List of top Mathematics Questions asked in KEAM

If \(θ1,θ2, θ3\) are the angles made by a line with the positive directions of the \(x,y,z\) axes, then the value of \(\cos 2\theta_1 + \cos 2\theta_2 + \cos 2\theta_3\) is

If the \(XZ\)-plane divides the straight line joining the points \((2,4,7)\) and \((3,-5,8)\) in the ratio \(α:1\),then the value of \(α\) is ?

Given the points \(A(6,-7,0),B(16,-19,-4),C(0,3,-6)\) and \(D(2,-5,10)\),the point of intersection of the lines \(AB\) and \(CD\) is

For a real number t ,the equation \((1+t)x^2 + (t-1)y^2 + t^2 - 1 = 0\) represents a hyperbola provided

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

The set of points of the form(t^2+t+1,t^2-t+1),where t is a real number, represents a/an

For \(i=1,2,3,4\), suppose the points\((\cosθi,\secθi)\) lie on the boundary of a circle,where \(θi∈[0,\frac{π}{6})\) are distinct. Then \(\cosθ_1\ \cosθ_2\ \cosθ_3\ \cosθ_4\) equals

For the circle \(C=x^2+y^2-6x+2y=0\),which of the following is incorrect:

The equation of the circle that can be inscribed in the square formed by \(x^2-8x+12=0\) and \(y^2-14y+45=0\) is ?

Suppose the line joining distinct points P and Q on \((x-2)^{2}+(y-1)^{2}=r^{2}\) is the diameter of \( (x-1)^2+(y-3)^2=4\).The value of r is

Suppose the point \(P(1,1)\) is translated to \(Q\) in the direction of y = 2x. If \(PQ = 1\),then Qis

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?

If (2,-6),(5,2) and (-2,2) constitute the vertices of a triangle then the the line joining the origin and its orthocentre is

\(∫^1_0\dfrac{x}{x^2-4}dx=?\)

The value of λ for which the vectors \(2i-3j+4k\) and \(-4i+λj-8k\) are collinear is

Let \(S=\){\(n∈NIn^3+3n^2+5n+3\) is not divisible by \(3\)}.Then, which of the following statements is true about \(S\)

The value of \(cos^{-1}(cos(\dfrac{7\pi}{4}))\) is