Mathematics Tes...

Let \(f(2)=2\) and \(f(x)=2\). Then, \(\lim _{x \rightarrow 2} \frac{x f(2)-2 f(x)}{x-2}\) is given by:

Find the value of \(\lim _{{x} \rightarrow 5} \frac{{x}^{2}-25}{{x}^{2}-2 {x}-10}\)

Find the equation of the plane through the line of intersection of the planes \(x+y+z=1\) and \(2 x+3 y+4 z=5\) which is perpendicular to the plane \(x-y+z=0 ?\)

Find the 5th term form the end in the expansion of \(\left(x-\frac{1}{x}\right)^{12} ?\)

The middle term of A.P. 5, 12, 19, ..., 215 is:

Find the standard deviation of \(15,20,18,22,25\)?

Let \(\vec{a}=\hat{i}-\hat{j}, \vec{b}=\hat{j}-\hat{k}, \vec{c}=\hat{k}-\hat{i}\). If \(\vec{d}\) is a unit vector such that \(\vec{a} \vec{d}=0=[\vec{b} \vec{c} \vec{d}],\) then \(\vec{d}\) equals:

\(\tan ^{-1} \frac{1}{4}+\tan ^{-1} \frac{2}{9}\) is equal to:

What is the angle between the two lines whose direction numbers are \((\sqrt{3}-1,-\sqrt{3}-1,4)\) and \((-\sqrt{3}-1, \sqrt{3}-1,4)\)?

Tangents are drawn to the hyperbola \(4 x^{2}-y^{2}=36\) at the points \(P\) and \(Q\). If these tangents intersect at the point \(T(0,3)\) then find the area of \(\triangle P T Q\).

Each of four particles move along an \(x\)-axis. Their coordinates (in meters) as functions of time (in seconds) are given by:

a) particle \(1: x(t)=3.5-2.7 t^{3}\)

b) particle \(2: x ( t )=3.5+2.7 t ^{3}\)

c) particle \(3: x(t)=3.5-2.7 t^{2}\)

d) particle \(4: x(t)=3.5-3.4 t-2.7 t^{2}\)

Which of these particles have constant acceleration?

If \(a_{1}, a_{2}, a_{3}, \ldots, a_{9}\) are in \(G . P_{.}\), then what is the value of the determinant \(\left|\begin{array}{lll}\ln a_{1} & \ln a_{2} & \ln a_{3} \\ \ln a_{4} & \ln a_{5} & \ln a_{6} \\ \ln a_{7} & \ln a_{8} & \ln a_{9}\end{array}\right| ?\)

Find the area between \(y=2 x^{2}\) and \(y+6 x-8=0\).

Construct a \(3 \times 2\) matrix whose elements are given by \(a _{ ij }=\frac{1}{3}|2 i + j |\).