Mathematics Tes...

Find the degree of the differential equation\(y=x \frac{d y}{d x}+\left(\frac{d y}{d x}\right)^{-1}\).

\(\tan ^{2} x-3 \sec ^{2} x+3=0\), then the value of \(x\left(0 \leq x \leq 90^{\circ}\right)\) is:

Find the roots of \(a^{2} x^{2}-3 a b x+2 b^{2}=0\)

A box contains 2 blue caps, 4 red caps, 5 greens caps, and 1 yellow cap. If four caps are picked at random, the probability that none of them are green is:

The equation which has the sum of its roots as \(3\) is:

The equation of the normal at the point \((1,1)\) on the curve \(2 y+x^{2}=3\) is:

Consider the following Linear Programming Problem (LPP).

Maximise \(Z=x_{1}+2 x_{2}\)

Subject to:

\(x_{1} \leq 2\)

\(x_{2} \leq 2\)

\(x_{1}+x_{2} \leq 2\)

\(x_{1}, x_{2} \geq 0\) (i.e., +ve decision variables)

A box contains \(4\) tennis balls, \(6\) season balls and \(8\) dues balls. \(3\) balls are randomly drawn frThe arithmetic mean of \(9\) terms is given as \(49\). If the mean of first \(7\) terms is \(37\) , find the mean of last \(2\) terms.om the box. What is the probability that the balls are different?

Three houses are available in a locality. Three persons apply for the houses. Each applies for one house without consulting others. The probability that all the threeapply for the same house is:

If the equation \(3 x^{2}+7 x y+2 y^{2}+5 x+5 y+k=0\) represents a pair of straight lines, then the value of \(k\) is: