Mathematics Tes...

If \(\alpha\) and \(\beta\) are the roots of the equation \(x^{2}-2 x+4=0\), then what is the value of \(\alpha^{3}+\beta^{3}\) ?

If \(A=\left\{x \mid x^{2}-5 x-6=0\right\}\) and \(B=\left\{y \mid y^{2}-7 y-8=0\right\}\). Then find \(A \cup(A \cap B)\) ?

If the correlation coefficient between \(x\) and \(y\) is \(0.6\) covariance is 27 variance of \(y\) is 25 , then what is the variance of \(x\)?

\(\lim _{x \rightarrow \infty}\left(\frac{x-5}{x-2}\right)^{(x-3)}\) equals:

For all positive integral values of \(n, 3^{3 n}-2 n+1\) is divisible by:

The function \(f(x)\) is defined as:

\(f(x)=\left\{\begin{array}{c}b x^{2}-a, \text { if } x<-1 \\ a x^{2}-b x-2, \text { if } x \geq-1\end{array}\right.\)

If \(f^{\prime}(x)\) is differentiable everywhere, the equation whose roots are \(a\) and \(b\) is:

There were two women participating in a chess tournament. Every participant played two games with the other participants. The number of games that the men played between themselves proved to exceed by \(66\) the number of games that the men played with the women. The number of participants is:

If one end of a diameter of the circle \(x^{2}+y^{2}-4 x-6 y+11=0\) is \((3,4),\) then find the coordinates of the other end of the diameter.

Solve the differential equation \(\frac{d y}{d x}+y \cos x=3 \cos x\).

The polar coordinate of a point \((1, \sqrt{−3})\) is -

Equation of angle bisectors between \(x\) and \(y\)-axes are:

If the points \((a, 0),\left(a t_{1}^{2}, 2 a t_{1}\right)\) and \(\left(a t_{2}^{2}, 2 a t_{2}\right)\) are collinear, write the value of \(t_{1} t_{2}\)

Find the angle between two vectors \((\vec{a}=2 \hat{i}+\hat{j}-3 \hat{k})\) and \((\vec{b}=3 \hat{i}-2 \hat{j}-\hat{k})\).