Question

Find the equation of tangent to the curve x² + 3y = 3, which is parallel to line y – 4x + 5 = 0.

Find the point on the curve y = x³ – 11x + 5 at which the equation of tangent is y = x – 11.

A bag contains (2n + 1) coins. It is known that (n – 1) of these coins have a head on both sides, whereas the rest of the coins are fair. A coin is picked up at random from the bag and is tossed. If the probability that the toss results in a head is 31/42, determine the value of n.

Find the particular solution of the differential equation satisfying the given condition ${\frac{d y}{d x}}=y\tan x,$ given that y = 1, when x = 0.

For the following matrices A and B, verify that [AB]’ = B’A’ where, A = $\left(\begin{array}{l }1 \\ -4 \\ 3\end{array}\right)$ , B = $\left(\begin{array}{l l l }-1 & 2 & 1\end{array}\right)$

Two farmers X and Y cultivate only three varieties of rice namely Basmati, Permal and Naura. The sale in rupees of these varieties of rice by both the farmers in the months of September and October are given by the following matrices A and B.

Find the particular solution of the following differential equation given that at x = 2, y = 1 $x\,{\frac{d y}{d x}}\,+\,2y=x^{2},\,(x\,\neq\,0).$