Mathematics Tes...

If$a{\sin }^2\theta +b{\cos }^2\theta =c$,then find the value of$\sqrt{\frac{c-b}{a-c}}$

What is the radius of the circle$2x^2+2y^2-3x+5y-7=0?$

Consider the following statements:

1. The magnitude of \(\vec{a} \times \vec{b}\) is same as the area of a triangle with sides \(\vec{a}\) and \(\vec{b}\)

2. If \(\vec{a} \times \vec{b}=\overrightarrow{0}\) where \(\vec{a} \neq \overrightarrow{0}, \vec{b} \neq \overrightarrow{0},\) then \(\vec{a}=\lambda \vec{b}\)

Which of the above statement is/are correct?

Find the value of${\int }_0^1\frac{{\tan }^{-1}x}{1+x^2}dx$:

A fair coin tossed repeatedly. If the head appears on the first three tosses, then the probability of the tail appearing on the fourth toss equals.

Find the value of \(\cot ^{-1}(\sqrt{3})\).

A point \(\mathrm{R}\) with \({x}\)-coordinate 4 lies on the line segment joining thepoints \(\mathrm{P}(2,-3,4)\) and \(\mathrm{Q}(8,0,10)\). Find the coordinates of the point \(\mathrm{R}\).

Solve the following integral:

\(\int\sqrt{1+\sin 2 x d x}\)

In a survey, it was found that \(21\) people liked product \(A, 26\) liked product \(B\) and \(29\) liked product \(C\). If \(14\) people liked products \(A\) and \(B\), \(12\) people liked products \(C\) and \(A, 14\) people liked products \(B\) and \(C\) and \(8\) liked all the three products. Find how many liked product \(C\) only.

What is \(\int \frac{d x}{2^{x}-1}\) equal to?