Choose the correct statement about Sinking Fund?

Which of the following is correct about the Sinking Fund?

The area (in sq. units) of the region in the first quadrant bounded by \(y=3 \sqrt{1-x^2}, x \in[0,1]\) and the x-axis is equal to

Consider the following L.P.P.
Max. \(z=5 x+2 y\), subject to \(-2 x-3 y \leq-6, x-2 y \leq 2,3 x+2 y \leq 12,-3 x+2 y \leq 3\) and \(x, y \geq 0\) then

Cofactor of \(a_{12}\) in \(A=\left[\begin{array}{ccc}1 & 2 & 3 \\ 4 & -5 & 6 \\ 0 & 1 & -1\end{array}\right]\) is:

\(\int_{0}^{1} (x^3 + 3x^2)e^x dx =\)

Match List - I with List - II

List - I	List - II
(A) \(\int \frac{d x}{a^2-x^2}\)	(I) \(\frac{1}{2 a} \log \left|\frac{x-a}{x+a}\right|+C\)
(B) \(\int \frac{d x}{x^2-a^2}\)	(II) \(\frac{1}{2 a} \log \left|\frac{a+x}{a-x}\right|+C\)
(C) \(\int \frac{d x}{x^2+a^2}\)	(III) \(\sin ^{-1}\left(\frac{x}{a}\right)+C\)
(D) \(\int \frac{d x}{\sqrt{a^2-x^2}}\)	(IV) \(\frac{1}{a} \tan ^{-1} \frac{x}{a}+C\)

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General solution of the differential equation \(\frac{d y}{d x}=e^{\frac{5^2}{5}}+x y\) is :

Match List-I with List-II:

List-I (AC Circuit)	List-II (Phase Angle)
(A) Phase Difference between current and voltage in a pure inductive ac circuit	(I) zero
(B) Phase Difference between current and voltage in a pure resistive ac circuit	(II) \(\pi/2\), current lags voltage
(C) Phase Difference between current and voltage in a pure capacitive ac circuit	(III) \(\tan^{-1}(\frac{X_L - X_C}{R})\)
(D) Phase Difference between current and voltage in a series LCR circuit	(IV) \(\pi/2\), current leads voltage

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Arrange the following electromagnetic waves in the ascending order of their wavelengths.
(A) Radio waves
(B) Gamma rays
(C) Infrared rays
(D) Ultraviolet rays
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Select the statements which are true for oogenesis?
(A). Ovulation occurs at the secondary oocyte stage.
(B). Polar body is larger than the secondary oocyte.
(C). No more oogonia is formed after birth in the ovary.
(D). The sperm and the ovum nucleus fuse before the formation of the second polar body.
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The mass of NaOH required to make a 500 mL solution of 0.5 molarity is

Read the passage carefully to answer the questions given below
Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans (tobacco budworm, armyworm), coleopterans (beetles) and dipterans (flies, mosquitoes). In Bacillus thuringiensis the toxin is coded by a gene crylAc named cry. There are a number of them, for example, the proteins encoded by the genes crylAc and cryllAb control the cotton bollworms, that of crylAb controls corn borer. Using conventional methods of diagnosis (serum and urine analysis, etc.) early detection is not possible. Recombinant DNA technology, Polymerase Chain Reaction (PCR) and Enzyme Linked Immuno-sorbent Assay (ELISA) are some of the techniques that serve the purpose of early diagnosis. The first clinical gene therapy was given in 1990 to a 4-year old girl with adenosine deaminase (ADA) deficiency. This enzyme is crucial for the immune system to function. The disorder is caused due to the deletion of the gene for adenosine deaminase. RNAi takes place in all eukaryotic organisms as a method of cellular defense. This method involves silencing of a specific mRNA due to a complementary dsRNA molecule that binds to and prevents translation of the mRNA.
RNAi involves involves silencing of a specific mRNA due to a complementary__________ molecule that binds to and prevents translation of the mRNA.