Which of the following functions from \(Z\) to \(Z\) is a bijective function? (where \(Z\) is set of integers)

The degree of the differential equation \(\frac{d^2 y}{d x^2}+\left(\frac{d y}{d x}\right)^3=\left(\frac{d^3 y}{d x^3}\right)^2\) is :

\(\int_0^a \frac{\sqrt{x}}{\sqrt{x}+\sqrt{a-x}} d x\) is equal to

A small start-up started making wafers and distributing them to the retailers. After a week, average sales per week were found to be 150 packets. So, to increase the sales, a strategy was used to change the packaging and add a chocolate worth Rs. 5 as a free gift with the pack. After this, a sample of 17 shops was taken, which showed that sales went up with mean 165 and a standard deviation of 25. Check whether the strategy was effective \(5 \%\), level of significance? [Given \(\left.t_{16}(0.05)=2.12\right]\)

Match List-I with List-II

List-I	List-II
(A) Maximum value of \(f(x)=\sin ^2 x-\cos ^2 x \forall x \in(\pi, 2 \pi)\)	(I) \(0\)
(B) Minimum value of \(f(x)=\sin x \cdot \cos x\)	(II) 1
(C) Point of Minima of \(f(x)=x^x(x>0)\)	(III) \(-\frac{1}{2}\)
(D) Maximum value of \(f(x)=-x^{2026}\)	(IV) \(\frac{1}{e}\)

Choose the correct answer from the options given below :

The differential equation representing the family of curves \(y=a \sin (x+b)\), where \(a\) and \(b\) are arbitrary constants is

Let R be the relation in the set \(\{a, b, c\}\) given by \(R=\{(a, b),(b, b),(a, a),(a, c),(c, c),(c, b)\}\) Choose the correct answer from the options below :

The peak value of the electric field associated with an electromagnetic wave traveling through vacuum is \( 8.1 \, \text{N}\cdot\text{C}^{-1} \). The peak value of the associated magnetic field will be:

Read the passage carefully and answer the questions
The coordination compounds are of great importance. These compounds are widely present in the mineral, plants and animal world and are known to play many important functions in the area of analytical chemistry, metallurgy, biological systems, industry and medicine. For example, coordination compounds find use in many qualitative and quantitative chemical analysis. Some important metal extraction and purification make use of complex formation. Hardness of water can be estimated by stable complex formation of Ca\(^{2+}\) and Mg\(^{2+}\)
In photography undecomposed AgBr is removed as ___________

8. An ammeter having internal resistance of \( 0.81 \, \Omega \) can read upto 1A. To convert it into an ammeter reading 0 - 10 A we have to connect :

Read the following paragraph and answer the given questions.
Repeated amplification is achieved by the use of a thermostable DNA polymerase (isolated from a bacterium, Thermus aquaticus), which remain active during the high temperature induced denaturation of double stranded DNA. The separated DNA fragments can be visualised only after staining the DNA with a compound known as ethidium bromide followed by exposure to UV radiation. The separated bands of DNA are cut out from the agarose gel and extracted from the gel piece. The convention for naming these enzymes is the first letter of the name comes from the genus and the second two letters come from the species of the prokaryotic cell from which they were isolated, e.g., EcoRI comes from Escherichia coli RY 13. In EcoRI, the letter 'R' is derived from the name of strain. Roman numbers following the names indicate the order in which the enzymes were isolated from that strain of bacteria. Stanley Cohen and Herbert Boyer accomplished this in 1972 by isolating the antibiotic resistance gene by cutting out a piece of DNA from a plasmid which was responsible for conferring antibiotic resistance. Since the DNA is enclosed within the membranes, we have to break the cell open to release DNA, RNA, protein, polysaccharides etc. The RNA can be removed by treatment with ribonuclease whereas proteins can be removed by treatment with protease. Other molecules can be removed by appropriate treatments and purified DNA ultimately precipitates out after the addition of chilled ethanol.

In agarose gel electrophoresis, the separated DNA fragments can be visualized with the help of compound known as:

Identify the symptoms of Amoebiasis from the following.
(A) Constipation
(B) Diarrhoea and vomitting
(C) Abdominal pain and cramps
(D) Excess mucous and blood clots in stool
Choose the correct answer from the options given below:

A series LCR circuit with an inductor, a capacitor and a resistor of resistance 50 Ω is connected to an ac source of 24 V, 50 Hz. The impedance of the circuit is 56 Ω. The average power dissipated in the circuit is