Match List-I with List-II

List-I (Differential Equation)	List-II (Integrating Factor)
(A) \(\frac{d y}{d x}+2 x y=1\)	(I) \(x\)
(B) \(x \frac{d y}{d x}+2 x y=1\)	(II) \(e^{2 x}\)
(C) \(x \frac{d y}{d x}+y=1\)	(III) \(x^2\)
(D) \(x \frac{d y}{d x}+2 y=2\)	(IV) \(e^{x^2}\)

Choose the correct answer from the options given below :

\(f(x)=\left\{\begin{array}{ll}\frac{\sqrt{1+p x}-\sqrt{1-p x}}{x}, & -1 \leq x<0 \\\frac{2 x+1}{x-2}, & 0 \leq x \leq 1\end{array}\right.\)
is continuous in the interval \([-1,1]\), then \(p\) is equal to :

The corner points of the feasible region determined by the system of linear constraints are \((0, 0), (0, 40), (20, 40), (60, 20), (60, 0)\). The objective function is \(Z = 4x + 3y\).
Compare the quantity in Column A and Column B
Column A : Column B :
Maximum of Z 325

A coin is tossed 7 times. The probability of getting at least 4 heads is:

Let \(A=\{1,2,3\}\), then the possible equivalence relations on \(A\) are :
(A) \(\{(1,1),(2,2),(3,3)\}\)
(B) \(\{(1,1),(2,2),(3,3),(1,2),(2,1)\}\)
(C) \(\{(1,1),(2,2),(3,3),(1,2),(2,1),(1,3)\}\)
(D) \(\{(1,1),(2,2),(3,3),(1,3),(3,1)\}\)
Choose the correct answer from the options given below :

Out of students in a school, it is known that \(65 \%\) reside in hostel and \(35 \%\) are day scholars. Previous year results report that \(40 \%\) of the students who reside in hostel attain A grade and 20% of day scholars attain A grade in their annual examination.At the end of the year, one student is chosen at random from the class.
If the selected student attains grade A, find the probability that the student is a hosteller.

For the objective function \(z=p x+q y\), where \(p, q>0\) the corner points of the feasible region determined by the system of linear constraints are \((0,10),(5,5),(15,15)\) and \((0,20)\), condition on \(p\) and \(q\) so that maximum of \(z\) occurs at both the points \((15,15)\) and \((0,20)\) is :

Identify the carbohydrate which is not a polysaccharide

Light ray travels from an rarer medium to an denser medium. Which of the following is incorrect if \( (0^{\circ} < i < 90^{\circ}) \).

Read the following passage carefully and answer the given questions.
The B-lymphocytes produce an army of proteins in response to pathogens. Each antibody molecule has four peptide chains, two small called light chains and two longer called heavy chains. Virus-infected cells secrete proteins called interferons which protect non-infected cells from further viral infection. Symptoms of allergic reactions include sneezing, watery eyes, running nose and difficulty in breathing. The use of drugs like anti-histamine, adrenalin and steroids quickly reduce the symptoms of allergy. Lymphoid organs are the organs where origin and/or maturation and proliferation of lymphocytes occur. The primary lymphoid organs are bone marrow and thymus. After maturation the lymphocytes migrate to secondary lymphoid organs like spleen, lymph nodes, tonsils, Peyer's patches of small intestine and appendix. Heroin commonly called smack is chemically diacetylmorphine which is a white, odourless, bitter crystalline compound. This is obtained by acetylation of morphine, which is extracted from the latex of poppy plant Papaver somniferum.
Which one of the following is not a feature of an antibody:

The vector equation of line passing through \((-1,3,-2)\) and perpendicular to the lines \(\frac{x+4}{1}=\frac{y}{2}=\frac{z-3}{3}\) and \(\frac{x+2}{-3}=\frac{y+5}{2}=\frac{z-6}{5}\) is

Read the following passage given below and answer the question.
Aldehydes and ketones undergo nucleophilic addition reactions. A nucleophile attacks the electrophilic carbon atom of polar carbonyl group from perpendicular to plane of \(sp^2\) hybridised orbitals of carbonyl carbon. The hybridisation of carbon changes from \(sp^2\) to \(sp^3\) and a tetrahedral alkoxide intermediate is formed. This captures \(H^+\) to give neutral product. In carboxylic acids, carbonyl carbon is less electrophilic than carbonyl carbon in aldehydes and ketones.How will you convert acetaldehyde to lactic acid ?

The relation R on the set of real numbers defined by \(R=\left\{(a, b): a \leq b^2\right\}\) is
(A) Reflexive
(B) Not symmetric
(C) Neither reflexive nor transitive
(D) Transitive
Choose the correct answer from the options given below: