On 1st April 2024, person ' \(X\) ' purchased a machinery costing ₹ 65000 and spent ₹ 10000 on its installation. The estimated effective life of the machinery is 5 years with a scrap value of ₹ 10000 . The annual depreciation using the straight-line method with the accounting year ending on 31st March 2025 is :

match List - I with List - II

List - I (function)	List - II (inceasing on the interval)
(A) f(x) = -\(x^2\) - 2x + 1	(I) \((-\infty,-1)\)
(B) f(x) = \(x^2\) + 1	(II) \((1, \infty)\)
(C) f(x) = \(x^2\) - 2x + 3	(III) \((-\infty, 0)\)
(D) f(x) = \(- x^2\)	(IV) \((0, \infty)\)

Choose the correct answert from the option given below :

Let \(\vec{a}=\hat{i}+2 \hat{j}+3 \hat{k}\) and \(\vec{b}=-2 \hat{i}+3 \hat{j}-4 \hat{k}\), then which of the following statements are correct?
(A) \(|\vec{a}|=\sqrt{14}\)
(B) \(|\vec{b}|=29\)
(C) \(\vec{a} \cdot \vec{b}=8\)
(D) Angle between \(\vec{a}\) and \(\vec{b}\) is \(\cos ^{-1}\left(\frac{-8}{\sqrt{406}}\right)\)
Choose the correct answert from the option given below :

According to Bohr's Model :
(A) The radius of the orbiting electron is directly proportional to \({'n'. } \)
(B) The speedof the orbiting electron is directly proportional to \(\frac{1}{n} \)
(C) The magnitude of the total energy of the orbiting electron is directly proportional to \(\frac{1}{n^2} \)
(D) The radius of the orbiting electron is directly proportional to \( =n^2 \)
Correct options :

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

Solution of the differential equation \(\frac{d y}{d x}=\sqrt{1+x^2+y^2+x^2 y^2}\) is : (Here \(C\) is an arbitrary costant)

Let two independent random samples of sizes \(n_1\) and \(n_2\) respectively have been drawn from the same normal population. Let \(\overline{X_1}\) and \(\overline{X_2}\) be the means and let \(s_1\) and \(s_2\) be their standard deviations. In order to test whether the the two sample means \(\overline{X_1}\) and \(\overline{X_2}\) differ significantly or not, the \(t\)-test statistic is given by

There are two kinds of nucleases - exonucleases and endonucleases. Exonucleases remove nucleotides from the ends of the DNA whereas, endonucleases make cuts at specific positions within the DNA. The cutting of DNA by restriction endonucleases results in the fragments of DNA. These fragments can be separated by a technique known as gel electrophoresis. Since DNA fragments are negatively charged molecules they can be separated by forcing them to move towards the anode under an electric field through a medium/matrix. Small volume cultures cannot yield appreciable quantities of products. To produce in large quantities, the development of bioreactors, where large volumes (100 - 1000 litres) of culture can be processed, was required. Thus, bioreactors can be thought of as vessels in which raw materials are biologically converted into specific products, individual enzymes, etc., using microbial plant, animal or human cells. PCR stands for Polymerase Chain Reaction. In this reaction, multiple copies of the gene (or DNA) of interest are synthesised in vitro using two sets of primers (small chemically synthesised oligonucleotides that are complementary to the regions of DNA) and the enzyme DNA polymerase.
Which one of the following enzymes remove nucleotides from the ends of the DNA?

The angle between thee curves \(x y=\sqrt{2}\) and \(x^2-y^2=1\) at \((\sqrt{2}, 1)\) is:

Two nuclei have mass numbers 125 and 27, respectively. The mass density ratio of their nuclei will be

Which is/are Non-biodegradable polymers ?
(A) Nylon 6, 6
(B) Nylon-2, Nylon-6
(C) PHBV
(D) Phenol formaldehyde resin
(E) Dacron
Choose the correct answer from the options given below :

Gause's 'Competitive Exclusion Principle' states that :

In a diffraction pattern due to a narrow slit of width a, alternate dark and bright fringe pattern is obtained on a screen kept at distance D from the slit. Choose the correct option.
(A) The angular width of central maximum is given by 2D/a, linear width is given by 2D\lambda/a
(B) When the size of aperture, a is quite large, the diffraction effect is negligible,
(C) For light of smaller wavelength, angular width of central maximum increases, while linear width decreases,
(D) Angular width of central maximum does not decrease while linear width decreases on decreasing distance of screen from slit.
Choose the correct answer from the options given below: