Mathematics Tes...

The ends of the base of an isosceles triangle are at \(2,0\) and \(0,1\) and the equation of one side is \(x=2\) then the orthocentre of the triangle is:

If \(\left|\begin{array}{ccc}1+a x & 1+b x & 1+c x \\ 1+a_{1} x & 1+b_{1} x & 1+c_{1} x \\ 1+a_{2} x & 1+b_{2} x & 1+c_{2} x\end{array}\right|=A_{0}+A_{1} x+A_{2} x^{2}+A_{3} x^{3},\) then \(A_{0}\) is equal to ______.

In class of 105 students out of three subjects Maths, Physics, Chemistry each student studies at least one subject. In Maths 47, in Physics 50, and in Chemistry 52 students studies, 16 in Maths and Physics, 17 in Maths and Chemistry and 16 in Physics and Chemistry students both subjects.

What will be the number of those students who study only two subjects?

\(\lim x \rightarrow 0\left\{\frac{1+\tan x}{1+\sin x}\right\}^{\operatorname{cosec} x}\) is equal to

Let\(f(x)=\left\{\begin{array}{ll}\frac{\tan x-\cot x}{x-\frac{\pi}{4}}, & x \neq \frac{\pi}{4} \\ a, & x=\frac{\pi}{4}\end{array}\right.\)the value of \(a\) so that \(f(x)\) is continuous at \(x=\frac{\pi}{4}\) is:

The coefficient of \(x^{n}\) in the expansion of \(\left(\frac{1+x}{1-x}\right)^{2}\), is:

\(\int \frac{1}{x}(\log x) d x\) is equal to:

Five letters are sent to different persons and addresses on the five envelopes are written lat random. The probability that all the letters do not reach the correct destiny is:

Let \(\vec{a}=a_{1} \hat{i}+a_{2} \hat{j}+a_{3} \hat{k} ,~ \vec{b}=b_{1} \hat{i}+b_{2} \hat{j}+b_{3} \hat{k}\) be three non-zero vectors such that \(\vec{c}\) is a vector perpendicular to both \(\vec{a}\) and \(\vec{b}\). If the angle between \(\vec{a} \) and \( \vec{b}\) is \(\frac{\pi}{6}\) then \(\left|\begin{array}{lll} a_{1} & b_{1} & c_{1} \\ a_{2} & b_{2} & c_{2} \\ a_{3} & b_{3} & c_{3} \end{array}\right|=?\)