Mathematics Tes...

The improper integral \(\int_{0}^{\infty} \mathrm{e}^{-2 \mathrm{t}}\) dt converges to:

If \(\left(1+x-2 x^{2}\right)^{6}=1+a_{1} x+a_{2} x^{2}+\ldots \ldots+a_{12} x^{12}\), then the expression \(a_{2}+\) \(a_{4}+a_{6}+\ldots \ldots+a_{12}\) has the value:

There are \(6\) persons arranged in a row. Another person has to shake hands with \(3\) of them so that he should not shake hands with two consecutive persons. In how many distinct possible combinations can the handshakes take place?

In the figure, \(P Q L\) and \(PRM\) are tangents to the circle with centre \(O\) at the points \(Q\) and \(R\), respectively and \(S\) is a point on the circle such that \(\angle SQL =50^{\circ}\) and \(\angle SRM =\) \(60^{\circ}\). Then \(\angle Q S R\) is equal to:

The solution of the differential equation \(\frac{d y}{d x}=\sec \left(\frac{y}{x}\right)+\frac{y}{x}\) is:

If \(f(x)=2 x-x^{2},\) then what is the value of \(f(x+2)+f(x-2)\) when \(x=0\)?

If \(\mathrm{A}+\mathrm{B}=90^{\circ}\), then \(\frac{\tan \mathrm{A} \tan \mathrm{B}+\tan \mathrm{A} \cot \mathrm{B}}{\sin \mathrm{A} \sec \mathrm{B}}-\frac{\sin ^2 \mathrm{~B}}{\cos ^2 \mathrm{~A}}\) is equal to:

If the determinant \(\left|\begin{array}{ccc}a & b & a \alpha+b \\ b & c & b \alpha+c \\ a \alpha+b & b \alpha+c & 0\end{array}\right|\)is equal to zero, then consider thefollowing statements

I. a, b, c are in A.P.

II. α is a root of the equation ax² + 2bx + c = 0.

Which of the above statements is/are correct?