If A is a square matrix such that \(A^2=A\) and I is the identity matrix of the same order as A, then \((I+A)^2-3 A\) is equal to

The integrating factor of the differential equation \(\left(x \log _e x\right) \frac{d y}{d x}+y=2 \log _e x\) is:

If f(a - x) = f(x), then \(\int_0^a x f(x) d x\) is equal to

In a 500 m race, the ratio of speeds of two participants \(A\) and \(B\) is \(4: 5\).
If \(A\) has a start of 180 m , then the distance by which \(A\) wins is :

If \(y=A \sin x+B \cos x\), then which of the following is correct?

In a 900 meters race, Ram gives Shyam a start of 150 meters and defeats him by 50 seconds. If the speed of Ram is 4.5 m/sec, then the speed of Shyam is

The value of the integral \(\int \frac{\log x^3}{x} d x\) is :

Match List-I with List-II

List-I (Characteristics)	List-II (Examples)
(A) Symbiotic association with roots of leguminous plants	(I) Glomus
(B) Fixes atmospheric nitrogen while free living in the soil	(II) Rhizobium
(C) Symbiotic association of fungi and plants	(III) Anabaena
(D) Cyanobacteria which can fix atmospheric nitrogen	(IV) Azotobacte

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The velocity and acceleration vectors of a particle moving in a magnetic field are given by : \(\vec{v}=3 \hat{i}+4 \hat{j}\) and \(\vec{a}=2 \hat{i}+\hat{j}\) respectively, Then :
(A) the magnetic field is along \(z\)-direction
(B) \(v=3\)
(C) the kinetic energy of the particle is constant
(D) the acceleration is in x-z plane
(E) the particle is moving in \(x-y\) plane

Match List - I with List - II

List - I	List - II
(A) Denaturation	(I) Sequence of amino acids in a protein
(B) Primary structure of protein	(II) alpha-Helix and beta-pleated sheets
(C) Quaternary structure of protein	(III) \(2\) degree and \(3\) degree structures gets destroyed
(D) Secondary structure of protein	(IV) The spatial arrangement of subunits (containing \(2\) or more polypeptide chains) with respect to each other

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There are two thin parallel charged sheets having surface charge density \( \sigma \) placed at a small distance apart. Which of the following statements are correct?
(A) If both the sheets are positively charged, then the electric field between them is \( \sigma/\epsilon_0 \)
(B) If both the sheets are negatively charged, then the electric field between them is \( \sigma/\epsilon_0 \)
(C) If the left sheet is positively charged and the right sheet is negatively charged the field between them is \( \sigma/\epsilon_0 \)
(D) If the right sheet is positively charged and the left sheet is negatively charged then the field between them is \( \sigma/\epsilon_0 \)
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Match List I with List II

LIST I	LIST II
A. Buna-S	I. Polyamide
B. Nylon 6,6	II. Homopolymer
C. Polythene	III. Terepthalic acid,ethylene glycol
D. Terylene	IV. Copolymer

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The physical quantity which does not change when X-rays of wavelength \( 10^{-10} \, \text{m} \), or visible light of wavelength 400 nm, or radio waves of 500 m wavelength pass through glass is