List of top Mathematics Questions asked in WBJEE

The approximate value of $\sin \, 31^{\circ}$ is

If $\int \, f(x) \, \sin \, x \, \cos \, x \, dx = \frac{1}{2(b^2 - a^2)} \log f(x) + c$, where c is the constant of integration , then f(x) =

Let $\vec{\alpha } = \hat{i} + \hat{j} + \hat{k} , \vec{\beta} = \hat{i} - \hat{j} - \hat{k}$ and $\vec{\gamma} = - \hat{i} + \hat{j} - \hat{k}$ be three vectors. A vector $\vec{\delta} $, in the plane of $\vec{\alpha}$ and $\vec{\beta}$, whose projection on $\vec{\gamma}$ is $\frac{1}{\sqrt{3}}$, is given by

The value of $\displaystyle\lim_{n \to \infty} \frac{1}{n} \left\{ \sec^2 \frac{\pi}{4 n} + \sec^2 \frac{2 \pi }{4n} + ..... \sec^2 \frac{n \pi}{4n} \right\}$ 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

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 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

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

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

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

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

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

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

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

The point $P \,(3, 6)$ is first reflected on the line $y = x$ and then the image point $Q$ is again reflected on the line $y = - x$ to get the image point $Q'$. Then the circumcentre of the $\Delta PQQ'$ is

For real $x$, the greatest value of $\frac{x^{2}+2x+4}{2x^{2}+4x+9}$ is

Let $A(2, -3)$ and $B (-2, 1)$ be two angular points of $\Delta ABC$. If the centroid of the triangle moves on the line $2x + 3y = 1$, then the locus of the angular point $C$ is given by

Let $f(x) = x^{13} + x^{11} + x^9 + x^7 + x^5 + x^3 + x + 19$. Then $f(x) = 0$ has

Transforming to parallel axes through a point $(p, q)$, the equation $2x^2 + 3xy + 4y^2 + x + 18y + 25 = 0$ becomes $2x^2 + 3xy + 4y^2 = 1$. Then

The locus of the mid-points of the chords of the circle $x^2 + y^2 + 2x - 2y - 2 = 0$ which make an angle of $90�$ at the centre is

If $\omega$ is an imaginary cube root of unity, then the value of $\left(2-\omega\right)\left(2-\omega^{2}\right)+2\left(3-\omega\right)\left(3-\omega^{2}\right)+.....+\left(n-1\right)\left(n-\omega\right)\left(n-\omega^{2}\right)$

If $PQ$ is a double ordinate of the hyperbola $\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$ such that $\Delta OPQ$ is equilateral, $O$ being the centre. Then the eccentricity e satisfies