Mathematics Tes...

If \(f: R \rightarrow R\) and \(g: R \rightarrow R\) are two mappings defined as \(f(x)=2 x\) and \(g(x)=x^{2}+2\), then the value of \((f+g)(2)\) is:

If \((a, b)\) be the orthocentre of the triangle whose vertices are \((1,2),(2,3)\) and \((3,1)\), and \(I_1=\int_a^b x \sin \left(4 x-x^2\right) d x, I_2=\int_a^b \sin \left(4 x-x^2\right) d x\), then \(36 \frac{I_1}{I_2}\) is equal to :

The slope of the line perpendicular to the line passing through the points \((3,2)\) and \((1,-1)\) is:

If \(\int_0^1 \frac{1}{\sqrt{3+x}+\sqrt{1+x}} d x=a+b \sqrt{2}+c \sqrt{3}\), where \(a, b, c\) are rational numbers, then \(2 a+3 b-4 c\) is equal to :

Let \(a_1, a_2, a_3, \ldots, a_n\) be \(n\) positive consecutive terms of an arithmetic progression. If \(d>0\) is its common difference, then :

\(\lim _{n \rightarrow \infty} \sqrt{\frac{d}{n}}\left(\frac{1}{\sqrt{a_1}+\sqrt{a_2}}+\frac{1}{\sqrt{a_2}+\sqrt{a_3}}+\ldots \ldots .+\frac{1}{\sqrt{a_{n-1}}+\sqrt{a_n}}\right) \text { is }\)

If \(2 \tan ^2 \theta-5 \sec \theta=1\) has exactly 7 solutions in the interval \(\left[0, \frac{n \pi}{2}\right]\), for the least value of \(n \in N\) then \(\sum_{k=1}^n \frac{k}{2^k}\) is equal to:

If the mirror image of the point \((2,4,7)\) in the plane \(3 x-y+4 z=2\) is \((\mathrm{a}, \mathrm{b}, \mathrm{c})\), then \(2 \mathrm{a}+\mathrm{b}+2 \mathrm{c}\) is equal to:

If \(A=\left[\begin{array}{ccc}3 & 4 & 9 \\ 11 & 6 & 7 \\ 8 & 9 & 5\end{array}\right]\) and \(|2 \mathrm{~A}|=\mathrm{k}\) then find the value of \(\mathrm{k}\)?

The optimal value of the objective function is attained at the points ________________.

If \(P\) and \(Q\) are two sets, then \((P-Q) \cup(Q-P) \cup(P \cap Q)\) will be: