Mathematics Tes...

A medicine is known to be 50% effective to cure a patient. If the medicine is given to 4 patients, what is the probability that at least one patient is cured by this medicine?

If \(1+\sin \theta+\sin ^{2} \theta+\ldots\) upto \(\infty=2 \sqrt{3}+4,\) then \(\theta=\)

If \(a\) denotes the number of permutations of \(x+2\) things taken all at a time, \(b\) the number of permutations of \(x\) things being taken 11 at a time and \(c\) the number of permutations of \(x-11\) things taken all at a time such that \(a=182 b c\), then the value of \(x\) is:

Find the value of \(\left|\begin{array}{lll}0 & c & b \\ c & 0 & a \\ b & a & 0\end{array}\right|^{2}\)

The set of all real \(x\) satisfying the inequality \(\frac{3-|x|}{4-|x|} \geq 0\):

Find the maximum value of15sin θ + 20cos θ.

Mean of marks of a class, having 40 students, in a subject are 70. If marks of a student were mistakenly read as 87 instead of 78, then what is the actual mean marks?

Let \(R\) be the relation on the set \(R\) of all real numbers, defined by \(a R b\) if \(f|a-b| \leq 1\). Then, \(R\) is: