematics
Let $z_1$ and $z_2$ be two non-zero complex numbers. Then
WBJEE - 2022
WBJEE
Mathematics
Complex numbers
Let $p(x_0)$ be a polynomial with real coefficients, $p(0) = 1$ and $p'(x)>0$ for all $x \in \mathbb{R}$. Then
WBJEE - 2022
WBJEE
Mathematics
Polynomials
The line $y = x + 5$ touches
WBJEE - 2022
WBJEE
Mathematics
Coordinate Geometry
Let $R$ and $S$ be two equivalence relations on a non-void set $A$. Then
WBJEE - 2022
WBJEE
Mathematics
Relations and functions
Twenty meters of wire is available to fence off a flower bed in the form of a circular sector. What must the radius of the circle be, if the area of the flower bed is greatest?
WBJEE - 2022
WBJEE
Mathematics
Geometry
Consider the equation $y - y_1 = m(x - x_1)$. If $m$ and $x_1$ are fixed, and different lines are drawn for different values of $y_1$, then
WBJEE - 2022
WBJEE
Mathematics
Straight lines
The solution of $\det(A - \lambda I_2) = 0$ is $4$ and $8$, and $A = \begin{pmatrix} 2 & 3 \\ x & y \end{pmatrix}$. Then
WBJEE - 2022
WBJEE
Mathematics
Determinants
If $\alpha$ is a unit vector, $\beta = \hat{i} + \hat{j} - \hat{k}$, $\gamma = \hat{i} + \hat{k}$, then the maximum value of $|\alpha \beta \gamma|$ is
WBJEE - 2022
WBJEE
Mathematics
Vectors
The value of $a$ for which the sum of the squares of the roots of the equation $x^2 - (a - 2)x - (a - 1) = 0$ assumes the least value is
WBJEE - 2022
WBJEE
Mathematics
Quadratic Equations
From the point $(-1, -6)$, two tangents are drawn to $y^2 = 4x$. Then the angle between the two tangents is
WBJEE - 2022
WBJEE
Mathematics
Parabola
Chords of an ellipse are drawn through the positive end of the minor axis. Their midpoint lies on
WBJEE - 2022
WBJEE
Mathematics
Ellipse
The maximum value of $f(x) = e^{\sin x} + e^{\cos x}$, where $x \in \mathbb{R}$, is
WBJEE - 2022
WBJEE
Mathematics
Maxima and Minima
If $x$ satisfies the inequality $\log_2 5x^2 + (\log_5 x)^2<2$, then $x$ belongs to
WBJEE - 2022
WBJEE
Mathematics
linear inequalities in one variable
Let $f$ be a non-negative function defined in $[0, \pi/2]$, $f'$ exists and is continuous for all $x$, and $\int_0^x \sqrt{1 - (f'(t))^2} dt = \int_0^x f(t) dt$ and $f(0) = 0$. Then
WBJEE - 2022
WBJEE
Mathematics
Some Properties of Definite Integrals
A straight line meets the coordinate axes at $A$ and $B$. A circle is circumscribed about the triangle $OAB$, with $O$ being the origin. If $m$ and $n$ are the distances of the tangent from the origin to the points $A$ and $B$ respectively, the diameter of the circle is
WBJEE - 2022
WBJEE
Mathematics
Coordinate Geometry
If $I$ is the greatest of $I_1 = \int_0^1 e^{-x} \cos^2 x \, dx$, $I_2 = \int_0^1 e^{-x^2} \cos^2 x \, dx$, $I_3 = \int_0^1 e^{-x^2} \, dx$, $I_4 = \int_0^1 e^{-\frac{x^2}{2}} \, dx$, then
WBJEE - 2022
WBJEE
Mathematics
Some Properties of Definite Integrals
If the transformation $z = \log \tan \frac{x}{2}$ reduces the differential equation $\frac{d^2y}{dx^2} + \cot x \frac{dy}{dx} + 4y \csc^2 x = 0$ into the form $\frac{d^2y}{dz^2} + ky = 0$, then $k$ is equal to
WBJEE - 2022
WBJEE
Mathematics
Differential equations
Let the tangent and normal at any point $P(at^2, 2at), (a>0)$, on the parabola $y^2 = 4ax$ meet the axis of the parabola at $T$ and $G$ respectively. Then the radius of the circle through $P$, $T$, and $G$ is
WBJEE - 2022
WBJEE
Mathematics
Parabola
$\lim_{x \to \infty} \left[ \frac{x^2 + 1}{x + 1} - ax - b \right], \, (a, b \in \mathbb{R}) = 0$. Then
WBJEE - 2022
WBJEE
Mathematics
Limits
$PQ$ is a double ordinate of the hyperbola $\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1$ such that $\triangle OPQ$ is an equilateral triangle, with $O$ being the center of the hyperbola. Then the eccentricity $e$ of the hyperbola satisfies
WBJEE - 2022
WBJEE
Mathematics
Hyperbola
The number of zeros at the end of $\angle 100$ is
WBJEE - 2022
WBJEE
Mathematics
Number Systems
If $|z - 25i| \leq 15$, the maximum $\arg(z) -$ minimum $\arg(z)$ is equal to
WBJEE - 2022
WBJEE
Mathematics
Complex numbers
If $P_1P_2$ and $P_3P_4$ are two focal chords of the parabola $y^2 = 4ax$, then the chords $P_1P_3$ and $P_2P_4$ intersect on the
WBJEE - 2022
WBJEE
Mathematics
Parabola
Prev
1
...
8
9
10
11
12
...
26
Next