Mathematics Tes...

If \(\alpha, \beta\) are the roots of \(a x^{2}+b x+c=0,\) find the value of \(\frac{1}{a \alpha+b}+\frac{1}{a \beta+b}\):

Find the vector along the sum of the vectors\(\vec{a}=2 \hat{i}+2 \hat{j}-5 \hat{k}\) and \(\vec{b}=2 \hat{i}+\hat{j}+3 \hat{k}\).

What is the most probable number of successes in 10 trials with probability of success \(\frac{2}{3}\)?

\(3 \tan ^{-1} x+\cot ^{-1} x=\pi\) then \(x\) equal to:

If \(5 \times^{ n } P _{3}=4 \times^{( n +1)} P _{3}\), find \(n\)?

The shaded region given below represents the constraints (other than \(x \geq 0, y \geq 0\) ):

What is the number of outcomes when a coin is tossed and then a die is rolled only in case a head is shown on the coin?

If the matrix \(\left[\begin{array}{ccc}\cos \theta & \sin \theta & 0 \\ \sin \theta & \cos \theta & 0 \\ 0 & 0 & 1\end{array}\right]\) is singular, then \(\theta\) is equal to :

The roots of the equation$3x^2-2x+4=0$ are:

If \(n=(2017) !\), then what is \(\frac{1}{\log _{2} n}+\frac{1}{\log _{3} n}+\frac{1}{\log _{4} n}+\cdots+\frac{1}{\log _{2017} n}\) equal to \(?\)