List of top Mathematics Questions on Algebra asked in WBJEE

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

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:

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:

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 \(0<\alpha<\beta<\gamma<\frac{\pi}{2}\) 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?