In a circuit where current 31 enters at \(A\), with semicircular sections \(A B C\) and \(A D C\) of equal radii r , resistances 2 R and R respectively, the magnetic field at the center is :

Which of the following statements are correct.
A. Every polynomial function is continuous.
B. Every constant function is continuous.
C. Modulus function is not continuous.
D. Identity function on real numbers is not continuous.
E. Every differentiable function is continuous.
Choose the correct answer from the options given below:

For the problem \(\max Z=a x+b y, x \geq 0, y \geq 0\), which of the following is NOT a valid constraint to make it a linear programming problem?

The value of \(\int \frac{\left(x^4-x\right)^{1 / 4}}{x^5} d x\) is equal to (where \(C\) is an arbitrary constant) :

Find the maximum value of the function sin x(1 + cos x) is:

A machine costing \(\operatorname{Rs} 3,00,000\) will have its scrap value of \(\operatorname{Rs} 50, 000\). The company at present plans to put \(\operatorname{Rs} 36, 650\) per annum at the end of each year in a sinking fund at the rate \(5 \%\) per annum for the replacement of the machine after its useful life. Suppose the new machine will cost \(\operatorname{Rs} 4,00,000\) at that time, then the useful life (approx.) of the machine is :
[Given: \((1.4775)^{\frac{1}{8}} \approx 1.05\) ]

If \(A=\left[\begin{array}{cc}2-x & 1 \\ 3 & y+2\end{array}\right]\) and \(B=\left[\begin{array}{cc}y & 1 \\ 3 & 2 x+1\end{array}\right]\) are such that A = B, then values of z and y are respectively :

The conductivity of an ionic solution depends on:
A. The nature of the electrolyte added
B. The Volume of the container
C. The size of the ions and their solvation
D. Pressure
E. Concentration of the electrolytes
Choose the correct answer from the options given below :

Read the passage carefully and answer the following questions
Aldehydes, carboxylic acids and ketones are widespread in the animal and plant kingdoms. They play a pivotal role in various biochemical processes of life. Their presence in nature adds fragrance and flavor. These compounds are widely used in food products, pharmaceuticals, paints, resins and other important product industries. These compounds are prepared by various laboratory methods, which mainly include oxidation, formylation, acylation and reduction. Due to the polar nature of the carbonyl group in aldehydes and ketones, they can exhibit different reactions like nucleophilic addition. They do exhibit redox and various condensation reactions which lead to the formation of various important compounds. On the other hand, the carboxylic acids are mainly prepared by oxidation and hydrolysis of different compounds. The carboxylic acid consists of a carbonyl group and the hydroxy group (attached to the carbonyl carbon atom). This makes it possible for the carboxylic acid to participate in various chemical reactions which involve cleavage of the C-OH bond and the O-H bond along with the reactions involving the complete - COOH group.
The IUPAC name of following compound is \(OHC-C_6H_4-CHO-p\)

The value of \(\tan \frac{1}{2}\left\{\sin ^{-1}\left(\frac{2 x}{1+x^2}\right)+\cos ^{-1}\left(\frac{1-y^2}{1+y^2}\right)\right\}\) if \(|x|<1, y>0\) and \(x y<1\) is:

The probability of obtaining an even prime number on each die, when a pair of dice is rolled, is:

A metal foil of thickness (3/4)d is introduced between two plates of a capacitor of capacitance C. The distance between the plates of the capacitor is d. The new capacitance of the capacitor will be

Which of the following is not the correctly matched pair of organism and its respective cell wall degrading enzyme