The interval where the function \(f(x)=2 x^3-9 x^2+12 x+15\) is decreasing, is :

For what value of \(k\), the matrix \(A=\left[\begin{array}{ll}1 & 3 \\ k & 4\end{array}\right]\) is singular ?

The number of vectors of unit length perpendicular to both the vectors \(\vec{a} = \hat{i} + 2\hat{j} + 3\hat{k}\) and \(\vec{b} = \hat{i} - \hat{j} + 3\hat{k}\) is:

The rate of change of volume of a sphere with respect to its surface area, when radius is 4 cm, is equal to

For the objective function \(Z = 3x + 5y\) subject to constraints \(x + 3y ≥ 3, x + y ≥ 2, x ≥ 0, y ≥ 0\):

If the straight lines \(x=1+s, y=-3-\lambda s, z=1+\lambda s\) and \(x=\frac{t}{2}, y=1+t, z=2-t\) with parameters s and \(t\) respectively, are coplanar, then \(\lambda\) is equal to :

The order and degree of the differential equation \(\frac{d^3 y}{d x^3}=\frac{y}{2}+\left(\frac{d y}{d x}\right)^3\), respectively are :

Which of the following statements is correct for a charged metallic shell?

Which of the following matrices is not invertible?

Figure shows a coil C connected to a galvanometer G. When the North-pole of a bar magnet is pushed towards the coil, the pointer in the galvanometer deflects. Regarding this set up, the following statements are given:
(A) It indicates the presence of electric current in the coil.
(B) The deflection is found to be smaller when the magnet is pushed towards the coil faster.
(C) There is repulsion in the moving magnet and the magnetic pole induced in the coil facing towards the N pole of the magnet.
(D) If the bar magnet does not move, there is no induced current in the coil.
Choose the correct answer from the options given below:

Read the following passage carefully and answer the given questions.
Insulin consists of two short polypeptide chains- chain A and chain B, that are linked together by disulphide bridges. Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans, coleopterans and dipterans. Bt toxin protein is converted into an active form of toxin due to the alkaline pH of the gut which solubilise the crystals. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (alpha-1-antitrypsin) used to treat emphysema. Plants, bacteria, fungi and animals whose genes have been altered by manipulation are called Genetically Modified Organisms (GMO). GM plants have been useful in many ways. Genetic modification has: (i) made crops more tolerant to abiotic stresses. (ii) reduced reliance on chemical pesticides (pest-resistant crops). (iii) helped to reduce post harvest losses. (iv) increased efficiency of mineral usage by plants (this prevents early exhaustion of fertility of soil). (v) enhanced nutritional value of food.
The beetles that infest Bt cotton plant are killed:

Which of the following is not true with reference to evaporation of liquid?

We should not allow mosquitoes to breed in our surroundings because they