In an influenza epidemic, the number of cases diagnosed in a week were as follows:

Day	Monday	Tuesday	Wednesday	Thursday	Friday	Saturday	Sunday
Number of Cases	10	12	8	16	9	14	4

The 3-day moving averages are :

The general solution of the differential equation \(x d y+\left(y-e^x\right) d x=0\) is :
where C is constant of integration

The sides of an equilateral triangle are increasing at the rate of 2 cm/s. The rate at which the area increases, when side is 10 cm is:

Which of the following statements are correct?
(A) If elements of a row (or column) of a determinant are multiplied with cofactors of any other row (or column), then their sum is zero.
(B) The value of determinant is equal to the sum of the product of elements of any row (or column) with their corresponding cofactors.
(C) If any two rows (or columns) of a determinant are interchanged, their sign of determinant does not change.
(D) The value of determinant remains unchanged if its rows and columns are interchanged.
(E) A square matrix A has inverse if and only if A is singular.
Choose the correct answer from the options given below:

If \(A =\left(\begin{array}{cc}2 & 3 \\ 5 & -2\end{array}\right)\), be such that \(A ^{-1}=K A\), then the value of \(K\) is :

The points on the curve \(\frac{x^2}{16}+\frac{y^2}{25}=1\) at which tangents are parallel to \(x\)-axis are:

The integral \(\int e^x(\tan x+\log \sec x) d x\) is equal to :

The properties which depend on the number of solute particles irrespective of their nature relative to the total number of particles in the solution are called colligative properties. These are relative lowering of vapour pressure of the solvent, depression of freeaing point of the solvent, elevation of boiling point of the solvent and osmotic pressure of the solution. All of these properties help in calculating the observed molar mass of the solute.
Determination of osmotic pressure is considered best for the determination of molecular mass of the solute.
Which ssolution has the highest boiling point ?

Read the following passage carefully and answer the given questions.
Insulin consists of two short polypeptide chains- chain A and chain B, that are linked together by disulphide bridges. Some strains of Bacillus thuringiensis produce proteins that kill certain insects such as lepidopterans, coleopterans and dipterans. Bt toxin protein is converted into an active form of toxin due to the alkaline pH of the gut which solubilise the crystals. Transgenic animals that produce useful biological products can be created by the introduction of the portion of DNA (or genes) which codes for a particular product such as human protein (alpha-1-antitrypsin) used to treat emphysema. Plants, bacteria, fungi and animals whose genes have been altered by manipulation are called Genetically Modified Organisms (GMO). GM plants have been useful in many ways. Genetic modification has: (i) made crops more tolerant to abiotic stresses. (ii) reduced reliance on chemical pesticides (pest-resistant crops). (iii) helped to reduce post harvest losses. (iv) increased efficiency of mineral usage by plants (this prevents early exhaustion of fertility of soil). (v) enhanced nutritional value of food.
Which one of the followings is not true about insulin?

A Bond has a coupon rate of 10\% per annum paid semi annually and the coupon payment made is ₹ 50 , so the face value of the bond is :

For \(SN_2\) reaction, the increasing order of the reactivity of the following alkyl halides is:
(A) \(CH _3 CH _2 CH _2 CH _2 Br\)
(B) \(CH 3 CH 2 CH ( Br ) CH 3\)
(C) \(( CH 3) 3 CBr\)
(D) \(( CH 3) 2 CHCH 2 Br\)

Variation caused by mutation, according to Hugo deVries are :

When a slab of insulating material 4 mm thick is introduced between the plates of a parallel plate capacitor of separation 4 mm, it is found that the distance between the plates has to be increased by 3.2 mm to restore the capacity to its original value. The dielectric constant of the material is :