Mathematics Tes...

The angle between the lines \(2 x=3 y=-z\) and \(6 x=-y=-4 z\) is:

Using the principle of Mathematical Induction, \(3^{\mathrm{n}}>2^{\mathrm{n}}\) is true for:

Calculate the scalar product of the following vectors.

\(a=\{-2,3,11\}\) and \( b=\{5,7,-4\}\)

In a binomial distribution \(\mathrm{B}\left(\mathrm{n}, \mathrm{p}=\frac{1}{4}\right)\), if the probability of at least one success is greater than or equal to \(\frac{9}{10}\), then \(\mathrm{n}\) is greater than:

How many combinations are possible while selecting four letters from the word ‘\(SMOKEJACK\)’ with the condition that ‘\(J\)’ must appear in it?

If, for a positive integer \(n\), the quadratic equation,

\(x(x+1)+(x+1)(x+2)+\ldots \)

\( +(x+\overline{ n -1})(x+ n )=10 n\)

has two consecutive integral solutions, then \(n\) is equal to:

If \(\cos ^{-1} x+\cos ^{-1} y+\cos ^{-1} z=\pi\), then:

If \(z_{1}=2-i\) and \(z_{2}=1+i\), then \(\left|\frac{z_{1}+z_{2}+1}{z_{1}-z_{2}+1}\right|\) is:

Let \(\mathrm{y}=\mathrm{y}(\mathrm{x})\) be a function of \(\mathrm{x}\) satisfying \(\mathrm{y} \sqrt{1-\mathrm{x}^2}=k-x \sqrt{1-\mathrm{y}^2}\) where \(\mathrm{k}\) is a constant and \(\mathrm{y}\left(\frac{1}{2}\right)=-\frac{1}{4}\). Then \(\frac{\mathrm{d} \mathrm{y}}{\mathrm{dx}}\) at \(\mathrm{x}=\frac{1}{2}\), is equal to: