List of top Questions asked in WBJEE

In a certain town, $60\%$ of the families own a car, $30\%$own a house and $20\%$ own both a car and a house. If a family is randomly chosen, what is the probability that this family owns a car or a house but not both ?

The length of a metal wire is $L_1$ when the tension is $T_1$ and $L_2$ when the tension is $T_2$. The unstretched length of the wire is

For all real values of \(a_0, a_1, a_2, a_3\) satisfying \(a_{0}+\frac{a_{1}}{2}+\frac{a_{2}}{3}+\frac{a_{3}}{4}=0\), the equation \(a_{0}+a_{1}x+a_{2}x^{2}+a_{3}x^{3}=0\) has a real root in the interval

If the four points with position vectors $-2\hat{i}+\hat{j}+k, \hat{i} +\hat{j}+\hat{k}, \hat{j}-\hat{k}, $ and $\lambda\hat{j}+\hat{k}$ are coplanar, then $\lambda=$

The minimum value of $\cos\,\theta + \sin\,\theta+\frac{2}{\sin\,2\theta}$ for $\theta\,\in \left(0, \pi/2\right)$ is

A fair coin is tossed a fixed number of times. If the probability of getting exactly $3$ heads equals the probability of getting exactly $5$ heads, then the probability of getting exactly one head is

The area of the region bounded by the curve $y = x^3$, its tangent at $(1, 1)$ and $x-axis$ is

Consider the following salts: $NaCl,\, HgCl_2,\, Hg_2Cl_2,\, CuCl_2,\, CuCl$ and $AgCl$. Identify the correct set of insoluble salts in water

In a mixture, two enantiomers are found to be present in $85\%$ and $15\%$ respectively. The enantiomeric excess $(e, e)$ is

A simple pendulum of length $L$ swings in a vertical plane. The tension of the string when it makes an angle $\theta$ with the vertical and the bob of mass m moves with a speed $v$ is ($g$ is the gravitational acceleration

If $\sin^{-1}\left(x-\frac{x^{2}}{2}+\frac{x^{3}}{4}-\frac{x^{4}}{8}+...\right)-\frac{\pi}{6}$ where $\left|x\right| < 2$ then the value of $x$ is

If $f \left(x\right)=\begin{vmatrix}1&x&x+1\\ 2x&x\left(x-1\right)&\left(x-1\right)x\\ 3x\left(x-1\right)&x\left(x-1\right)\left(x-2\right)&\left(x-1\right)\end{vmatrix}$ Then $f (100)$ is equal to

A straight conductor $0.1\, m$ long moves in a uniform magnetic field $0.1\, T$. The velocity of the conductor is $15\, m / s$ and is directed perpendicular to the field. The emf induced between the two ends of the conductor is

Two particles, $A$ and $B$, having equal charges, after being accelerated through the same potential difference enter into a region of uniform magnetic field and the particles describe circular paths of radii $R_{1}$ and $R_{2}$, respectively. The ratio of the masses of $A$ and $B$ is

Two particles $A$ and $B$ are moving as shown in the figure. Their total angular momentum about the point $O$ is

The value of \(\lambda\), such that the following system of equations \(2x - y - 2z = 2\); \(x - 2y + z = -4\); \(x + y + \lambda z = 4\) has no solution, is

If $f:[0, \pi / 2) \rightarrow R$ is defined as $f(\theta)=\begin{vmatrix}1 & \tan \theta & 1 \\ -\tan \theta & 1 & \tan \theta \\ -1 & -\tan \theta & 1\end{vmatrix}$. Then, the range of $f$ is

Area of the region bounded by $y = |x|$ and $y = -|x| + 2$ is

The trigonometric equation $\sin^{-1}x = 2 \sin^{-1}2a$ has a real solution if

Particle $A$ moves along $X$-axis with a uniform velocity of magnitude $10\, m / s$. Particle $B$ moves with uniform velocity $20\, m / s$ along a direction making an angle of $60^{\circ}$ with the positive direction of $X$-axis as shown in the figure. The relative velocity of $B$ with respect to that of $A$ is

The RMS velocity of $CO$ gas molecules at $27^{\circ}$C is approximately $1000\, m/s$. For $N_2$ molecules at $600 \,K$ the RMS velocity is approximately

For the reaction $A+2 B \longrightarrow C$, the reaction rate is doubled, if the concentration of $A$ is doubled. The rate is increased by four times when concentrations of both $A$ and $B$ are increased by four times. The order of the reaction is

Addition of sodium thiosulphate solution to a solution of silver nitrate gives $X$ as white precipitate, insoluble in water but soluble in excess thiosulphate solution to give $Y$. On boiling in water, $Y$ gives $Z . X, Y$ and $Z$ respectively are

Block $B$ lying on a table weighs $W$. The coefficient of static friction between the block and the table is $\mu$. Assume that the cord between $B$ and the knot is horizontal. The maximum weight of the block $A$ for which the system will be stationary is

Two copper spheres having same radii, one solid and other hollow, are charged to the same potential. Which of the following statements is correct?