Mathematics Tes...

The value of \(\int_{\pi / 4}^{3 \pi / 4} \frac{d x}{1+\cos x}\) is:

The position vectors of \(A, B, C\) are \(\hat{i}+\hat{j}+\hat{k}, 4 \hat{i}+\hat{j}+\hat{k}, 4 \hat{i}+5 \hat{j}+\hat{k}\). Then the position vector of the circumcentre of the triangle \(ABC\) is:

Find the coefficient of \(x^{11}\) in the expansion of \(\left(x^{3}-\frac{1}{x^{4}}\right)^{13}\):

There are 10 people seated in two rows (5 in 1 row) and there are two types of food items. Each row can be served any of the two food items but it must be different from the other row. In how many ways the food can be served?

Two equal circles of radius \(r\) intersect such that each passes through the centre of the other. The length of the common chord of the circles is:

Find the general solution of the differential equation \(y d x=(y-x) d y\).

What is \(\lim _{x \rightarrow 1} \frac{x+x^{2}+x^{3}-3}{x-1}\) equal to?

\((\sin \alpha+\operatorname{cosec} \alpha)^{2}+(\cos \alpha+\sec \alpha)^{2}\) is equals to:

The cofactor of the element 4 in the determinant \(\left[\begin{array}{lll}1 & 2 & 3 \\ 4 & 5 & 6 \\ 5 & 8 & 9\end{array}\right]\) is:

The triangle \(ABC\) is defined by the vertices \(A =(0,7,10), B =(-1,6,6)\) and \(C =(-4,9,6)\). Let \(D\) be the foot of the attitude from \(B\) to the side \(AC\) then \(BD\) is: