List of top Mathematics Questions asked in WBJEE

Consider the curve \(x=1-3t^{2},\ y=t-3t^{3}\). The tangent to the curve at the point is inclined at an angle \(\phi\) to \(OX\) and the tangent at \(P(-2,2)\) meets the curve again at \(Q\). Then:

If a differentiable function satisfies \[ (x-y)f(x+y) - (x+y)f(x-y) = 2(x^2y-y^3), \qquad \forall x,y\in\mathbb{R} \] and \(f(1)=2\), then:

Let \(Z_{1},Z_{2}\) be the roots of the equation \(Z^{2}+pZ+q=0\), where the coefficients \(p\) and \(q\) may be complex numbers and also let \(A,B\) represent \(Z_{1},Z_{2}\) respectively in the complex plane. If \(\angle AOB=\alpha\ne0\) and \(OA=OB\), where \(O\) is the origin, then the value of \(\frac{p^{2}}{q}\sec^{2}\frac{\alpha}{2}\) will be:

The equation \(x^{3}+5x^{2}+px+q=0\) and \(x^{3}+7x^{2}+px+r=0\) have two roots in common. If the third root of each equation is represented by \(x_{1}\) and \(x_{2}\) respectively, then \(\gcd(x_{1},x_{2})\) will be:

Tangent at a point \(P_{1}\) (other than \((0,0)\)) on the curve \(y=x^{3}\) meets the curve again at \(P_{2}\). The tangent at \(P_{2}\) meets the curve at \(P_{3}\) and so on. Then the abscissae of \(P_{1},P_{2},P_{3},\ldots,P_{n}\) form:

The point of intersection of \(\vec{r}\times\vec{a}=\vec{b}\times\vec{a}\) and \(\vec{r}\times\vec{b}=\vec{a}\times\vec{b}\), where \(\vec{a}=\hat{i}+\hat{j}\) and \(\vec{b}=2\hat{i}-\hat{k}\) is:

The position vectors of two adjacent sides of a rectangle \(OACB\) are \(\vec{a}\) and \(\vec{b}\) respectively, where \(O\) is the origin. If \(16|\vec{a}\times\vec{b}|=3(|\vec{a}|+|\vec{b}|)^{2}\) and \(\theta\) be the acute angle between the diagonals \(OC\) and \(AB\), then the value of \(\tan\left(\frac{\theta}{2}\right)\) is:

If \(a=\lim_{n\rightarrow\infty}\cos^{2n}x\), \((x=n\pi)\) and \(b=\lim_{n\rightarrow\infty}\cos^{2n}x\), \((x\ne m\pi)\), then numerical value of the area of the triangle whose vertices are \((a,b)\), \((-2,1)\) and \((2,1)\) is:

Let \(A=[a,\infty)\) denotes the domain, then \(f:[a,\infty)\rightarrow B\) which is defined by \(f(x)=2x^{3}-3x^{2}+6\) will have an inverse for the smallest real value of \(a\) if:

A mapping is selected at random from all mappings \(f:A\rightarrow A\) where set \(A=\{1,2,3,\dots,n\}\). If the probability that the mapping is injective is \(\frac{3}{32}\), then the value of \(n\) is:

The true set of values of \(K\) for which \(\sin^{-1}\left(\frac{1}{1+\sin^{2}x}\right)=\frac{K\pi}{6}\) may have a solution is:

If the locus of mid point of any normal chord of the parabola \(y^{2}=4x\) is \(x-\lambda=\frac{\mu}{y^{2}}+\frac{y^{2}}{\nu}\), \(\lambda,\mu,\nu\in\mathbb{N}\), then \((\lambda+\mu+\nu)\) equals to:

If \(\int\frac{\csc^{2}x-2010}{\cos^{2010}x}dx=-\frac{f(x)}{(g(x))^{2010}}+c\), where \(f\left(\frac{\pi}{4}\right)=1\), then the number of solutions of the equation \(\frac{f(x)}{g(x)}=\{x\}\) in \([0,2\pi]\) is/are (where \(\{\cdot\}\) represents fractional part function):

On the set \(\mathbb{R}\) of real numbers the relation \(\rho\), defined by \(x\rho y\) \((x,y\in\mathbb{R})\) iff:

If \(0<\alpha<\beta<\gamma<\frac{\pi}{2}\) then the equation \(\frac{1}{x-\sin\alpha}+\frac{1}{x-\sin\beta}+\frac{1}{x-\sin\gamma}=0\) has:

Which of the following statements is always true?