Match List-I with List-II
An urn contains 4 white and 3 red balls. In a random draw of three balls, the probability of

List-I	List-II
(A) No red ball is	(I) \(\frac{12}{35}\)
(B) Only 1 red ball is	(II) \(\frac{1}{35}\)
(C) Exactly 2 red balls is	(III) \(\frac{4}{35}\)
(D) No white ball is	(IV) \(\frac{18}{35}\)

Choose the correct answer from the options given below :

Consider the following hypothesis test:
\(\begin{aligned} & H_0: \mu=20 \\ & H_a: \mu \neq 20\end{aligned}\)
A sample of 40 provided a sample mean of 19. The standard deviation is 3. Then the value of the t-test statistic is:

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

The number of all possible matrices of order \(3 \times 3\) with each entry 2 or 3 is:

Match List - I with List - II

List - I	List - II
(A) The degree of the differential equation \(\left(\frac{d^2 y}{d x^2}\right)^2+\left(\frac{d y}{d x}\right)=x \sin \left(\frac{d y}{d x}\right)\)	(I) 4
(B) The degree of differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^{1 / 4}+x^{1 / 5}=0\)	(II) 1
(C) The degree of differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^3+6 y^5=0\)	(III) Not defined
(D) The degree of differential equation \(1+\left(\frac{d y}{d x}\right)^4=7\left(\frac{d^2 y}{d x^2}\right)^3\)	(IV) 3

Choose the correct answer from the options given below:

Let A = \(\left[\begin{array}{ccc}152 & 105 & 3 \\ 149 & 25 & 35 \\ 2 & 1 & 0\end{array}\right]\) . If \(A_{i j}\) denotes the co-factor of an element \(a_{i j}\) of the matrix A, then the value of \(a_{11} A_{21}+a_{12} A_{22}+a_{13} A_{23}\) is equal to

Area of the region bounded by the curve \(x^2=4 y, x\)-axis and \(x=3\) is:

A spherical ice ball is melting at the rate of \(100 \pi \mathrm{~cm}^3 / \mathrm{min}\). The rate at which its radius is decreasing when its radius is 15 cm, 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.
Baculoviruses are-

A beam of light of wavelength 500 nm from a distant source falls on a single slit of width \( 10^{-4} \, \text{m} \), and the resulting diffraction pattern is observed on a screen 2 m away. The width of the central bright fringe is:

Arrange the following electrodes in increasing order of strength as an oxidizing agent.
(A) \(Ni ^{2+}+2 e^{-} \rightarrow Ni (s) \quad E^0=-0.25 V\)
(B) \(Cu ^{2+}+2 e^{-} \rightarrow Cu (s) \quad E^0=0.34 V\)
(C) \(Br _2+2 e^{-} \rightarrow 2 Br ^{-} \quad E^0=1.09 V\)
(D) \(O _2(g)+2 H ^{+}+2 e^{-} \rightarrow H _2 O _2 \quad E^0=0.68 V\)
Choose the correct answer from the options given below :

Given that the value of a determinant of order three is zero; which one of the following is not correct?

The radius of the first orbit in Bohr's hydrogen atom is 0.53\(\text{\AA}\). The radius of fourth orbit of this atom will be: