Mathematics Tes...

The length of the perpendicular from the origin to a line is 7 and the line makes an angle of 150 degrees with the positive direction of the y-axis then, the equation of a line is:

The absolute maximum value of y = x³ – 3x + 2 in 0 ≤ x ≤ 2 is

Suppose $z_1, z_2, z_3$ are the vertices of an equilateral triangle inscribed in the circle$\left|z\right| = 2$. If$z_1=1+\sqrt{3}i$, then$z_2$ and$z_3$, respectively are:

If \(A =\left[\begin{array}{cc}1 & -5 \\ -3 & 7\end{array}\right]\) and \(B =\left[\begin{array}{ll}8 & 4 \\ 1 & 3\end{array}\right]\) then the value of \(( AB )^{T}\) is:

Consider the following statements in respect of the differential equation

$\frac{d^{2}y}{d{x}^2}+\cos \left(\frac{dy}{dx}\right)=0$

1. The degree of the differential equation is not defined.

2. The order of the differential equation is 2

Which of the above statements is correct?

Evaluate the integral \(\int_{1}^{2} \frac{1}{x(1+\log x)^{2}} d x\).

In An A.P. twenty fifth term is 70 more than to fifteen term. Find the common differences.

Consider the following statements in respect of a vector \(\vec{c}=\vec{a}+\vec{b}\), where \(|\vec{a}|=|\vec{b}| \neq 0\) :

1. \(\vec{c}\) is perpendicular to \((\vec{a}-\vec{b})\).

2. \(\vec{c}\) is perpendicular to \(\vec{a} \times \vec{b}\).

Which of the above statement is/are correct?

What is the value of \(\cos \left\{\cos ^{-1} \frac{4}{5}+\cos ^{-1} \frac{12}{13}\right\} ?\)

A box contains 5 green pencils and 7 yellow pencils. Two pencils are chosen at random from the box without replacement. What is the probability they are both yellow?