Let \(A=\left[\begin{array}{cc}\cos \theta & -\sin \theta \\ \sin \theta & \cos \theta\end{array}\right]\) and \(I=\left[\begin{array}{ll}1 & 0 \\ 0 & 1\end{array}\right]\). If \(A^T+A=I\), then:

If the function \(f(x)=x^2+k x+7\) is strictly increasing in the interval [-2, 2], then

If it is 7:00 pm currently in the clock, what will the clock show (in am or pm) after 674 hours?

Area of the triangle ABC with vertices \(\left(a, a^2\right),\left(b, b^2\right)\) and \(\left(c, c^2\right)\) is equal to :

The area (in sq., units) of the region bounded by the parabola \(y^2=4 x\) and the line \(x=1\) is:

In which of the following intervals, the function \(f(x)=-x^2-2 x+15\) is decreasing ?

The value of the integral \(I=\int_0^1 \frac{1}{\sqrt{x^2+2 x+3}} d x\) is :

Let the matrix \(A=\left[\begin{array}{ll}2 & 3 \\ 1 & 4\end{array}\right]\). Then which of the following are true?
(A) \(\operatorname{adj} A =\left[\begin{array}{cc}4 & -3 \\ -1 & 2\end{array}\right]\)
(B) \(\operatorname{det}( A )=5\)
(C) \(\operatorname{det}(\operatorname{adj} A )=25\)
(D) If \(A^3=\left[\begin{array}{ll}a & b \\ c & d\end{array}\right]\), then \(a+b=c+d\)
Choose the correct answer from the options given below :

In reference to the radio waves, choose the incorrect statements:
(A) Radio waves are the longest wavelength electromagnetic waves.
(B) Radio waves are deviated by electric and magnetic fields.
(C) Radio waves are diffracted easily.
(D) Radio waves are not electromagnetic waves.
Choose the correct answer from the options given below:

The electric field intensity at a distance of 20 cm from the centre of a small conducting sphere is \(1.5 \times 10^3 \text{ N}⋅­­C^{-1}\) and is directed towards the sphere. The charge on the sphere is:

The marginal cost of production of \(X\) units of a commodity is \(56+\frac{3}{2} x\).
It is known that fixed costs are Rs.115.
Then the total cost of producing 50 units is :-

Read the following passage carefully and answer the given questions.
Bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. Baculoviruses are pathogens that attack insects and other arthropods. The majority of baculoviruses used as biological control agents are in the genus Nucleopolyhedrovirus. These viruses are excellent candidates for species-specific, narrow spectrum insecticidal applications. They have been shown to have no negative impacts on plants, mammals, birds, fish or even on non-target insects. BOD refers to the amount of the oxygen that would be consumed if all the organic matter in one liter of water were oxidised by bacteria. The sewage water is treated till the BOD is reduced. Cheese, is one of the oldest food items in which microbes were used. Different varieties of cheese are known by their characteristic texture, flavour and taste. For example, the large holes in ‘Swiss cheese’ are due to production of a large amount of CO₂ by a bacterium named Propionibacterium sharmanii.
The greater the BOD of waste water-

An object is placed at a distance of 10 cm from a concave mirror of focal length 15 cm. The magnification of the image is