List of top Questions asked in KEAM

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 ?

An average frictional force of 80N is required to stop an object at a distance of 25m. If the initial speed of the object is 20m/s,the mass of the object is:

A biased die is rolled such that the probability of getting k dots,1≤k≤6, on the upper face of the die is proportional to k. Then the probability that five dots appear on the upper face of the die is

A planet has an escape speed of 10km/s,The radius of the planet is 10,000km. The acceleration due to gravity of the planet at its surface is:

\(∫xlog(1+x^2)dx=\)?

If, \(x∈(0,π)\) satisfies the equation \(6^{1+sinx+sin^2x....}=36\) ,then the value of \(x\) is_____.

If \(x\) is a real number such that \(tanx+cotx=2\),then \(x=\)?

The value of a(≠0) for which the equation \(\frac{1}{2}(x-2)^2+1=\sin(\frac{a}{x})\) holds is/are

Let P(x)=cos²x+sin⁴x,for any x∈R.Then which of the following options is correct for all x?

In a triangle ABC,if \(cos^{2}A-sin^{2}B+cos^{2}C=0\) ,then the value of \(cosAcosBcosC\) is

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

A projectile is thrown at a speed V and at an angle with the horizontal. If the speed at its maximum height is \(\frac{V}{3}\),then the value of tan θ is:

If the coefficients of \((5r+4)th\) term and \((r-1)th\) term in the expansion of \((1+x)^{25}\) are equal, then \(r\) is

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

Two satellites A and B are moving around the earth in a circular orbit of radius 2R,respectively. If the kinetic energy of the satellite A is two-times the kinetic energy of the satellite B,the ratio of their masses (m_A:m_B) is:

The number of solutions of the equation \( \dfrac{1}{2}(x^3+1)=(2x-1)^{⅓}\) is

A horizontal force is exerted on a 20 kg box to slide it up on an inclined plane with an angle of 30°. The frictional force retarding the motion is 80 N. If the box moves with a constant speed, then the magnitude of the force is:(Take g=10 ms^-2)

Consider a vector addition \(\vec{P}\)+\(\vec{Q}\)=\(\vec{R}\). If \(\vec{P}\)=|\(\vec{P}\)|\(\hat{i}\),|\(\vec{Q}\)|=10 and\(\vec{R}\)= 3 |\(\vec{P}\)|\(\hat{j}\),then |\(\vec{P}\)| is: