A is a square matrix of order 3 such that |A| = 13. The value of | - 3A| is:

If the sum of the lengths of the hypotenuse and one of the other two sides of a right angled triangle is fixed, then the area of the triangle is maximum, when the angle between them is :

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 :

Consider the differential equation \(x d y=\left(y+2 x^3\right) d x\). Then which of the following are TRUE?
(A) It is a homogeneous differential equation.
(B) Product of the order and degree of the differential equation is one.
(C) Integrating factor is \(x\).
(D) General solution of the differential equation is \(y=x^3+C x\), where \(C\) is an arbitrary constant.
Choose the correct answer from the options given below :

If it is given that at \(x = 1\) the function \(f(x)=x^4-62 x^2+2 a x+8\) attains its maximum value on the interval [0, 2], then the value of a is:

The area of the region bounded by the line \(y = 2 x\) and the \(x\)-axis between \(x = - 2\) and \(x = 2\) is

The area enclosed between \(y^2=4 x\) and \(x^2=4 y\) is:

The matrix \(A=\left[\begin{array}{lll}0 & 0 & 5 \\ 0 & 5 & 0 \\ 0 & 0 & 5\end{array}\right]\) is a:

If \(\left|\begin{array}{cc}2 & 3-x \\ x & 1\end{array}\right|=0\), then the values of x are:

Read the passage carefully and answer the questions
The osmotic pressure is one of the four colligative properties which depends on the number of particles of solute in the solution, irrespective of their nature. The osmotic pressure is equal to the product of concentration, gas constant and temperature. It is the most commonly used property for the determination of the molar mass of biomolecules. In many situations, the molecules get dissociated or associated when they are dissolved in a solvent, thereby changing the number of molecules in the solution. As a result, an abnormal molecular mass is obtained. The extent of dissociation or association is given by van't Hoff factor (i), which is the ratio of normal molar mass to abnormal molar mass. It is related with the degree of association or ionization. The introduction of van't Hoff factor in the osmotic pressure equation modifies the equation.
Which one of the following has minimum osmotic pressure at 298 K ?

A letter is known to have come either from KOLKATA or TATANAGAR. On the envelope just two consecutive letters TA are visible. The probability that letter has come from TATANAGAR is

When a current carrying coil is placed in a uniform external magnetic field with its magnetic moment antiparallel to the external magnetic field, then
(A) its potential energy is minimum
(B) its potential energy is maximum
(C) torque on it is maximum
(D) torque on it is zero
(E) coil is in unstable equilibrium
Choose the correct answer from the options given below:

Two events \(E\) and \(F\) are independent. If \(P(E)=0.3, P(E \cup F)=0.5\), then \(P(E / F)-P(F / E)\) equals :