List of top Questions asked in KEAM

Suppose a and b are lengths of major and minor axes of an ellipse that passes through the points (4,3) and (-1,4). If the major axis of the ellipse lies along the x-axis , then the value of \(\frac{1}{a^2}+\frac{16}{b^2}\) is

Suppose the line mx-y+ 5m-4=0 meets the lines x+3y+2=0, 2x+3y+4=0 and x-y-5=0 at the points R. S and T, respectively. If R, S and T are at distances r1, r2 and r3, respectively, from (-5,-4) and \((\frac{15}{r_1})^2+(\frac{10}{r_2})^2=(\frac{6}{r_3})^2\) then the value of m is

A point moves in such a way that it remains equidistant from each of the lines \(3x±2y= 5\). Then the path along which the point moves is?

If the two sides AB and AC of a triangle are along \(4x-3y-17 = 0\) and \(3x+4y-19= 0\), then the equation of the bisector of the angle between AB and AC is ?

A thin particle moves from \((0,1)\) and gets reflected upon hitting the x-axis at \((√3,0)\). Then the slope of the reflected line is ?

The line perpendicular to \(4x-5y+1=0\) and passing through the point of intersection of the straight line \(x+2y-10=0\) and \(2x+y+5=0\) is ?

If a straight line in XY plane is passes through \((-a,-b),(a,b),(k,k),(a^2,a^3)\) for some real number \(a,b\) and \(k\),where \(a≠0\),then which of the following option is correct?

\(∫^1_0\dfrac{x}{x^2-4}dx=?\)

Which order is correct in spectrochemical series of ligands:

The tetrahedral crystal field splitting is only____of the octahedral splitting.

Match the following complexes (P) with the geometry (Q)

	P		Q
a	[Cu(NH₃)₄]²⁺	i	Tetrahedral
b	[Ag(NH₃)₂]⁺	ii	Octahedral
c	Fe(CO)₅	iii	Square planar
d	[Cr(H₂O)₆]³⁺	iv	Triagonal bipyramidal
e	[NiCl₄]^2-	v	Linear