Mathematics Tes...

If the repetition is not allowed, how many numbers lying between \(1000\) and \(10,000\) can be formed with the digits \(1, 2, 3, 4\), and \(5\)?

The exponent of \(x\) occurring in the \(7^{\text {th }}\) term of expansion of \(\left(\frac{3 x}{2}-\frac{8}{7 x}\right)^{9}\) is:

The value of \(\int_{2}^{8} \frac{\sqrt{10-x}}{\sqrt{x}+\sqrt{10-x}} d x\) is:

The modulus of \(5+4 i\) is:

If letters of the work \(KUBER\) are written in all possible orders and arranged as in a dictionary, then the rank of the word \(KUBER\) will be:

A box of \(600\) bulbs contains \(12\) defective bulbs. One bulb is taken out at random from this box. Then the probability that it is non-defective bulb is:

Consider three sets \(E_{1}=\{1,2,3\}, F_{1}=\{1,3,4\}\) and \(G_{1}=\{2,3,4,5\}\). Two elements are chosen at random, without replacement, from the set \(E_{1}\), and let \(S_{1}\) denote the set of these chosen elements. Let \(E_{2}=E_{1}-S_{1}\) and \(F_{2}=F_{1} \cup S_{1} .\) Now two elements are chosen at random, without replacement, from the set \(F_{2}^{2}\) and let \(S_{2}\) dentoe the set of these chosen elements.

Let \(G_{2}=G_{1} \cup S_{2}\). Finally, two elements are chosen at random, without replacement from the set \(G_{2}\) and let \(S_{3}\) denote the set of these chosen elements.

Let \(E_{3}=E_{2} \cup S_{3}\). Given that \(E_{1}=E_{3}\), let \(p\) be the conditional probability of the event \(S_{1}=\{1,2\}\). Then the value of \(p\) is:

Evaluate the expression \((\mathrm{y}+1)^{4}-(\mathrm{y}-1)^{4}\).

In the figure given below, if \(\mathrm{O}\) is the centre of the circle, \(\angle \mathrm{AOB}=\angle \mathrm{EOF}=\angle \mathrm{COD}=60^{\circ}\) and \(A B=4\) units, then find \(E F+C D\).