Mathematics Tes...

Find the vector equation of the line passing through the point with position vector \(\hat{i}-2 \hat{j}+5 \hat{k}\) and perpendicular to the plane \(\vec{r} \cdot(2 \hat{i}-3 \hat{j}-\hat{k})=0\).

What is the probability of solving a given problem if three students \((A, B\) and \(C)\), try it independently, with respective probabilities \(\frac{4}{7}, \frac{3}{8}\) and \(\frac{1}{2}\)?

Given that, E = {2, 4, 6, 8, 10}, if n represents a member (component) of E, write the set containing all the numbers represented by (n + 1):

If \(y=\frac{4+3 x^{3}}{6 x^{4}}\), then find the value of \(\frac{d y}{d x}\).

A man starts repaying his loan as first installment of Rs.1000 . If he increases the installment by Rs. 50 every month. What amount will he pay in the 20th installment ?

If the distances of P (x, y) from A (4, 1) and B (-1, 4) are equal, then which of the following is true?

There are \(49\) cards in a box numbered from \(1\) to \(49\). Every card is numbered with only \(1\) number. Probability of picking up a card, the number printed on which is a multiple of \(5\) but not that of \(10\) or \(15\) is:

A sequence \(b_{0}, b_{1}, b_{2} \ldots\) is defined by letting \(b_{0}=5\) and \(b_{k}=4+b_{k-1}\) for all natural numbers \(k\). Show that \(b_{n}=5+4 n\) for all: