Mathematics Tes...

Compute: \(\lim _{x \rightarrow 0} \frac{1-\cos \left(x^{2}\right)}{x^{4}}=?\)

If \(\log \left(2^{ J } \times 5^{ K } \times 7^{ L }\right)\) is arithmetic mean of \(\log \left(2^5 \times 5^4 \times 7^2\right)\), log \(\left(2^7 \times 5^2 \times 7^5\right), \log \left(2^6 \times 5^8 \times 7^4\right)\) and \(\log \left(2^2 \times 5^2 \times 7\right)\) then find value \(5 J +4 K +2 L ^2\)

If \(n=(2017) !\), then what is \(\frac{1}{\log _{2} n}+\frac{1}{\log _{3} n}+\frac{1}{\log _{4} n}+\cdots+\frac{1}{\log _{2017} n}\) equal to \(?\)

If \(\sin \theta+\cos \theta=\sqrt{2} \cos \theta,\) then what is \((\cos \theta-\sin \theta)\) equal to?

If \(\frac{d y}{d x}=1+x+y+x y\) and \(y(-1)=0\), then function \(y\) is

If Matrix \(A=\left[\begin{array}{ll}1 & 2 \\ 4 & 3\end{array}\right]\) such that \(A x=1,\) then \(x=\)

Find the equation of line through (-4,1,3) and parallel to the plane \(x+y+z=3\) while the line intersects another line whose equation is \(x+y-z=0=x+2 y-3 z+5\):

If the \(4^{\text {th }}, 7^{\text {th }}\) and \(10^{\text {th }}\) terms of a G.P. be \(a, b\), c respectively, then the relation between \(a, b, c\) is:

If the vectors \(\vec{a}=2 \hat{i}-3 \hat{j}-\hat{k}\) and \(\vec{b}=\hat{i}+4 \hat{j}-2 \hat{k}\) represent the two sides of any triangle, then the area of that triangle is: