List of top Questions asked in KEAM

\(ABCD\) is a square with side \(a\). If \(AB\) and \(AD\) are along the coordinate axes, then the equation of the circle passing through the vertices \( A, B \) and \( D \) is

The line segment joining \( (5,0) \) and \( (10\cos\theta, 10\sin\theta) \) is divided internally in the ratio \(2:3\) at \(P\). If \(\theta\) varies, then the locus of \(P\) is

The point on the circle \( (x-1)^2 + (y-1)^2 = 1 \) which is nearest to the circle \( (x-5)^2 + (y-5)^2 = 4 \) is

The parametric form of equation of the circle \( x^2 + y^2 - 6x + 2y - 28 = 0 \) is

A circle passes through the point \( (6,2) \). If segments of the straight lines \( x+y=6 \) and \( x+2y=4 \) are two diameters of the circle, then its radius is

If the straight line \( 5x + y = k \) forms a triangle with the coordinate axes of area \(10\) sq. units, then the values of \(k\) are

If a straight line is perpendicular to \( 2x + 8y = 10 \) and meets the x-axis at \( (5,0) \), then it meets the y-axis at

The distance between the point \( (1,2) \) and the point of intersection of the lines \( 2x + y = 2 \) and \( x + 2y = 2 \) is

If \( p_1 \) and \( p_2 \) are respectively length of perpendiculars from the origin to the straight lines \( x\sec\theta + y\cosec\theta = a \) and \( x\cos\theta - y\sin\theta = a\cos 2\theta \), then \( 4p_1^2 + p_2^2 = \)

If the points \( A(3,4) \), \( B(x_1,y_1) \) and \( C(x_2,y_2) \) are such that both \( 3,x_1,x_2 \) and \( 4,y_1,y_2 \) are in A.P., then

If coordinates of the circumcentre and the orthocentre of a triangle are respectively \( (5,5) \) and \( (2,2) \), then the coordinates of the centroid are:

Let \( A(0,0) \) and \( B(8,0) \) be two vertices of a right angled triangle whose hypotenuse is \( BC \). If the circumcentre is \( (4,2) \), then the point \( C \) is:

If \( 0 \le x \le 2\pi \), then the number of solutions of the equation \( \sin^8 x + \cos^8 x = 1 \) is

If \( \cos^{-1}x > \sin^{-1}x \), then \(x\) lies in the interval

If \( \cos^{-1}x + \cos^{-1}y = \frac{2\pi}{7} \), then the value of \( \sin^{-1}x + \sin^{-1}y \) is equal to

\( 2\tan^{-1}\left(\frac{1}{3}\right) + \tan^{-1\left(\frac{1}{4}\right) = \)}

If \( \sin(\theta+\phi) = n \sin(\theta-\phi), \; n \neq 1 \), then the value of \( \frac{\tan\theta}{\tan\phi} \) is

The period of the function \( f(x) = \cos 4x + \tan 3x \) is

The value of \( \tan 15^\circ + \tan 75^\circ \) is equal to

If \( x = 5 + 2\sec \theta \) and \( y = 5 + 2\tan \theta \), then \( (x-5)^2 - (y-5)^2 \) is equal to

If \( \tan \frac{\theta}{2} = \frac{1}{2} \), then the value of \( \sin \theta \) is

Consider the two statements \(P\): He is intelligent and \(Q\): He is strong. Then the symbolic form of the statement “It is not true that he is either intelligent or strong” is

Let \(p, q, r\) be three statements. Then \( \sim (p \vee (q \wedge r)) \) is equal to

For any two statements \(p\) and \(q\), the statement \( \sim(p \vee q) \vee (\sim p \wedge q) \) is equivalent to

The area and perimeter of a rectangle are \(A\) and \(P\) respectively. Then \(P\) and \(A\) satisfy the inequality