For \(x>1, \int \frac{e^{7 \log x}-e^{5 \log x}}{e^{5 \log x}-e^{4 \log x}} d x\) equals.

The area of the smaller region of the circle \(x^2+y^2=8\) cut off by the line \(x=2\) is

Radiation of frequency \(2 v _0\) incident on a metal with threshold frequency \(v _0\) results in maximum kinetic energy of photoelectrons as :

The cartesian equation of the plane whose intercepts on the coordinate axes are 2, -3 and 4 is:

Which of the following statements are correct in reference to the linear programming problem (LPP):
Maximize \(Z =5 x +2 y, Z =5 x +2 y, Z =5 x +2 y\)
subject to the following constraints
\(3 x+5 y \leq 15,5 x+2 y \leq 10, x \geq 0, y \geq 0\)
(A) The LPP has a unique optimal solution at \((2,0)\) only.
(B) The feasible region is bounded with corner points \((0,0),(2,0),(20 / 19,45 / 19)\) and \((0,3)\).
(C) The optimal value is unique, but there are an infinite number of optimal solutions.
(D) The feasible region is unbounded.
Choose the correct answer from the options given below:

If the vectors \(\hat{i}-2 x \hat{j}+3 y \hat{k}\) and \(\hat{i}+2 x \hat{j}-3 y \hat{k}\) are perpendicular, then the locus of \((x, y)\) is:

The remainder, when \(5^{60}\) is divided by 7 , is :

"The rate constant of a first order reaction follows the equation 
 \(log\ k = 8.0 - \frac{5000}{T}\)
 The activation energy \((E_a)\) for the reaction is:
 (Given \(R = 8.3\ JK^{-1}\ mol^{-1}\))"

The kinetic energy of an electron in a given orbit in a hydrogen atom is : (symbols have their usual meaning)

Select the correct name for the following reaction:

Match List I with List - II.

List-I (Transformer)	List-II
(A) Flux leakage	(I) Laminated core
(B) Energy loss due to resistance of winding	(II) By winding the primary and secondary one over the other
(C) Eddy current loss	(III) Using thick wires
(D) Hysteresis	(IV) By using soft iron core

Choose the correct answer from the options given below :

Read the following paragraph carefully and answer the given questions.
In the year 1963 the two enzymes responsible for restricting the growth of bacteriophage in E. coli were isolated. The first restriction endonuclease - Hind II, whose functioning depended on a specific DNA nucleotide sequence was characterized five years later. It was found that Hind II always cut DNA molecules at a particular point by recognizing a specific sequence of six base pairs. This specific base sequence is known as the recognition sequence for Hind II. Besides Hind II, today we know more than 900 restriction enzymes that have been isolated from over 230 strains of bacteria, each of which recognize different recognition sequences.
In EcoR I the latter 'R' is derived from the -

Which of the following is incorrect with reference to drug abuse?