The vector equation of the line passing through points \(A(3,4,-7)\) and \(B(1,-1,6)\) is:

Let \(\Delta=\left|\begin{array}{ccc}x & 2 & x \\ x^2 & x & 6 \\ x & x & 6\end{array}\right|=p x^4+q x^3+r x^2+s x+t\), then the value of \(5 p+4 q+3 r+2 s+t\) is equal to :

If A and B are events such that \(P(A \mid B)=P(B \mid A)\), then :

The position vector of a point which divides the line joining the points with position vectors \((\vec{a}-2 \vec{b})\) and \((2 \vec{a}+\vec{b})\) externally in the ratio \(2 : 1\), is

The rise and fall of share market is an example of

The value of \(m\) so that the lines \(\frac{1-x}{3}=\frac{7 y-14}{2 m}=\frac{z-3}{2}\) and \(\frac{7-7 x}{3 m}=\frac{y-5}{1}=\frac{6-z}{5}\) are at right angle is :

If A is a square matrix such that \(A^2=A\), then \(|A|\) equals :

Which of the following statements about electromagnetic waves is/are correct?
A. Visible Light can be polarised but X-rays cannot.
B. X-rays in vacuum travel faster than visible light waves in vacuum.
C. The energy of X-ray photon is greater than that of a visible light photon.
D. Radio waves are produced by the accelerated motion of charges in conducting wires.
E. An electric dipole is a basic source of electromagnetic waves.
Choose the correct answer from the options given below:

If a matrix has 24 elements, which of the following cannot be the possible order of the matrix?

A charged particle enters a uniform magnetic field at an angle of \(45 ^\circ\) with the field. The path along which the particle moves in the field will be

Read the following passage carefully and answer the given questions.
During anaerobic sludge digestion, bacteria produce a mixture of gases such as methane, hydrogen sulphide and carbon dioxide. These gases form biogas and can be used as source of energy as it is inflammable. The bioactive molecule, cyclosporin A, that is used as an immunosuppressive agent in organ-transplant patients, is produced by the fungus Trichoderma polysporum. You must have noticed that bottled fruit juices bought from the market are clearer as compared to those made at home. This is because the bottled juices are clarified by the use of pectinases and proteases. Statins produced by the yeast Monascus purpureus have been commercialised as blood-cholesterol lowering agents. It acts by competitively inhibiting the enzyme responsible for synthesis of cholesterol. The BOD test measures the rate of uptake of oxygen by micro-organisms in a sample of water and thus, indirectly, BOD is a measure of the organic matter present in the water.
Statins, used as blood-cholesterol lowering agents are produced by -

Different stages of oogenesis are given below. Arrange them in the sequence of their occurrence
A. Completion of first meiotic division of primary oocyte
B. Release of ovum from the ovary.
C. Primary oocyte in the primary follicle formation.
D. Graafian follicle

ZSM-5 is a catalyst used for.