Mathematics Tes...

Let \(A(\vec{a}), B(\vec{b}), C(\vec{c})\) be the vertices of the triangle \(A B C\) and let \(D E F\) be the midpoints of the sides \(B C, C A, A B\) respectively. If \(P\) divides the median \(AD\) in the ratio \(2: 1\) then the position vector of \(P\) is:

Let \(y=3 x^{2}+2\). If \(x\) changes from 10 to 10.1, then what is the total change in y?

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

What is the value of

\(\frac{\sin 34^{\circ} \cos 236^{\circ}-\sin 56^{\circ} \sin 124^{\circ}}{\cos 28^{\circ} \cos 88^{\circ}+\cos 178^{\circ} \sin 208^{\circ}}\)

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

If \(A\) and \(B\) are two events such that \(P ( A \cup B )\)= \(\frac{5}{6}\) , \(P ( A \cap B )\) = \(\frac{1} {3}\), \(P ( B )\) = \(\frac{1}2\), then the events \(A\) and \(B\) are:

\(60 \%\) of the employees of a company are college graduates. Of these, \(10 \%\) are in sales. Of the employees who did not graduate from college, \(80 \%\) are in sales. The probability that an employee selected at random is in sales is:

The equation of a parabola which passes through the intersection of a straight line x + y = 0 and the circle x² + y² + 4y = 0 is:

The shaded region given below represents the constraints (other than \(x \geq 0, y \geq 0\) ):

Using the principle of mathematical induction, prove that \(1 \times 3+2 \times 3^{2}+3 \times 3^{3}+\ldots+n \times 3^{n}=\frac{(2 n-1) 3^{n+1}+3}{4}\) for all: