Mathematics Tes...

Suppose \(\sin 2 \theta=\cos 3 \theta\), here \(0<\theta<\pi / 2\) then what is the value of \(\cos 2 \theta ?\)

The sum of the first 20 terms of the series \(\sqrt{5}+\sqrt{20}+\sqrt{45}+\sqrt{80}+\ldots\) is

Let the equations of two sides of a triangle be 3x−2y+6=0 and 4x+5y−20=0. If the orthocentre of this triangle is at (1,1), then the equation of its third side is:

How many words can be formed by using all the letters of the word ‘DAUGHTER’ so that the vowels always come together?

The equation of the locus of a point equidistant from the point A(1, 3) and B(-2, 1) is:

If \(A\) and \(B\) are two events such that \(P(A) \neq 0\) and \(P(A) \neq 1\), then \(P\left(\frac{\overline{A}}{\overline{B}}\right)\) is:

Solve the differential equation \(\sin x \frac{d y}{d x}+\frac{y}{\sin x}=x \sin x e^{\cot x}\)

Integrating factor of \(\left(1-x^2\right) \frac{d y}{d x}-x y=1\) is:

Mean of 100 observations is 50 and standard deviation is 10. If 5 is added to each observation, then what will be the new mean and new standard deviation respectively?

What is the value of \(7^{\frac{1}{7}} \times 7^{\frac{1}{7^{2}}} \times 7^{\frac{1}{7^{3}}} \times \ldots\infty\) ?