List of top Questions asked in WBJEE- 2017

The velocity of a particle executing a simple harmonic motion is $13\, ms^{-1}$, when its distance from the equilibrium position (Q) is 3 m and its velocity is $12 \, ms^{-1}$, when it is 5 m away from The frequency of the simple harmonic motion is

Let $F(x) = e^x, G(x) = e^{-x}$ and $H(x) = G(F(x))$, where $x$ is a real variable. Then $\frac{dH}{dx}$ at $x = 0$ is

When $BaCl_2$ is added to an aqueous salt solution, a white precipitate is obtained. The anion among $CO_3^{ 2-}, SO_3^{ 2-}$ and $SO_4^{ 2-}$ that was present in the solution can be :

$C_{6}H_{5}F^{18}$ is a $F^{18}$ radio-isotope labelled organic compound. $F^{18}$ decays by positron emission. the product resulting on decay is

A solid rectangular sheet has two different coefficients of linear expansion $\alpha_{1}$ and $\alpha_{2}$ along its length and breadth respectively. The coefficient of surface expansion is (for $\alpha_{1} t < < 1, \alpha_{2} t < < 1$)

A parallel beam of light is incident on a glass prism in the shape of a quarter cylinder of radius $R \,= \,0.05\, m$ and refractive index n = $1.5$ placed on a horizontal table as shown in the figure. Beyond the cylinder, a patch of light is found whose nearest distance $x$ from the cylinder is

The magnetic field due to a current in a straight wire segment of length $L$ at a point on its perpendicular bisector at a distance $r (r >> L)$

A uniform string of length $L$ and mass $M$ is fixed at both ends while it is subject to a tension $T$. It can vibrate at frequencies $(v)$ given by the formula (where $n = 1, 2, 3, .....$)

The common chord of the circles $x^2 + y^2 - 4x - 4y = 0$ and $2x^2 + 2y^2 = 32$ subtends at the origin an angle equal to

Let $A=\begin{pmatrix}x+2&3x\\ 3&x+2\end{pmatrix}, B=\begin{pmatrix}x&0\\ 5&x+2\end{pmatrix}$. Then all solutions of the equation det $(AB) = 0$ is

Out of $7$ consonants and $4$ vowels, words are formed each having $3$ consonants and $2$ vowels. The number of such words that can be formed is

The equation of the plane through \((1, 2, -3)\) and \((2, -2, 1)\) and parallel to \(X-\)axis is

In a close-packed body-centred cubic lattice of potassium, the correct relation between the atomic radius $(r)$ of potassium and the edge-length $(a)$ of the cube is

Reduction of the lactol  OH with sodium borohydride gives

The ground state magnetic property of $B_2$ and $C_2$ molecules will be

The probability that a non leap year selected at random will have $53$ Sundays is

The axis of the parabola $x^2 + 2xy + y^2 - 5x + 5y - 5 = 0$ is

A uniform capillary tube of length $l$ and inner radius $r$ with its upper end sealed is submerged vertically into water. The outside pressure is $p_0$ and surface tension of water is $\gamma$. When a length $x$ of the capillary is submerged into water, it is found that water levels inside and outside the capillary coincide. The value of $x$ is

A positive charge $Q$ is situated at the centre of a cube. The electric flux through any face of the cube is (in $SI$ units)

The line segment joining the foci of the hyperbola $x^2 - y^2 + 1 = 0$ is one of the diameters of a circle. The equation of the circle is

Let P be the foot of the perpendicular from focus S of hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ on the line $bx - ay = 0$ and let $C$ be the centre of hyperbola. Then the area of the rectangle whose sides are equal to that of $SP$ and $CP$ is

For any vector $x$, where $\hat{ i }, \hat{ j }, \hat{ k }$ have their usual meanings the value of $( x \times \hat{ i })^{2}+( x \times \hat{ j })^{2}+( x \times \hat{ k })^{2}$ where $\hat{ i }, \hat{ j }, \mathbf { k }$ have their usual meanings, is equal to

Mean of $n$ observations $x_{1}, x_{2}, ........ , x_{n}$ is $\bar{x}.$ If an observation $x_q$ is replaced by $x'_q$ then the new mean is

The integrating factor of the first order differential equation $x^{2}\left(x^{2}-1\right) \frac{dy}{dx}+x\left(x^{2}+1\right)y=x^{2}-1$ is

Let $d_1$ and $d_2$ be the lengths of the perpendiculars drawn from any point of the line $7x - 9y + 10 = 0$ upon the lines $3x + 4y = 5$ and $12x + 5y = 7$ respectively. Then