Mathematics Tes...

Find \(\cot \left[\tan ^{-1} \frac{1}{2}+\tan ^{-1} \frac{1}{8}\right]=?\)

Find the area of the region bounded by the curves \(y=x^{3}+4 x+2\), the line \(x=0, x=4\) and the \(x\)-axis.

The value of the \(\sin 1^{\circ}+\sin 2^{\circ}+\ldots+\sin 359^{\circ}\) is equal to:

If nth term of a series is given by T_n = 3n + 2, where n is a natural number then find the value of\(S_{n}=\sum_{k=1}^{n} T_{k}=?\)

Let \(A=\left[a_{i j}\right]\) be a square matrix of order 3 such that \(a_{i j}=2^{j-i}\), for all \(\mathrm{i}, \mathrm{i}=1,2,3\). Then, the matrix \(\mathrm{A}^2+\mathrm{A}^3+\ldots \ldots+\mathrm{A}^{10}\) is equal to :

If two sides of a triangle are represented by \(x^2-7 x y+6 y^2=\) 0 and the centroid is \((1,0)\), then the equation of third side is

A class of \(30\) students occupy a classroom containing \(5\) rows of seats, with \(8\) seats in each row. If the student seat themselves at random, the probability that the sixth seat in the fifth row will be empty is:

If \(a_1, a_2, \ldots \ldots \ldots \ldots, a_n\) are in H.P., then the expression \(a_1 a_2+a_2 a_3+\ldots \ldots \ldots \ldots+a_{n-1} a_n\) is equal to:

Solve the differential equation \(x d y-2 y d x=0\)

If \(|\overrightarrow{\mathrm{a}}|=10,|\overrightarrow{\mathrm{b}}|=2\) and \(\overrightarrow{\mathrm{a}}. \overrightarrow{\mathrm{b}}=12\), then what is the value of \(|\overrightarrow{\mathrm{a}} \times \overrightarrow{\mathrm{b}}| ?\)