The real valued function \(f(x)=x^{15}+5 x^9+10\) is increasing for __________ .

For the function \(f(x)=e^{-2 x}(2-x)^2\), the point of local maxima is:

If \(A\) is a square matrix of order 3 such that \(|A|=2\), then the value of \(|\operatorname{adj}(\operatorname{adj} A)|\) is :

If \(m\) and \(n\) are respectively the order and degree of the differential equation
\(\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)^3+y=4 x\),
then the value of \((m+n)\) is :

A man wishes to ensure that he gets Rs. 75,000/- at the end of each year indefinitely. The amount that he invest now to produce the desired cash flow, if money is worth 2.5% compounded annually is:

The image of the point \((3,-2,1)\) in the plane \(3 x-y+4 z=2\) is:

The function \(f(x)=\frac{x}{2}+\frac{2}{x}, x \neq 0\) is increasing on :
(A) \((-\infty,-2)\)
(B) \((-2,2)\)
(C) \((2, \infty)\)
(D) \((-1,1)\)
Choose the correct answer from the options given below :

The minimum value of \(Z = 2x + y\) subjected to \(x + y ≥ 10, 2x + 3y ≤ 26, x, y ≥ 0\) is

The value of \(\int_0^{\pi / 2} \log _e\left(\frac{5+2 \sin x}{5+2 \cos x}\right) d x\) is

When light passes from air to glass, then

The domain of the function \(f(x)=\sin ^{-1}(2 x-3)\) is :

Read the passage and answer the question given below.
When a host is exposed to antigens, which may be in the form of living or dead microbes or other proteins, antibodies are produced in the host body. This type of immunity is called active immunity. Active immunity is slow and takes time to give its full effective response. Injecting the microbes deliberately during immunisation or infectious organisms gaining access into body during natural infection induce active immunity. When antibodies are directly given to protect the body against foreign agents, it is called passive immunity.
Production of antibodies against antigens in the body is:

If \(A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\), then \(A^2=\)