Mathematics Tes...

In a group of 600 students, there are 575 students who can speak Marathi and 300 can speak Hindi. What is the number of students who can speak Marathi only?

I. \(3 x^{2}-2 \sqrt{21} x+7=0\)

II. \(3 y^{2}+\sqrt{3 y}-2=0\)

I. \(10 x^{2}-59 x+45=0\)

II. \(9 y^{2}-100 y+100=0\)

I. \(2 x^{2}+11 x+12=0\)

II. \(y^{2}-y-2=0\)

\(\left|\begin{array}{ccc}1 & \cos \alpha & \cos \beta \\ \cos \alpha & 1 & \cos \gamma \\ \cos \beta & \cos \gamma & 1\end{array}\right|=\left|\begin{array}{ccc}0 & \cos \alpha & \cos \beta \\ \cos \alpha & 0 & \cos \gamma \\ \cos \beta & \cos \gamma & 0\end{array}\right|\) then :

A pair of dice is thrown and the numbers appearing have sum greater than or equal to \(10\). The probability of getting a sum of \(10\) is:

A line makes an angle \(\alpha,\beta, \gamma\) with the \(X, Y, Z\) axes. Then \(\sin ^2 \alpha+\sin ^2 \beta+\) \(\sin ^2 \gamma\) is equal to: